%!PS-Adobe-2.0 %%Creator: dvips(k) 2023.1 (TeX Live 2023) Copyright 2023 Radical Eye Software %%Title: arXiv:2411.05492v1 [cs.IT] 8 Nov 2024 %%CreationDate: Mon Nov 11 05:13:57 2024 %%Pages: 15 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: NimbusRomNo9L-Regu NimbusRomNo9L-MediItal %%+ NimbusRomNo9L-Medi NimbusRomNo9L-ReguItal %%DocumentPaperSizes: Letter %%EndComments %%BeginDefaults %%ViewingOrientation: 1 0 0 1 %%EndDefaults %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -R2 -P pk -z main.dvi -o %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2024.11.11:0513 %%BeginProcSet: tex.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /dir 0 def/dyy{/dir 0 def}B/dyt{/dir 1 def}B/dty{/dir 2 def}B/dtt{/dir 3 def}B/p{dir 2 eq{-90 rotate show 90 rotate}{dir 3 eq{-90 rotate show 90 rotate}{show}ifelse}ifelse}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)(LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse} forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{ BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat {BDot}imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B /M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M} B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{ 0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: psfrag.pro 0 0 %% %% This is file `psfrag.pro', %% generated with the docstrip utility. %% %% The original source files were: %% %% psfrag.dtx (with options: `filepro') %% %% Copyright (c) 1996 Craig Barratt, Michael C. 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TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll }repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def /TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{ setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{ /currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC /Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC /Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0 setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0 setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61 0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC /Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0 setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87 0.68 0.32 setcmykcolor}DC/BrickRed{0 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0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1 0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11 0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0 setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0 0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC /Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0 setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0 0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0 1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC /PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0 setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{ 0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor} DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70 setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0 setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1 setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end %%EndProcSet %%BeginProcSet: hps.pro 0 0 %! /HPSdict 20 dict dup begin/braindeaddistill 50 def/rfch{dup length 1 sub 1 exch getinterval}bind def/splituri{dup(#)search{exch pop}{()exch} ifelse dup(file:)anchorsearch{pop exch pop 3 -1 roll pop false}{pop 3 -1 roll exch pop true}ifelse}bind def/lookuptarget{exch rfch dup /TargetAnchors where{pop TargetAnchors dup 3 -1 roll known{exch get true }{pop(target unknown:)print == false}ifelse}{pop pop (target dictionary unknown\012)print false}ifelse}bind def/savecount 0 def/stackstopped{count counttomark sub/savecount exch store stopped count savecount sub 1 sub dup 0 gt{{exch pop}repeat}{pop}ifelse}bind def /tempstring 128 string def/targetvalidate{1 index dup length 127 gt exch tempstring cvs dup(/)search{pop pop pop exch pop true exch}{pop}ifelse token{pop length 0 ne}{true}ifelse or not}bind def/targetdump-hook where {pop}{/targetdump-hook{dup mark exch gsave initmat setmatrix{{mark/Dest 4 2 roll targetvalidate{aload pop exch pop/Page 3 1 roll/View exch[exch /FitH exch]/DEST pdfmark}{cleartomark}ifelse}forall}stackstopped pop grestore}bind def}ifelse/baseurl{mark exch 1 dict dup 3 -1 roll/Base exch put/URI exch/DOCVIEW{pdfmark}stackstopped pop}bind def /externalhack systemdict/PDF known def/oldstyle true def/initmat matrix currentmatrix def/actiondict 2 dict dup/Subtype/URI put def /weblinkhandler{dup 3 1 roll mark 4 1 roll/Title 4 1 roll splituri 3 -1 roll dup length 0 gt{cvn/Dest exch 4 2 roll}{pop}ifelse{externalhack{ /HTTPFile exch}{actiondict dup 3 -1 roll/URI exch put/Action exch} ifelse}{externalhack{/HTTPFile exch}{/File exch/Action/GoToR}ifelse} ifelse counttomark 2 sub -1 roll aload pop/Rect 4 1 roll/Border 3 1 roll /Color exch oldstyle{/LNK}{/Subtype/Link/ANN}ifelse gsave initmat setmatrix{pdfmark}stackstopped grestore}bind def/externalhandler where{ pop}{/externalhandler{2 copy{weblinkhandler}exec{/externalhack externalhack not store 2 copy{weblinkhandler}exec{/externalhack externalhack not store/oldstyle false store 2 copy{weblinkhandler}exec{ (WARNING: external refs disabled\012)print/externalhandler{pop pop}bind store externalhandler}{pop pop}ifelse}{pop pop/externalhack externalhack not store}ifelse}{pop pop/externalhandler{weblinkhandler pop}bind store} ifelse}bind def}ifelse/pdfmnew{dup type/stringtype eq{externalhandler}{ exch dup rfch exch 3 -1 roll lookuptarget{mark 4 1 roll/Title 4 1 roll aload pop exch pop/Page 3 1 roll/View exch[exch/FitH exch]5 -1 roll aload pop/Rect 4 1 roll/Border 3 1 roll/Color exch/LNK gsave initmat setmatrix pdfmark grestore}{pop pop}ifelse}ifelse}bind def/pdfmold{dup type/stringtype eq{externalhandler}{exch dup rfch exch 3 -1 roll lookuptarget{mark 4 1 roll/Title 4 1 roll aload pop exch pop/Page 3 1 roll/View exch[exch/FitH exch]5 -1 roll aload pop pop 0 3 getinterval /Rect 3 1 roll/Border exch/LNK gsave initmat setmatrix pdfmark grestore} {pop pop}ifelse}ifelse}bind def/pdfm where{pop}{/pdfm /currentdistillerparams where{pop currentdistillerparams dup /CoreDistVersion known{/CoreDistVersion get}{0}ifelse dup braindeaddistill le{(WARNING: switching to old pdfm because version =) print ==/pdfmold}{pop/pdfmnew}ifelse load}{/pdfmark where{pop{dup type /stringtype eq{externalhandler}{2 copy mark 3 1 roll{pdfmnew} stackstopped{2 copy mark 3 1 roll{pdfmold}stackstopped{ (WARNING: pdfm disabled\012)print/pdfm{pop pop}store}{ (WARNING: new pdfm failed, switching to old pdfm\012)print/pdfm/pdfmold load store}ifelse}{/pdfm/pdfmnew load store}ifelse pop pop}ifelse}}{{ pop pop}}ifelse}ifelse bind def}ifelse end def %%EndProcSet TeXDict begin @defspecial systemdict /pdfmark known{userdict /?pdfmark systemdict /exec get put}{userdict /?pdfmark systemdict /pop get put userdict /pdfmark systemdict /cleartomark get put}ifelse /DvipsToPDF{72.27 mul Resolution div} def/PDFToDvips{72.27 div Resolution mul} def/BPToDvips{72 div Resolution mul}def product (Ghostscript) search {pop pop pop revision 927 gt}{pop false} ifelse{/BorderArrayPatch{} def}{/BorderArrayPatch{[exch{dup dup type/integertype eq exch type/realtype eq or{BPToDvips}if}forall]}def} ifelse /HyperBorder {1 PDFToDvips} def/H.V {pdf@hoff pdf@voff null} def/H.B {/Rect[pdf@llx pdf@lly pdf@urx pdf@ury]} def/H.S {currentpoint HyperBorder add /pdf@lly exch def dup DvipsToPDF 72 add /pdf@hoff exch def HyperBorder sub /pdf@llx exch def} def/H.L {2 sub dup/HyperBasePt exch def PDFToDvips /HyperBaseDvips exch def currentpoint HyperBaseDvips sub /pdf@ury exch def/pdf@urx exch def} def/H.A {H.L currentpoint exch pop vsize 72 sub exch DvipsToPDF HyperBasePt sub sub /pdf@voff exch def} def/H.R {currentpoint HyperBorder sub /pdf@ury exch def HyperBorder add /pdf@urx exch def currentpoint exch pop vsize 72 sub exch DvipsToPDF sub /pdf@voff exch def} def @fedspecial end %%BeginFont: NimbusRomNo9L-ReguItal %!PS-AdobeFont-1.0: NimbusRomNo9L-ReguItal 1.05 %%CreationDate: Wed Dec 22 1999 % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % (URW)++,Copyright 1999 by (URW)++ Design & Development % See the file COPYING (GNU General Public License) for license conditions. % As a special exception, permission is granted to include this font % program in a Postscript or PDF file that consists of a document that % contains text to be displayed or printed using this font, regardless % of the conditions or license applying to the document itself. 12 dict begin /FontInfo 10 dict dup begin /version (1.05) readonly def /Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def /Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def /FullName (Nimbus Roman No9 L Regular Italic) readonly def /FamilyName (Nimbus Roman No9 L) readonly def /Weight (Regular) readonly def /ItalicAngle -15.5 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /NimbusRomNo9L-ReguItal def /PaintType 0 def /WMode 0 def /FontBBox {-169 -270 1010 924} readonly def /FontType 1 def /FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def /Encoding StandardEncoding def currentdict end currentfile eexec D9D66F633B846A989B9974B0179FC6CC445BC2C03103C68570A7B354A4A280AE 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cleartomark %%EndFont %%BeginFont: NimbusRomNo9L-Medi %!PS-AdobeFont-1.0: NimbusRomNo9L-Medi 1.05 %%CreationDate: Wed Dec 22 1999 % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % (URW)++,Copyright 1999 by (URW)++ Design & Development % See the file COPYING (GNU General Public License) for license conditions. % As a special exception, permission is granted to include this font % program in a Postscript or PDF file that consists of a document that % contains text to be displayed or printed using this font, regardless % of the conditions or license applying to the document itself. 12 dict begin /FontInfo 10 dict dup begin /version (1.05) readonly def /Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def /Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def /FullName (Nimbus Roman No9 L Medium) readonly def /FamilyName (Nimbus Roman No9 L) readonly def /Weight (Bold) readonly def /ItalicAngle 0.0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /NimbusRomNo9L-Medi def /PaintType 0 def /WMode 0 def /FontBBox {-168 -341 1000 960} readonly def /FontType 1 def /FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def /Encoding StandardEncoding def currentdict end currentfile eexec D9D66F633B846A989B9974B0179FC6CC445BC2C03103C68570A7B354A4A280AE 6FBF7F9888E039AB60FCAF852EB4CE3AFEB979D5EA70FDE44A2AE5C8C0166C27 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: NimbusRomNo9L-Regu %!PS-AdobeFont-1.0: NimbusRomNo9L-Regu 1.05 %%CreationDate: Wed Dec 22 1999 % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % (URW)++,Copyright 1999 by (URW)++ Design & Development % See the file COPYING (GNU General Public License) for license conditions. % As a special exception, permission is granted to include this font % program in a Postscript or PDF file that consists of a document that % contains text to be displayed or printed using this font, regardless % of the conditions or license applying to the document itself. 12 dict begin /FontInfo 10 dict dup begin /version (1.05) readonly def /Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def /Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def /FullName (Nimbus Roman No9 L Regular) readonly def /FamilyName (Nimbus Roman No9 L) readonly def /Weight (Regular) readonly def /ItalicAngle 0.0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /NimbusRomNo9L-Regu def /PaintType 0 def /WMode 0 def /FontBBox {-168 -281 1000 924} readonly def /FontType 1 def /FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def /Encoding StandardEncoding def currentdict end currentfile eexec D9D66F633B846A989B9974B0179FC6CC445BC2C03103C68570A7B354A4A280AE 6FBF7F9888E039AB60FCAF852EB4CE3AFEB979D5EA70FDE44A2AE5C8C0166C27 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: NimbusRomNo9L-MediItal %!PS-AdobeFont-1.0: NimbusRomNo9L-MediItal 1.05 %%CreationDate: Wed Dec 22 1999 % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % (URW)++,Copyright 1999 by (URW)++ Design & Development % See the file COPYING (GNU General Public License) for license conditions. % As a special exception, permission is granted to include this font % program in a Postscript or PDF file that consists of a document that % contains text to be displayed or printed using this font, regardless % of the conditions or license applying to the document itself. 12 dict begin /FontInfo 10 dict dup begin /version (1.05) readonly def /Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def /Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def /FullName (Nimbus Roman No9 L Medium Italic) readonly def /FamilyName (Nimbus Roman No9 L) readonly def /Weight (Bold) readonly def /ItalicAngle -15.3 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /NimbusRomNo9L-MediItal def /PaintType 0 def /WMode 0 def /FontBBox {-200 -324 996 964} readonly def /FontType 1 def /FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def /Encoding StandardEncoding def currentdict end currentfile eexec D9D66F633B846A989B9974B0179FC6CC445BC2C03103C68570A7B354A4A280AE 6FBF7F9888E039AB60FCAF852EB4CE3AFEB979D5EA70FDE44A2AE5C8C0166C27 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1027 3838 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.2.10) cvn H.B /ANN pdfmark end 1027 3838 a 0 TeXcolorgray Fx(\))i(much)f(more)g (challenging)-192 3938 y(to)c(solv)o(e.)-192 4073 y SDict begin H.S end -192 4073 a -192 4073 a SDict begin 12 H.A end -192 4073 a -192 4073 a SDict begin [/View [/XYZ H.V]/Dest (section.3) cvn /DEST pdfmark end -192 4073 a -161 4174 a Fx(I)t(I)t(I)t(.)45 b(P)t Fy(R)q(O)t(P)t(O)t(S)t(E)t(D)26 b Fx(C)t(D)f(A)t Fy(L)t(G)t(O)t(R)t(I)t(T)t(H)t(M)t(S)g(F)t(O)t(R)h Fx(D)t Fy(E)t(V)t(I)t(C)t(E)e Fx(A)q Fy(C)t(T)t(I)t(V)t(I)t(T)t(Y)645 4274 y Fx(D)t Fy(E)t(T)t(E)t(C)t(T)t(I)t(O)t(N)-109 4417 y Fx(In)31 b(this)h(section,)f(we)h(focus)f(on)g(designing)f(ef)n (\002cient)h(algorithms)-192 4517 y(for)f(solving)f(the)h(MLE)g (problem)f(\()p 0 0 1 TeXcolorrgb 885 4518 a SDict begin H.S end 885 4518 a 0 0 1 TeXcolorrgb -1 x Fx(10)p 0 0 1 TeXcolorrgb 968 4460 a SDict begin H.R end 968 4460 a 968 4517 a SDict begin 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-85 y Fj(n)2000 37 y Fx(such)28 b(that)2726 140 y SDict begin H.S end 2726 140 a 2726 140 a SDict begin 12 H.A end 2726 140 a 2726 140 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.11) cvn /DEST pdfmark end 2726 140 a Fo(R)2798 152 y Fr(n)2866 140 y Ft(=)23 b Fo(R)3036 69 y Fh(1)p 3037 78 29 3 v 3037 111 a(2)3026 150 y Fr(n)3079 73 y Fk(\000)3117 140 y Fo(R)3199 69 y Fh(1)p 3200 78 V 3200 111 a(2)3189 150 y Fr(n)3242 73 y Fk(\001)3280 90 y Fr(H)3343 140 y Fu(:)588 b Fx(\(11\))2000 327 y(Let)29 b Fo(X)2219 339 y Fr(n)2286 327 y Ft(=)23 b Fo(R)2456 256 y Fh(1)p 2457 265 V 2457 298 a(2)2446 336 y Fr(n)2518 327 y Fs(\012)18 b Fo(s)2645 339 y Fr(n)2713 327 y Fs(2)23 b Fn(C)2845 296 y Fr(LM)6 b Fq(\002)p Fr(r)3043 304 y Fj(n)3094 327 y Fu(:)29 b Fx(Then)f(we)h(ha)n(v)o(e)2590 486 y SDict begin H.S end 2590 486 a 2590 486 a SDict begin 12 H.A end 2590 486 a 2590 486 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.12) cvn /DEST pdfmark end 2590 486 a Fo(X)2669 498 y Fr(n)2714 486 y 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3108 y(\014)-110 3129 y Fo(I)-68 3141 y Fr(r)-37 3149 y Fj(n)27 3129 y Ft(+)18 b Fu(d)c Fo(X)252 3095 y Fr(H)246 3150 y(n)315 3129 y Fl(\006)384 3095 y Fq(\000)p Fp(1)384 3150 y Fi(a)473 3129 y Fo(X)552 3141 y Fr(n)597 3058 y Fk(\014)597 3108 y(\014)648 3129 y Ft(=)22 b Fs(j)q Fo(I)801 3141 y Fr(r)832 3149 y Fj(n)895 3129 y Ft(+)c Fu(d)c Fl(\003)p Fs(j)23 b Ft(=)1254 3024 y Fr(r)1285 3032 y Fj(n)1237 3050 y Fk(Y)1236 3227 y Fr(i)p Fp(=1)1343 3129 y Ft(\(1)c(+)f Fu(d)c(\025)1624 3141 y Fr(i)1652 3129 y Ft(\))p Fu(;)55 b Fx(\(21\))-192 3349 y(which)27 b(is)h(a)f(polynomial)e(of)i(de)o (gree)f Fu(r)974 3361 y Fr(n)1047 3349 y Fx(in)i Fu(d:)g Fx(Second,)e(the)h(term)g(in)-192 3448 y(\()p 0 0 1 TeXcolorrgb -164 3450 a SDict begin H.S end -164 3450 a 0 0 1 TeXcolorrgb -2 x Fx(19b)p 0 0 1 TeXcolorrgb -40 3392 a SDict begin H.R end -40 3392 a -40 3448 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.19b) cvn H.B /ANN pdfmark end -40 3448 a 0 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Fr(H)416 4067 y Fk(\000)454 4134 y Fo(I)496 4146 y Fr(r)527 4154 y Fj(n)591 4134 y Ft(+)18 b Fu(d)c Fo(X)816 4100 y Fr(H)810 4155 y(n)879 4134 y Fl(\006)948 4100 y Fq(\000)p Fp(1)948 4155 y Fi(a)1037 4134 y Fo(X)1116 4146 y Fr(n)1161 4067 y Fk(\001)1199 4081 y Fq(\000)p Fp(1)1302 4134 y Fo(\021)207 4268 y Ft(=)23 b Fo(\030)340 4234 y Fr(H)402 4268 y Fo(V)36 b Ft(\()p Fo(I)568 4280 y Fr(r)599 4288 y Fj(n)663 4268 y Ft(+)18 b Fu(d)c Fl(\003)p Ft(\))902 4226 y Fq(\000)p Fp(1)1005 4268 y Fo(V)1082 4234 y Fr(H)1145 4268 y Fo(\021)207 4402 y Ft(=)307 4380 y(\026)295 4402 y Fo(\030)340 4368 y Fr(H)416 4402 y Ft(\()p Fo(I)490 4414 y Fr(r)521 4422 y Fj(n)585 4402 y Ft(+)k Fu(d)c Fl(\003)p Ft(\))824 4360 y Fq(\000)p Fp(1)938 4401 y Ft(\026)927 4402 y Fo(\021)207 4595 y Ft(=)319 4490 y Fr(r)350 4498 y Fj(n)295 4516 y Fk(X)301 4693 y Fr(i)p Fp(=1)504 4517 y Ft(\026)496 4539 y Fu(\030)536 4509 y Fq(\003)532 4560 y Fr(i)594 4539 y Ft(\026)-48 b Fu(\021)629 4551 y Fr(i)p 438 4576 277 4 v 438 4652 a 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Fo(I)91 2535 y Fr(r)122 2543 y Fj(n)185 2523 y Ft(+)18 b Fu(d)c Fo(X)410 2488 y Fr(H)404 2543 y(n)474 2523 y Fl(\006)543 2488 y Fq(\000)p Fp(1)543 2543 y Fi(a)632 2523 y Fo(X)711 2535 y Fr(n)755 2452 y Fk(\014)755 2502 y(\014)806 2523 y Ft(=)918 2418 y Fr(r)949 2426 y Fj(n)894 2444 y Fk(X)900 2621 y Fr(i)p Fp(=1)1028 2523 y Ft(log\(1)k(+)g Fu(d)c(\025)1415 2535 y Fr(i)1443 2523 y Ft(\))806 2792 y(=)918 2687 y Fr(r)949 2695 y Fj(n)894 2713 y Fk(X)900 2890 y Fr(i)p Fp(=1)1028 2792 y Fu(d)g(\025)1133 2804 y Fr(i)1179 2792 y Ft(+)k Fu(o)p Ft(\()p Fu(d)p Ft(\))806 2997 y(=)23 b Fu(d)14 b Ft(tr)1030 2930 y Fk(\000)1068 2997 y Fo(X)1153 2963 y Fr(H)1147 3017 y(n)1216 2997 y Fl(\006)1285 2963 y Fq(\000)p Fp(1)1285 3017 y Fi(a)1374 2997 y Fo(X)1453 3009 y Fr(n)1498 2930 y Fk(\001)1554 2997 y Ft(+)k Fu(o)p Ft(\()p Fu(d)p Ft(\))p Fu(;)1762 3097 y SDict begin H.S end 1762 3097 a 1762 3097 a SDict begin 15 H.A end 1762 3097 a 1762 3097 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.25) cvn /DEST pdfmark end 1762 3097 a Fx(\(25\))-192 3238 y(where)42 b(the)h(little-)p Fu(o)g Fx(notation)e Fu(o)p Ft(\()p Fu(d)p Ft(\))j Fx(satis\002es)g (the)f(condition)e(that)-192 3338 y Fu(o)p Ft(\()p Fu(d)p Ft(\))p Fu(=d)24 b Fs(!)f Ft(0)g Fx(as)h Fu(d)f Fs(!)g Ft(0)p Fu(:)g Fx(Further)m(,)e(we)j(apply)e(the)h(T)-7 b(aylor)22 b(e)o(xpansion)-192 3438 y(to)29 b(obtain)-92 3558 y Fk(\000)-54 3625 y Fo(I)c Ft(+)18 b Fu(d)c Fo(X)238 3591 y Fr(H)232 3646 y(n)301 3625 y Fl(\006)370 3591 y Fq(\000)p Fp(1)370 3646 y Fi(a)459 3625 y Fo(X)538 3637 y Fr(n)583 3558 y Fk(\001)621 3572 y Fq(\000)p Fp(1)734 3625 y Ft(=)848 3522 y Fq(1)822 3547 y Fk(X)821 3725 y Fr(k)q Fp(=0)956 3558 y Fk(\000)994 3625 y Fs(\000)p Fu(d)g Fo(X)1201 3591 y Fr(H)1195 3646 y(n)1264 3625 y Fl(\006)1333 3591 y Fq(\000)p Fp(1)1333 3646 y Fi(a)1422 3625 y Fo(X)1501 3637 y Fr(n)1545 3558 y Fk(\001)1583 3572 y Fr(k)734 3833 y Ft(=)22 b Fo(I)863 3845 y Fr(r)894 3853 y Fj(n)958 3833 y Fs(\000)c Fu(d)c Fo(X)1183 3798 y Fr(H)1177 3853 y(n)1246 3833 y Fl(\006)1315 3798 y Fq(\000)p Fp(1)1315 3853 y Fi(a)1404 3833 y Fo(X)1483 3845 y Fr(n)1546 3833 y Ft(+)k Fu(o)p Ft(\()p Fu(d)p Ft(\))p Fu(:)1762 3932 y SDict begin H.S end 1762 3932 a 1762 3932 a SDict begin 15 H.A end 1762 3932 a 1762 3932 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.26) cvn /DEST pdfmark end 1762 3932 a Fx(\(26\))-192 4074 y(Substituting)38 b(\()p 0 0 1 TeXcolorrgb 277 4075 a SDict begin H.S end 277 4075 a 0 0 1 TeXcolorrgb -1 x Fx(25)p 0 0 1 TeXcolorrgb 360 4017 a SDict begin H.R end 360 4017 a 360 4074 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.25) cvn H.B /ANN pdfmark end 360 4074 a 0 TeXcolorgray Fx(\))h(and)g(\()p 0 0 1 TeXcolorrgb 615 4075 a SDict begin H.S end 615 4075 a 0 0 1 TeXcolorrgb -1 x Fx(26)p 0 0 1 TeXcolorrgb 698 4017 a SDict begin H.R end 698 4017 a 698 4074 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.26) cvn H.B /ANN 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Fp(2)1060 484 y Ft(Re)1172 392 y Fk(\020)1221 484 y Ft(\()p Fo(y)22 b Fs(\000)p 1407 437 V 18 w Fo(y)1459 504 y Fi(a)1505 484 y Ft(\))1537 442 y Fr(H)1614 484 y Fl(\006)1683 450 y Fq(\000)p Fp(1)1683 504 y Fi(a)1772 484 y Fo(X)1851 496 y Fr(n)1910 417 y Fk(\000)1948 484 y Fo(I)1990 496 y Fr(r)2021 504 y Fj(n)2085 484 y Fs(\000)c Fu(d)c Fo(X)2310 450 y Fr(H)2304 504 y(n)2373 484 y Fl(\006)2442 450 y Fq(\000)p Fp(1)2442 504 y Fi(a)2531 484 y Fo(X)2610 496 y Fr(n)2655 417 y Fk(\001)2707 484 y Fo(X)2792 450 y Fr(H)2786 504 y(n)2855 484 y Fl(\006)2924 450 y Fq(\000)p Fp(1)2924 504 y Fi(a)3027 417 y Fk(\000)p 3065 416 56 4 v 67 x Fo(h)3120 496 y Fr(n)3184 484 y Fs(\012)k Fo(s)3311 496 y Fr(n)3356 417 y Fk(\001)3394 392 y(\021)827 656 y Fs(\000)g Fu(d)953 622 y Fp(3)1004 589 y Fk(\000)p 1042 588 V 67 x Fo(h)1098 668 y Fr(n)1161 656 y Fs(\012)h Fo(s)1289 668 y Fr(n)1334 589 y Fk(\001)1372 602 y Fr(H)1449 656 y Fl(\006)1518 622 y Fq(\000)p Fp(1)1518 677 y Fi(a)1607 656 y Fo(X)1686 668 y Fr(n)1744 589 y Fk(\000)1782 656 y Fo(I)1824 668 y Fr(r)1855 676 y Fj(n)1919 656 y Fs(\000)f Fu(d)c Fo(X)2144 622 y Fr(H)2138 677 y(n)2207 656 y Fl(\006)2276 622 y Fq(\000)p Fp(1)2276 677 y Fi(a)2365 656 y Fo(X)2444 668 y Fr(n)2489 589 y Fk(\001)2541 656 y Fo(X)2626 622 y Fr(H)2620 677 y(n)2689 656 y Fl(\006)2758 622 y Fq(\000)p Fp(1)2758 677 y Fi(a)2861 589 y Fk(\000)p 2899 588 V 67 x Fo(h)2954 668 y Fr(n)3018 656 y Fs(\012)k Fo(s)3145 668 y Fr(n)3190 589 y Fk(\001)3242 656 y Fu(:)3954 656 y SDict begin H.S end 3954 656 a 3954 656 a SDict begin 15 H.A end 3954 656 a 3954 656 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.27) cvn /DEST pdfmark end 3954 656 a Fx(\(27\))p -192 812 4284 4 v 0 TeXcolorgray -192 1066 a(updating)36 b(and)i(storing)f Fl(\006)634 1036 y Fq(\000)p Fp(1)634 1086 y Fi(a)762 1066 y Fx(by)g(taking)g(adv)n(antage)f(of)i (the)g(lo)n(w-)-192 1165 y(rank)32 b(properties)f(of)i(the)g(near)n (-\002eld)f(correlation)f(matrices.)h(Belo)n(w)-5 b(,)-192 1265 y(we)29 b(formally)e(present)h(the)g(assumption)g(for)f(this)i (speci\002c)g(case.)-192 1276 y SDict begin H.S end -192 1276 a -192 1276 a SDict begin 12 H.A end -192 1276 a -192 1276 a SDict begin [/View [/XYZ H.V]/Dest (assumption.1) cvn /DEST pdfmark end -192 1276 a 0 TeXcolorgray 0 TeXcolorgray -109 1375 a Fw(Assumption)35 b(1:)h Fx(Assume)g(that)g (there)f(e)o(xists)h Fu(N)1379 1387 y Fp(corr)1534 1375 y Fs(\024)h Fu(N)45 b Fx(such)-192 1475 y(that)24 b(for)f Ft(1)g Fs(\024)g Fu(n)f Fs(\024)h Fu(N)458 1487 y Fp(corr)576 1475 y Fu(;)i Fx(the)f(correlation)e(matrix)h Fo(R)1447 1487 y Fr(n)1518 1475 y Fx(of)g(de)n(vice)g Fu(n)-192 1574 y Fx(is)h(a)f(lo)n(w-rank)e(positi)n(v)o(e)h(semide\002nite)h (matrix,)f(and)g(for)g Fu(N)1572 1586 y Fp(corr)1698 1574 y Ft(+)8 b(1)23 b Fs(\024)-192 1674 y Fu(n)h Fs(\024)f Fu(N)t(;)30 b Fx(the)f(correlation)e(matrix)i(is)g Fo(R)1017 1686 y Fr(n)1087 1674 y Ft(=)24 b Fu(g)1216 1686 y Fr(n)1260 1674 y Fo(I)1302 1686 y Fr(M)1376 1674 y Fu(;)30 b Fx(where)e Fu(g)1701 1686 y Fr(n)1770 1674 y Fu(>)c Ft(0)-192 1774 y Fx(is)37 b(the)f(lar)o(ge-scale)f(f)o(ading)g(coef)n(\002cient.)g(W) -7 b(e)37 b(further)e(assume)h(that)-192 1873 y(the)g(summation)e(of)h (the)h(correlation)d(matrices)j(of)f(the)h(\002rst)g Fu(N)1782 1885 y Fp(corr)-192 1973 y Fx(de)n(vices)28 b(is)h(rank-de\002cient,)d(i.e.,)360 2240 y SDict begin H.S end 360 2240 a 360 2240 a SDict begin 12 H.A end 360 2240 a 360 2240 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.30) cvn /DEST pdfmark end 360 2240 a Fu(r)399 2206 y Fq(0)446 2240 y Fm(,)c Ft(rank)711 2098 y Fk( )777 2136 y Fr(N)830 2144 y Fh(corr)795 2161 y Fk(X)792 2337 y Fr(n)p Fp(=1)946 2240 y Fo(R)1018 2252 y Fr(n)1064 2098 y Fk(!)1153 2240 y Fu(<)g(M)t(:)414 b Fx(\(30\))-109 2540 y(Notice)39 b(that)g Fu(r)355 2510 y Fq(0)422 2540 y Fs(\024)529 2478 y Fk(P)617 2499 y Fr(N)670 2507 y Fh(corr)617 2565 y Fr(n)p Fp(=1)796 2518 y Ft(\026)790 2540 y Fu(`)825 2552 y Fr(n)870 2540 y Fu(:)g Fx(Then,)f(a)i(suf)n (\002cient)f(condition)-192 2640 y(for)44 b(Assumption)p 0 0 1 TeXcolorrgb 397 2640 a SDict begin H.S end 397 2640 a 0 0 1 TeXcolorrgb Fx(1)p 0 0 1 TeXcolorrgb 439 2583 a SDict begin H.R end 439 2583 a 439 2640 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (assumption.1) cvn H.B /ANN pdfmark end 439 2640 a 0 TeXcolorgray 45 w Fx(to)h(hold)f(is)i(that)f(there)f (are)h(fe)n(w)g(near)n(-\002eld)-192 2740 y(de)n(vices)35 b(\(i.e.,)f Fu(N)343 2752 y Fp(corr)497 2740 y Fx(is)i(small\))f(and)g (fe)n(w)g(scatterers)g(in)g(the)g(near)n(-)-192 2839 y(\002eld)k(channels)e(\(i.e.,)519 2817 y Ft(\026)513 2839 y Fu(`)548 2851 y Fr(n)632 2839 y Fx(is)j(small\).)e(The)g(follo)n (wing)f(proposition)-192 2939 y(demonstrates)30 b(that)g(under)g (Assumption)p 0 0 1 TeXcolorrgb 1087 2939 a SDict begin H.S end 1087 2939 a 0 0 1 TeXcolorrgb Fx(1)p 0 0 1 TeXcolorrgb 1128 2882 a SDict begin H.R end 1128 2882 a 1128 2939 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (assumption.1) cvn H.B /ANN pdfmark end 1128 2939 a 0 TeXcolorgray Fx(,)h Fo(R)1252 2951 y Fr(n)1329 2939 y Fx(\()p Ft(1)c Fs(\024)g Fu(n)g Fs(\024)g Fu(N)1754 2951 y Fp(corr)1873 2939 y Fx(\))-192 3039 y(can)37 b(be)g(transformed)d(into)j(a)g(matrix) f(where)h(only)f(the)g(upper)n(-left)-192 3138 y Fu(r)-153 3108 y Fq(0)-110 3138 y Fs(\002)18 b Fu(r)12 3108 y Fq(0)65 3138 y Fx(submatrix)27 b(is)i(nonzero.)-192 3149 y SDict begin H.S end -192 3149 a -192 3149 a SDict begin 12 H.A end -192 3149 a -192 3149 a SDict begin [/View [/XYZ H.V]/Dest (proposition.1) cvn /DEST pdfmark end -192 3149 a 0 TeXcolorgray 0 TeXcolorgray -109 3248 a Fw(Pr)l(oposition)h(1:)h Fx(Under)g(Assumption)p 0 0 1 TeXcolorrgb 1085 3248 a SDict begin H.S end 1085 3248 a 0 0 1 TeXcolorrgb Fx(1)p 0 0 1 TeXcolorrgb 1126 3192 a SDict begin H.R end 1126 3192 a 1126 3248 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (assumption.1) cvn H.B /ANN pdfmark end 1126 3248 a 0 TeXcolorgray Fx(,)h(there)f(e)o(xists)g(a)h(unitary)-192 3348 y(matrix)c Fo(U)33 b Fs(2)23 b Fn(C)285 3318 y Fr(M)7 b Fq(\002)p Fr(M)515 3348 y Fx(such)29 b(that)102 3550 y SDict begin H.S end 102 3550 a 102 3550 a SDict begin 12 H.A end 102 3550 a 102 3550 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.31) cvn /DEST pdfmark end 102 3550 a Fo(U)177 3516 y Fr(H)241 3550 y Fo(R)313 3562 y Fr(n)358 3550 y Fo(U)k Ft(=)23 b(diag\()752 3529 y Fk(b)730 3550 y Fo(R)802 3562 y Fr(n)848 3550 y Fu(;)14 b Fl(0)p Ft(\))p Fu(;)97 b Ft(1)23 b Fs(\024)f Fu(n)h Fs(\024)g Fu(N)1465 3562 y Fp(corr)1583 3550 y Fu(;)156 b Fx(\(31\))-192 3755 y(where)69 3734 y Fk(b)48 3755 y Fo(R)120 3767 y Fp(1)157 3755 y Fu(;)216 3734 y Fk(b)194 3755 y Fo(R)266 3767 y Fp(2)304 3755 y Fu(;)14 b(:)g(:)g(:)g(;)510 3734 y Fk(b)489 3755 y Fo(R)561 3767 y Fr(N)614 3775 y Fh(corr)758 3755 y Fs(2)38 b Fn(C)905 3725 y Fr(r)938 3700 y Ff(0)966 3725 y Fq(\002)p Fr(r)1051 3700 y Ff(0)1077 3755 y Fu(:)f Fx(The)f(matrix)g Fo(U)47 b Fx(can)36 b(be)-192 3855 y(computed)23 b(by)i(performing)d(the)j(eigen)m(v)n(alue)e (decomposition)f(on)j(the)-192 3954 y(matrix)54 3892 y Fk(P)141 3913 y Fr(N)194 3921 y Fh(corr)141 3979 y Fr(n)p Fp(=1)315 3954 y Fo(R)387 3966 y Fr(n)432 3954 y Fu(;)30 b Fx(i.e.,)e(\002nding)f(a)i(unitary)e(matrix)h Fo(U)39 b Fx(such)28 b(that)-124 4235 y SDict begin H.S end -124 4235 a -124 4235 a SDict begin 12 H.A end -124 4235 a -124 4235 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.32) cvn /DEST pdfmark end -124 4235 a Fo(U)-49 4201 y Fr(H)29 4093 y Fk( )95 4130 y Fr(N)148 4138 y Fh(corr)113 4156 y Fk(X)110 4332 y Fr(n)p Fp(=1)264 4235 y Fo(R)336 4247 y Fr(n)382 4093 y Fk(!)461 4235 y Fo(U)33 b Ft(=)23 b(diag\()p Fu(\025)881 4247 y Fp(1)919 4235 y Fu(;)14 b(\025)1004 4247 y Fp(2)1042 4235 y Fu(;)g(:)g(:)g(:)f(;)h(\025)1274 4247 y Fr(r)1307 4231 y Ff(0)1334 4235 y Fu(;)g Ft(0)p Fu(;)g(:)g(:)g(:)f(;)h Ft(0\))p Fu(;)68 b Fx(\(32\))-192 4501 y(where)28 b Fu(\025)88 4513 y Fp(1)149 4501 y Fs(\025)22 b Fu(\025)284 4513 y Fp(2)345 4501 y Fs(\025)h Fu(:)14 b(:)g(:)23 b Fs(\025)f Fu(\025)688 4513 y Fr(r)721 4497 y Ff(0)771 4501 y Fu(>)h Ft(0)p Fu(:)-26 4611 y Fw(Pr)l(oof:)28 b Fx(Please)h(see)g(Appendix)p 0 0 1 TeXcolorrgb 949 4611 a SDict begin H.S end 949 4611 a 0 0 1 TeXcolorrgb Fx(B)p 0 0 1 TeXcolorrgb 1004 4555 a SDict begin H.R end 1004 4555 a 1004 4611 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (section*.12) cvn H.B /ANN pdfmark end 1004 4611 a 0 TeXcolorgray Fx(.)p 1852 4611 49 49 v -109 4721 a(Furthermore,)d(once)h(the)h (matrix)g Fo(U)39 b Fx(is)29 b(obtained,)d(we)j(can)f(trans-)-192 4821 y(form)18 b(the)h(MLE)g(problem)f(\()p 0 0 1 TeXcolorrgb 630 4822 a SDict begin H.S end 630 4822 a 0 0 1 TeXcolorrgb -1 x Fx(10)p 0 0 1 TeXcolorrgb 712 4764 a SDict begin H.R end 712 4764 a 712 4821 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.2.10) cvn H.B /ANN pdfmark end 712 4821 a 0 TeXcolorgray Fx(\))i(to)f(obtain)f(a)i(more)e(tractable)g (problem)-192 4920 y(as)29 b(presented)e(in)i(the)g(follo)n(wing)d (theorem.)-192 4931 y SDict begin H.S end -192 4931 a -192 4931 a SDict begin 12 H.A end -192 4931 a -192 4931 a SDict begin [/View [/XYZ H.V]/Dest (theorem.2) cvn /DEST pdfmark end -192 4931 a 0 TeXcolorgray 0 TeXcolorgray -109 5030 a Fw(Theor)m(em)34 b(2:)g Fx(The)g(follo)n(wing)f(problem)g (is)i(equi)n(v)n(alent)e(to)h(prob-)-192 5130 y(lem)29 b(\()p 0 0 1 TeXcolorrgb -10 5131 a SDict begin H.S end -10 5131 a 0 0 1 TeXcolorrgb -1 x Fx(10)p 0 0 1 TeXcolorrgb 72 5073 a SDict begin H.R end 72 5073 a 72 5130 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.2.10) cvn H.B /ANN pdfmark end 72 5130 a 0 TeXcolorgray Fx(\):)152 5130 y SDict begin H.S end 152 5130 a 152 5130 a SDict begin 12 H.A end 152 5130 a 152 5130 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.33) cvn /DEST pdfmark end 152 5130 a -87 5333 a Ft(minimize)56 5383 y Fi(a)373 5333 y Ft(log)14 b Fs(j)p Fl(\006)586 5299 y Fq(0)586 5354 y Fi(a)632 5333 y Fs(j)k Ft(+)g(\()q Fo(y)841 5299 y Fq(0)882 5333 y Fs(\000)p 965 5287 53 4 v 18 w Fo(y)1018 5299 y Fq(0)1018 5354 y Fi(a)1064 5333 y Ft(\))1096 5287 y Fr(H)1173 5333 y Ft(\()p Fl(\006)1274 5299 y Fq(0)1274 5354 y Fi(a)1320 5333 y Ft(\))1352 5287 y Fq(\000)p Fp(1)1455 5333 y Ft(\()q Fo(y)1540 5299 y Fq(0)1581 5333 y Fs(\000)p 1665 5287 V 19 w Fo(y)1717 5299 y Fq(0)1717 5354 y Fi(a)1763 5333 y Ft(\))1725 5461 y SDict begin H.S end 1725 5461 a 1725 5461 a SDict begin 15 H.A end 1725 5461 a 1725 5461 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.33a) cvn /DEST pdfmark end 1725 5461 a Fx(\(33a\))-73 5586 y Ft(sub)5 b(ject)14 b(to)83 b Fu(a)403 5598 y Fr(n)471 5586 y Fs(2)23 b Ft([0)p Fu(;)14 b Ft(1])p Fu(;)27 b Fs(8)14 b Fu(n)22 b Ft(=)h(1)p Fu(;)14 b Ft(2)p Fu(;)g(:)g(:)g(:)e(;)i (N)t(;)1720 5586 y SDict begin H.S end 1720 5586 a 1720 5586 a SDict begin 15 H.A end 1720 5586 a 1720 5586 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.33b) cvn /DEST pdfmark end 1720 5586 a Fx(\(33b\))p 0 TeXcolorgray 0 TeXcolorgray 2000 1066 a(where)2080 1216 y Fl(\006)2149 1182 y Fq(0)2149 1237 y Fi(a)2218 1216 y Ft(=)2306 1149 y Fk(\000)2344 1216 y Fo(U)2419 1182 y Fr(H)2501 1216 y Fs(\012)k Fo(I)2626 1228 y Fr(L)2677 1149 y Fk(\001)2715 1216 y Fl(\006)2784 1228 y Fi(a)2830 1149 y Fk(\000)2868 1216 y Fo(U)28 b Fs(\012)18 b Fo(I)3087 1228 y Fr(L)3137 1149 y Fk(\001)2218 1370 y Fp(\()p Fr(a)p Fp(\))2230 1424 y Ft(=)2329 1319 y Fr(N)2382 1327 y Fh(corr)2347 1345 y Fk(X)2344 1521 y Fr(n)p Fp(=1)2499 1424 y Fu(a)2543 1436 y Fr(n)2601 1424 y Ft(diag)q(\()2808 1403 y Fk(b)2787 1424 y Fo(R)2859 1436 y Fr(n)2905 1424 y Fu(;)c Fl(0)p Ft(\))k Fs(\012)3123 1356 y Fk(\000)3161 1424 y Fo(s)3205 1436 y Fr(n)3250 1424 y Fo(s)3294 1389 y Fr(H)3294 1444 y(n)3357 1356 y Fk(\001)2380 1706 y Ft(+)2599 1602 y Fr(N)2569 1627 y Fk(X)2463 1805 y Fr(n)p Fp(=)p Fr(N)2608 1813 y Fh(corr)2710 1805 y Fp(+1)2808 1706 y Fu(a)2852 1718 y Fr(n)2911 1706 y Fu(g)2951 1718 y Fr(n)2996 1706 y Fo(I)3038 1718 y Fr(M)3130 1706 y Fs(\012)3213 1638 y Fk(\000)3251 1706 y Fo(s)3295 1718 y Fr(n)3341 1706 y Fo(s)3385 1671 y Fr(H)3385 1726 y(n)3448 1638 y Fk(\001)3504 1706 y Ft(+)g Fu(\033)3637 1671 y Fp(2)3634 1726 y Fr(w)3688 1706 y Fo(I)3730 1718 y Fr(LM)3850 1706 y Fu(;)3954 1706 y SDict begin H.S end 3954 1706 a 3954 1706 a SDict begin 15 H.A end 3954 1706 a 3954 1706 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.34) cvn /DEST pdfmark end 3954 1706 a Fx(\(34\))2120 1920 y Fo(y)2172 1886 y Fq(0)2218 1920 y Ft(=)2306 1853 y Fk(\000)2344 1920 y Fo(U)2419 1886 y Fr(H)2501 1920 y Fs(\012)g Fo(I)2626 1932 y Fr(L)2677 1853 y Fk(\001)2728 1920 y Fo(y)s Fu(;)3954 1920 y SDict begin H.S end 3954 1920 a 3954 1920 a SDict begin 15 H.A end 3954 1920 a 3954 1920 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.35) cvn /DEST pdfmark end 3954 1920 a Fx(\(35\))p 2097 2080 53 4 v 2097 2127 a Fo(y)2149 2093 y Fq(0)2149 2148 y Fi(a)2218 2127 y Ft(=)23 b Fn(E)8 b Ft([)p Fo(y)2430 2093 y Fq(0)2460 2127 y Ft(])23 b(=)2594 2060 y Fk(\000)2632 2127 y Fo(U)2707 2093 y Fr(H)2789 2127 y Fs(\012)18 b Fo(I)2914 2139 y Fr(L)2964 2060 y Fk(\001)p 3016 2080 V 3016 2127 a Fo(y)3068 2147 y Fi(a)3137 2073 y Fp(\()p Fr(b)p Fp(\))3146 2127 y Ft(=)3275 2023 y Fr(N)3244 2048 y Fk(X)3241 2224 y Fr(n)p Fp(=1)3380 2127 y Fu(a)3424 2139 y Fr(n)3483 2060 y Fk(\000)3521 2127 y Fo(U)3596 2093 y Fr(H)p 3660 2059 56 4 v 3660 2127 a Fo(h)3716 2139 y Fr(n)3761 2060 y Fk(\001)3817 2127 y Fs(\012)g Fo(s)3944 2139 y Fr(n)3990 2127 y Fu(:)3954 2302 y SDict begin H.S end 3954 2302 a 3954 2302 a SDict begin 15 H.A end 3954 2302 a 3954 2302 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.36) cvn /DEST pdfmark end 3954 2302 a Fx(\(36\))2166 2438 y Fw(Pr)l(oof:)28 b Fx(Please)h(see)g(Appendix)p 0 0 1 TeXcolorrgb 3141 2439 a SDict begin H.S end 3141 2439 a 0 0 1 TeXcolorrgb -1 x Fx(C)p 0 0 1 TeXcolorrgb 3196 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Fq(0)2459 3086 y Fs(j)14 b Fo(a)p Ft(\))23 b(=)f Fu(p)p Ft(\()p Fo(y)17 b Fs(j)d Fo(a)p Ft(\))k Fs(\001)3013 3015 y Fk(\014)3013 3065 y(\014)3041 3086 y Fo(U)3116 3051 y Fr(H)3198 3086 y Fs(\012)g Fo(I)3323 3098 y Fr(L)3373 3015 y Fk(\014)3373 3065 y(\014)3424 3086 y Ft(=)k Fu(p)p Ft(\()p Fo(y)17 b Fs(j)d Fo(a)p Ft(\))p Fu(:)158 b Fx(\(37\))2000 3236 y(Therefore,)35 b(problem)h(\()p 0 0 1 TeXcolorrgb 2729 3237 a SDict begin H.S end 2729 3237 a 0 0 1 TeXcolorrgb -1 x Fx(33)p 0 0 1 TeXcolorrgb 2812 3179 a SDict begin H.R end 2812 3179 a 2812 3236 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.33) cvn H.B /ANN pdfmark end 2812 3236 a 0 TeXcolorgray Fx(\))h(\(i.e.,)g(minimizing)f Fs(\000)14 b Ft(log)g Fu(p)p Ft(\()p Fo(y)3812 3206 y Fq(0)3849 3236 y Fs(j)g Fo(a)p Ft(\))p Fx(\))38 b(is)2000 3336 y(equi)n(v)n(alent)27 b(to)h(problem)f(\()p 0 0 1 TeXcolorrgb 2798 3337 a SDict begin H.S end 2798 3337 a 0 0 1 TeXcolorrgb -1 x Fx(10)p 0 0 1 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[/XYZ H.V]/Dest (subsection.4.2) cvn /DEST pdfmark end 2000 -163 a 100 x Fw(B.)41 b(Identi\002ability)26 b(of)j(T)-5 b(rue)29 b(Activity)g(V)-9 b(ector)2083 76 y Fx(The)21 b(phase)f(transition)g(analysis)i(in)f([)p 0 0 1 TeXcolorrgb 3183 77 a SDict begin H.S end 3183 77 a 0 0 1 TeXcolorrgb -1 x Fx(7)p 0 0 1 TeXcolorrgb 3224 21 a SDict begin H.R end 3224 21 a 3224 76 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (cite.chen2022phase) cvn H.B /ANN pdfmark end 3224 76 a 0 TeXcolorgray Fx(])g(demonstrates)f(that,)h(a)g(cru-) 2000 176 y(cial)f(condition)e(for)h(the)h(MLE)f(model)g(\()p 0 0 1 TeXcolorrgb 3164 177 a SDict begin H.S end 3164 177 a 0 0 1 TeXcolorrgb -1 x Fx(10)p 0 0 1 TeXcolorrgb 3246 119 a SDict begin H.R end 3246 119 a 3246 176 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.2.10) cvn H.B /ANN pdfmark end 3246 176 a 0 TeXcolorgray Fx(\))h(to)g(perform)e(ef)n(fecti) n(v)o(ely)g(is)2000 276 y(that)27 b(the)g(true)g(acti)n(vity)f (indicator)g(v)o(ector)g Fo(a)3322 245 y Fq(\016)3387 276 y Fx(needs)g(to)h(be)g(uniquely)2000 375 y(identi\002able.)g(This)h (implies)f(that)h(there)g(should)f(be)g(no)h(other)f(v)o(ector)2000 475 y Fo(a)2053 445 y Fq(0)2104 475 y Fs(6)p Ft(=)i Fo(a)2251 445 y Fq(\016)2320 475 y Fx(such)j(that)f Fu(p)p Ft(\()p Fo(y)17 b Fs(j)d Fo(a)2891 445 y Fq(0)2914 475 y Ft(\))29 b(=)f Fu(p)p Ft(\()p Fo(y)17 b Fs(j)d Fo(a)3298 445 y Fq(\016)3336 475 y Ft(\))p Fu(:)33 b Fx(W)-7 b(e)32 b(no)n(w)f(in)m(v)o (estigate)2000 574 y(the)24 b(identi\002ability)f(of)g Fo(a)2744 544 y Fq(\016)2806 574 y Fx(in)h(both)f(Case)p 0 0 1 TeXcolorrgb 3253 574 a SDict begin H.S end 3253 574 a 0 0 1 TeXcolorrgb Fx(I)p 0 0 1 TeXcolorrgb 3281 519 a SDict begin H.R end 3281 519 a 3281 574 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (Item.1) cvn H.B /ANN pdfmark end 3281 574 a 0 TeXcolorgray 24 w Fx(and)g(Case)p 0 0 1 TeXcolorrgb 3635 574 a SDict begin H.S end 3635 574 a 0 0 1 TeXcolorrgb Fx(II)p 0 0 1 TeXcolorrgb 3690 519 a SDict begin H.R end 3690 519 a 3690 574 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (Item.2) cvn H.B /ANN pdfmark end 3690 574 a 0 TeXcolorgray Fx(.)h(Since)g(both)2000 674 y Fu(p)p Ft(\()p Fo(y)17 b Fs(j)d Fo(a)p Ft(\))28 b Fx(and)g Fu(p)p Ft(\()p Fo(y)17 b Fs(j)d Fo(a)2669 644 y Fq(\016)2707 674 y Ft(\))29 b Fx(are)f(multi)n(v)n(ariate)f(Gaussian)i(distrib)n (utions,)2000 774 y(their)h(equi)n(v)n(alence)f(implies)i(that)g(their) f(corresponding)e(means)i(and)2000 873 y(co)o(v)n(ariances)25 b(must)h(be)h(identical.)f(Therefore,)e(the)j(identi\002ability)f(of) 2000 973 y Fo(a)2053 943 y Fq(\016)2113 973 y Fx(is)d(equi)n(v)n(alent) d(to)i(the)g(condition)f(that)h(there)f(is)i(no)f(other)f Fo(a)3868 943 y Fq(0)3914 973 y Fs(6)p Ft(=)h Fo(a)4054 943 y Fq(\016)2000 1073 y Fx(such)i(that)p 2326 1026 53 4 v 24 w Fo(y)2379 1093 y Fi(a)2421 1076 y Ff(0)2470 1073 y Ft(=)p 2558 1026 V 23 w Fo(y)2610 1093 y Fi(a)2652 1076 y Ff(\016)2716 1073 y Fx(and)g Fl(\006)2930 1085 y Fi(a)2972 1068 y Ff(0)3021 1073 y Ft(=)f Fl(\006)3178 1085 y Fi(a)3220 1068 y Ff(\016)3259 1073 y Fu(:)i Fx(Furthermore,)c (we)k(de\002ne)2081 1262 y Fs(N)2149 1274 y Fp(I)2200 1262 y Fm(,)2288 1170 y Fk(n)2343 1262 y Fo(x)e Fs(2)g Fn(R)2553 1227 y Fr(N)2622 1166 y Fk(\014)2622 1216 y(\014)2622 1266 y(\014)2664 1199 y(P)2751 1220 y Fr(N)2751 1287 y(n)p Fp(=1)2894 1262 y Fu(x)2941 1274 y Fr(n)2987 1262 y Fo(R)3059 1274 y Fr(n)3123 1262 y Fs(\012)3206 1194 y Fk(\000)3244 1262 y Fo(s)3288 1274 y Fr(n)3333 1262 y Fo(s)3377 1232 y Fr(H)3377 1282 y(n)3441 1194 y Fk(\001)3502 1262 y Ft(=)f Fl(0)p Fu(;)2870 1436 y Fx(and)3033 1374 y Fk(P)3121 1394 y Fr(N)3121 1461 y(n)p Fp(=1)3264 1436 y Fu(x)3311 1448 y Fr(n)p 3370 1368 56 4 v 3370 1436 a Fo(h)3426 1448 y Fr(n)3489 1436 y Fs(\012)c Fo(s)3616 1448 y Fr(n)3685 1436 y Ft(=)k Fl(0)3820 1344 y Fk(o)3875 1436 y Fu(;)3954 1436 y SDict begin H.S end 3954 1436 a 3954 1436 a SDict begin 15 H.A end 3954 1436 a 3954 1436 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.49) cvn /DEST pdfmark end 3954 1436 a Fx(\(49\))2055 1610 y Fs(N)2123 1622 y Fp(I)r(I)2200 1610 y Fm(,)2288 1518 y Fk(n)2343 1610 y Fo(x)h Fs(2)g Fn(R)2553 1576 y Fr(N)2622 1515 y Fk(\014)2622 1565 y(\014)2622 1615 y(\014)2664 1548 y(P)2751 1569 y Fr(N)2751 1635 y(n)p Fp(=1)2894 1610 y Fu(x)2941 1622 y Fr(n)2987 1610 y Fu(g)3027 1622 y Fr(n)3072 1610 y Fo(I)3114 1622 y Fr(M)3206 1610 y Fs(\012)3289 1543 y Fk(\000)3327 1610 y Fo(s)3371 1622 y Fr(n)3417 1610 y Fo(s)3461 1580 y Fr(H)3461 1631 y(n)3524 1543 y Fk(\001)3585 1610 y Ft(=)g Fl(0)p Fu(;)2870 1785 y Fx(and)3033 1722 y Fk(P)3121 1743 y Fr(N)3121 1810 y(n)p Fp(=1)3264 1785 y Fu(x)3311 1797 y Fr(n)p 3370 1717 56 4 v 3370 1785 a Fo(h)3426 1797 y Fr(n)3489 1785 y Fs(\012)18 b Fo(s)3616 1797 y Fr(n)3685 1785 y Ft(=)k Fl(0)3820 1693 y Fk(o)3875 1785 y Fu(;)3954 1785 y SDict begin H.S end 3954 1785 a 3954 1785 a SDict begin 15 H.A end 3954 1785 a 3954 1785 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.50) cvn /DEST pdfmark end 3954 1785 a Fx(\(50\))2128 1940 y Fs(C)28 b Fm(,)2288 1872 y Fk(\010)2346 1940 y Fo(x)23 b Fs(2)g Fn(R)2556 1905 y Fr(N)2639 1869 y Fk(\014)2639 1919 y(\014)2681 1940 y Fu(x)2728 1952 y Fr(n)2796 1940 y Fs(\025)g Ft(0)28 b Fx(if)h Fu(a)3078 1905 y Fq(\016)3139 1940 y Ft(=)23 b(0)p Fu(;)k(x)3366 1952 y Fr(n)3435 1940 y Fs(\024)c Ft(0)28 b Fx(if)h Fu(a)3717 1905 y Fq(\016)3778 1940 y Ft(=)23 b(1)3908 1872 y Fk(\011)3969 1940 y Fu(:)3954 2039 y SDict begin H.S end 3954 2039 a 3954 2039 a SDict begin 15 H.A end 3954 2039 a 3954 2039 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.51) cvn /DEST pdfmark end 3954 2039 a Fx(\(51\))2000 2200 y(The)h (identi\002ability)g(of)h Fo(a)2775 2170 y Fq(\016)2838 2200 y Fx(in)f(Case)p 0 0 1 TeXcolorrgb 3114 2200 a SDict begin H.S end 3114 2200 a 0 0 1 TeXcolorrgb Fx(I)p 0 0 1 TeXcolorrgb 3142 2144 a SDict begin H.R end 3142 2144 a 3142 2200 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Fs(\\)19 b(C)27 b Ft(=)c Fs(f)p Fl(0)p Fs(g)p Fu(:)2000 2502 y SDict begin H.S end 2000 2502 a 2000 2502 a SDict begin 12 H.A end 2000 2502 a 2000 2502 a SDict begin [/View [/XYZ H.V]/Dest (theorem.3) cvn /DEST pdfmark end 2000 2502 a 0 TeXcolorgray 0 TeXcolorgray 2083 2602 a Fw(Theor)m(em)g(3:)g Fx(If)g Fs(N)2639 2614 y Fp(I)r(I)2702 2602 y Fs(\\)9 b(C)28 b Ft(=)23 b Fs(f)p Fl(0)p Fs(g)p Fu(;)g Fx(then)g Fs(N)3339 2614 y Fp(I)3376 2602 y Fs(\\)9 b(C)28 b Ft(=)23 b Fs(f)p Fl(0)p Fs(g)f Fx(also)i(holds)2000 2702 y(true.)2166 2805 y Fw(Pr)l(oof:)k Fx(Please)h(see)g(Appendix)p 0 0 1 TeXcolorrgb 3141 2805 a SDict begin H.S end 3141 2805 a 0 0 1 TeXcolorrgb Fx(D)p 0 0 1 TeXcolorrgb 3201 2750 a SDict begin H.R end 3201 2750 a 3201 2805 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (section*.14) cvn H.B /ANN pdfmark end 3201 2805 a 0 TeXcolorgray Fx(.)p 4043 2805 49 49 v 2083 2909 a(Theorem)p 0 0 1 TeXcolorrgb 2416 2910 a SDict begin H.S end 2416 2910 a 0 0 1 TeXcolorrgb -1 x Fx(3)p 0 0 1 TeXcolorrgb 2458 2852 a SDict begin H.R end 2458 2852 a 2458 2909 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (theorem.3) cvn H.B /ANN pdfmark end 2458 2909 a 0 TeXcolorgray 34 w Fx(highlights)i(a)j(k)o(e)o(y)f(observ)n(ation)e(that)i(the)g (identi\002a-)2000 3008 y(bility)d(of)g Fo(a)2359 2978 y Fq(\016)2428 3008 y Fx(is)h(more)e(lik)o(ely)h(to)h(hold)e(in)i(Case) p 0 0 1 TeXcolorrgb 3496 3008 a SDict begin H.S end 3496 3008 a 0 0 1 TeXcolorrgb Fx(I)p 0 0 1 TeXcolorrgb 3524 2953 a SDict begin H.R end 3524 2953 a 3524 3008 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (Item.1) cvn H.B /ANN pdfmark end 3524 3008 a 0 TeXcolorgray 30 w Fx(than)f(in)h(Case)p 0 0 1 TeXcolorrgb 4016 3008 a SDict begin H.S end 4016 3008 a 0 0 1 TeXcolorrgb Fx(II)p 0 0 1 TeXcolorrgb 4071 2953 a SDict begin H.R end 4071 2953 a 4071 3008 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (Item.2) cvn H.B /ANN pdfmark end 4071 3008 a 0 TeXcolorgray Fx(.)2000 3108 y(Furthermore,)20 b(the)i(scaling)g(la)o(w)h(results)g(in)f([)p 0 0 1 TeXcolorrgb 3338 3109 a SDict begin H.S end 3338 3109 a 0 0 1 TeXcolorrgb -1 x Fx(6)p 0 0 1 TeXcolorrgb 3379 3051 a SDict begin H.R end 3379 3051 a 3379 3108 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (cite.fengler2021non) cvn H.B /ANN pdfmark end 3379 3108 a 0 TeXcolorgray Fx(]\226[)p 0 0 1 TeXcolorrgb 3477 3109 a SDict begin H.S end 3477 3109 a 0 0 1 TeXcolorrgb -1 x Fx(8)p 0 0 1 TeXcolorrgb 3518 3051 a SDict begin H.R end 3518 3051 a 3518 3108 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (cite.wang2023covariance) cvn H.B /ANN pdfmark end 3518 3108 a 0 TeXcolorgray Fx(])g(sho)n(w)h(that)f(when)2000 3208 y(the)31 b(system)g(parameters)f(satisfy)h Fu(K)i Ft(=)28 b Fs(O)r Ft(\()p Fu(L)3393 3177 y Fp(2)3430 3208 y Ft(\))k Fx(and)e(under)g(certain)2000 3307 y(methods)35 b(of)h(generating)e(signature)i(sequences,)f Fs(N)3615 3319 y Fp(I)r(I)3693 3307 y Fs(\\)25 b(C)42 b Ft(=)37 b Fs(f)p Fl(0)p Fs(g)2000 3407 y Fx(holds.)47 b(Therefore,)e Fs(N)2713 3419 y Fp(I)2775 3407 y Fs(\\)33 b(C)63 b Ft(=)c Fs(f)p Fl(0)p Fs(g)47 b Fx(also)h(holds)g(under)e(these)2000 3507 y(conditions,)36 b(implying)h(that)h(the)h(number)d(of)i(acti)n(v) o(e)g(de)n(vices)f(that)2000 3606 y(can)26 b(be)h(correctly)e(detected) h(by)g(the)g(MLE)h(problem)e(\()p 0 0 1 TeXcolorrgb 3647 3607 a SDict begin H.S end 3647 3607 a 0 0 1 TeXcolorrgb -1 x Fx(10)p 0 0 1 TeXcolorrgb 3729 3550 a SDict begin H.R end 3729 3550 a 3729 3606 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.2.10) cvn H.B /ANN pdfmark end 3729 3606 a 0 TeXcolorgray Fx(\))i(in)g(Case)p 0 0 1 TeXcolorrgb 4064 3606 a SDict begin H.S end 4064 3606 a 0 0 1 TeXcolorrgb Fx(I)p 0 0 1 TeXcolorrgb 4092 3551 a SDict begin H.R end 4092 3551 a 4092 3606 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (Item.1) cvn H.B /ANN pdfmark end 4092 3606 a 0 TeXcolorgray 2000 3706 a Fx(is)i(at)g(least)g Fu(K)g Ft(=)23 b Fs(O)r Ft(\()p Fu(L)2699 3676 y Fp(2)2736 3706 y Ft(\))p Fu(:)2083 3809 y Fx(Notice)30 b(that)h(if)p 2573 3742 56 4 v 31 w Fo(h)2628 3821 y Fr(n)2700 3809 y Ft(=)26 b Fl(0)31 b Fx(for)f(all)h Fu(n;)g Fx(then)f(sets)h Fs(N)3613 3821 y Fp(I)3673 3809 y Fx(and)f Fs(N)3892 3821 y Fp(I)r(I)3977 3809 y Fx(can)2000 3909 y(be)e(represented)f(as) 2511 4096 y Fs(N)2579 4108 y Fp(I)2630 4096 y Ft(=)2717 4003 y Fk(n)2773 4096 y Fo(x)c Fs(2)g Fn(R)2983 4061 y Fr(N)3066 4000 y Fk(\014)3066 4050 y(\014)3066 4100 y(\014)3093 4096 y Fl(\011)3167 4061 y Fp(\()p Fr(I)5 b Fp(\))3258 4096 y Fo(x)22 b Ft(=)h Fl(0)3481 4003 y Fk(o)3550 4096 y Fu(;)3954 4096 y SDict begin H.S end 3954 4096 a 3954 4096 a SDict begin 15 H.A end 3954 4096 a 3954 4096 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.52) cvn 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271.333 M 72 271.333 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 256.683 M 72 256.683 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 248.113 M 72 248.113 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 242.033 M 72 242.033 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 237.317 M 72 237.317 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 233.463 M 72 233.463 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 230.205 M 72 230.205 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 227.383 M 72 227.383 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 224.894 M 72 224.894 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 222.667 M 72 222.667 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 208.017 M 72 208.017 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 199.447 M 72 199.447 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 193.366 M 72 193.366 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 188.65 M 72 188.65 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 184.797 M 72 184.797 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 181.539 M 72 181.539 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 178.716 M 72 178.716 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 176.227 M 72 176.227 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 174 M 72 174 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 159.35 M 72 159.35 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 150.78 M 72 150.78 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 144.7 M 72 144.7 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 139.983 M 72 139.983 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 136.13 M 72 136.13 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 132.872 M 72 132.872 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 130.05 M 72 130.05 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 127.56 M 72 127.56 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 110.683 M 72 110.683 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 102.113 M 72 102.113 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 96.033 M 72 96.033 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 91.317 M 72 91.317 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 87.463 M 72 87.463 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 84.205 M 72 84.205 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 81.383 M 72 81.383 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 78.894 M 72 78.894 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 76.667 M 72 76.667 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 62.017 M 72 62.017 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 53.447 M 72 53.447 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 47.366 M 72 47.366 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 42.65 M 72 42.65 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 38.797 M 72 38.797 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 35.539 M 72 35.539 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 32.716 M 72 32.716 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 30.227 M 72 30.227 L S GR GS [0.5 0 0 0.5 0 0] CT 0.873 GC 1 LJ N 456 320 M 72 320 L S GR GS [0.5 0 0 0.5 0 0] CT 0.873 GC 1 LJ N 456 222.667 M 72 222.667 L S GR GS [0.5 0 0 0.5 0 0] CT 0.873 GC 1 LJ N 456 125.333 M 72 125.333 L S GR GS [0.5 0 0 0.5 0 0] CT 0.873 GC 1 LJ N 456 28 M 72 28 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 320 M 456 320 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 28 M 456 28 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 126.857 320 M 126.857 316.17 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 236.571 320 M 236.571 316.17 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 346.286 320 M 346.286 316.17 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 320 M 456 316.17 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 126.857 28 M 126.857 31.83 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 236.571 28 M 236.571 31.83 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 346.286 28 M 346.286 31.83 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 28 M 456 31.83 L S GR GS [0.5 0 0 0.5 63.42857 163.39999] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT -11 20 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 118.28571 163.39999] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT -11 20 moveto 1 -1 scale (20) t GR GR GS [0.5 0 0 0.5 173.14285 163.39999] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT -11 20 moveto 1 -1 scale (30) t GR GR GS [0.5 0 0 0.5 228 163.39999] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT -11 20 moveto 1 -1 scale (40) t GR GR GS [0.5 0 0 0.5 69 186.5] CT 0.149 GC /Times-Roman 20.9 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (Signature sequence length \() t GR GR GS [0.5 0 0 0.5 185 186.5] CT 0.149 GC /Times-Italic 20.9 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (L) t GR GR GS [0.5 0 0 0.5 191 186.5] CT 0.149 GC /Times-Roman 20.9 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (\)) t GR GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 320 M 72 28 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 320 M 456 28 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 320 M 75.83 320 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 222.667 M 75.83 222.667 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 125.333 M 75.83 125.333 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 28 M 75.83 28 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 320 M 452.17 320 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 222.667 M 452.17 222.667 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 125.333 M 452.17 125.333 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 28 M 452.17 28 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 320 M 73.915 320 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 305.35 M 73.915 305.35 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 296.78 M 73.915 296.78 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 290.7 M 73.915 290.7 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 285.983 M 73.915 285.983 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 282.13 M 73.915 282.13 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 278.872 M 73.915 278.872 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 276.05 M 73.915 276.05 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 273.56 M 73.915 273.56 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 271.333 M 73.915 271.333 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 256.683 M 73.915 256.683 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 248.113 M 73.915 248.113 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 242.033 M 73.915 242.033 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 237.317 M 73.915 237.317 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 233.463 M 73.915 233.463 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 230.205 M 73.915 230.205 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 227.383 M 73.915 227.383 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 224.894 M 73.915 224.894 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 222.667 M 73.915 222.667 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 222.667 M 73.915 222.667 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 208.017 M 73.915 208.017 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 199.447 M 73.915 199.447 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 193.366 M 73.915 193.366 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 188.65 M 73.915 188.65 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 184.797 M 73.915 184.797 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 181.539 M 73.915 181.539 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 178.716 M 73.915 178.716 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 176.227 M 73.915 176.227 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 174 M 73.915 174 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 159.35 M 73.915 159.35 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 150.78 M 73.915 150.78 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 144.7 M 73.915 144.7 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 139.983 M 73.915 139.983 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 136.13 M 73.915 136.13 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 132.872 M 73.915 132.872 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 130.05 M 73.915 130.05 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 127.56 M 73.915 127.56 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 125.333 M 73.915 125.333 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 110.683 M 73.915 110.683 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 102.113 M 73.915 102.113 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 96.033 M 73.915 96.033 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 91.317 M 73.915 91.317 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 87.463 M 73.915 87.463 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 84.205 M 73.915 84.205 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 81.383 M 73.915 81.383 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 78.894 M 73.915 78.894 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 76.667 M 73.915 76.667 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 62.017 M 73.915 62.017 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 53.447 M 73.915 53.447 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 47.366 M 73.915 47.366 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 42.65 M 73.915 42.65 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 38.797 M 73.915 38.797 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 35.539 M 73.915 35.539 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 32.716 M 73.915 32.716 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 30.227 M 73.915 30.227 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 28 M 73.915 28 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 320 M 454.085 320 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 305.35 M 454.085 305.35 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 296.78 M 454.085 296.78 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 290.7 M 454.085 290.7 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 285.983 M 454.085 285.983 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 282.13 M 454.085 282.13 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 278.872 M 454.085 278.872 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 276.05 M 454.085 276.05 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 273.56 M 454.085 273.56 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 271.333 M 454.085 271.333 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 256.683 M 454.085 256.683 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 248.113 M 454.085 248.113 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 242.033 M 454.085 242.033 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 237.317 M 454.085 237.317 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 233.463 M 454.085 233.463 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 230.205 M 454.085 230.205 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 227.383 M 454.085 227.383 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 224.894 M 454.085 224.894 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 222.667 M 454.085 222.667 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 222.667 M 454.085 222.667 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 208.017 M 454.085 208.017 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 199.447 M 454.085 199.447 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 193.366 M 454.085 193.366 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 188.65 M 454.085 188.65 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 184.797 M 454.085 184.797 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 181.539 M 454.085 181.539 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 178.716 M 454.085 178.716 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 176.227 M 454.085 176.227 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 174 M 454.085 174 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 159.35 M 454.085 159.35 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 150.78 M 454.085 150.78 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 144.7 M 454.085 144.7 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 139.983 M 454.085 139.983 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 136.13 M 454.085 136.13 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 132.872 M 454.085 132.872 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 130.05 M 454.085 130.05 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 127.56 M 454.085 127.56 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 125.333 M 454.085 125.333 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 110.683 M 454.085 110.683 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 102.113 M 454.085 102.113 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 96.033 M 454.085 96.033 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 91.317 M 454.085 91.317 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 87.463 M 454.085 87.463 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 84.205 M 454.085 84.205 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 81.383 M 454.085 81.383 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 78.894 M 454.085 78.894 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 76.667 M 454.085 76.667 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 62.017 M 454.085 62.017 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 53.447 M 454.085 53.447 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 47.366 M 454.085 47.366 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 42.65 M 454.085 42.65 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 38.797 M 454.085 38.797 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 35.539 M 454.085 35.539 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 32.716 M 454.085 32.716 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 30.227 M 454.085 30.227 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 28 M 454.085 28 L S GR GS [0.5 0 0 0.5 14.5 165] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 160.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-6) t GR GR GS [0.5 0 0 0.5 14.5 116.5] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 112] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-4) t GR GR GS [0.5 0 0 0.5 14.5 67.5] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 63] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-2) t GR GR GS [0.5 0 0 0.5 17 19] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 28 14.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (0) t GR GR GS [0 -0.5 0.5 0 12.6 86.99993] CT 0.149 GC /Times-Roman 20.9 F GS [1 0 0 1 0 0] CT -128 -5 moveto 1 -1 scale (Probability of error \(PM = PF\)) t GR GR GS [0.5 0 0 0.5 0 0] CT 0 0.447 0.741 RC 1 LJ 3 LW N 72 68.663 M 126.857 112.173 L 181.714 142.341 L 236.571 159.945 L 291.429 183.286 L 346.286 178.716 L 401.143 192.787 L 456 206.325 L 456.046 206.342 L S GR GS [0.5 0 0 0.5 36 34.33126] CT 0 0.447 0.741 RC N 0 -3.5 M 1.933 -3.5 3.5 -1.933 3.5 0 C 3.5 0 L 3.5 1.933 1.933 3.5 0 3.5 C -1.933 3.5 -3.5 1.933 -3.5 0 C -3.5 -1.933 -1.933 -3.5 0 -3.5 C cp 0 -6.5 M -3.59 -6.5 -6.5 -3.59 -6.5 0 C -6.5 3.59 -3.59 6.5 0 6.5 C 3.59 6.5 6.5 3.59 6.5 0 C 6.5 0 L 6.5 -3.59 3.59 -6.5 0 -6.5 C cp f GR GS [0.5 0 0 0.5 63.42857 56.08644] CT 0 0.447 0.741 RC N /f223118758{0 -3.5 M 1.933 -3.5 3.5 -1.933 3.5 0 C 3.5 0 L 3.5 1.933 1.933 3.5 0 3.5 C -1.933 3.5 -3.5 1.933 -3.5 0 C -3.5 -1.933 -1.933 -3.5 0 -3.5 C cp 0 -6.5 M -3.59 -6.5 -6.5 -3.59 -6.5 0 C -6.5 3.59 -3.59 6.5 0 6.5 C 3.59 6.5 6.5 3.59 6.5 0 C 6.5 0 L 6.5 -3.59 3.59 -6.5 0 -6.5 C cp}def f223118758 f GR GS [0.5 0 0 0.5 90.85715 71.1706] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 118.28571 79.97264] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 145.71429 91.64315] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 173.14285 89.35815] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 200.57143 96.39366] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 228 103.16239] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 0 0] CT 0.851 0.325 0.098 RC 1 LJ 3 LW N 72 59.736 M 126.857 103.488 L 181.714 144.966 L 236.571 181.041 L 291.429 216.586 L 346.286 233.075 L 401.143 238.525 L 456 283.757 L S GR GS [0.5 0 0 0.5 36 29.86793] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 63.42857 51.74397] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 90.85715 72.48281] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 118.28571 90.52061] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 145.71429 108.29316] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 173.14285 116.53774] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 200.57143 119.26244] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 228 141.8783] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.929 0.694 0.125 RC 1 LJ 3 LW N 72 55.707 M 126.857 91.067 L 181.714 134.895 L 236.571 173.535 L 291.429 210.506 L 346.286 223.875 L 401.143 283.757 L 456 315.048 L S GR GS [0.5 0 0 0.5 36 27.85357] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 63.42857 45.5335] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 90.85715 67.44736] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 118.28571 86.76773] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 145.71429 105.25298] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 173.14285 111.93738] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 200.57143 141.8783] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 228 157.52415] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.494 0.184 0.557 RC 1 LJ 3 LW N 72 48.041 M 126.857 63.438 L 181.714 93.077 L 236.571 132.375 L 291.429 186.005 L 346.286 242.033 L 391.973 320.035 L S GR GS [0.5 0 0 0.5 36 24.02039] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 63.42857 31.71884] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 90.85715 46.53828] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 118.28571 66.18729] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 145.71429 93.00237] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 173.14285 121.01654] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 0 0] CT 1 GC N 453 122 M 453 31 L 229 31 L 229 122 L cp f GR GS [0.5 0 0 0.5 149.855 22.17918] CT N 3.875 2.291 M 4.453 3.026 5.328 3.456 QT 6.203 3.885 7.141 3.885 QT 7.922 3.885 8.594 3.573 QT 9.266 3.26 9.773 2.706 QT 10.281 2.151 10.547 1.44 QT 10.813 0.729 10.813 -0.052 QT 10.813 -0.177 10.969 -0.177 QT 11.172 -0.177 L 11.313 -0.177 11.313 -0.021 QT 11.313 0.87 10.969 1.698 QT 10.625 2.526 10 3.151 QT 9.375 3.776 8.57 4.127 QT 7.766 4.479 6.875 4.479 QT 5.656 4.479 4.57 3.987 QT 3.484 3.495 2.672 2.635 QT 1.859 1.776 1.406 0.643 QT 0.953 -0.49 0.953 -1.709 QT 0.953 -2.927 1.406 -4.052 QT 1.859 -5.177 2.672 -6.044 QT 3.484 -6.912 4.57 -7.396 QT 5.656 -7.88 6.875 -7.88 QT 7.75 -7.88 8.547 -7.505 QT 9.344 -7.13 9.938 -6.443 QT 10.938 -7.834 L 11.031 -7.88 11.047 -7.88 QT 11.172 -7.88 L 11.219 -7.88 11.266 -7.841 QT 11.313 -7.802 11.313 -7.74 QT 11.313 -3.146 L 11.313 -3.005 11.172 -3.005 QT 10.859 -3.005 L 10.703 -3.005 10.703 -3.146 QT 10.703 -3.646 10.508 -4.248 QT 10.313 -4.849 10.016 -5.396 QT 9.719 -5.943 9.313 -6.349 QT 8.359 -7.287 7.125 -7.287 QT 6.188 -7.287 5.328 -6.865 QT 4.469 -6.443 3.875 -5.693 QT 3.25 -4.896 3.008 -3.88 QT 2.766 -2.865 2.766 -1.709 QT 2.766 -0.552 3.008 0.471 QT 3.25 1.495 3.875 2.291 QT cp f GR GS [0.5 0 0 0.5 149.855 22.17918] CT N 13.038 2.432 M 13.038 1.416 13.834 0.784 QT 14.631 0.151 15.741 -0.107 QT 16.85 -0.365 17.866 -0.365 QT 17.866 -1.068 L 17.866 -1.552 17.647 -2.013 QT 17.428 -2.474 17.022 -2.771 QT 16.616 -3.068 16.131 -3.068 QT 14.991 -3.068 14.413 -2.568 QT 14.725 -2.568 14.944 -2.318 QT 15.163 -2.068 15.163 -1.755 QT 15.163 -1.412 14.92 -1.169 QT 14.678 -0.927 14.35 -0.927 QT 14.006 -0.927 13.764 -1.169 QT 13.522 -1.412 13.522 -1.755 QT 13.522 -2.646 14.334 -3.084 QT 15.147 -3.521 16.131 -3.521 QT 16.819 -3.521 17.514 -3.224 QT 18.209 -2.927 18.655 -2.38 QT 19.1 -1.834 19.1 -1.099 QT 19.1 2.729 L 19.1 3.057 19.241 3.338 QT 19.381 3.62 19.678 3.62 QT 19.959 3.62 20.1 3.338 QT 20.241 3.057 20.241 2.729 QT 20.241 1.635 L 20.741 1.635 L 20.741 2.729 L 20.741 3.104 20.538 3.448 QT 20.334 3.791 19.998 3.995 QT 19.663 4.198 19.272 4.198 QT 18.772 4.198 18.413 3.815 QT 18.053 3.432 18.006 2.901 QT 17.694 3.541 17.084 3.916 QT 16.475 4.291 15.772 4.291 QT 15.116 4.291 14.491 4.104 QT 13.866 3.916 13.452 3.502 QT 13.038 3.088 13.038 2.432 QT cp 14.413 2.432 M 14.413 3.026 14.85 3.44 QT 15.288 3.854 15.881 3.854 QT 16.428 3.854 16.881 3.573 QT 17.334 3.291 17.6 2.823 QT 17.866 2.354 17.866 1.823 QT 17.866 0.057 L 17.084 0.057 16.28 0.315 QT 15.475 0.573 14.944 1.112 QT 14.413 1.651 14.413 2.432 QT cp f GR GS [0.5 0 0 0.5 149.855 22.17918] CT N 21.463 4.151 M 21.463 1.385 L 21.463 1.245 21.619 1.245 QT 21.822 1.245 L 21.916 1.245 21.947 1.385 QT 22.431 3.854 24.244 3.854 QT 25.056 3.854 25.595 3.487 QT 26.134 3.12 26.134 2.354 QT 26.134 1.807 25.713 1.416 QT 25.291 1.026 24.713 0.885 QT 23.572 0.666 L 22.994 0.541 22.525 0.284 QT 22.056 0.026 21.759 -0.404 QT 21.463 -0.834 21.463 -1.396 QT 21.463 -2.146 21.861 -2.623 QT 22.259 -3.099 22.884 -3.31 QT 23.509 -3.521 24.244 -3.521 QT 25.119 -3.521 25.759 -3.052 QT 26.259 -3.474 L 26.259 -3.521 26.338 -3.521 QT 26.463 -3.521 L 26.509 -3.521 26.548 -3.474 QT 26.588 -3.427 26.588 -3.38 QT 26.588 -1.146 L 26.588 -0.99 26.463 -0.99 QT 26.259 -0.99 L 26.103 -0.99 26.103 -1.146 QT 26.103 -2.037 25.611 -2.576 QT 25.119 -3.115 24.228 -3.115 QT 23.463 -3.115 22.9 -2.834 QT 22.338 -2.552 22.338 -1.865 QT 22.338 -1.396 22.744 -1.091 QT 23.15 -0.787 23.697 -0.646 QT 24.838 -0.443 L 25.431 -0.302 25.931 0.01 QT 26.431 0.323 26.728 0.807 QT 27.025 1.291 27.025 1.901 QT 27.025 2.51 26.806 2.963 QT 26.588 3.416 26.213 3.713 QT 25.838 4.01 25.322 4.151 QT 24.806 4.291 24.244 4.291 QT 23.181 4.291 22.431 3.588 QT 21.806 4.26 L 21.806 4.291 21.713 4.291 QT 21.619 4.291 L 21.463 4.291 21.463 4.151 QT cp f GR GS [0.5 0 0 0.5 149.855 22.17918] CT N 31.879 4.291 M 30.848 4.291 29.981 3.752 QT 29.114 3.213 28.614 2.299 QT 28.114 1.385 28.114 0.37 QT 28.114 -0.615 28.567 -1.513 QT 29.02 -2.412 29.833 -2.966 QT 30.645 -3.521 31.645 -3.521 QT 32.411 -3.521 32.989 -3.255 QT 33.567 -2.99 33.942 -2.529 QT 34.317 -2.068 34.512 -1.435 QT 34.708 -0.802 34.708 -0.052 QT 34.708 0.182 34.52 0.182 QT 29.598 0.182 L 29.598 0.354 L 29.598 1.776 30.168 2.784 QT 30.739 3.791 32.036 3.791 QT 32.551 3.791 32.997 3.565 QT 33.442 3.338 33.77 2.916 QT 34.098 2.495 34.208 2.026 QT 34.223 1.963 34.27 1.924 QT 34.317 1.885 34.379 1.885 QT 34.52 1.885 L 34.708 1.885 34.708 2.088 QT 34.458 3.057 33.661 3.674 QT 32.864 4.291 31.879 4.291 QT cp 29.614 -0.24 M 33.504 -0.24 L 33.504 -0.88 33.325 -1.537 QT 33.145 -2.193 32.731 -2.63 QT 32.317 -3.068 31.645 -3.068 QT 30.676 -3.068 30.145 -2.169 QT 29.614 -1.271 29.614 -0.24 QT cp f GR GS [0.5 0 0 0.5 149.855 22.17918] CT N 41.383 4.104 M 41.383 3.51 L 43.226 3.51 43.226 2.963 QT 43.226 -6.365 L 43.226 -6.912 41.383 -6.912 QT 41.383 -7.505 L 46.633 -7.505 L 46.633 -6.912 L 44.804 -6.912 44.804 -6.365 QT 44.804 2.963 L 44.804 3.51 46.633 3.51 QT 46.633 4.104 L 41.383 4.104 L cp f GR GS [0.5 0 0 0.5 149.855 22.17918] CT N 56.586 4.104 M 54.383 -2.084 L 54.226 -2.459 53.945 -2.544 QT 53.664 -2.63 53.133 -2.63 QT 53.133 -3.224 L 56.633 -3.224 L 56.633 -2.63 L 55.633 -2.63 55.633 -2.209 QT 55.633 -2.177 55.64 -2.154 QT 55.648 -2.13 55.648 -2.084 QT 57.273 2.495 L 58.695 -1.49 L 58.461 -2.084 L 58.336 -2.459 58.047 -2.544 QT 57.758 -2.63 57.226 -2.63 QT 57.226 -3.224 L 60.57 -3.224 L 60.57 -2.63 L 59.57 -2.63 59.57 -2.209 QT 59.57 -2.146 59.586 -2.084 QT 61.289 2.713 L 62.836 -1.63 L 62.867 -1.755 62.867 -1.865 QT 62.867 -2.224 62.562 -2.427 QT 62.258 -2.63 61.883 -2.63 QT 61.883 -3.224 L 64.773 -3.224 L 64.773 -2.63 L 64.258 -2.63 63.89 -2.357 QT 63.523 -2.084 63.351 -1.63 QT 61.32 4.104 L 61.258 4.291 61.07 4.291 QT 60.929 4.291 L 60.726 4.291 60.679 4.104 QT 58.961 -0.74 L 57.242 4.104 L 57.148 4.291 56.976 4.291 QT 56.851 4.291 L 56.633 4.291 56.586 4.104 QT cp f GR GS [0.5 0 0 0.5 149.855 22.17918] CT N 65.686 4.104 M 65.686 3.51 L 66.279 3.51 66.647 3.416 QT 67.014 3.323 67.014 2.963 QT 67.014 -1.677 L 67.014 -2.334 66.764 -2.482 QT 66.514 -2.63 65.764 -2.63 QT 65.764 -3.224 L 68.217 -3.412 L 68.217 2.963 L 68.217 3.323 68.537 3.416 QT 68.858 3.51 69.404 3.51 QT 69.404 4.104 L 65.686 4.104 L cp 66.42 -6.334 M 66.42 -6.709 66.701 -6.99 QT 66.983 -7.271 67.342 -7.271 QT 67.592 -7.271 67.811 -7.146 QT 68.029 -7.021 68.154 -6.794 QT 68.279 -6.568 68.279 -6.334 QT 68.279 -5.959 67.998 -5.677 QT 67.717 -5.396 67.342 -5.396 QT 66.983 -5.396 66.701 -5.677 QT 66.42 -5.959 66.42 -6.334 QT cp f GR GS [0.5 0 0 0.5 149.855 22.17918] CT N 71.654 2.057 M 71.654 -2.63 L 70.248 -2.63 L 70.248 -3.068 L 71.358 -3.068 71.881 -4.107 QT 72.404 -5.146 72.404 -6.349 QT 72.889 -6.349 L 72.889 -3.224 L 75.295 -3.224 L 75.295 -2.63 L 72.889 -2.63 L 72.889 2.026 L 72.889 2.729 73.123 3.26 QT 73.358 3.791 73.983 3.791 QT 74.561 3.791 74.818 3.237 QT 75.076 2.682 75.076 2.026 QT 75.076 1.026 L 75.561 1.026 L 75.561 2.057 L 75.561 2.588 75.365 3.112 QT 75.17 3.635 74.787 3.963 QT 74.404 4.291 73.858 4.291 QT 72.842 4.291 72.248 3.682 QT 71.654 3.073 71.654 2.057 QT cp f GR GS [0.5 0 0 0.5 149.855 22.17918] CT N 77.07 4.104 M 77.07 3.51 L 77.664 3.51 78.031 3.416 QT 78.398 3.323 78.398 2.963 QT 78.398 -5.959 L 78.398 -6.412 78.265 -6.615 QT 78.133 -6.818 77.875 -6.865 QT 77.617 -6.912 77.07 -6.912 QT 77.07 -7.505 L 79.601 -7.693 L 79.601 -1.849 L 79.961 -2.552 80.601 -2.982 QT 81.242 -3.412 82.008 -3.412 QT 83.179 -3.412 83.773 -2.849 QT 84.367 -2.287 84.367 -1.115 QT 84.367 2.963 L 84.367 3.323 84.742 3.416 QT 85.117 3.51 85.695 3.51 QT 85.695 4.104 L 81.804 4.104 L 81.804 3.51 L 82.383 3.51 82.758 3.416 QT 83.133 3.323 83.133 2.963 QT 83.133 -1.068 L 83.133 -1.896 82.89 -2.435 QT 82.648 -2.974 81.914 -2.974 QT 80.914 -2.974 80.281 -2.185 QT 79.648 -1.396 79.648 -0.38 QT 79.648 2.963 L 79.648 3.323 80.023 3.416 QT 80.398 3.51 80.976 3.51 QT 80.976 4.104 L 77.07 4.104 L cp f GR GS [0.5 0 0 0.5 149.855 22.17918] CT N 94.13 -9.846 M 94.13 -10.44 L 100.27 -10.44 L 100.27 -9.846 L 94.13 -9.846 L cp f GR GS [0.5 0 0 0.5 149.855 22.17918] CT N 92.176 2.838 M 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456 258.308 M 454.085 258.308 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 254.074 M 454.085 254.074 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 250.34 M 454.085 250.34 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 247 M 454.085 247 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 225.025 M 454.085 225.025 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 212.17 M 454.085 212.17 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 203.05 M 454.085 203.05 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 195.975 M 454.085 195.975 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 190.195 M 454.085 190.195 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 185.308 M 454.085 185.308 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 181.074 M 454.085 181.074 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 177.34 M 454.085 177.34 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 174 M 454.085 174 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 152.025 M 454.085 152.025 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 139.17 M 454.085 139.17 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 130.05 M 454.085 130.05 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 122.975 M 454.085 122.975 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 117.195 M 454.085 117.195 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 112.308 M 454.085 112.308 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 108.074 M 454.085 108.074 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 104.34 M 454.085 104.34 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 101 M 454.085 101 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 79.025 M 454.085 79.025 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 66.17 M 454.085 66.17 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 57.05 M 454.085 57.05 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 49.975 M 454.085 49.975 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 44.195 M 454.085 44.195 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 39.308 M 454.085 39.308 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 35.074 M 454.085 35.074 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 31.34 M 454.085 31.34 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 28 M 454.085 28 L S GR GS [0.5 0 0 0.5 14.5 165] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 160.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-4) t GR GR GS [0.5 0 0 0.5 14.5 128.5] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 124] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-3) t GR GR GS [0.5 0 0 0.5 14.5 92] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 87.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-2) t GR GR GS [0.5 0 0 0.5 14.5 55.5] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 51] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-1) t GR GR GS [0.5 0 0 0.5 17 19] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 28 14.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (0) t GR GR GS [0 -0.5 0.5 0 12.6 86.99993] CT 0.149 GC /Times-Roman 20.9 F GS [1 0 0 1 0 0] CT -128 -5 moveto 1 -1 scale (Probability of error \(PM = PF\)) t GR GR GS [0.5 0 0 0.5 0 0] CT 0 0.447 0.741 RC 1 LJ 3 LW N 71.954 238.135 M 72 238.145 L 120 233.144 L 168 220.517 L 216 223.714 L 264 215.904 L 312 210.156 L 360 194.529 L 408 189.32 L 456 180.89 L S GR GS [0.5 0 0 0.5 36 119.07239] CT 0 0.447 0.741 RC N 0 -3.5 M 1.933 -3.5 3.5 -1.933 3.5 0 C 3.5 0 L 3.5 1.933 1.933 3.5 0 3.5 C -1.933 3.5 -3.5 1.933 -3.5 0 C -3.5 -1.933 -1.933 -3.5 0 -3.5 C cp 0 -6.5 M -3.59 -6.5 -6.5 -3.59 -6.5 0 C -6.5 3.59 -3.59 6.5 0 6.5 C 3.59 6.5 6.5 3.59 6.5 0 C 6.5 0 L 6.5 -3.59 3.59 -6.5 0 -6.5 C cp f GR GS [0.5 0 0 0.5 60 116.57185] CT 0 0.447 0.741 RC N /f223118758{0 -3.5 M 1.933 -3.5 3.5 -1.933 3.5 0 C 3.5 0 L 3.5 1.933 1.933 3.5 0 3.5 C -1.933 3.5 -3.5 1.933 -3.5 0 C -3.5 -1.933 -1.933 -3.5 0 -3.5 C cp 0 -6.5 M -3.59 -6.5 -6.5 -3.59 -6.5 0 C -6.5 3.59 -3.59 6.5 0 6.5 C 3.59 6.5 6.5 3.59 6.5 0 C 6.5 0 L 6.5 -3.59 3.59 -6.5 0 -6.5 C cp}def f223118758 f GR GS [0.5 0 0 0.5 84 110.25869] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 108 111.85685] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 132 107.95214] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 156 105.07776] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 180 97.26459] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 204 94.65998] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 228 90.44501] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 0 0] CT 0.851 0.325 0.098 RC 1 LJ 3 LW N 71.954 270.183 M 72 270.123 L 120 266.492 L 168 250.145 L 216 235.538 L 264 218.424 L 312 202.451 L 360 185.7 L 408 173.875 L 456 155.127 L S GR GS [0.5 0 0 0.5 36 135.06148] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 60 133.2459] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 84 125.0726] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 108 117.76877] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 132 109.21178] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 156 101.22571] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 180 92.85014] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 204 86.9375] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 228 77.56362] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.929 0.694 0.125 RC 1 LJ 3 LW N 71.954 296.293 M 72 296.311 L 120 274.336 L 168 255.424 L 216 233.357 L 264 203.762 L 312 178.735 L 360 161.762 L 408 143.467 L 456 125.048 L S GR GS [0.5 0 0 0.5 36 148.15535] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 60 137.16776] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 84 127.71186] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 108 116.67838] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 132 101.88104] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 156 89.36742] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 180 80.88094] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 204 71.7335] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 228 62.52399] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.494 0.184 0.557 RC 1 LJ 3 LW N 71.954 313.679 M 72 313.628 L 120 232.543 L 168 187.712 L 216 148.206 L 264 124.666 L 312 107.012 L 360 95.196 L 408 87.826 L 456 81.773 L S GR GS [0.5 0 0 0.5 36 156.81389] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 60 116.27132] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 84 93.85578] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 108 74.10312] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 132 62.33285] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 156 53.50588] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 180 47.59778] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 204 43.913] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 228 40.8865] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 0 0] CT 1 GC N 296 113 M 296 22 L 72 22 L 72 113 L cp f GR GS [0.5 0 0 0.5 71.35499 17.67918] CT N 3.875 2.291 M 4.453 3.026 5.328 3.456 QT 6.203 3.885 7.141 3.885 QT 7.922 3.885 8.594 3.573 QT 9.266 3.26 9.773 2.706 QT 10.281 2.151 10.547 1.44 QT 10.813 0.729 10.813 -0.052 QT 10.813 -0.177 10.969 -0.177 QT 11.172 -0.177 L 11.313 -0.177 11.313 -0.021 QT 11.313 0.87 10.969 1.698 QT 10.625 2.526 10 3.151 QT 9.375 3.776 8.57 4.127 QT 7.766 4.479 6.875 4.479 QT 5.656 4.479 4.57 3.987 QT 3.484 3.495 2.672 2.635 QT 1.859 1.776 1.406 0.643 QT 0.953 -0.49 0.953 -1.709 QT 0.953 -2.927 1.406 -4.052 QT 1.859 -5.177 2.672 -6.044 QT 3.484 -6.912 4.57 -7.396 QT 5.656 -7.88 6.875 -7.88 QT 7.75 -7.88 8.547 -7.505 QT 9.344 -7.13 9.938 -6.443 QT 10.938 -7.834 L 11.031 -7.88 11.047 -7.88 QT 11.172 -7.88 L 11.219 -7.88 11.266 -7.841 QT 11.313 -7.802 11.313 -7.74 QT 11.313 -3.146 L 11.313 -3.005 11.172 -3.005 QT 10.859 -3.005 L 10.703 -3.005 10.703 -3.146 QT 10.703 -3.646 10.508 -4.248 QT 10.313 -4.849 10.016 -5.396 QT 9.719 -5.943 9.313 -6.349 QT 8.359 -7.287 7.125 -7.287 QT 6.188 -7.287 5.328 -6.865 QT 4.469 -6.443 3.875 -5.693 QT 3.25 -4.896 3.008 -3.88 QT 2.766 -2.865 2.766 -1.709 QT 2.766 -0.552 3.008 0.471 QT 3.25 1.495 3.875 2.291 QT cp f GR GS [0.5 0 0 0.5 71.35499 17.67918] CT N 13.038 2.432 M 13.038 1.416 13.834 0.784 QT 14.631 0.151 15.741 -0.107 QT 16.85 -0.365 17.866 -0.365 QT 17.866 -1.068 L 17.866 -1.552 17.647 -2.013 QT 17.428 -2.474 17.022 -2.771 QT 16.616 -3.068 16.131 -3.068 QT 14.991 -3.068 14.413 -2.568 QT 14.725 -2.568 14.944 -2.318 QT 15.163 -2.068 15.163 -1.755 QT 15.163 -1.412 14.92 -1.169 QT 14.678 -0.927 14.35 -0.927 QT 14.006 -0.927 13.764 -1.169 QT 13.522 -1.412 13.522 -1.755 QT 13.522 -2.646 14.334 -3.084 QT 15.147 -3.521 16.131 -3.521 QT 16.819 -3.521 17.514 -3.224 QT 18.209 -2.927 18.655 -2.38 QT 19.1 -1.834 19.1 -1.099 QT 19.1 2.729 L 19.1 3.057 19.241 3.338 QT 19.381 3.62 19.678 3.62 QT 19.959 3.62 20.1 3.338 QT 20.241 3.057 20.241 2.729 QT 20.241 1.635 L 20.741 1.635 L 20.741 2.729 L 20.741 3.104 20.538 3.448 QT 20.334 3.791 19.998 3.995 QT 19.663 4.198 19.272 4.198 QT 18.772 4.198 18.413 3.815 QT 18.053 3.432 18.006 2.901 QT 17.694 3.541 17.084 3.916 QT 16.475 4.291 15.772 4.291 QT 15.116 4.291 14.491 4.104 QT 13.866 3.916 13.452 3.502 QT 13.038 3.088 13.038 2.432 QT cp 14.413 2.432 M 14.413 3.026 14.85 3.44 QT 15.288 3.854 15.881 3.854 QT 16.428 3.854 16.881 3.573 QT 17.334 3.291 17.6 2.823 QT 17.866 2.354 17.866 1.823 QT 17.866 0.057 L 17.084 0.057 16.28 0.315 QT 15.475 0.573 14.944 1.112 QT 14.413 1.651 14.413 2.432 QT cp f GR GS [0.5 0 0 0.5 71.35499 17.67918] CT N 21.463 4.151 M 21.463 1.385 L 21.463 1.245 21.619 1.245 QT 21.822 1.245 L 21.916 1.245 21.947 1.385 QT 22.431 3.854 24.244 3.854 QT 25.056 3.854 25.595 3.487 QT 26.134 3.12 26.134 2.354 QT 26.134 1.807 25.713 1.416 QT 25.291 1.026 24.713 0.885 QT 23.572 0.666 L 22.994 0.541 22.525 0.284 QT 22.056 0.026 21.759 -0.404 QT 21.463 -0.834 21.463 -1.396 QT 21.463 -2.146 21.861 -2.623 QT 22.259 -3.099 22.884 -3.31 QT 23.509 -3.521 24.244 -3.521 QT 25.119 -3.521 25.759 -3.052 QT 26.259 -3.474 L 26.259 -3.521 26.338 -3.521 QT 26.463 -3.521 L 26.509 -3.521 26.548 -3.474 QT 26.588 -3.427 26.588 -3.38 QT 26.588 -1.146 L 26.588 -0.99 26.463 -0.99 QT 26.259 -0.99 L 26.103 -0.99 26.103 -1.146 QT 26.103 -2.037 25.611 -2.576 QT 25.119 -3.115 24.228 -3.115 QT 23.463 -3.115 22.9 -2.834 QT 22.338 -2.552 22.338 -1.865 QT 22.338 -1.396 22.744 -1.091 QT 23.15 -0.787 23.697 -0.646 QT 24.838 -0.443 L 25.431 -0.302 25.931 0.01 QT 26.431 0.323 26.728 0.807 QT 27.025 1.291 27.025 1.901 QT 27.025 2.51 26.806 2.963 QT 26.588 3.416 26.213 3.713 QT 25.838 4.01 25.322 4.151 QT 24.806 4.291 24.244 4.291 QT 23.181 4.291 22.431 3.588 QT 21.806 4.26 L 21.806 4.291 21.713 4.291 QT 21.619 4.291 L 21.463 4.291 21.463 4.151 QT cp f GR GS [0.5 0 0 0.5 71.35499 17.67918] CT N 31.879 4.291 M 30.848 4.291 29.981 3.752 QT 29.114 3.213 28.614 2.299 QT 28.114 1.385 28.114 0.37 QT 28.114 -0.615 28.567 -1.513 QT 29.02 -2.412 29.833 -2.966 QT 30.645 -3.521 31.645 -3.521 QT 32.411 -3.521 32.989 -3.255 QT 33.567 -2.99 33.942 -2.529 QT 34.317 -2.068 34.512 -1.435 QT 34.708 -0.802 34.708 -0.052 QT 34.708 0.182 34.52 0.182 QT 29.598 0.182 L 29.598 0.354 L 29.598 1.776 30.168 2.784 QT 30.739 3.791 32.036 3.791 QT 32.551 3.791 32.997 3.565 QT 33.442 3.338 33.77 2.916 QT 34.098 2.495 34.208 2.026 QT 34.223 1.963 34.27 1.924 QT 34.317 1.885 34.379 1.885 QT 34.52 1.885 L 34.708 1.885 34.708 2.088 QT 34.458 3.057 33.661 3.674 QT 32.864 4.291 31.879 4.291 QT cp 29.614 -0.24 M 33.504 -0.24 L 33.504 -0.88 33.325 -1.537 QT 33.145 -2.193 32.731 -2.63 QT 32.317 -3.068 31.645 -3.068 QT 30.676 -3.068 30.145 -2.169 QT 29.614 -1.271 29.614 -0.24 QT cp f GR GS [0.5 0 0 0.5 71.35499 17.67918] CT N 41.383 4.104 M 41.383 3.51 L 43.226 3.51 43.226 2.963 QT 43.226 -6.365 L 43.226 -6.912 41.383 -6.912 QT 41.383 -7.505 L 46.633 -7.505 L 46.633 -6.912 L 44.804 -6.912 44.804 -6.365 QT 44.804 2.963 L 44.804 3.51 46.633 3.51 QT 46.633 4.104 L 41.383 4.104 L cp f GR GS [0.5 0 0 0.5 71.35499 17.67918] CT N 56.586 4.104 M 54.383 -2.084 L 54.226 -2.459 53.945 -2.544 QT 53.664 -2.63 53.133 -2.63 QT 53.133 -3.224 L 56.633 -3.224 L 56.633 -2.63 L 55.633 -2.63 55.633 -2.209 QT 55.633 -2.177 55.64 -2.154 QT 55.648 -2.13 55.648 -2.084 QT 57.273 2.495 L 58.695 -1.49 L 58.461 -2.084 L 58.336 -2.459 58.047 -2.544 QT 57.758 -2.63 57.226 -2.63 QT 57.226 -3.224 L 60.57 -3.224 L 60.57 -2.63 L 59.57 -2.63 59.57 -2.209 QT 59.57 -2.146 59.586 -2.084 QT 61.289 2.713 L 62.836 -1.63 L 62.867 -1.755 62.867 -1.865 QT 62.867 -2.224 62.562 -2.427 QT 62.258 -2.63 61.883 -2.63 QT 61.883 -3.224 L 64.773 -3.224 L 64.773 -2.63 L 64.258 -2.63 63.89 -2.357 QT 63.523 -2.084 63.351 -1.63 QT 61.32 4.104 L 61.258 4.291 61.07 4.291 QT 60.929 4.291 L 60.726 4.291 60.679 4.104 QT 58.961 -0.74 L 57.242 4.104 L 57.148 4.291 56.976 4.291 QT 56.851 4.291 L 56.633 4.291 56.586 4.104 QT cp f GR GS [0.5 0 0 0.5 71.35499 17.67918] CT N 65.686 4.104 M 65.686 3.51 L 66.279 3.51 66.647 3.416 QT 67.014 3.323 67.014 2.963 QT 67.014 -1.677 L 67.014 -2.334 66.764 -2.482 QT 66.514 -2.63 65.764 -2.63 QT 65.764 -3.224 L 68.217 -3.412 L 68.217 2.963 L 68.217 3.323 68.537 3.416 QT 68.858 3.51 69.404 3.51 QT 69.404 4.104 L 65.686 4.104 L cp 66.42 -6.334 M 66.42 -6.709 66.701 -6.99 QT 66.983 -7.271 67.342 -7.271 QT 67.592 -7.271 67.811 -7.146 QT 68.029 -7.021 68.154 -6.794 QT 68.279 -6.568 68.279 -6.334 QT 68.279 -5.959 67.998 -5.677 QT 67.717 -5.396 67.342 -5.396 QT 66.983 -5.396 66.701 -5.677 QT 66.42 -5.959 66.42 -6.334 QT cp f GR GS [0.5 0 0 0.5 71.35499 17.67918] CT N 71.654 2.057 M 71.654 -2.63 L 70.248 -2.63 L 70.248 -3.068 L 71.358 -3.068 71.881 -4.107 QT 72.404 -5.146 72.404 -6.349 QT 72.889 -6.349 L 72.889 -3.224 L 75.295 -3.224 L 75.295 -2.63 L 72.889 -2.63 L 72.889 2.026 L 72.889 2.729 73.123 3.26 QT 73.358 3.791 73.983 3.791 QT 74.561 3.791 74.818 3.237 QT 75.076 2.682 75.076 2.026 QT 75.076 1.026 L 75.561 1.026 L 75.561 2.057 L 75.561 2.588 75.365 3.112 QT 75.17 3.635 74.787 3.963 QT 74.404 4.291 73.858 4.291 QT 72.842 4.291 72.248 3.682 QT 71.654 3.073 71.654 2.057 QT cp f GR GS [0.5 0 0 0.5 71.35499 17.67918] CT N 77.07 4.104 M 77.07 3.51 L 77.664 3.51 78.031 3.416 QT 78.398 3.323 78.398 2.963 QT 78.398 -5.959 L 78.398 -6.412 78.265 -6.615 QT 78.133 -6.818 77.875 -6.865 QT 77.617 -6.912 77.07 -6.912 QT 77.07 -7.505 L 79.601 -7.693 L 79.601 -1.849 L 79.961 -2.552 80.601 -2.982 QT 81.242 -3.412 82.008 -3.412 QT 83.179 -3.412 83.773 -2.849 QT 84.367 -2.287 84.367 -1.115 QT 84.367 2.963 L 84.367 3.323 84.742 3.416 QT 85.117 3.51 85.695 3.51 QT 85.695 4.104 L 81.804 4.104 L 81.804 3.51 L 82.383 3.51 82.758 3.416 QT 83.133 3.323 83.133 2.963 QT 83.133 -1.068 L 83.133 -1.896 82.89 -2.435 QT 82.648 -2.974 81.914 -2.974 QT 80.914 -2.974 80.281 -2.185 QT 79.648 -1.396 79.648 -0.38 QT 79.648 2.963 L 79.648 3.323 80.023 3.416 QT 80.398 3.51 80.976 3.51 QT 80.976 4.104 L 77.07 4.104 L cp f GR GS [0.5 0 0 0.5 71.35499 17.67918] CT N 94.13 -9.846 M 94.13 -10.44 L 100.27 -10.44 L 100.27 -9.846 L 94.13 -9.846 L cp f GR GS [0.5 0 0 0.5 71.35499 17.67918] CT N 92.176 2.838 M 92.098 2.838 92.02 2.752 QT 91.942 2.666 91.942 2.573 QT 91.942 2.432 93.348 1.151 QT 93.348 1.073 93.34 1.026 QT 93.333 0.979 93.333 0.932 QT 93.333 0.198 93.45 -0.56 QT 93.567 -1.318 93.77 -2.076 QT 93.973 -2.834 94.278 -3.654 QT 94.583 -4.474 94.895 -5.099 QT 95.442 -6.209 96.09 -7.044 QT 96.739 -7.88 97.536 -7.88 QT 98.067 -7.88 98.301 -7.513 QT 98.536 -7.146 98.536 -6.584 QT 98.536 -3.474 94.395 0.729 QT 94.333 1.463 94.333 1.776 QT 94.333 3.901 95.301 3.901 QT 95.723 3.901 96.129 3.682 QT 96.536 3.463 96.833 3.206 QT 97.129 2.948 97.661 2.432 QT 97.692 2.401 97.754 2.401 QT 97.848 2.401 97.934 2.502 QT 98.02 2.604 98.02 2.698 QT 98.02 2.745 97.942 2.807 QT 97.176 3.541 96.575 3.948 QT 95.973 4.354 95.27 4.354 QT 94.379 4.354 93.942 3.588 QT 93.504 2.823 93.395 1.76 QT 92.926 2.213 92.27 2.807 QT 92.254 2.838 92.176 2.838 QT cp 94.536 -0.084 M 95.442 -1.037 96.231 -2.099 QT 97.02 -3.162 97.551 -4.341 QT 98.083 -5.521 98.083 -6.63 QT 98.083 -7.443 97.52 -7.443 QT 96.911 -7.443 96.278 -5.998 QT 95.645 -4.552 95.2 -2.865 QT 94.754 -1.177 94.536 -0.084 QT cp f GR GS [0.5 0 0 0.5 71.35499 17.67918] CT N 99.817 6.466 M 99.817 6.388 99.833 6.356 QT 100.723 2.778 L 100.817 2.45 100.817 2.185 QT 100.817 1.669 100.473 1.669 QT 100.098 1.669 99.911 2.122 QT 99.723 2.575 99.551 3.263 QT 99.551 3.294 99.52 3.317 QT 99.489 3.341 99.458 3.341 QT 99.317 3.341 L 99.27 3.341 99.247 3.294 QT 99.223 3.247 99.223 3.216 QT 99.348 2.685 99.465 2.325 QT 99.583 1.966 99.84 1.669 QT 100.098 1.372 100.473 1.372 QT 100.926 1.372 101.27 1.653 QT 101.614 1.935 101.614 2.372 QT 101.973 1.903 102.458 1.638 QT 102.942 1.372 103.473 1.372 QT 103.911 1.372 104.215 1.513 QT 104.52 1.653 104.7 1.95 QT 104.88 2.247 104.88 2.653 QT 104.88 3.153 104.653 3.849 QT 104.426 4.544 104.098 5.403 QT 103.942 5.794 103.942 6.122 QT 103.942 6.481 104.208 6.481 QT 104.676 6.481 104.989 5.981 QT 105.301 5.481 105.442 4.903 QT 105.458 4.841 105.536 4.841 QT 105.676 4.841 L 105.723 4.841 105.755 4.864 QT 105.786 4.888 105.786 4.935 QT 105.786 4.95 105.77 4.981 QT 105.614 5.653 105.208 6.231 QT 104.801 6.81 104.192 6.81 QT 103.77 6.81 103.465 6.513 QT 103.161 6.216 103.161 5.81 QT 103.161 5.591 103.255 5.341 QT 103.411 4.95 103.606 4.403 QT 103.801 3.856 103.926 3.356 QT 104.051 2.856 104.051 2.481 QT 104.051 2.138 103.919 1.903 QT 103.786 1.669 103.458 1.669 QT 103.02 1.669 102.645 1.864 QT 102.27 2.06 101.997 2.38 QT 101.723 2.7 101.505 3.138 QT 100.676 6.403 L 100.645 6.575 100.497 6.692 QT 100.348 6.81 100.176 6.81 QT 100.036 6.81 99.926 6.716 QT 99.817 6.622 99.817 6.466 QT cp f GR GS [0.5 0 0 0.5 71.35499 17.67918] CT N 112.966 1.838 M 112.825 1.838 112.732 1.737 QT 112.638 1.635 112.638 1.51 QT 112.638 1.37 112.732 1.268 QT 112.825 1.166 112.966 1.166 QT 123.638 1.166 L 123.763 1.166 123.857 1.268 QT 123.95 1.37 123.95 1.51 QT 123.95 1.635 123.857 1.737 QT 123.763 1.838 123.638 1.838 QT 112.966 1.838 L cp 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/I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /bullet /Euro /bullet /quotesinglbase /florin /quotedblbase /ellipsis /dagger /daggerdbl /circumflex /perthousand /Scaron /guilsinglleft /OE /bullet /Zcaron /bullet /bullet /quoteleft /quoteright /quotedblleft /quotedblright /bullet /endash /emdash /asciitilde /trademark /scaron /guilsinglright /oe /bullet /zcaron /Ydieresis /space /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /sfthyphen /registered /macron /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /middot /cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def %%EndResource %FOPBeginFontReencode /Courier-Oblique findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Courier-Oblique exch definefont pop /Courier-BoldOblique findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Courier-BoldOblique exch definefont pop /Courier-Bold findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Courier-Bold exch definefont pop /Helvetica findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Helvetica exch definefont pop /Helvetica-Oblique findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Helvetica-Oblique exch definefont pop /Helvetica-Bold findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Helvetica-Bold exch definefont pop /Helvetica-BoldOblique findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Helvetica-BoldOblique exch definefont pop /Times-Roman findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Times-Roman exch definefont pop /Times-Italic findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Times-Italic exch definefont pop /Times-Bold findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Times-Bold exch definefont pop /Times-BoldItalic findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Times-BoldItalic exch definefont pop /Courier findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Courier exch definefont pop %FOPEndFontReencode %%EndProlog %%Page: 1 1 %%PageBoundingBox: 0 0 252 189 %%BeginPageSetup [1 0 0 -1 0 189] CT %%EndPageSetup GS [0.5 0 0 0.5 0 0] CT 1 GC N 0 0 504 378 re f GR GS [0.5 0 0 0.5 0 0] CT 1 GC N 0 0 504 378 re f GR GS [0.5 0 0 0.5 0 0] CT 1 GC N 72 320 M 456 320 L 456 28 L 72 28 L cp f GR GS [0.5 0 0 0.5 0 0] CT 0.873 GC 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0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 162.38 M 72 162.38 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 157.756 M 72 157.756 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 153.846 M 72 153.846 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 150.46 M 72 150.46 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 147.472 M 72 147.472 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 127.22 M 72 127.22 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 116.936 M 72 116.936 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 109.64 M 72 109.64 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 103.98 M 72 103.98 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 99.356 M 72 99.356 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 95.446 M 72 95.446 L S GR GS [0.5 0 0 0.5 0 0] CT 0.775 GC [1 3] 0 setdash 2 LJ N 456 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95.446 M 73.915 95.446 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 92.06 M 73.915 92.06 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 89.072 M 73.915 89.072 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 86.4 M 73.915 86.4 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 68.82 M 73.915 68.82 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 58.536 M 73.915 58.536 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 51.24 M 73.915 51.24 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 45.58 M 73.915 45.58 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 40.956 M 73.915 40.956 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 37.046 M 73.915 37.046 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 33.66 M 73.915 33.66 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 30.672 M 73.915 30.672 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 28 M 73.915 28 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 320 M 454.085 320 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 302.42 M 454.085 302.42 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 292.136 M 454.085 292.136 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 284.84 M 454.085 284.84 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 279.18 M 454.085 279.18 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 274.556 M 454.085 274.556 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 270.646 M 454.085 270.646 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 267.26 M 454.085 267.26 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 264.272 M 454.085 264.272 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 261.6 M 454.085 261.6 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 261.6 M 454.085 261.6 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 244.02 M 454.085 244.02 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 233.736 M 454.085 233.736 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 226.44 M 454.085 226.44 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 220.78 M 454.085 220.78 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 216.156 M 454.085 216.156 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 212.246 M 454.085 212.246 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 208.86 M 454.085 208.86 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 205.872 M 454.085 205.872 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 203.2 M 454.085 203.2 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 185.62 M 454.085 185.62 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 175.336 M 454.085 175.336 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 168.04 M 454.085 168.04 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 162.38 M 454.085 162.38 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 157.756 M 454.085 157.756 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 153.846 M 454.085 153.846 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 150.46 M 454.085 150.46 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 147.472 M 454.085 147.472 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 144.8 M 454.085 144.8 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 127.22 M 454.085 127.22 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 116.936 M 454.085 116.936 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 109.64 M 454.085 109.64 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 103.98 M 454.085 103.98 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 99.356 M 454.085 99.356 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 95.446 M 454.085 95.446 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 92.06 M 454.085 92.06 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 89.072 M 454.085 89.072 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 86.4 M 454.085 86.4 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 68.82 M 454.085 68.82 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 58.536 M 454.085 58.536 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 51.24 M 454.085 51.24 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 45.58 M 454.085 45.58 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 40.956 M 454.085 40.956 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 37.046 M 454.085 37.046 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 33.66 M 454.085 33.66 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 30.672 M 454.085 30.672 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 28 M 454.085 28 L S GR GS [0.5 0 0 0.5 14.5 165] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 160.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-5) t GR GR GS [0.5 0 0 0.5 14.5 136] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 131.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-4) t GR GR GS [0.5 0 0 0.5 14.5 106.5] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 102] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-3) t GR GR GS [0.5 0 0 0.5 14.5 77.5] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 73] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-2) t GR GR GS [0.5 0 0 0.5 14.5 48] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 43.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-1) t GR GR GS [0.5 0 0 0.5 17 19] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 28 14.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (0) t GR GR GS [0 -0.5 0.5 0 12.6 86.99993] CT 0.149 GC /Times-Roman 20.9 F GS [1 0 0 1 0 0] CT -128 -5 moveto 1 -1 scale (Probability of error \(PM = PF\)) t GR GR GS [0.5 0 0 0.5 0 0] CT 0 0.447 0.741 RC 1 LJ 3 LW N 72 94.37 M 126.857 150.144 L 181.714 185.549 L 236.571 211.259 L 291.429 221.35 L 346.286 234.693 L 401.143 261.6 L 456 278.9 L S GR GS [0.5 0 0 0.5 36 47.18518] CT 0 0.447 0.741 RC N 0 -3.5 M 1.933 -3.5 3.5 -1.933 3.5 0 C 3.5 0 L 3.5 1.933 1.933 3.5 0 3.5 C -1.933 3.5 -3.5 1.933 -3.5 0 C -3.5 -1.933 -1.933 -3.5 0 -3.5 C cp 0 -6.5 M -3.59 -6.5 -6.5 -3.59 -6.5 0 C -6.5 3.59 -3.59 6.5 0 6.5 C 3.59 6.5 6.5 3.59 6.5 0 C 6.5 0 L 6.5 -3.59 3.59 -6.5 0 -6.5 C cp f GR GS [0.5 0 0 0.5 63.42857 75.07224] CT 0 0.447 0.741 RC N /f223118758{0 -3.5 M 1.933 -3.5 3.5 -1.933 3.5 0 C 3.5 0 L 3.5 1.933 1.933 3.5 0 3.5 C -1.933 3.5 -3.5 1.933 -3.5 0 C -3.5 -1.933 -1.933 -3.5 0 -3.5 C cp 0 -6.5 M -3.59 -6.5 -6.5 -3.59 -6.5 0 C -6.5 3.59 -3.59 6.5 0 6.5 C 3.59 6.5 6.5 3.59 6.5 0 C 6.5 0 L 6.5 -3.59 3.59 -6.5 0 -6.5 C cp}def f223118758 f GR GS [0.5 0 0 0.5 90.85715 92.77474] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 118.28571 105.62964] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 145.71429 110.67506] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 173.14285 117.34666] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 200.57143 130.8] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 228 139.44995] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 0 0] CT 0.851 0.325 0.098 RC 1 LJ 3 LW N 72 84.167 M 126.857 143.67 L 181.714 201.829 L 236.571 244.734 L 291.429 299.748 L 346.286 317.328 L S GR GS [0.5 0 0 0.5 36 42.08325] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 63.42857 71.83506] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 90.85715 100.91435] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 118.28571 122.36717] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 145.71429 149.87381] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 173.14285 158.66388] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.929 0.694 0.125 RC 1 LJ 3 LW N 72 79.53 M 126.857 136.919 L 181.714 200.655 L 236.571 261.6 L 291.429 295.389 L 346.286 305.014 L S GR GS [0.5 0 0 0.5 36 39.76493] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 63.42857 68.45929] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 90.85715 100.32745] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 118.28571 130.8] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 145.71429 147.6945] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 173.14285 152.50696] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.494 0.184 0.557 RC 1 LJ 3 LW N 72 84.344 M 126.857 117.903 L 181.714 147.238 L 236.571 180.358 L 291.429 205.716 L 346.286 225.068 L 401.143 263.05 L 456 275.27 L S GR GS [0.5 0 0 0.5 36 42.17195] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 63.42857 58.95154] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 90.85715 73.61924] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 118.28571 90.17897] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 145.71429 102.85808] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 173.14285 112.53419] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 200.57143 131.52486] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 228 137.63522] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 0 0] CT 1 GC N 452 122 M 452 32 L 229 32 L 229 122 L cp f GR GS [0.5 0 0 0.5 149.69716 22.60578] CT N 3.875 2.291 M 4.453 3.026 5.328 3.456 QT 6.203 3.885 7.141 3.885 QT 7.922 3.885 8.594 3.573 QT 9.266 3.26 9.773 2.706 QT 10.281 2.151 10.547 1.44 QT 10.813 0.729 10.813 -0.052 QT 10.813 -0.177 10.969 -0.177 QT 11.172 -0.177 L 11.313 -0.177 11.313 -0.021 QT 11.313 0.87 10.969 1.698 QT 10.625 2.526 10 3.151 QT 9.375 3.776 8.57 4.127 QT 7.766 4.479 6.875 4.479 QT 5.656 4.479 4.57 3.987 QT 3.484 3.495 2.672 2.635 QT 1.859 1.776 1.406 0.643 QT 0.953 -0.49 0.953 -1.709 QT 0.953 -2.927 1.406 -4.052 QT 1.859 -5.177 2.672 -6.044 QT 3.484 -6.912 4.57 -7.396 QT 5.656 -7.88 6.875 -7.88 QT 7.75 -7.88 8.547 -7.505 QT 9.344 -7.13 9.938 -6.443 QT 10.938 -7.834 L 11.031 -7.88 11.047 -7.88 QT 11.172 -7.88 L 11.219 -7.88 11.266 -7.841 QT 11.313 -7.802 11.313 -7.74 QT 11.313 -3.146 L 11.313 -3.005 11.172 -3.005 QT 10.859 -3.005 L 10.703 -3.005 10.703 -3.146 QT 10.703 -3.646 10.508 -4.248 QT 10.313 -4.849 10.016 -5.396 QT 9.719 -5.943 9.313 -6.349 QT 8.359 -7.287 7.125 -7.287 QT 6.188 -7.287 5.328 -6.865 QT 4.469 -6.443 3.875 -5.693 QT 3.25 -4.896 3.008 -3.88 QT 2.766 -2.865 2.766 -1.709 QT 2.766 -0.552 3.008 0.471 QT 3.25 1.495 3.875 2.291 QT cp f GR GS [0.5 0 0 0.5 149.69716 22.60578] CT N 13.038 2.432 M 13.038 1.416 13.834 0.784 QT 14.631 0.151 15.741 -0.107 QT 16.85 -0.365 17.866 -0.365 QT 17.866 -1.068 L 17.866 -1.552 17.647 -2.013 QT 17.428 -2.474 17.022 -2.771 QT 16.616 -3.068 16.131 -3.068 QT 14.991 -3.068 14.413 -2.568 QT 14.725 -2.568 14.944 -2.318 QT 15.163 -2.068 15.163 -1.755 QT 15.163 -1.412 14.92 -1.169 QT 14.678 -0.927 14.35 -0.927 QT 14.006 -0.927 13.764 -1.169 QT 13.522 -1.412 13.522 -1.755 QT 13.522 -2.646 14.334 -3.084 QT 15.147 -3.521 16.131 -3.521 QT 16.819 -3.521 17.514 -3.224 QT 18.209 -2.927 18.655 -2.38 QT 19.1 -1.834 19.1 -1.099 QT 19.1 2.729 L 19.1 3.057 19.241 3.338 QT 19.381 3.62 19.678 3.62 QT 19.959 3.62 20.1 3.338 QT 20.241 3.057 20.241 2.729 QT 20.241 1.635 L 20.741 1.635 L 20.741 2.729 L 20.741 3.104 20.538 3.448 QT 20.334 3.791 19.998 3.995 QT 19.663 4.198 19.272 4.198 QT 18.772 4.198 18.413 3.815 QT 18.053 3.432 18.006 2.901 QT 17.694 3.541 17.084 3.916 QT 16.475 4.291 15.772 4.291 QT 15.116 4.291 14.491 4.104 QT 13.866 3.916 13.452 3.502 QT 13.038 3.088 13.038 2.432 QT cp 14.413 2.432 M 14.413 3.026 14.85 3.44 QT 15.288 3.854 15.881 3.854 QT 16.428 3.854 16.881 3.573 QT 17.334 3.291 17.6 2.823 QT 17.866 2.354 17.866 1.823 QT 17.866 0.057 L 17.084 0.057 16.28 0.315 QT 15.475 0.573 14.944 1.112 QT 14.413 1.651 14.413 2.432 QT cp f GR GS [0.5 0 0 0.5 149.69716 22.60578] CT N 21.463 4.151 M 21.463 1.385 L 21.463 1.245 21.619 1.245 QT 21.822 1.245 L 21.916 1.245 21.947 1.385 QT 22.431 3.854 24.244 3.854 QT 25.056 3.854 25.595 3.487 QT 26.134 3.12 26.134 2.354 QT 26.134 1.807 25.713 1.416 QT 25.291 1.026 24.713 0.885 QT 23.572 0.666 L 22.994 0.541 22.525 0.284 QT 22.056 0.026 21.759 -0.404 QT 21.463 -0.834 21.463 -1.396 QT 21.463 -2.146 21.861 -2.623 QT 22.259 -3.099 22.884 -3.31 QT 23.509 -3.521 24.244 -3.521 QT 25.119 -3.521 25.759 -3.052 QT 26.259 -3.474 L 26.259 -3.521 26.338 -3.521 QT 26.463 -3.521 L 26.509 -3.521 26.548 -3.474 QT 26.588 -3.427 26.588 -3.38 QT 26.588 -1.146 L 26.588 -0.99 26.463 -0.99 QT 26.259 -0.99 L 26.103 -0.99 26.103 -1.146 QT 26.103 -2.037 25.611 -2.576 QT 25.119 -3.115 24.228 -3.115 QT 23.463 -3.115 22.9 -2.834 QT 22.338 -2.552 22.338 -1.865 QT 22.338 -1.396 22.744 -1.091 QT 23.15 -0.787 23.697 -0.646 QT 24.838 -0.443 L 25.431 -0.302 25.931 0.01 QT 26.431 0.323 26.728 0.807 QT 27.025 1.291 27.025 1.901 QT 27.025 2.51 26.806 2.963 QT 26.588 3.416 26.213 3.713 QT 25.838 4.01 25.322 4.151 QT 24.806 4.291 24.244 4.291 QT 23.181 4.291 22.431 3.588 QT 21.806 4.26 L 21.806 4.291 21.713 4.291 QT 21.619 4.291 L 21.463 4.291 21.463 4.151 QT cp f GR GS [0.5 0 0 0.5 149.69716 22.60578] CT N 31.879 4.291 M 30.848 4.291 29.981 3.752 QT 29.114 3.213 28.614 2.299 QT 28.114 1.385 28.114 0.37 QT 28.114 -0.615 28.567 -1.513 QT 29.02 -2.412 29.833 -2.966 QT 30.645 -3.521 31.645 -3.521 QT 32.411 -3.521 32.989 -3.255 QT 33.567 -2.99 33.942 -2.529 QT 34.317 -2.068 34.512 -1.435 QT 34.708 -0.802 34.708 -0.052 QT 34.708 0.182 34.52 0.182 QT 29.598 0.182 L 29.598 0.354 L 29.598 1.776 30.168 2.784 QT 30.739 3.791 32.036 3.791 QT 32.551 3.791 32.997 3.565 QT 33.442 3.338 33.77 2.916 QT 34.098 2.495 34.208 2.026 QT 34.223 1.963 34.27 1.924 QT 34.317 1.885 34.379 1.885 QT 34.52 1.885 L 34.708 1.885 34.708 2.088 QT 34.458 3.057 33.661 3.674 QT 32.864 4.291 31.879 4.291 QT cp 29.614 -0.24 M 33.504 -0.24 L 33.504 -0.88 33.325 -1.537 QT 33.145 -2.193 32.731 -2.63 QT 32.317 -3.068 31.645 -3.068 QT 30.676 -3.068 30.145 -2.169 QT 29.614 -1.271 29.614 -0.24 QT cp f GR GS [0.5 0 0 0.5 149.69716 22.60578] CT N 41.383 4.104 M 41.383 3.51 L 43.226 3.51 43.226 2.963 QT 43.226 -6.365 L 43.226 -6.912 41.383 -6.912 QT 41.383 -7.505 L 46.633 -7.505 L 46.633 -6.912 L 44.804 -6.912 44.804 -6.365 QT 44.804 2.963 L 44.804 3.51 46.633 3.51 QT 46.633 4.104 L 41.383 4.104 L cp f GR GS [0.5 0 0 0.5 149.69716 22.60578] CT N 56.586 4.104 M 54.383 -2.084 L 54.226 -2.459 53.945 -2.544 QT 53.664 -2.63 53.133 -2.63 QT 53.133 -3.224 L 56.633 -3.224 L 56.633 -2.63 L 55.633 -2.63 55.633 -2.209 QT 55.633 -2.177 55.64 -2.154 QT 55.648 -2.13 55.648 -2.084 QT 57.273 2.495 L 58.695 -1.49 L 58.461 -2.084 L 58.336 -2.459 58.047 -2.544 QT 57.758 -2.63 57.226 -2.63 QT 57.226 -3.224 L 60.57 -3.224 L 60.57 -2.63 L 59.57 -2.63 59.57 -2.209 QT 59.57 -2.146 59.586 -2.084 QT 61.289 2.713 L 62.836 -1.63 L 62.867 -1.755 62.867 -1.865 QT 62.867 -2.224 62.562 -2.427 QT 62.258 -2.63 61.883 -2.63 QT 61.883 -3.224 L 64.773 -3.224 L 64.773 -2.63 L 64.258 -2.63 63.89 -2.357 QT 63.523 -2.084 63.351 -1.63 QT 61.32 4.104 L 61.258 4.291 61.07 4.291 QT 60.929 4.291 L 60.726 4.291 60.679 4.104 QT 58.961 -0.74 L 57.242 4.104 L 57.148 4.291 56.976 4.291 QT 56.851 4.291 L 56.633 4.291 56.586 4.104 QT cp f GR GS [0.5 0 0 0.5 149.69716 22.60578] CT N 65.686 4.104 M 65.686 3.51 L 66.279 3.51 66.647 3.416 QT 67.014 3.323 67.014 2.963 QT 67.014 -1.677 L 67.014 -2.334 66.764 -2.482 QT 66.514 -2.63 65.764 -2.63 QT 65.764 -3.224 L 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107.0128] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 121.33334 109.64291] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 142.66667 118.41414] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 164 131.4366] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 185.33334 135.43056] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 206.66667 155.84875] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 228 158.67177] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 0 0] CT 0.851 0.325 0.098 RC 1 LJ 3 LW N 72 87.652 M 114.667 149.039 L 157.333 180.851 L 200 207.777 L 242.667 221.22 L 285.333 227.248 L 328 252.129 L 370.667 264.836 L 413.333 287.856 L 456 294.104 L S GR GS [0.5 0 0 0.5 36 43.82582] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 57.33333 74.5197] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 78.66666 90.42567] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 100 103.88875] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 121.33334 110.61021] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 142.66667 113.62404] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 164 126.0647] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 185.33334 132.41803] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 206.66667 143.92815] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 228 147.05193] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.929 0.694 0.125 RC 1 LJ 3 LW N 72 90.854 M 114.667 148.719 L 157.333 180.789 L 200 210.805 L 242.667 215.611 L 285.333 220.894 L 328 246.528 L 370.667 248.913 L 413.333 264.617 L 456 260.169 L S GR GS [0.5 0 0 0.5 36 45.4269] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 57.33333 74.35938] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 78.66666 90.39451] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 100 105.40234] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 121.33334 107.80525] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 142.66667 110.44677] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 164 123.2638] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 185.33334 124.45657] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 206.66667 132.3083] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 228 130.08472] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.494 0.184 0.557 RC 1 LJ 3 LW N 72 70.408 M 114.667 83.676 L 157.333 96.257 L 200 102.824 L 242.667 109.099 L 285.333 114.243 L 328 119.72 L 370.667 121.043 L 413.333 127.468 L 456 129.711 L S GR GS [0.5 0 0 0.5 36 35.20391] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 57.33333 41.83801] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 78.66666 48.1286] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 100 51.41206] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 121.33334 54.54972] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 142.66667 57.12136] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 164 59.85987] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 185.33334 60.52142] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 206.66667 63.73381] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 228 64.85548] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 0 0] CT 1 GC N 461 109 M 461 20 L 259 20 L 259 109 L cp f GR GS [0.5 0 0 0.5 164.83746 16.55524] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (MLE) t GR GR GS [0.5 0 0 0.5 0 0] CT 0 0.447 0.741 RC 1 LJ 3 LW N 265.015 33.11 M 325.164 33.11 L S GR GS [0.5 0 0 0.5 147.54466 16.55524] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 164.83746 27.01841] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] 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263.195 M 454.085 263.195 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 258.308 M 454.085 258.308 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 254.074 M 454.085 254.074 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 250.34 M 454.085 250.34 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 247 M 454.085 247 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 225.025 M 454.085 225.025 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 212.17 M 454.085 212.17 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 203.05 M 454.085 203.05 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 195.975 M 454.085 195.975 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 190.195 M 454.085 190.195 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 185.308 M 454.085 185.308 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 181.074 M 454.085 181.074 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 177.34 M 454.085 177.34 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 174 M 454.085 174 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 152.025 M 454.085 152.025 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 139.17 M 454.085 139.17 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 130.05 M 454.085 130.05 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 122.975 M 454.085 122.975 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 117.195 M 454.085 117.195 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 112.308 M 454.085 112.308 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 108.074 M 454.085 108.074 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 104.34 M 454.085 104.34 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 101 M 454.085 101 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 79.025 M 454.085 79.025 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 66.17 M 454.085 66.17 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 57.05 M 454.085 57.05 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 49.975 M 454.085 49.975 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 44.195 M 454.085 44.195 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 39.308 M 454.085 39.308 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 35.074 M 454.085 35.074 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 31.34 M 454.085 31.34 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 28 M 454.085 28 L S GR GS [0.5 0 0 0.5 14.5 165] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 160.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-4) t GR GR GS [0.5 0 0 0.5 14.5 128.5] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 124] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-3) t GR GR GS [0.5 0 0 0.5 14.5 92] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 87.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-2) t GR GR GS [0.5 0 0 0.5 14.5 55.5] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 51] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-1) t GR GR GS [0.5 0 0 0.5 17 19] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 28 14.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (0) t GR GR GS [0 -0.5 0.5 0 12.6 86.99993] CT 0.149 GC /Times-Roman 20.9 F GS [1 0 0 1 0 0] CT -128 -5 moveto 1 -1 scale (Probability of error \(PM = PF\)) t GR GR GS [0.5 0 0 0.5 0 0] CT 0 0.447 0.741 RC 1 LJ 3 LW N 72 93.601 M 114.667 159.636 L 157.333 195.827 L 200 227.089 L 242.667 241.312 L 285.333 256.705 L 328 263.73 L 370.667 271.363 L 413.333 277.553 L 456 295.37 L S GR GS [0.5 0 0 0.5 36 46.80075] CT 0 0.447 0.741 RC N 0 -3.5 M 1.933 -3.5 3.5 -1.933 3.5 0 C 3.5 0 L 3.5 1.933 1.933 3.5 0 3.5 C -1.933 3.5 -3.5 1.933 -3.5 0 C -3.5 -1.933 -1.933 -3.5 0 -3.5 C cp 0 -6.5 M -3.59 -6.5 -6.5 -3.59 -6.5 0 C -6.5 3.59 -3.59 6.5 0 6.5 C 3.59 6.5 6.5 3.59 6.5 0 C 6.5 0 L 6.5 -3.59 3.59 -6.5 0 -6.5 C cp f GR GS [0.5 0 0 0.5 57.33333 79.81824] CT 0 0.447 0.741 RC N /f223118758{0 -3.5 M 1.933 -3.5 3.5 -1.933 3.5 0 C 3.5 0 L 3.5 1.933 1.933 3.5 0 3.5 C -1.933 3.5 -3.5 1.933 -3.5 0 C -3.5 -1.933 -1.933 -3.5 0 -3.5 C cp 0 -6.5 M -3.59 -6.5 -6.5 -3.59 -6.5 0 C -6.5 3.59 -3.59 6.5 0 6.5 C 3.59 6.5 6.5 3.59 6.5 0 C 6.5 0 L 6.5 -3.59 3.59 -6.5 0 -6.5 C cp}def f223118758 f GR GS [0.5 0 0 0.5 78.66666 97.91331] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 100 113.54463] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 121.33334 120.65611] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 142.66667 128.35236] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 164 131.86484] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 185.33334 135.6814] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 206.66667 138.77666] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 228 147.68513] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 0 0] CT 0.851 0.325 0.098 RC 1 LJ 3 LW N 72 70.336 M 114.667 88.555 L 157.333 106.449 L 200 121.159 L 242.667 136.854 L 285.333 147.182 L 328 161.543 L 370.667 171.318 L 413.333 174.789 L 456 183.616 L S GR GS [0.5 0 0 0.5 36 35.16793] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 57.33333 44.27774] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 78.66666 53.22456] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 100 60.57962] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 121.33334 68.42725] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 142.66667 73.59124] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 164 80.77167] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 185.33334 85.65907] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 206.66667 87.39445] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 228 91.80778] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.929 0.694 0.125 RC 1 LJ 3 LW N 72 76.688 M 114.667 99.806 L 157.333 114.006 L 200 130.752 L 242.667 145.029 L 285.333 153.95 L 328 164.289 L 370.667 172.468 L 413.333 168.395 L 456 174.7 L S GR GS [0.5 0 0 0.5 36 38.34391] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 57.33333 49.90321] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 78.66666 57.00276] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 100 65.37595] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 121.33334 72.51434] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 142.66667 76.97478] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 164 82.1444] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 185.33334 86.23421] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 206.66667 84.1977] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 228 87.35012] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.494 0.184 0.557 RC 1 LJ 3 LW N 72 66.837 M 114.667 85.276 L 157.333 111.875 L 200 137.177 L 242.667 158.888 L 285.333 178.193 L 328 200.296 L 370.667 219.8 L 413.333 231.069 L 456 243.69 L S GR GS [0.5 0 0 0.5 36 33.41845] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 57.33333 42.63802] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 78.66666 55.93746] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 100 68.58863] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 121.33334 79.44406] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 142.66667 89.09671] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 164 100.14789] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 185.33334 109.90007] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 206.66667 115.53456] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 228 121.84506] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 0 0] CT 1 GC N 450 121 M 450 33 L 249 33 L 249 121 L cp f GR GS [0.5 0 0 0.5 159.66254 22.98159] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (MLE) t GR GR GS [0.5 0 0 0.5 0 0] CT 0 0.447 0.741 RC 1 LJ 3 LW N 254.985 45.963 M 314.836 45.963 L S GR GS [0.5 0 0 0.5 142.45534 22.98159] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 159.66254 33.3272] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (AMP) t GR GR GS [0.5 0 0 0.5 0 0] CT 0.851 0.325 0.098 RC 1 LJ 3 LW N 254.985 66.654 M 314.836 66.654 L S GR GS [0.5 0 0 0.5 142.45534 33.32719] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 159.66254 43.67281] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (OAMP) t GR GR GS [0.5 0 0 0.5 0 0] CT 0.929 0.694 0.125 RC 1 LJ 3 LW N 254.985 87.346 M 314.836 87.346 L S GR GS [0.5 0 0 0.5 142.45534 43.67281] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 159.66254 54.01841] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (Mismatched MLE) t GR GR GS [0.5 0 0 0.5 0 0] CT 0.494 0.184 0.557 RC 1 LJ 3 LW N 254.985 108.037 M 314.836 108.037 L S GR GS [0.5 0 0 0.5 142.45534 54.01841] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 10.0 ML N 249 121 M 249 33 L 450 33 L 450 121 L cp S GR %%Trailer %%Pages: 1 %%EOF %%EndDocument @endspecial 0 TeXcolorgray 102 x Fy(\(a\))26 b(Detection)j(under)e (correlated)j(Rician)2000 843 y(f)o(ading)25 b(channels.)p 0 TeXcolorgray 3067 666 a @beginspecial 2 @llx 0 @lly 233 @urx 180 @ury 1230 @rwi @setspecial %%BeginDocument: pe_compare_Rayleigh_L.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: (MATLAB, The Mathworks, Inc. 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License terms: http://www.apache.org/licenses/LICENSE-2.0) /bd{bind def}bind def /ld{load def}bd /GR/grestore ld /GS/gsave ld /RM/rmoveto ld /C/curveto ld /t/show ld /L/lineto ld /ML/setmiterlimit ld /CT/concat ld /f/fill ld /N/newpath ld /S/stroke ld /CC/setcmykcolor ld /A/ashow ld /cp/closepath ld /RC/setrgbcolor ld /LJ/setlinejoin ld /GC/setgray ld /LW/setlinewidth ld /M/moveto ld /re {4 2 roll M 1 index 0 rlineto 0 exch rlineto neg 0 rlineto cp } bd /_ctm matrix def /_tm matrix def /BT { _ctm currentmatrix pop matrix _tm copy pop 0 0 moveto } bd /ET { _ctm setmatrix } bd /iTm { _ctm setmatrix _tm concat } bd /Tm { _tm astore pop iTm 0 0 moveto } bd /ux 0.0 def /uy 0.0 def /F { /Tp exch def /Tf exch def Tf findfont Tp scalefont setfont /cf Tf def /cs Tp def } bd /ULS {currentpoint /uy exch def /ux exch def} bd /ULE { /Tcx currentpoint pop def gsave newpath cf findfont cs scalefont dup /FontMatrix get 0 get /Ts exch def /FontInfo get dup /UnderlinePosition get Ts mul /To exch def /UnderlineThickness get Ts mul /Tt exch def ux uy To add moveto Tcx uy To add lineto Tt setlinewidth stroke grestore } bd /OLE { /Tcx currentpoint pop def gsave newpath cf findfont cs scalefont dup /FontMatrix get 0 get /Ts exch def /FontInfo get dup /UnderlinePosition get Ts mul /To exch def /UnderlineThickness get Ts mul /Tt exch def ux uy To add cs add moveto Tcx uy To add cs add lineto Tt setlinewidth stroke grestore } bd /SOE { /Tcx currentpoint pop def gsave newpath cf findfont cs scalefont dup /FontMatrix get 0 get /Ts exch def /FontInfo get dup /UnderlinePosition get Ts mul /To exch def /UnderlineThickness get Ts mul /Tt exch def ux uy To add cs 10 mul 26 idiv add moveto Tcx uy To add cs 10 mul 26 idiv add lineto Tt setlinewidth stroke grestore } bd /QT { /Y22 exch store /X22 exch store /Y21 exch store /X21 exch store currentpoint /Y21 load 2 mul add 3 div exch /X21 load 2 mul add 3 div exch /X21 load 2 mul /X22 load add 3 div /Y21 load 2 mul /Y22 load add 3 div /X22 load /Y22 load curveto } bd /SSPD { dup length /d exch dict def { /v exch def /k exch def currentpagedevice k known { /cpdv currentpagedevice k get def v cpdv ne { /upd false def /nullv v type /nulltype eq def /nullcpdv cpdv type /nulltype eq def nullv nullcpdv or { /upd true def } { /sametype v type cpdv type eq def sametype { v type /arraytype eq { /vlen v length def /cpdvlen cpdv length def vlen cpdvlen eq { 0 1 vlen 1 sub { /i exch def /obj v i get def /cpdobj cpdv i get def obj cpdobj ne { /upd true def exit } if } for } { /upd true def } ifelse } { v type /dicttype eq { v { /dv exch def /dk exch def /cpddv cpdv dk get def dv cpddv ne { /upd true def exit } if } forall } { /upd true def } ifelse } ifelse } if } ifelse upd true eq { d k v put } if } if } if } forall d length 0 gt { d setpagedevice } if } bd /RE { % /NewFontName [NewEncodingArray] /FontName RE - findfont dup length dict begin { 1 index /FID ne {def} {pop pop} ifelse } forall /Encoding exch def /FontName 1 index def currentdict definefont pop end } bind def %%EndResource %%BeginResource: procset (Apache XML Graphics EPS ProcSet) 1.0 0 %%Version: 1.0 0 %%Copyright: (Copyright 2002-2003 The Apache Software Foundation. License terms: http://www.apache.org/licenses/LICENSE-2.0) /BeginEPSF { %def /b4_Inc_state save def % Save state for cleanup /dict_count countdictstack def % Count objects on dict stack /op_count count 1 sub def % Count objects on operand stack userdict begin % Push userdict on dict stack /showpage { } def % Redefine showpage, { } = null proc 0 setgray 0 setlinecap % Prepare graphics state 1 setlinewidth 0 setlinejoin 10 setmiterlimit [ ] 0 setdash newpath /languagelevel where % If level not equal to 1 then {pop languagelevel % set strokeadjust and 1 ne % overprint to their defaults. {false setstrokeadjust false setoverprint } if } if } bd /EndEPSF { %def count op_count sub {pop} repeat % Clean up stacks countdictstack dict_count sub {end} repeat b4_Inc_state restore } bd %%EndResource %FOPBeginFontDict %%IncludeResource: font Courier-Oblique %%IncludeResource: font Courier-BoldOblique %%IncludeResource: font Courier-Bold %%IncludeResource: font ZapfDingbats %%IncludeResource: font Symbol %%IncludeResource: font Helvetica %%IncludeResource: font Helvetica-Oblique %%IncludeResource: font Helvetica-Bold %%IncludeResource: font Helvetica-BoldOblique %%IncludeResource: font Times-Roman %%IncludeResource: font Times-Italic %%IncludeResource: font Times-Bold %%IncludeResource: font Times-BoldItalic %%IncludeResource: font Courier %FOPEndFontDict %%BeginResource: encoding WinAnsiEncoding /WinAnsiEncoding [ /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quotesingle /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /bullet /Euro /bullet /quotesinglbase /florin /quotedblbase /ellipsis /dagger /daggerdbl /circumflex /perthousand /Scaron /guilsinglleft /OE /bullet /Zcaron /bullet /bullet /quoteleft /quoteright /quotedblleft /quotedblright /bullet /endash /emdash /asciitilde /trademark /scaron /guilsinglright /oe /bullet /zcaron /Ydieresis /space /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /sfthyphen /registered /macron /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /middot /cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def %%EndResource %FOPBeginFontReencode /Courier-Oblique findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Courier-Oblique exch definefont pop /Courier-BoldOblique findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Courier-BoldOblique exch definefont pop /Courier-Bold findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Courier-Bold exch definefont pop /Helvetica findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Helvetica exch definefont pop /Helvetica-Oblique findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Helvetica-Oblique exch definefont pop /Helvetica-Bold findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Helvetica-Bold exch definefont pop /Helvetica-BoldOblique findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Helvetica-BoldOblique exch definefont pop /Times-Roman findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Times-Roman exch definefont pop /Times-Italic findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Times-Italic exch definefont pop /Times-Bold findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Times-Bold exch definefont pop /Times-BoldItalic findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Times-BoldItalic exch definefont pop /Courier findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WinAnsiEncoding def currentdict end /Courier exch definefont pop %FOPEndFontReencode %%EndProlog %%Page: 1 1 %%PageBoundingBox: 0 0 252 189 %%BeginPageSetup [1 0 0 -1 0 189] CT %%EndPageSetup GS [0.5 0 0 0.5 0 0] CT 1 GC N 0 0 504 378 re f GR GS [0.5 0 0 0.5 0 0] CT 1 GC N 0 0 504 378 re f GR GS [0.5 0 0 0.5 0 0] CT 1 GC N 72 320 M 456 320 L 456 28 L 72 28 L cp f GR GS [0.5 0 0 0.5 0 0] CT 0.873 GC 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1 LJ N 72 267.26 M 73.915 267.26 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 264.272 M 73.915 264.272 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 261.6 M 73.915 261.6 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 261.6 M 73.915 261.6 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 244.02 M 73.915 244.02 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 233.736 M 73.915 233.736 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 226.44 M 73.915 226.44 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 220.78 M 73.915 220.78 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 216.156 M 73.915 216.156 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 212.246 M 73.915 212.246 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 208.86 M 73.915 208.86 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 205.872 M 73.915 205.872 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 203.2 M 73.915 203.2 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 185.62 M 73.915 185.62 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 175.336 M 73.915 175.336 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 168.04 M 73.915 168.04 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 162.38 M 73.915 162.38 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 157.756 M 73.915 157.756 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 153.846 M 73.915 153.846 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 150.46 M 73.915 150.46 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 147.472 M 73.915 147.472 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 144.8 M 73.915 144.8 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 127.22 M 73.915 127.22 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 116.936 M 73.915 116.936 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 109.64 M 73.915 109.64 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 103.98 M 73.915 103.98 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 99.356 M 73.915 99.356 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 95.446 M 73.915 95.446 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 92.06 M 73.915 92.06 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 89.072 M 73.915 89.072 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 86.4 M 73.915 86.4 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 68.82 M 73.915 68.82 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 58.536 M 73.915 58.536 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 51.24 M 73.915 51.24 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 45.58 M 73.915 45.58 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 40.956 M 73.915 40.956 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 37.046 M 73.915 37.046 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 33.66 M 73.915 33.66 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 30.672 M 73.915 30.672 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 28 M 73.915 28 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 320 M 454.085 320 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 302.42 M 454.085 302.42 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 292.136 M 454.085 292.136 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 284.84 M 454.085 284.84 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 279.18 M 454.085 279.18 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 274.556 M 454.085 274.556 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 270.646 M 454.085 270.646 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 267.26 M 454.085 267.26 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 264.272 M 454.085 264.272 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 261.6 M 454.085 261.6 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 261.6 M 454.085 261.6 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 244.02 M 454.085 244.02 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 233.736 M 454.085 233.736 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 226.44 M 454.085 226.44 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 220.78 M 454.085 220.78 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 216.156 M 454.085 216.156 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 212.246 M 454.085 212.246 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 208.86 M 454.085 208.86 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 205.872 M 454.085 205.872 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 203.2 M 454.085 203.2 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 185.62 M 454.085 185.62 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 175.336 M 454.085 175.336 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 168.04 M 454.085 168.04 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 162.38 M 454.085 162.38 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 157.756 M 454.085 157.756 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 153.846 M 454.085 153.846 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 150.46 M 454.085 150.46 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 147.472 M 454.085 147.472 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 144.8 M 454.085 144.8 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 127.22 M 454.085 127.22 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 116.936 M 454.085 116.936 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 109.64 M 454.085 109.64 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 103.98 M 454.085 103.98 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 99.356 M 454.085 99.356 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 95.446 M 454.085 95.446 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 92.06 M 454.085 92.06 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 89.072 M 454.085 89.072 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 86.4 M 454.085 86.4 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 68.82 M 454.085 68.82 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 58.536 M 454.085 58.536 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 51.24 M 454.085 51.24 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 45.58 M 454.085 45.58 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 40.956 M 454.085 40.956 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 37.046 M 454.085 37.046 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 33.66 M 454.085 33.66 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 30.672 M 454.085 30.672 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 28 M 454.085 28 L S GR GS [0.5 0 0 0.5 14.5 165] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 160.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-5) t GR GR GS [0.5 0 0 0.5 14.5 136] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 131.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-4) t GR GR GS [0.5 0 0 0.5 14.5 106.5] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 102] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-3) t GR GR GS [0.5 0 0 0.5 14.5 77.5] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 73] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-2) t GR GR GS [0.5 0 0 0.5 14.5 48] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 43.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-1) t GR GR GS [0.5 0 0 0.5 17 19] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 28 14.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (0) t GR GR GS [0 -0.5 0.5 0 12.6 86.99993] CT 0.149 GC /Times-Roman 20.9 F GS [1 0 0 1 0 0] CT -128 -5 moveto 1 -1 scale (Probability of error \(PM = PF\)) t GR GR GS [0.5 0 0 0.5 0 0] CT 0 0.447 0.741 RC 1 LJ 3 LW N 72 75.197 M 114.667 130.963 L 157.333 167.594 L 200 203.578 L 242.667 219.285 L 285.333 233.395 L 328 247.676 L 370.667 265.633 L 413.333 282.86 L 456 284.225 L S GR GS [0.5 0 0 0.5 36 37.59846] CT 0 0.447 0.741 RC N 0 -3.5 M 1.933 -3.5 3.5 -1.933 3.5 0 C 3.5 0 L 3.5 1.933 1.933 3.5 0 3.5 C -1.933 3.5 -3.5 1.933 -3.5 0 C -3.5 -1.933 -1.933 -3.5 0 -3.5 C cp 0 -6.5 M -3.59 -6.5 -6.5 -3.59 -6.5 0 C -6.5 3.59 -3.59 6.5 0 6.5 C 3.59 6.5 6.5 3.59 6.5 0 C 6.5 0 L 6.5 -3.59 3.59 -6.5 0 -6.5 C cp f GR GS [0.5 0 0 0.5 57.33333 65.48146] CT 0 0.447 0.741 RC N /f223118758{0 -3.5 M 1.933 -3.5 3.5 -1.933 3.5 0 C 3.5 0 L 3.5 1.933 1.933 3.5 0 3.5 C -1.933 3.5 -3.5 1.933 -3.5 0 C -3.5 -1.933 -1.933 -3.5 0 -3.5 C cp 0 -6.5 M -3.59 -6.5 -6.5 -3.59 -6.5 0 C -6.5 3.59 -3.59 6.5 0 6.5 C 3.59 6.5 6.5 3.59 6.5 0 C 6.5 0 L 6.5 -3.59 3.59 -6.5 0 -6.5 C cp}def f223118758 f GR GS [0.5 0 0 0.5 78.66666 83.79715] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 100 101.78914] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 121.33334 109.64259] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 142.66667 116.69727] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 164 123.83825] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 185.33334 132.81645] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 206.66667 141.42976] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 228 142.11244] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 0 0] CT 0.851 0.325 0.098 RC 1 LJ 3 LW N 72 66.116 M 114.667 119.369 L 157.333 162.138 L 200 189.381 L 242.667 212.766 L 285.333 226.528 L 328 254.421 L 370.667 261.531 L 413.333 261.482 L 456 261.542 L S GR GS [0.5 0 0 0.5 36 33.05788] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 57.33333 59.6844] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 78.66666 81.0689] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 100 94.69025] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 121.33334 106.3831] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 142.66667 113.26405] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 164 127.21046] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 185.33334 130.76543] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 206.66667 130.74081] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 228 130.77112] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.929 0.694 0.125 RC 1 LJ 3 LW N 72 75.285 M 114.667 125.555 L 157.333 163.129 L 200 196.96 L 242.667 218.779 L 285.333 221.732 L 328 253.379 L 370.667 270.866 L 413.333 264.451 L 456 279.195 L S GR GS [0.5 0 0 0.5 36 37.6426] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 57.33333 62.7776] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 78.66666 81.56453] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 100 98.47984] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 121.33334 109.38969] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 142.66667 110.86611] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 164 126.68956] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 185.33334 135.43277] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 206.66667 132.22528] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 228 139.59726] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.494 0.184 0.557 RC 1 LJ 3 LW N 72 51.489 M 114.667 64.083 L 157.333 78.65 L 200 98.265 L 242.667 116.427 L 285.333 132.716 L 328 148.716 L 370.667 167.346 L 413.333 176.462 L 456 184.941 L S GR GS [0.5 0 0 0.5 36 25.74427] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 57.33333 32.04163] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 78.66666 39.32494] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 100 49.13268] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 121.33334 58.21345] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 142.66667 66.358] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 164 74.35824] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 185.33334 83.67319] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 206.66667 88.23093] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 228 92.47054] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 0 0] CT 1 GC N 456 116 M 456 28 L 255 28 L 255 116 L cp f GR GS [0.5 0 0 0.5 162.66254 20.48159] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (MLE) t GR GR GS [0.5 0 0 0.5 0 0] CT 0 0.447 0.741 RC 1 LJ 3 LW N 260.985 40.963 M 320.836 40.963 L S GR GS [0.5 0 0 0.5 145.45534 20.48159] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 162.66254 30.8272] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (AMP) t GR GR GS [0.5 0 0 0.5 0 0] CT 0.851 0.325 0.098 RC 1 LJ 3 LW N 260.985 61.654 M 320.836 61.654 L S GR GS [0.5 0 0 0.5 145.45534 30.8272] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 162.66254 41.1728] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (OAMP) t GR GR GS [0.5 0 0 0.5 0 0] CT 0.929 0.694 0.125 RC 1 LJ 3 LW N 260.985 82.346 M 320.836 82.346 L S GR GS [0.5 0 0 0.5 145.45534 41.17281] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 162.66254 51.51841] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (Mismatched MLE) t GR GR GS [0.5 0 0 0.5 0 0] CT 0.494 0.184 0.557 RC 1 LJ 3 LW N 260.985 103.037 M 320.836 103.037 L S GR GS [0.5 0 0 0.5 145.45534 51.51841] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 10.0 ML N 255 116 M 255 28 L 456 28 L 456 116 L cp S GR %%Trailer %%Pages: 1 %%EOF %%EndDocument @endspecial 0 TeXcolorgray 102 x(\(b\))91 b(Detection)j(under)e (correlated)3067 843 y(Rayleigh)26 b(f)o(ading)f(channels.)p 0 TeXcolorgray 0 TeXcolorgray 2000 967 a(Fig.)32 b(7)66 b(Detection)36 b(performance)e(comparison)g(of)e(the)h(MLE)e(approach)j (and)f(the)2000 1042 y(benchmarks)25 b(for)f(dif)n(ferent)i Fd(L)p Fy(')l(s.)p 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 2000 1131 a SDict begin H.S end 2000 1131 a 2000 1131 a SDict begin 12 H.A end 2000 1131 a 2000 1131 a SDict begin [/View [/XYZ H.V]/Dest (figure.caption.10) cvn /DEST pdfmark end 2000 1131 a 828 x @beginspecial 2 @llx 0 @lly 239 @urx 180 @ury 1230 @rwi @setspecial %%BeginDocument: pe_compare_Rician_N.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: (MATLAB, The Mathworks, Inc. 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153.44476] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (Mismatched MLE) t GR GR GS [0.5 0 0 0.5 0 0] CT 0.494 0.184 0.557 RC 1 LJ 3 LW N 274.985 306.89 M 334.836 306.89 L S GR GS [0.5 0 0 0.5 152.45534 153.44476] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 10.0 ML N 269 320 M 269 231 L 470 231 L 470 320 L cp S GR %%Trailer %%Pages: 1 %%EOF %%EndDocument @endspecial 0 TeXcolorgray 102 x Fy(\(a\))g(Detection)j(under)e (correlated)j(Rician)2000 2136 y(f)o(ading)25 b(channels.)p 0 TeXcolorgray 3067 1959 a @beginspecial 2 @llx 0 @lly 239 @urx 180 @ury 1230 @rwi @setspecial %%BeginDocument: pe_compare_Rayleigh_N.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: (MATLAB, The Mathworks, Inc. 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73.915 129.787 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 125.333 M 73.915 125.333 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 96.033 M 73.915 96.033 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 78.894 M 73.915 78.894 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 66.733 M 73.915 66.733 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 57.3 M 73.915 57.3 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 49.593 M 73.915 49.593 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 43.077 M 73.915 43.077 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 37.433 M 73.915 37.433 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 32.454 M 73.915 32.454 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 72 28 M 73.915 28 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 320 M 454.085 320 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 290.7 M 454.085 290.7 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 273.56 M 454.085 273.56 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 261.4 M 454.085 261.4 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 251.967 M 454.085 251.967 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 244.26 M 454.085 244.26 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 237.744 M 454.085 237.744 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 232.099 M 454.085 232.099 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 227.12 M 454.085 227.12 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 222.667 M 454.085 222.667 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 193.366 M 454.085 193.366 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 176.227 M 454.085 176.227 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 164.066 M 454.085 164.066 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 154.634 M 454.085 154.634 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 146.927 M 454.085 146.927 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 140.41 M 454.085 140.41 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 134.766 M 454.085 134.766 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 129.787 M 454.085 129.787 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 125.333 M 454.085 125.333 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 96.033 M 454.085 96.033 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 78.894 M 454.085 78.894 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 66.733 M 454.085 66.733 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 57.3 M 454.085 57.3 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 49.593 M 454.085 49.593 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 43.077 M 454.085 43.077 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 37.433 M 454.085 37.433 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 32.454 M 454.085 32.454 L S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 2 setlinecap 1 LJ N 456 28 M 454.085 28 L S GR GS [0.5 0 0 0.5 14.5 165] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 160.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-3) t GR GR GS [0.5 0 0 0.5 14.5 116.5] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 112] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-2) t GR GR GS [0.5 0 0 0.5 14.5 67.5] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 25.5 63] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (-1) t GR GR GS [0.5 0 0 0.5 17 19] CT 0.149 GC /Helvetica 19 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (10) t GR GR GS [0.5 0 0 0.5 28 14.5] CT 0.149 GC /Helvetica 15.2 F GS [1 0 0 1 0 0] CT 0 0 moveto 1 -1 scale (0) t GR GR GS [0 -0.5 0.5 0 12.6 86.99993] CT 0.149 GC /Times-Roman 20.9 F GS [1 0 0 1 0 0] CT -128 -5 moveto 1 -1 scale (Probability of error \(PM = PF\)) t GR GR GS [0.5 0 0 0.5 0 0] CT 0 0.447 0.741 RC 1 LJ 3 LW N 72 319.201 M 114.667 289.191 L 157.333 272.391 L 200 253.693 L 242.667 233.211 L 285.333 208.767 L 328 188.597 L 370.667 165.899 L 413.333 142.339 L 456 125.463 L S GR GS [0.5 0 0 0.5 36 159.60071] CT 0 0.447 0.741 RC N 0 -3.5 M 1.933 -3.5 3.5 -1.933 3.5 0 C 3.5 0 L 3.5 1.933 1.933 3.5 0 3.5 C -1.933 3.5 -3.5 1.933 -3.5 0 C -3.5 -1.933 -1.933 -3.5 0 -3.5 C cp 0 -6.5 M -3.59 -6.5 -6.5 -3.59 -6.5 0 C -6.5 3.59 -3.59 6.5 0 6.5 C 3.59 6.5 6.5 3.59 6.5 0 C 6.5 0 L 6.5 -3.59 3.59 -6.5 0 -6.5 C cp f GR GS [0.5 0 0 0.5 57.33333 144.59561] CT 0 0.447 0.741 RC N /f223118758{0 -3.5 M 1.933 -3.5 3.5 -1.933 3.5 0 C 3.5 0 L 3.5 1.933 1.933 3.5 0 3.5 C -1.933 3.5 -3.5 1.933 -3.5 0 C -3.5 -1.933 -1.933 -3.5 0 -3.5 C cp 0 -6.5 M -3.59 -6.5 -6.5 -3.59 -6.5 0 C -6.5 3.59 -3.59 6.5 0 6.5 C 3.59 6.5 6.5 3.59 6.5 0 C 6.5 0 L 6.5 -3.59 3.59 -6.5 0 -6.5 C cp}def f223118758 f GR GS [0.5 0 0 0.5 78.66666 136.19543] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 100 126.84666] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 121.33334 116.60548] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 142.66667 104.38332] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 164 94.29849] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 185.33334 82.94961] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 206.66667 71.1693] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 228 62.73136] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 0 0] CT 0.851 0.325 0.098 RC 1 LJ 3 LW N 72 307.542 M 114.667 291.49 L 157.333 277.319 L 200 252.715 L 242.667 230.209 L 285.333 198.311 L 328 171.909 L 370.667 140.795 L 413.333 120.597 L 456 108.242 L S GR GS [0.5 0 0 0.5 36 153.77115] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 57.33333 145.74496] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 78.66666 138.65935] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 100 126.35758] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 121.33334 115.10473] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 142.66667 99.15566] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 164 85.95437] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 185.33334 70.39741] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 206.66667 60.29852] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 228 54.12094] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.929 0.694 0.125 RC 1 LJ 3 LW N 72 304.936 M 114.667 293.651 L 157.333 268.431 L 200 240.798 L 242.667 208.533 L 285.333 180.716 L 328 152.793 L 370.667 131.183 L 413.333 117.169 L 456 106.138 L S GR GS [0.5 0 0 0.5 36 152.46808] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 57.33333 146.82558] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 78.66666 134.21559] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 100 120.39904] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 121.33334 104.26646] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 142.66667 90.35787] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 164 76.3966] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 185.33334 65.59172] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 206.66667 58.58469] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 228 53.06883] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.494 0.184 0.557 RC 1 LJ 3 LW N 72 198.429 M 114.667 141.486 L 157.333 113.523 L 200 96.492 L 242.667 86.009 L 285.333 78.981 L 328 74.564 L 370.667 71.281 L 413.333 69.167 L 456 67.474 L S GR GS [0.5 0 0 0.5 36 99.21465] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 57.33333 70.74294] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 78.66666 56.76173] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 100 48.24597] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 121.33334 43.00468] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 142.66667 39.49031] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 164 37.28182] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 185.33334 35.64034] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 206.66667 34.58364] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 228 33.73708] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 0 0] CT 1 GC N 456 320 M 456 231 L 255 231 L 255 320 L cp f GR GS [0.5 0 0 0.5 162.66254 122.05524] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (MLE) t GR GR GS [0.5 0 0 0.5 0 0] CT 0 0.447 0.741 RC 1 LJ 3 LW N 260.985 244.11 M 320.836 244.11 L S GR GS [0.5 0 0 0.5 145.45534 122.05524] CT 0 0.447 0.741 RC N f223118758 f GR GS [0.5 0 0 0.5 162.66254 132.51842] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (AMP) t GR GR GS [0.5 0 0 0.5 0 0] CT 0.851 0.325 0.098 RC 1 LJ 3 LW N 260.985 265.037 M 320.836 265.037 L S GR GS [0.5 0 0 0.5 145.45534 132.51842] CT 0.851 0.325 0.098 RC 10.0 ML 3 LW N -4 -4 M -4 4 L 4 4 L 4 -4 L cp S GR GS [0.5 0 0 0.5 162.66254 142.98158] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (OAMP) t GR GR GS [0.5 0 0 0.5 0 0] CT 0.929 0.694 0.125 RC 1 LJ 3 LW N 260.985 285.963 M 320.836 285.963 L S GR GS [0.5 0 0 0.5 145.45534 142.98158] CT 0.929 0.694 0.125 RC 10.0 ML 3 LW N 0 -6.665 M -5.772 3.332 L 5.772 3.332 L cp S GR GS [0.5 0 0 0.5 162.66254 153.44476] CT /Times-Roman 17.1 F GS [1 0 0 1 0 0] CT 0 6 moveto 1 -1 scale (Mismatched MLE) t GR GR GS [0.5 0 0 0.5 0 0] CT 0.494 0.184 0.557 RC 1 LJ 3 LW N 260.985 306.89 M 320.836 306.89 L S GR GS [0.5 0 0 0.5 145.45534 153.44476] CT 0.494 0.184 0.557 RC 10.0 ML 3 LW N -5 0 M 0 6.65 L 5 0 L 0 -6.65 L cp S GR GS [0.5 0 0 0.5 0 0] CT 0.149 GC 10.0 ML N 255 320 M 255 231 L 456 231 L 456 320 L cp S GR %%Trailer %%Pages: 1 %%EOF %%EndDocument @endspecial 0 TeXcolorgray 102 x(\(b\))91 b(Detection)j(under)e (correlated)3067 2136 y(Rayleigh)26 b(f)o(ading)f(channels.)p 0 TeXcolorgray 0 TeXcolorgray 2000 2261 a(Fig.)32 b(8)66 b(Detection)36 b(performance)e(comparison)g(of)e(the)h(MLE)e(approach)j (and)f(the)2000 2335 y(benchmarks)25 b(for)f(dif)n(ferent)i Fd(N)7 b Fy(')l(s.)p 0 TeXcolorgray 0 TeXcolorgray 2000 2613 a Fx(the)32 b(mismatched)f(MLE)g(performing)e(w)o(orse)j(than)g (these)g(methods.)2000 2713 y(Moreo)o(v)o(er)m(,)k(MLE)k(outperforms)d 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(all)i(the)f(homogeneous)d(terms)j(in)g(\()p 0 0 1 TeXcolorrgb 1628 1203 a SDict begin H.S end 1628 1203 a 0 0 1 TeXcolorrgb -1 x Fx(27)p 0 0 1 TeXcolorrgb 1711 1145 a SDict begin H.R end 1711 1145 a 1711 1202 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.27) cvn H.B /ANN pdfmark end 1711 1202 a 0 TeXcolorgray Fx(\))g(and)-192 1301 y(denote)27 b Fu(c)94 1313 y Fr(i)122 1301 y Ft(\()p Fo(a)p Ft(\))i Fx(as)g(the)g(coef)n(\002cient)e(of)i Fu(d)1016 1271 y Fr(i)1043 1301 y Fu(;)g(i)23 b Ft(=)g(2)p Fu(;)14 b Ft(3)p Fu(;)g Ft(4)p Fu(:)27 b Fx(Speci\002cally)-5 b(,)-109 1482 y Fu(p)-67 1494 y Fp(appro)n(x)136 1482 y Ft(\()p Fu(d)p Ft(\))23 b(=)g Fu(f)9 b Ft(\()p Fo(a)p Ft(\)+)113 1609 y([)p Fs(r)p Fu(f)g Ft(\()p Fo(a)p Ft(\)])395 1634 y Fr(n)454 1609 y Fu(d)19 b Ft(+)f Fu(c)635 1621 y Fp(2)672 1609 y Ft(\()p Fo(a)p Ft(\))c Fu(d)846 1575 y Fp(2)902 1609 y Ft(+)k Fu(c)1021 1621 y Fp(3)1058 1609 y Ft(\()p Fo(a)p Ft(\))c Fu(d)1232 1575 y Fp(3)1288 1609 y Ft(+)k Fu(c)1407 1621 y Fp(4)1444 1609 y Ft(\()p Fo(a)p Ft(\))c Fu(d)1618 1575 y Fp(4)1656 1609 y Fu(:)1762 1609 y SDict begin H.S end 1762 1609 a 1762 1609 a SDict begin 15 H.A end 1762 1609 a 1762 1609 a SDict begin [/View [/XYZ H.V]/Dest (equation.Appendix.A.60) cvn /DEST pdfmark end 1762 1609 a Fx(\(60\))-192 1765 y(Since)28 b Fu(c)57 1777 y Fp(2)94 1765 y Ft(\()p Fo(a)p Ft(\))p Fu(;)g(c)298 1777 y Fp(3)336 1765 y Ft(\()p Fo(a)p Ft(\))p Fu(;)g Fx(and)f Fu(c)688 1777 y Fp(4)725 1765 y Ft(\()p Fo(a)p Ft(\))i Fx(are)f(continuous)d (and)i Fo(a)h Fx(is)h(in)f(the)-192 1864 y(bounded)c(re)o(gion)h Ft([0)p Fu(;)14 b Ft(1])526 1834 y Fr(N)588 1864 y Fu(;)27 b Fx(the)o(y)f(are)g(bounded.)e(That)i(is,)i(there)e(e)o(xist)-192 1964 y(constants)k Ft(\026)-44 b Fu(c)182 1976 y Fp(2)219 1964 y Fu(;)31 b Ft(\026)-44 b Fu(c)307 1976 y Fp(3)345 1964 y Fu(;)29 b Fx(and)g Ft(\026)-43 b Fu(c)582 1976 y Fp(4)642 1964 y Fu(>)22 b Ft(0)29 b Fx(such)f(that)413 2120 y SDict begin H.S end 413 2120 a 413 2120 a SDict begin 12 H.A end 413 2120 a 413 2120 a SDict begin [/View [/XYZ H.V]/Dest (equation.Appendix.A.61) cvn /DEST pdfmark end 413 2120 a Fs(j)p Fu(c)472 2132 y Fr(i)500 2120 y Ft(\()p Fo(a)p Ft(\))p Fs(j)23 b(\024)i Ft(\026)-44 b Fu(c)787 2132 y Fr(i)814 2120 y Fu(;)97 b(i)23 b Ft(=)g(2)p Fu(;)14 b Ft(3)p Fu(;)g Ft(4)p Fu(:)465 b Fx(\(61\))-192 2276 y(Therefore,)22 b(setting)j Fu(c)e Ft(=)g(2\()r(\026)-44 b Fu(c)685 2288 y Fp(2)733 2276 y Ft(+)13 b(\026)-44 b Fu(c)845 2288 y Fp(3)894 2276 y Ft(+)13 b(\026)-44 b Fu(c)1006 2288 y Fp(4)1043 2276 y Ft(\))p Fu(;)26 b Fx(for)e Fu(\026)f Fs(\025)f Fw(\006)12 b Ft(+)f Fu(c;)25 b Fx(we)g(ha)n(v)o(e)-192 2376 y(that)g(for)g(an)o(y)f Fu(d)f Fs(2)h Ft([)p Fs(\000)p Fu(a)502 2388 y Fr(n)547 2376 y Fu(;)j Ft(1)12 b Fs(\000)g Fu(a)772 2388 y Fr(n)817 2376 y Ft(])p Fu(;)26 b Fx(the)f(follo)n(wing)e(inequality)h(holds)-34 2564 y SDict begin H.S end -34 2564 a -34 2564 a SDict begin 12 H.A end -34 2564 a -34 2564 a SDict begin 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begin H.R end 638 2677 a 638 2734 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.Appendix.A.62) cvn H.B /ANN pdfmark end 638 2734 a 0 TeXcolorgray Fx(\))o(,)h(we)g(obtain)277 2900 y SDict begin H.S end 277 2900 a 277 2900 a SDict begin 12 H.A end 277 2900 a 277 2900 a SDict begin [/View [/XYZ H.V]/Dest (equation.Appendix.A.63) cvn /DEST pdfmark end 277 2900 a Fu(f)9 b Ft(\()p Fo(a)18 b Ft(+)g Fu(d)c Fo(e)616 2912 y Fr(n)661 2900 y Ft(\))23 b Fs(\024)g Fu(p)846 2912 y Fp(appro)n(x)1049 2900 y Ft(\()p Fu(d)p Ft(\))c(+)1268 2844 y Fu(\026)p 1268 2881 51 4 v 1272 2957 a Ft(2)1328 2900 y Fu(d)1371 2866 y Fp(2)1408 2900 y Fu(:)331 b Fx(\(63\))-109 3081 y(No)n(w)37 b(we)g(study)f(the)h(optimal)f(v)n(alue)h(of)f Fu(p)1233 3093 y Fp(appro)n(x)1436 3081 y Ft(\()p Fu(d)p Ft(\))25 b(+)1667 3044 y Fr(\026)p 1667 3062 41 4 v 1671 3110 a Fp(2)1718 3081 y Fu(d)1761 3051 y Fp(2)1836 3081 y Fx(to)-192 3181 y(obtain)38 b(the)g(desired)g(inequality)f(\()p 0 0 1 TeXcolorrgb 873 3183 a SDict begin H.S end 873 3183 a 0 0 1 TeXcolorrgb -2 x Fx(29)p 0 0 1 TeXcolorrgb 956 3124 a SDict begin H.R end 956 3124 a 956 3181 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.29) cvn H.B /ANN pdfmark end 956 3181 a 0 TeXcolorgray Fx(\))o(.)i(Notice)f(that)h(for)f (an)o(y)f Fu(d)42 b Fs(2)-192 3280 y Ft([)p Fs(\000)p Fu(a)-60 3292 y Fr(n)-15 3280 y Fu(;)27 b Ft(1)18 b Fs(\000)g Fu(a)222 3292 y Fr(n)268 3280 y Ft(])p Fu(;)-105 3462 y SDict begin H.S end -105 3462 a -105 3462 a SDict begin 12 H.A end -105 3462 a -105 3462 a SDict begin [/View [/XYZ H.V]/Dest (equation.Appendix.A.64) cvn /DEST pdfmark end -105 3462 a Fu(p)-63 3474 y Fp(appro)n(x)140 3462 y Ft(\()p Fu(d)p Ft(\))h(+)359 3406 y Fu(\026)p 359 3443 51 4 v 363 3519 a Ft(2)419 3462 y Fu(d)462 3428 y Fp(2)522 3462 y Fs(\024)k Fu(f)9 b Ft(\()p Fo(a)p Ft(\))18 b(+)g([)p Fs(r)p Fu(f)9 b Ft(\()p Fo(a)p Ft(\)])1160 3487 y Fr(n)1219 3462 y Fu(d)19 b 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1386 3987 188 4 v 1459 4063 a Ft(2)1584 4006 y Fu(d)1627 3972 y Fp(2)67 4172 y(\()p Fr(a)p Fp(\))79 4248 y Fs(\024)34 b Fu(f)9 b Ft(\()p Fo(a)p Ft(\))18 b Fs(\000)456 4191 y Ft(\()q(Pro)5 b(j)12 b(\()p Fu(a)739 4203 y Fr(n)803 4191 y Fs(\000)18 b Ft([)p Fs(r)p Fu(f)9 b Ft(\()p Fo(a)p Ft(\)])1168 4216 y Fr(n)1213 4191 y Ft(\))19 b Fs(\000)f Fu(a)1391 4203 y Fr(n)1436 4191 y Ft(\))1468 4149 y Fp(2)p 456 4229 1050 4 v 834 4305 a Ft(2\()p Fu(\026)g Ft(+)g Fu(c)p Ft(\))67 4474 y(=)23 b Fu(f)9 b Ft(\()p Fo(a)p Ft(\))18 b Fs(\000)450 4418 y Ft([)p Fl(v)q Ft(\()p Fo(a)p Ft(\)])664 4388 y Fp(2)664 4439 y Fr(n)p 433 4455 294 4 v 433 4531 a Ft(2\()p Fu(\026)g Ft(+)g Fu(c)p Ft(\))737 4474 y Fu(;)1762 4474 y SDict begin H.S end 1762 4474 a 1762 4474 a SDict begin 15 H.A end 1762 4474 a 1762 4474 a SDict begin [/View [/XYZ H.V]/Dest (equation.Appendix.A.65) cvn /DEST pdfmark end 1762 4474 a Fx(\(65\))-192 4671 y(where)28 b Ft(\()p Fu(a)p Ft(\))h Fx(is)h(deri)n(v)o(ed)d(from)-95 4893 y Ft(Pro)5 b(j)79 4776 y Fk(\022)140 4893 y Fu(a)184 4905 y Fr(n)248 4893 y Fs(\000)341 4836 y Ft([)p Fs(r)p Fu(f)k Ft(\()p Fo(a)p Ft(\)])623 4861 y Fr(n)p 341 4874 328 4 v 411 4950 a Fu(\026)18 b Ft(+)g Fu(c)678 4776 y Fk(\023)758 4893 y Fs(\000)g Fu(a)885 4905 y Fr(n)82 5102 y Ft(=)108 b(arg)13 b(min)170 5175 y Fr(d)p Fq(2)p Fp([)p Fq(\000)p Fr(a)357 5183 y Fj(n)397 5175 y Fr(;)e Fp(1)p Fq(\000)p Fr(a)549 5183 y Fj(n)589 5175 y Fp(])637 5102 y Fu(f)e Ft(\()p Fo(a)p Ft(\))18 b(+)g([)p Fs(r)p Fu(f)9 b Ft(\()p Fo(a)p Ft(\)])1187 5127 y Fr(n)1246 5102 y Fu(d)19 b Ft(+)1401 5046 y Fu(\026)f Ft(+)h Fu(c)p 1401 5083 188 4 v 1474 5159 a Ft(2)1598 5102 y Fu(d)1641 5067 y Fp(2)1762 5102 y SDict begin H.S end 1762 5102 a 1762 5102 a SDict begin 15 H.A end 1762 5102 a 1762 5102 a SDict begin [/View [/XYZ H.V]/Dest (equation.Appendix.A.66) cvn /DEST pdfmark end 1762 5102 a Fx(\(66\))-192 5317 y(and)29 b(the)g(properties)f(of)h(the)g (projection)f(operator)g Ft(Pro)5 b(j)n(\()p Fs(\001)p Ft(\))p Fu(:)31 b 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-192 5634 a SDict begin 12 H.A end -192 5634 a -192 5634 a SDict begin [/View [/XYZ H.V]/Dest (appendix.Appendix.B) cvn /DEST pdfmark end -192 5634 a 0 TeXcolorgray 0 TeXcolorgray 2819 -63 a SDict begin H.S end 2819 -63 a 2819 -63 a SDict begin 12 H.A end 2819 -63 a 2819 -63 a SDict begin [/View [/XYZ H.V]/Dest (section*.12) cvn /DEST pdfmark end 2819 -63 a 2 w Fx(A)t Fy(P)t(P)t(E)t(N)t(D)t(I)t(X)d Fx(B)2585 37 y(P)t Fy(R)q(O)t(O)t(F)h(O) t(F)f Fx(P)t Fy(R)q(O)t(P)t(O)t(S)t(I)t(T)t(I)t(O)t(N)p 0 0 1 TeXcolorrgb 3463 37 a SDict begin H.S end 3463 37 a 0 0 1 TeXcolorrgb 2 w Fx(1)p 0 0 1 TeXcolorrgb 3509 -20 a SDict begin H.R end 3509 -20 a 3509 37 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (proposition.1) cvn H.B /ANN pdfmark end 3509 37 a 0 TeXcolorgray 2083 167 a Fx(Let)30 b Fo(u)2281 179 y Fr(m)2373 167 y Fx(denote)f(the)h Fu(m)p Fx(-th)f(column)f(v)o(ector)h(of)g Fo(U)9 b Fu(:)31 b Fx(W)-7 b(e)31 b(observ)o(e)2000 267 y(from)c(\()p 0 0 1 TeXcolorrgb 2218 268 a SDict begin H.S end 2218 268 a 0 0 1 TeXcolorrgb -1 x Fx(32)p 0 0 1 TeXcolorrgb 2301 210 a SDict begin H.R end 2301 210 a 2301 267 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.32) cvn H.B /ANN pdfmark end 2301 267 a 0 TeXcolorgray Fx(\))i(that)2343 494 y SDict begin H.S end 2343 494 a 2343 494 a SDict begin 12 H.A end 2343 494 a 2343 494 a SDict begin [/View [/XYZ H.V]/Dest (equation.Appendix.B.67) cvn /DEST pdfmark end 2343 494 a -104 x Fr(N)2396 398 y Fh(corr)2360 415 y Fk(X)2358 591 y Fr(n)p Fp(=1)2512 494 y Fo(u)2569 460 y Fr(H)2569 515 y(m)2631 494 y Fo(R)2703 506 y Fr(n)2749 494 y Fo(u)2806 506 y Fr(m)2892 494 y Ft(=)22 b(0)p Fu(;)97 b(r)3180 460 y Fq(0)3222 494 y Ft(+)18 b(1)23 b Fs(\024)f Fu(m)h Fs(\024)g Fu(M)t(:)205 b Fx(\(67\))2000 729 y(Since)30 b Fo(R)2287 741 y Fr(n)2363 729 y Fx(is)h(positi)n(v)o(e)f (semide\002nite,)f Fo(u)3254 699 y Fr(H)3254 750 y(m)3316 729 y Fo(R)3388 741 y Fr(n)3434 729 y Fo(u)3491 741 y Fr(m)3584 729 y Fx(is)i(nonne)o(gati)n(v)o(e.)2000 829 y(Therefore,)20 b(\()p 0 0 1 TeXcolorrgb 2399 830 a SDict begin H.S end 2399 830 a 0 0 1 TeXcolorrgb -1 x Fx(67)p 0 0 1 TeXcolorrgb 2482 772 a SDict begin H.R end 2482 772 a 2482 829 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.Appendix.B.67) cvn H.B /ANN pdfmark end 2482 829 a 0 TeXcolorgray Fx(\))j(implies)g Fo(u)2858 799 y Fr(H)2858 849 y(m)2921 829 y Fo(R)2993 841 y Fr(n)3038 829 y Fo(u)3095 841 y Fr(m)3181 829 y Ft(=)g(0)p Fu(;)g Fx(which)f(is)i(equi)n(v)n(alent)d (to)2000 928 y Fo(R)2072 940 y Fr(n)2117 928 y Fo(u)2174 940 y Fr(m)2262 928 y Ft(=)k Fl(0)p Fu(;)30 b(r)2492 898 y Fq(0)2535 928 y Ft(+)19 b(1)24 b Fs(\024)h Fu(m)g Fs(\024)g Fu(M)t(;)30 b Ft(1)25 b Fs(\024)f Fu(n)h Fs(\024)g Fu(N)3489 940 y Fp(corr)3607 928 y Fu(:)30 b Fx(No)n(w)g(we)g(can)2000 1028 y(v)o(erify)d(that)h(only)g(the)g(upper)f(left)i Fu(r)3083 998 y Fq(0)3125 1028 y Fs(\002)18 b Fu(r)3247 998 y Fq(0)3300 1028 y Fx(submatrix)27 b(of)i Fo(U)3835 998 y Fr(H)3898 1028 y Fo(R)3970 1040 y Fr(n)4016 1028 y Fo(U)2000 1128 y Fx(is)g(nonzero.)d(This)j(completes)f(the)g(proof)f (of)h(Proposition)p 0 0 1 TeXcolorrgb 3793 1128 a SDict begin H.S end 3793 1128 a 0 0 1 TeXcolorrgb Fx(1)p 0 0 1 TeXcolorrgb 3835 1071 a SDict begin H.R end 3835 1071 a 3835 1128 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (proposition.1) cvn H.B /ANN pdfmark end 3835 1128 a 0 TeXcolorgray Fx(.)2000 1146 y SDict begin H.S end 2000 1146 a 2000 1146 a SDict begin 12 H.A end 2000 1146 a 2000 1146 a SDict begin [/View [/XYZ H.V]/Dest (appendix.Appendix.C) cvn /DEST pdfmark end 2000 1146 a 2819 1346 a SDict begin H.S end 2819 1346 a 2819 1346 a SDict begin 12 H.A end 2819 1346 a 2819 1346 a SDict begin [/View [/XYZ H.V]/Dest (section*.13) cvn /DEST pdfmark end 2819 1346 a 2 w Fx(A)t Fy(P)t(P)t(E)t(N)t(D)t(I)t(X)d Fx(C)2647 1446 y(P)t Fy(R)q(O)t(O)t(F)h (O)t(F)f Fx(T)t Fy(H)t(E)t(O)t(R)t(E)t(M)p 0 0 1 TeXcolorrgb 3401 1446 a SDict begin H.S end 3401 1446 a 0 0 1 TeXcolorrgb 2 w Fx(2)p 0 0 1 TeXcolorrgb 3447 1390 a SDict begin H.R end 3447 1390 a 3447 1446 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (theorem.2) cvn H.B /ANN pdfmark end 3447 1446 a 0 TeXcolorgray 2083 1577 a Fx(According)20 b(to)i(the)f(property)f(of)i(the)f(Kroneck)o(er)f(product,)g(for)h(an)o (y)2000 1676 y(matrices)28 b Fo(A)p Fu(;)14 b Fo(B)27 b Fs(2)d Fn(C)2651 1646 y Fr(M)6 b Fq(\002)p Fr(M)2881 1676 y Fx(and)28 b Fo(C)6 b Fu(;)14 b Fo(D)25 b Fs(2)e Fn(C)3376 1646 y Fr(L)p Fq(\002)p Fr(L)3529 1676 y Fu(;)2453 1836 y SDict begin H.S end 2453 1836 a 2453 1836 a SDict begin 12 H.A end 2453 1836 a 2453 1836 a SDict begin [/View [/XYZ H.V]/Dest (equation.Appendix.C.68) cvn /DEST pdfmark end 2453 1836 a Ft(\()p Fo(A)c Fs(\012)f Fo(C)6 b Ft(\))14 b(\()p Fo(B)22 b Fs(\012)c Fo(D)s Ft(\))23 b(=)g Fo(AB)g Fs(\012)18 b Fo(C)6 b(D)s Fu(:)314 b Fx(\(68\))2000 1995 y(Therefore,)40 b(we)j(can)g(v)o(erify)e(that)i Ft(\()p Fu(a)p Ft(\))h Fx(in)e(\()p 0 0 1 TeXcolorrgb 3385 1996 a SDict begin H.S end 3385 1996 a 0 0 1 TeXcolorrgb -1 x Fx(34)p 0 0 1 TeXcolorrgb 3468 1939 a SDict begin H.R end 3468 1939 a 3468 1995 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.34) cvn H.B /ANN pdfmark end 3468 1995 a 0 TeXcolorgray Fx(\))h(and)f Ft(\()p Fu(b)p Ft(\))i Fx(in)f(\()p 0 0 1 TeXcolorrgb 3982 1996 a SDict begin H.S end 3982 1996 a 0 0 1 TeXcolorrgb -1 x Fx(36)p 0 0 1 TeXcolorrgb 4064 1939 a SDict begin H.R end 4064 1939 a 4064 1995 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.36) cvn H.B /ANN pdfmark end 4064 1995 a 0 TeXcolorgray Fx(\))2000 2095 y(hold.)c(Furthermore,)g(since)h Fo(U)2973 2065 y Fr(H)3065 2095 y Fs(\012)27 b Fo(I)3199 2107 y Fr(L)3295 2095 y Fs(2)46 b Fn(C)3450 2065 y Fr(LM)6 b Fq(\002)p Fr(LM)3783 2095 y Fx(is)42 b(a)f(uni-)2000 2195 y(tary)g(matrix,)h(i.e.,)2616 2127 y Fk(\000)2654 2195 y Fo(U)d Fs(\012)28 b Fo(I)2894 2207 y Fr(L)2944 2127 y Fk(\001\000)3020 2195 y Fo(U)3095 2164 y Fr(H)3187 2195 y Fs(\012)g Fo(I)3322 2207 y Fr(L)3373 2127 y Fk(\001)3459 2195 y Ft(=)47 b Fo(I)3613 2207 y Fr(LM)3733 2195 y Fu(;)c Fx(we)f(ha)n(v)o(e)2000 2294 y Ft(log)14 b Fs(j)p Fl(\006)2213 2264 y Fq(0)2213 2315 y Fi(a)2259 2294 y Fs(j)23 b Ft(=)g(log)14 b Fs(j)p Fl(\006)2606 2306 y Fi(a)2652 2294 y Fs(j)29 b Fx(and)2012 2460 y SDict begin H.S end 2012 2460 a 2012 2460 a SDict begin 12 H.A end 2012 2460 a 2012 2460 a SDict begin [/View [/XYZ H.V]/Dest (equation.Appendix.C.69) cvn /DEST pdfmark end 2012 2460 a Ft(\()p Fo(y)2096 2426 y Fq(0)2138 2460 y Fs(\000)p 2221 2414 53 4 v 18 w Fo(y)2273 2426 y Fq(0)2273 2481 y Fi(a)2319 2460 y Ft(\))2352 2414 y Fr(H)2428 2460 y Ft(\()q Fl(\006)2530 2426 y Fq(0)2530 2481 y Fi(a)2576 2460 y Ft(\))2608 2414 y Fq(\000)p Fp(1)2711 2460 y Ft(\()p Fo(y)2795 2426 y Fq(0)2837 2460 y Fs(\000)p 2920 2414 V 18 w Fo(y)2972 2426 y Fq(0)2972 2481 y Fi(a)3018 2460 y Ft(\))24 b(=)e(\()q Fo(y)f Fs(\000)p 3347 2414 V 18 w Fo(y)3399 2481 y Fi(a)3445 2460 y Ft(\))3478 2419 y Fr(H)3555 2460 y Fl(\006)3624 2426 y Fq(\000)p Fp(1)3624 2481 y Fi(a)3726 2460 y Ft(\()q Fo(y)g Fs(\000)p 3912 2414 V 18 w Fo(y)3964 2481 y Fi(a)4011 2460 y Ft(\))14 b Fu(:)3954 2560 y Fx(\(69\))2000 2660 y(This)28 b(completes)g(the)h (proof)e(of)h(Theorem)p 0 0 1 TeXcolorrgb 3309 2660 a SDict begin H.S end 3309 2660 a 0 0 1 TeXcolorrgb Fx(2)p 0 0 1 TeXcolorrgb 3350 2603 a SDict begin H.R end 3350 2603 a 3350 2660 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (theorem.2) cvn H.B /ANN pdfmark end 3350 2660 a 0 TeXcolorgray Fx(.)2000 2678 y SDict begin H.S end 2000 2678 a 2000 2678 a SDict begin 12 H.A end 2000 2678 a 2000 2678 a SDict begin [/View [/XYZ H.V]/Dest (appendix.Appendix.D) cvn /DEST pdfmark end 2000 2678 a 2817 2878 a SDict begin H.S end 2817 2878 a 2817 2878 a SDict begin 12 H.A end 2817 2878 a 2817 2878 a SDict begin [/View [/XYZ H.V]/Dest (section*.14) cvn /DEST pdfmark end 2817 2878 a 2 w Fx(A)t Fy(P)t(P)t(E)t(N)t(D)t(I)t(X)d Fx(D)2647 2978 y(P)t Fy(R)q(O)t(O)t(F)h (O)t(F)f Fx(T)t Fy(H)t(E)t(O)t(R)t(E)t(M)p 0 0 1 TeXcolorrgb 3401 2979 a SDict begin H.S end 3401 2979 a 0 0 1 TeXcolorrgb 3403 2978 a Fx(3)p 0 0 1 TeXcolorrgb 3447 2922 a SDict begin H.R end 3447 2922 a 3447 2978 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (theorem.3) cvn H.B /ANN pdfmark end 3447 2978 a 0 TeXcolorgray 2083 3109 a Fx(W)-7 b(e)25 b(pro)o(v)o(e)d(Theorem)p 0 0 1 TeXcolorrgb 2751 3110 a SDict begin H.S end 2751 3110 a 0 0 1 TeXcolorrgb -1 x Fx(3)p 0 0 1 TeXcolorrgb 2793 3052 a SDict begin H.R end 2793 3052 a 2793 3109 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (theorem.3) cvn H.B /ANN pdfmark end 2793 3109 a 0 TeXcolorgray 24 w Fx(by)i(contradiction.)d(Suppose)i(there)g (e)o(xists)2000 3209 y(a)29 b(nonzero)d(v)o(ector)h Fo(x)c Fs(2)h(N)2822 3221 y Fp(I)2868 3209 y Fs(\\)19 b(C)5 b Fu(:)29 b Fx(Hence)f(we)h(ha)n(v)o(e)2164 3433 y SDict begin H.S end 2164 3433 a 2164 3433 a SDict begin 12 H.A end 2164 3433 a 2164 3433 a SDict begin [/View [/XYZ H.V]/Dest (equation.Appendix.D.70) cvn /DEST pdfmark end 2164 3433 a 2197 3329 a Fr(N)2166 3354 y Fk(X)2164 3529 y Fr(n)p Fp(=1)2303 3433 y Fu(x)2350 3445 y Fr(n)2395 3433 y Ft(\()p Fo(R)2499 3445 y Fr(n)2545 3433 y Ft(\))2577 3445 y Fr(m;m)2719 3433 y Fo(s)2763 3445 y Fr(n)2808 3433 y Fo(s)2852 3398 y Fr(H)2852 3453 y(n)2939 3433 y Ft(=)22 b Fl(0)p Fu(;)97 b(m)23 b Ft(=)f(1)p Fu(;)14 b Ft(2)p Fu(;)g(:)g(:)g(:)f(;)h(M)t(:)164 b Fx(\(70\))2000 3668 y(Since)28 b(in)h(Case)p 0 0 1 TeXcolorrgb 2497 3668 a SDict begin H.S end 2497 3668 a 0 0 1 TeXcolorrgb Fx(II)p 0 0 1 TeXcolorrgb 2553 3612 a SDict begin H.R end 2553 3612 a 2553 3668 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (Item.2) cvn H.B /ANN pdfmark end 2553 3668 a 0 TeXcolorgray Fx(,)g Fu(g)2643 3680 y Fr(n)2710 3668 y Ft(=)2826 3635 y Fp(1)p 2808 3649 70 4 v 2808 3696 a Fr(M)2888 3668 y Ft(tr)o(\()p Fo(R)3056 3680 y Fr(n)3102 3668 y Ft(\))p Fu(;)h Fx(we)e(ha)n(v)o(e)2058 3908 y SDict begin H.S end 2058 3908 a 2058 3908 a SDict begin 12 H.A end 2058 3908 a 2058 3908 a SDict begin [/View [/XYZ H.V]/Dest (equation.Appendix.D.71) cvn /DEST pdfmark end 2058 3908 a 2091 3804 a Fr(N)2061 3829 y Fk(X)2058 4005 y Fr(n)p Fp(=1)2197 3908 y Fu(x)2244 3920 y Fr(n)2290 3908 y Fu(g)2330 3920 y Fr(n)2375 3908 y Fo(s)2419 3920 y Fr(n)2464 3908 y Fo(s)2508 3874 y Fr(H)2508 3928 y(n)2594 3908 y Ft(=)2716 3852 y(1)p 2692 3889 90 4 v 2692 3965 a Fu(M)2842 3804 y Fr(M)2817 3829 y Fk(X)2805 4005 y Fr(m)p Fp(=1)2995 3804 y Fr(N)2964 3829 y Fk(X)2962 4005 y Fr(n)p Fp(=1)3101 3908 y Fu(x)3148 3920 y Fr(n)3193 3908 y Ft(\()p Fo(R)3297 3920 y Fr(n)3343 3908 y Ft(\))3375 3920 y Fr(m;m)3517 3908 y Fo(s)3561 3920 y Fr(n)3607 3908 y Fo(s)3651 3874 y Fr(H)3651 3928 y(n)3737 3908 y Ft(=)22 b Fl(0)p Fu(;)59 b Fx(\(71\))2000 4129 y(which)28 b(further)f(implies)2066 4359 y SDict begin H.S end 2066 4359 a 2066 4359 a SDict begin 12 H.A end 2066 4359 a 2066 4359 a SDict begin [/View [/XYZ H.V]/Dest (equation.Appendix.D.72) cvn /DEST pdfmark end 2066 4359 a 2099 4255 a Fr(N)2068 4280 y Fk(X)2066 4456 y Fr(n)p Fp(=1)2205 4359 y Fu(x)2252 4371 y Fr(n)2297 4359 y Fu(g)2337 4371 y Fr(n)2382 4359 y Fo(I)2424 4371 y Fr(M)2517 4359 y Fs(\012)2600 4292 y Fk(\000)2638 4359 y Fo(s)2682 4371 y Fr(n)2727 4359 y Fo(s)2771 4325 y Fr(H)2771 4380 y(n)2834 4292 y Fk(\001)2895 4359 y Ft(=)c Fo(I)3025 4371 y Fr(M)3117 4359 y Fs(\012)3200 4217 y Fk( )3299 4255 y Fr(N)3269 4280 y Fk(X)3266 4456 y Fr(n)p Fp(=1)3405 4359 y Fu(x)3452 4371 y Fr(n)3498 4359 y Fu(g)3538 4371 y Fr(n)3583 4359 y Fo(s)3627 4371 y Fr(n)3672 4359 y Fo(s)3716 4325 y Fr(H)3716 4380 y(n)3779 4217 y Fk(!)3868 4359 y Ft(=)f Fl(0)p Fu(:)3954 4521 y Fx(\(72\))2000 4621 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