基于增强空间调制的正交时频空间系统

<!DOCTYPE html><html lang="zh-CN" dir="ltr"><head>  <script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-TF44WCG2');</script>  <meta name="google-site-verification" content="qtQTnMSrK6sA-4pRLrqiSiCZUW4v-JjdBfmipk6pNRI"> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1"> <title>基于增强空间调制的正交时频空间系统</title> <meta name="description" content=""> <meta property="og:title" content="网上交易"> <meta property="og:type" content="website"> <meta property="og:url" content="#"> <meta property="og:image" content="#//assets/img/ogp.jpg"> <meta property="og:site_name" content="Transactions Online"> <meta property="og:description" content=""> <link rel="icon" href="https://global.ieice.org/assets/img/favicon.ico"> <link rel="apple-touch-icon" sizes="180x180" href="https://global.ieice.org/assets/img/apple-touch-icon.png"> <link rel="stylesheet" href="https://global.ieice.org/assets/css/header.css"> <link rel="stylesheet" href="https://global.ieice.org/assets/css/footer.css"> <link rel="stylesheet" href="https://global.ieice.org/assets/css/style.css"> <link rel="stylesheet" href="https://global.ieice.org/assets/css/2nd.css"> <link rel="stylesheet" href="https://global.ieice.org/assets/css/summary.css"> <link href="https://use.fontawesome.com/releases/v5.15.4/css/all.css" rel="stylesheet"> <link href="https://use.fontawesome.com/releases/v6.7.1/css/all.css" rel="stylesheet"> <link rel="stylesheet" type="text/css" href="https://unpkg.com/tippy.js@5.0.3/animations/shift-toward-subtle.css"> <link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/slick-carousel@1.8.1/slick/slick.css"> <link rel="stylesheet" href="https://use.typekit.net/mgs1ayn.css">  <script src="https://global.ieice.org/web/ui/js/custom.js"></script> <link href="https://global.ieice.org/web/ui/site.css" rel="stylesheet">   <meta name="DC.title" content="基于增强空间调制的正交时频空间系统"> <meta name="DC.creator" content="Anoop A"> <meta name="DC.creator" content="Christo K. THOMAS"> <meta name="DC.creator" content="Kala S"> <meta name="DC.date.issued" scheme="DCTERMS.W3CDTF" content="2024/11"> <meta name="DC.Date" content="2024/11/01"> <meta name="DC.citation.volume" content="E107-B"> <meta name="DC.citation.issue" content="11"> <meta name="DC.citation.spage" content="785"> <meta name="DC.citation.epage" content="796"> <meta name="DC.identifier" content="https://global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3206/_pdf"> <meta name="DCTERMS.abstract" content="本文提出了一种基于增强空间调制的新型正交时频空间 (ESM-OTFS)，以最大限度地发挥增强空间调制 (ESM) 和正交时频空间 (OTFS) 传输的优势。这种新型调制的主要目标是提高传输可靠性，满足未来无线通信系统对高传输速率和快速数据传输的苛刻要求。本文首先概述了 ESM-OTFS 中采用的系统模型和特定的信号处理技术。此外，还专门为 ESM-OTFS 提出了一种基于稀疏信号估计的新型检测器。稀疏信号估计是使用变分贝叶斯推理的完全分解后验近似来执行的，从而无需任何矩阵求逆即可获得低复杂度解。仿真结果表明，ESM-OTFS 优于传统的基于空间调制的 OTFS，新引入的检测算法优于其他线性检测方法。"> <meta name="DC.type" content=""> <meta name="DC.relation.ispartof" content="IEICE Transactions 关于通讯"> <meta name="DC.publisher" content="电子、信息和通信工程师协会">    <script async="" src="https://www.googletagmanager.com/gtag/js?id=G-FKRLDTXBR3"></script> <script> window.dataLayer = window.dataLayer || []; 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Non-English content has been machine-translated and may contain typographical errors or mistranslations. <span class="copyright js-modal-open" data-target="modal_copyright">Copyrights notice</span></p> <p class="close"><i class="fas fa-times-circle"></i></p> </div> <section class="summary_box">  <h3><span id="skip_info" class="notranslate"><span class="open_access2">Open Access</span><br><span class="TEXT-SUMMARY-TITLE" data-gt-block="">Enhanced Spatial Modulation Based Orthogonal Time Frequency Space System</span></span> <span class="sub"><span class="open_access2">开放存取</span><br><span class="TEXT-SUMMARY-TITLE" data-gt-block="">基于增强空间调制的正交时频空间系统</span></span> </h3> <p class="notranslate author" id="skip_info"><span class="TEXT-AUTHOR">Anoop A</span>, <span class="TEXT-AUTHOR">Christo K. THOMAS</span>, <span class="TEXT-AUTHOR">Kala S</span></p>  <div class="score_action_box"> <div class="score_box"> <ul> <li> <p class="score_name">全文浏览量</p> <p class="score">567</p> </li> </ul> </div> <div class="action_box"> <ul> <li> <span class="cap js-modal-open" data-tippy-content="Add to My Favorites" data-target="modal_sign_personal"> <a href="add_favorites/e107-b_11_785/"><i class="fas fa fa-star" style="color: #C0C0C0"></i></a> </span> </li>  <li class="share"><span class="cap toggle" data-tippy-content="share"><i class="fas fa-share-alt-square"></i></span> <div class="icon_box"> <p class="share_name">分享</p> <ul> <li class="mail js-modal-open" data-target="modal_mail"><i class="fa-solid fa-envelope"></i></li> <li><a href="https://www.facebook.com/sharer/sharer.php?u=https://zh-cn.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3206/_f" target="_blank"><i class="fa-brands fa-square-facebook"></i></a></li> <li><a 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solid 1px #b03527; text-align: center; width: 100px; height: 35px; line-height: 40px; border-radius: 25px; font-size: 14px; color: #b03527; margin-right: 10%; float: right; margin-top: -5%; margin-right: 235px; } .open_access2 { font-family: "noto-sans", sans-serif; font-weight: 400; font-style: normal; font-size: 14px; color: #fff; background-color: #b03527; padding: 2px 15px; border-radius: 5px; margin-left: 0px; position: relative; top: -1.5px; } //mail form .row { display: flex; align-items:center; padding: 5px; > label { width: 200px; } .input-box { width: 100%; .form-text { &.errors { border:1px solid red; } } span { display: none; color:red; padding-top: 5px; } } } .input-box.errors { span { display: block; } } .form-text.errors { + span { display: block; } } </style>   <div class="summary" id="Summary"> <h4>摘要：</h4> <div class="txt"> <p class="gt-block"> <span class="TEXT-COL">本文提出了一种基于增强空间调制的新型正交时频空间 (ESM-OTFS)，以最大限度地发挥增强空间调制 (ESM) 和正交时频空间 (OTFS) 传输的优势。这种新型调制的主要目标是提高传输可靠性，满足未来无线通信系统对高传输速率和快速数据传输的苛刻要求。本文首先概述了 ESM-OTFS 中采用的系统模型和特定的信号处理技术。此外，还专门为 ESM-OTFS 提出了一种基于稀疏信号估计的新型检测器。稀疏信号估计是使用变分贝叶斯推理的完全分解后验近似来执行的，从而无需任何矩阵求逆即可获得低复杂度解。仿真结果表明，ESM-OTFS 优于传统的基于空间调制的 OTFS，新引入的检测算法优于其他线性检测方法。</span> </p> </div> <div class="data"> <dl> <dt>出版物</dt> <dd> <span id="skip_info" class="notranslate"> <span class="TEXT-COL">IEICE TRANSACTIONS on Communications <a href="https://zh-cn.global.ieice.org/en_transactions/communications/E107-B_11">Vol.<span class="TEXT-COL">E107-B</span></a> No.<span class="TEXT-COL">11 pp.785-796</span> </span> </span></dd> </dl> <dl> <dt>发布日期</dt> <dd><span class="TEXT-COL">2024/11/01</span></dd> </dl> <dl> <dt>宣传</dt> <dd><span class="TEXT-COL"></span></dd> </dl> <dl> <dt>网络版ISSN</dt> <dd><span class="TEXT-COL">1745-1345</span></dd> </dl> <dl> <dt><span id="skip_info" class="notranslate">DOI</span></dt> <dd><span id="skip_info" class="notranslate"><span class="TEXT-COL">10.23919/transcom.2023EBP3206</span></span></dd> </dl> <dl> <dt>稿件类型</dt> <dd><span id="skip_info" class="notranslate"><span class="TEXT-COL">PAPER</span><br></span></dd> </dl> <dl> <dt>分类</dt> <dd><span class="TEXT-COL">无线通信技术</span></dd> </dl>  </div> </div> <div class="content">  <div class="txt"> <p> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ tex2jax: { inlineMath: [ ['$','$'], ["\$","\$"] ], displayMath: [ ['$$','$$'], ["\\[","\\]"] ], processEnvironments: true, processEscapes: true, ignoreClass: "mathjax-off" }, CommonHTML: { linebreaks: { automatic: true } }, "HTML-CSS": { linebreaks: { automatic: true } }, SVG: { linebreaks: { automatic: true } }, }); </script> <script async="" src="https://cdn.jsdelivr.net/npm/mathjax@2.7.5/MathJax.js?config=TeX-AMS-MML_HTMLorMML-full"></script> <link rel="stylesheet" type="text/css" href="https://global.ieice.org/full_text/full.css"> </p><div class="gt-block fj-sec" data-gt-block="">  <div> <h4 id="sec_1" class="gt-block headline" data-gt-block=""><span></span>1. 引言</h4> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>现代多载波调制技术在实现对可靠性和频谱效率有严格要求的未来无线通信方面发挥着重要作用，这一作用已得到广泛认可。未来的多载波调制方案有望处理高度衰落的无线场景，例如车对车通信、高速无人机和快速行驶的子弹头列车通信、车辆对基础设施通信等。最近提出的正交时频 (OTFS) 是一种可行的选择，可用于应对多载波调制方案中的高移动性条件 [1]。信息符号分布在延迟多普勒 (DD) 域中，而不是 OFDM 中的时频 (TF) 域中。DD 域信道特性使均衡器和信道估计的设计和设计相对容易，如 [2] 中所述。这些特性使 OTFS 成为未来实用无线通信的理想候选方案。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>[1] 中提出的 OTFS 非常有效地表示了高多普勒信道的时间波动特性。OTFS 使用二维 (2D) 基函数在 DD 域中传播信息 [4]。因此，我们可以说 OTFS 调制能够将 TF 域中随时间变化的信道转换为 DD 域中具有时不变特性的信道。OTFS 在双选择无线信道中非常有效，因为这些基函数涵盖了整个时频平面。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>在毫米波系统中对OTFS进行了性能评估，估计OTFS的误码率（BER）性能远优于正交频分复用（OFDM）[3]。通过在发射机端添加逆辛有限傅里叶变换（ISFFT）并在接收机端添加辛有限傅里叶变换（SFFT）[5]，可以将OTFS调制付诸实践。因此我们可以轻松地将OTFS集成到传统的OFDM系统中。[6]提出了一种简化的OTFS离散输入输出关系。在[7]中，作者研究表明OTFS在高移动信道中表现出优异的峰均功率比（PAPR）耐受性。[8]提出了一种利用嵌入式导频信号的OTFS系统信道估计新方法。[9]提出了一种OTFS的迭代检测器。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>多输入多输出 (MIMO) 技术因其能够提供高频谱效率而成为第四代和第五代无线网络的一部分。但是，与固定 MIMO 网络相比，MIMO 网络在具有高度移动性的环境中面临更多挑战。因此，传统 MIMO 信道存在许多重大缺陷，如 [10] 中所述。DD 域 OTFS 信道具有稀疏性，此特性有助于高阶 MIMO 网络缓解高多普勒环境中的信道均衡和信道估计。MIMO-OTFS 系统自诞生以来就得到了深入研究，[11]-[13] 对其详细的信号处理、检测方法和信道估计技术进行了研究。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>空间调制 (SM) 代表了无线通信领域的一项尖端技术，特别是通过利用空间维度传输附加信息来增强多输入多输出 (MIMO) 系统 [14]。该方法有效地将天线选择与符号调制相结合，大大降低了信道间干扰和系统复杂性。这意味着在 SM 的情况下，同一时刻只有一个发射天线处于工作状态，其他天线保持不活动状态。这使得 SM 成为一种具有高频谱效率、低复杂性和良好 BER 性能的调制方案。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>为了进一步提高频谱效率，提出了正交空间调制 (QSM) [22]。QSM 是 SM 的衍生技术，其独特之处在于将调制符号分为同相和正交分量。然后，将这些分量分配给两个不同的发射天线，每个天线由各自的索引位组激活，以传输同相和正交分量。随后，使用相互正交的载波传输这些调制信号分量。这种方法有效地防止了信道干扰并提高了分集增益。广义空间调制 (GSM) 是另一种创新的空间调制技术，它可以在任何给定时间选择性地激活一组天线进行传输 [23]。与 SM 相比，GSM 需要更复杂的信号处理和天线选择算法，从而导致计算复杂度增加，并且可能增加功耗 [24]。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>增强空间调制 (ESM) 最早是在 [16] 中提出的。ESM 是通过结合不同的思想而形成的。ESM 涉及使用主星座和辅星座。在 ESM 的情况下，当一个发射天线处于活动状态时，用于调制的信息符号从主星座中选择，而当两个发射天线处于活动状态时，使用辅星座调制信息符号，其他天线保持静默。在一次 ESM 传输中可以发送的信息比特总数取决于发射天线和星座符号组合的大小。因此，与传统 SM 相比，此属性增加了 ESM 的有效吞吐量。此外，辅星座是使用主星座的几何插值设计的，这优化了发射信号矢量之间的最小欧几里得距离。这种方法标志着 ESM 与传统 SM 和 GSM 之间的显著差异。当我们选择的信号星座将 ESM 的操作频谱效率保持在与传统 SM 相当的水平时，ESM 表现出卓越的性能。这种通过增加组合数来提高频谱效率的理念在 QSM 中也有所体现。然而，QSM 的最小平方欧几里德距离有所减小，性能不如 ESM。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>SM 表现出非凡的灵活性和适应性，使其能够与各种传输技术无缝集成。当与 OFDM 结合形成 SM-OFDM 时，这种方法能够抵抗频率选择性衰落，无需复杂的均衡方法，从而显著提高系统的频谱效率 [25]。虽然 OFDM 在具有多径传播的静态或低移动性环境中表现良好，但由于多普勒频移影响子载波的正交性，其性能在高移动性场景中会显著下降。为了解决这个问题，提出了基于 OTFS 的空间调制 (SM-OTFS) [15]，以在高多普勒频移和显著延迟扩展的环境中表现出色。作者在 [15] 中介绍了基于 MIMO 的 SM-OTFS，以提高频谱效率并降低检测复杂度。通过模拟证明，SM-OTFS 比空时编码 OTFS (STC-OTFS) 提供了显著的性能提升，尤其是在高移动性场景中。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>[26] 详细阐述了 SM-OTFS 方案的系统模型及其相关的信号处理技术，本文还提供了延迟多普勒信道上的平均误码率 (ASER) 和平均误码率 (ABER) 的闭式表达式。[26] 中，作者还强调了在高多普勒环境下 SM-OFDM 优于 SM-OTFS 的性能。[27] 概述了 OTFS（GSM-OTFS）系统上的广义空间调制的系统模型及其相关的信号处理技术，包括使用联合边界技术和矩生成函数 (MGF) 对平均 BER 性能进行理论分析。在论文 [27] 中，作者通过理论和仿真结果证明，与传统的 SM-OTFS 相比，GSM-OTFS 提供了更好的 BER 性能和频谱效率。即使 GSM-OTFS 系统与 SM-OTFS 相比提高了频谱效率和 BER 性能，它也带来了诸如系统复杂性增加、硬件需求、功耗和高级信号处理要求等挑战。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>[20] 中提出的基于 OTFS 的正交空间调制 (QSM-OTFS) 是另一种利用 QSM 的基于 OTFS 的索引调制。在论文 [20] 中，作者详细介绍了系统模型、信号处理步骤和性能分析，包括理论 ABER 分析和一种名为增强型最小均方误差 (EMMSE) 的创新检测技术，以降低检测复杂度。此外，它将提出的 QSM-OTFS 系统与传统的 SM-OTFS 系统进行了比较，突出了 ABER 性能方面的优势。受 ESM 和 OTFS 特点的启发，我们提出了一种基于 ESM 的新型 OTFS 方案，称为增强型基于调制的 OTFS (ESM-OTFS)，它在高移动场景中表现良好，并且与 SM-OTFS 相比具有更高的频谱效率。QSM-OTFS 具有与 ESM-OTFS 相同的频谱效率，但在相同信道条件下性能较差。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>增强型空间调制与正交时频空间 (ESM-OTFS) 调制相结合，为现代无线通信挑战提供了一种通用且高效的解决方案，特别是在需要高移动性和稳健性的环境中。ESM-OTFS 特别适合高移动性环境，例如高速列车、车载网络（车对车和车对基础设施通信）和无人机，因为它具有抗多普勒频移的能力，并且能够在高速下保持可靠的通信。这种创新方法还非常适合广泛的应用，包括 5G 及更高版本的无线系统、物联网 (IoT) 网络、卫星和深空通信以及水下声学通信，以及增强城市蜂窝网络的容量和可靠性。通过提供更高的频谱效率和对多普勒频移和多径传播的抗性，ESM-OTFS 脱颖而出，成为一种有前途的技术，可确保在各种具有挑战性的环境和应用中实现可靠的高速通信，推动当前和未来无线通信领域的进步。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>SM-OTFS 和 ESM-OTFS 的传输向量包含大量零项而非非零值，此属性使数据传输向量在大多数系统配置中成为稀疏向量。因此，利用稀疏信号估计方法来检测 ESM-OTFS 是一个不错的选择。稀疏贝叶斯学习 (SBL) 是稀疏信号估计中使用的流行技术之一。但它涉及在每次迭代中使用矩阵求逆，因此即使对于中等大小的数据集，计算量也是很大的。我们可以使用变分贝叶斯推理方法 [17]、[18] 来进行稀疏信号估计，而不是使用 SBL。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>变分贝叶斯推断 (VBI)，也称为变分贝叶斯，是贝叶斯统计和机器学习中用于近似概率模型中潜在变量的后验分布的一种方法。此方法在涉及复杂模型的情况下非常有用，因为使用精确推断或采样技术在计算上是困难的。VBI 背后的主要思想是用更简单、参数化的变分分布来近似真实的后验分布，这种分布更容易使用。这些变分分布通常从一类分布中选择，例如高斯分布。目标是找到最能近似真实后验的这种简单分布的参数。[19] 中提出的 SAVE（稀疏贝叶斯学习的空间交替变分估计）算法是一种出色的稀疏信号估计算法。受 SAVE 算法的启发，我们能够为新提出的 ESM-OTFS 设计出一种基于稀疏信号估计的新型检测器。</p> </div>  <div class="fj-pagetop"><a href="#top">页面顶部</a></div> </div> <div class="gt-block fj-sec" data-gt-block=""> <div> <h4 id="sec_2" class="gt-block headline" data-gt-block=""><span></span>2. 系统模型</h4> <div> <h5 id="sec_2_1" class="gt-block headline" data-gt-block=""><span></span>2.1 ESM调制</h5> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>空间调制 (SM) 是一种基于多输入多输出 (MIMO) 的无线通信技术，使用发射天线索引来传输信息符号。SM 涉及在任何给定时刻激活单个发射天线，并且所选天线用于从所选星座传输信号。如果 <span id="skip_info" class="notranslate">$N_{T}$</span> 是发射天线的数量， <span id="skip_info" class="notranslate">$s_{a}=2^{n_{a}}$</span> 是信号星座的大小，SM中传输的比特数为 <span id="skip_info" class="notranslate">$n_{a}+\log_{2}(N_{T})$</span>.</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>增强型空间调制通过根据 [16] 中确定的活跃天线数量从不同的星座发射不同的符号，提高了 SM 的效率和稳健性。这通过在单发射天线激活期间首先从主星座发射符号来实现，就像传统的 SM 一样。当启用两个发射天线时，符号从辅助星座发射。辅助星座的大小取主星座的一半，以便在单天线激活和双天线激活期间发射相同数量的信息位。由于信号是从两个不同的天线发射的，因此可以获得更高的分集增益，从而使其对干扰更具鲁棒性。为了最大化发射信号矢量之间的最小欧几里得距离，通过几何插值创建了辅助星座。这确保了辅助星座中的符号尽可能远，从而使接收器更难出错。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>在传统 SM 中，传输的信息比特数取决于发射天线的数量和用于调制的符号星座的大小。在 ESM 中，它由天线和星座符号组合决定。下图为具有 <span id="skip_info" class="notranslate">$2$</span> 表 1 列出了发射天线数、QPSK 作为主星座、BPSK 作为辅星座的情况。这里，传输的比特数或每信道使用的比特数 (bpcu) 为 <span id="skip_info" class="notranslate">$4$</span>.</p> <div id="table_1" class="fj-table-g"> <table> <tbody> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>表1</b>  欧洲安全与稳定委员会， <span id="skip_info" class="notranslate">$2$</span> 德克萨斯州 - <span id="skip_info" class="notranslate">$4$</span> BPCU。</p></td> </tr> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/t01.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/t01.jpg" class="fj-table-graphic"></a></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span><span id="skip_info" class="notranslate">$\text{QPSK}=\pm 1 \pm j$</span>、BPSK0 和 BPSK1 分别由下式给出 <span id="skip_info" class="notranslate">$\text{BPSK0}=\pm 1$</span> <span id="skip_info" class="notranslate">$\&$</span> <span id="skip_info" class="notranslate">$\text{BPSK1}=\pm j$</span>. 前两种组合 <span id="skip_info" class="notranslate">$C1$</span> 和 <span id="skip_info" class="notranslate">$C2$</span> 看起来像是来自其中一个天线的传输，并传送来自 QPSK 星座的一个符号。最后的组合 <span id="skip_info" class="notranslate">$C3$</span> 和 <span id="skip_info" class="notranslate">$C4$</span> 对应于从两个天线发出的辅助星座 BPSK0 或 BPSK1 的符号传输。</p> </div> <div> <h5 id="sec_2_2" class="gt-block headline" data-gt-block=""><span></span>2.2 OTFS信号调制与解调</h5> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>OTFS 调制是一种传输信息符号的方式，对多普勒频移具有鲁棒性。它的工作原理是在 DD 域中复用数据符号，这是表达对多普勒频移不变的信号的另一种方式。这使得 OTFS 成为高移动性应用的理想选择。让 <span id="skip_info" class="notranslate">$\{u[l,k],l=0,1,\ldots,M-1,k=0,1,\ldots,N-1\}$</span> 是 DD 域中的二维信息信号，其中 <span id="skip_info" class="notranslate">$M$</span> 表示子载波的数量， <span id="skip_info" class="notranslate">$N$</span> 表示 OFDM 符号或时隙的数量。时频 (TF) 域信号 <span id="skip_info" class="notranslate">$U[m,n]$</span> 从获得 <span id="skip_info" class="notranslate">$u[l,k]$</span> 通过逆辛有限傅里叶变换（ISFFT），即</p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} U\left[m, n\right]=\frac{1}{\sqrt{MN}}\sum_{l=0}^{M-1}\sum_{k=0}^{N-1}u\left[l, k\right]e^{j2\pi\left(\frac{nk}{N}-\frac{ml}{M}\right)} \tag{1} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""></p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>使用海森堡变换以及发射机侧脉冲整形信号 <span id="skip_info" class="notranslate">$p_{tx}(t)$</span>, <span id="skip_info" class="notranslate">$U[m,n]$</span> 转换为时域 (TD) 信号 <span id="skip_info" class="notranslate">$s(t)$</span> </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} s(t)=\displaystyle \sum_{m=0}^{M-1}\sum_{n=0}^{N-1}U[m,\ n]p_{\mathrm{t}\mathrm{x}}(t-mT)e^{j2\pi n\Delta f(t-mT)} \tag{2} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$\Delta f$</span> 和 <span id="skip_info" class="notranslate">$T$</span> 分别表示子载波间隔和OFDM符号周期， <span id="skip_info" class="notranslate">$\Delta f = \frac{1}{T}$</span>.</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>在接收器处，接收到的信号 <span id="skip_info" class="notranslate">$r(t)$</span> 与接收端脉冲整形信号匹配 <span id="skip_info" class="notranslate">$p_{rx}(t)$</span> 并使用 Wigner 变换将其转换为 TF 域，并得到交叉模糊性 <span id="skip_info" class="notranslate">$\Lambda_{p_{rx},r}(t,f)$</span> 给出为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \Lambda_{p_{rx},r}(t,f) = \int r(t^{*})p_{\mathrm{r}\mathrm{x}}(t^{*}-t)e^{j2\pi f(t^{*}-t)}\mathrm {d}t^{*} \tag{3} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""></p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>使用子载波间隔对结果信号进行采样 <span id="skip_info" class="notranslate">$\Delta f$</span> 以及帧持续时间 <span id="skip_info" class="notranslate">$T$</span>接收到的TF域信号为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} V[m, n]=\Lambda_{p_{\mathrm{rx},\mathrm{r}}(t, f)|_{t=nT,f=m\Delta f}} \tag{4} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> DD域信号 <span id="skip_info" class="notranslate">$v[l,k]$</span> 从获得 <span id="skip_info" class="notranslate">$V[m,n]$</span> 通过应用辛有限傅里叶变换 (SFFT)，得到如下结果 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} v\left[l, k\right]=\frac{1}{\sqrt{MN}}\sum_{m=0}^{M-1}\sum_{n=0}^{N-1}V\left[m, n\right]e^{-j2\pi\left(\frac{nk}{N}-\frac{ml}{M}\right)} \tag{5} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""></p> </div> <div> <h5 id="sec_2_3" class="gt-block headline" data-gt-block=""><span></span>2.3 OTFS系统模型</h5> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>考虑使用 DD 域名渠道 <span id="skip_info" class="notranslate">$P$</span> 通道抽头，每个延迟 <span id="skip_info" class="notranslate">$\tau_{i}$</span>，多普勒 <span id="skip_info" class="notranslate">$\nu_{i}$</span> 衰落信道增益 <span id="skip_info" class="notranslate">$\kappa_{i}$</span>. [1] 中 DD 域的信道脉冲响应可以表示为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \kappa(\displaystyle \tau, \nu)=\sum_{i=1}^{P}\kappa_{i}\delta(\tau-\tau_{i})\delta(\nu-\nu_{i}) \tag{6} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$\delta(.)$</span> 表示狄拉克-德尔塔函数。延迟和多普勒 <span id="skip_info" class="notranslate">$i^{th}$</span> 可以表述为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \displaystyle \tau_{i}=\frac{l_{i}}{M\Delta f}, \nu_{i}=\frac{k_{i}}{NT} \tag{7} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""></p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>给定 TD 输入信号 <span id="skip_info" class="notranslate">$s(t)$</span>，接收信号 <span id="skip_info" class="notranslate">$r(t)$</span> 给出为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} r(t) = \int _{\nu}\int _{\tau }\kappa(\tau,\nu)s(t-\tau)e^{j2\pi \nu(t-\tau)} \mathrm{d}\tau \mathrm {d}\nu \tag{8} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 代入方程 <span id="skip_info" class="notranslate">$(6)$</span> 在等式中 <span id="skip_info" class="notranslate">$(8)$</span> 产量如[5]所述。 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \begin{aligned} &r(t) = \\& \int _{\nu}\int _{\tau }\left(\sum_{i=1}^{P}\kappa_{i}\delta(\tau-\tau_{i})\delta(\nu-\nu_{i})\right)s(t-\tau) e^{j2\pi \nu(t-\tau)}\mathrm {d}\tau \mathrm {d}\nu \end{aligned} \tag{9} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 并可以简化为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} r(t)=\sum_{i=1}^{P}\kappa_{i}s(t-\tau_{i})e^{j2\pi \nu_{i}(t-\tau_{i})} + n(t) \tag{10} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$n(t)$</span> 是TD中的噪声信号。采样的TD信号 <span id="skip_info" class="notranslate">$r(p)$</span> 给出为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} r(p)=\sum_{i=1}^{P}\kappa_{i}s(p-\tau_{i})e^{j2\pi \nu_{i}(p-\tau_{i})} + n(p) \tag{11} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$p=0,1,2\ldots,NM-1$</span>.</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>它可以以矩阵形式表示如下 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} r = \begin{bmatrix} r_{0} \\ r_{1} \\ \vdots \\ r_{MN-1} \end{bmatrix}=\bigg(\sum_{i=1}^{P}\kappa_{i}\Pi^{l_{i}}\Delta^{k_{i}}\bigg)s+w = \breve{H}s+n \tag{12} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$\Pi=\begin{bmatrix} 0&\cdots&0&1\\ 1&\ddots&0&0\\ \vdots&\ddots&\ddots&\vdots\\ 0&\cdots&1&0 \end{bmatrix}$</span> 是维度为 <span id="skip_info" class="notranslate">$MN\times MN$</span>, <span id="skip_info" class="notranslate">$\Delta$</span> 是 <span id="skip_info" class="notranslate">$MN\times MN$</span> 维对角矩阵为 <span id="skip_info" class="notranslate">$\Delta=diag{\begin{Bmatrix}e^{j2\pi\frac{p}{MN}}\end{Bmatrix}}^{MN-1}_{p=0}$</span>, <span id="skip_info" class="notranslate">$\breve{H}$</span> 是维度为 <span id="skip_info" class="notranslate">$MN\times MN$</span>，同时不失一般性 <span id="skip_info" class="notranslate">$l_{i}$</span> 和 <span id="skip_info" class="notranslate">$k_{i}$</span> 被认为是整数。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>在接收端，接收信号矢量 <span id="skip_info" class="notranslate">$r$</span> 转换到DD域，DD域中的输入输出关系如下 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} v=Hu+w \tag{13} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 其中 w 是 DD 域中的噪声矢量， <span id="skip_info" class="notranslate">$H$</span> DD 域信道矩阵如下 <span id="skip_info" class="notranslate">$H=(F_{N}\otimes I_{M})\breve{H}(F^{H}_{N}\otimes I_{M})$</span> 假设发射机和接收机使用矩形脉冲整形滤波器， <span id="skip_info" class="notranslate">$F_{N}$</span> 是 <span id="skip_info" class="notranslate">$N$</span> 点离散傅里叶变换 (DFT) 矩阵， <span id="skip_info" class="notranslate">$F^{H}_{N}$</span> 是 <span id="skip_info" class="notranslate">$N$</span> 点逆离散傅里叶变换（IDFT）矩阵， <span id="skip_info" class="notranslate">$\otimes$</span> 是 Kronecker 乘积的操作员，并且 <span id="skip_info" class="notranslate">$I_{M}$</span> 是 <span id="skip_info" class="notranslate">$M$</span> 维单位矩阵。</p> </div> <div> <h5 id="sec_2_4" class="gt-block headline" data-gt-block=""><span></span>2.4 ESM-OTFS</h5> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>所提出的ESM-OTFS系统模型如图1所示。从图1可以看出，ESM-OTFS系统配备了 <span id="skip_info" class="notranslate">$N_{T}$</span> 发射天线和 <span id="skip_info" class="notranslate">$N_{R}$</span> 接收天线。下面详细描述了ESM-OTFS中使用的信号处理。随机比特序列 <span id="skip_info" class="notranslate">$b=[b_{0} \hspace{2mm} b_{1}\cdots b_{totbits}]$</span> DD 域中的 ESM-OTFS 框架进入 ESM-OTFS 系统，其中 <span id="skip_info" class="notranslate">$totbits=MNlog_{2}(\mathbb{C} )$</span> 和 <span id="skip_info" class="notranslate">$\mathbb{C}$</span> 是ESM星座的大小。ESM调制的映射规则如表2所示。对于每个 <span id="skip_info" class="notranslate">$\mathbb{C}$</span> 传入比特时，根据给出的映射规则选择一个 ESM 传输向量。对于每个 <span id="skip_info" class="notranslate">$MN$</span> ESM-OTFS 帧的时隙中，每个时隙分配一个星座符号 <span id="skip_info" class="notranslate">$N_T$</span> 发射天线。这些 <span id="skip_info" class="notranslate">$MN$</span> 符号进入相应发射天线的 OTFS 块创建器单元，并形成相应天线的发射 DD 域向量。</p> <div id="fig_1" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f01.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f01.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>图。 1</b>  ESM-OTFS系统的系统模型。</p></td> </tr> </tbody> </table> </div> <div id="table_2" class="fj-table-g"> <table> <tbody> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>表2</b>  ESM 映射规则 <span id="skip_info" class="notranslate">$N_{T}=2$</span> 并以QSPK为主星座。</p></td> </tr> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/t02.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/t02.jpg" class="fj-table-graphic"></a></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>ESM-OTFS的传输速率可以表示为 <span id="skip_info" class="notranslate">$R_{ESM-OTFS}=MNlog_{2}(\mathbb{C})$</span> 而在相同设置下，SM-OTFS 的传输速率为 <span id="skip_info" class="notranslate">$R_{SM-OTFS}=MNlog_{2}(s_{a})$</span> 哪里 <span id="skip_info" class="notranslate">$s_{a}$</span> 是调制阶数或调制星座图的大小。由于发射天线与主、辅星座符号组合形成的ESM星座图大小大于SM调制阶数的大小，因此在相同MIMO环境下，ESM-OTFS的传输速率远优于SM-OTFS。ESM-OTFS帧的数据传输矩阵维数为 <span id="skip_info" class="notranslate">$MN \times N_T$</span> 并给出如下 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \mathbf{X_{ESM}}=\begin{bmatrix}\mathbf{x}_{0,0}^{1} & \ldots & \mathbf{x}_{0,0}^{i} & \ldots & \mathbf{x}_{0,0}^{N_{T}}\\[1.5mm] \mathbf{x}_{0,1}^{1} & \ldots & \mathbf{x}_{0,1}^{i} & \ldots & \mathbf{x}_{0,1}^{N_{T}}\\\vdots & \ddots & \vdots & \ddots & \vdots\\ \mathbf{x}_{0,N-1}^{1} & \ldots & \mathbf{x}_{0,N-1}^{i} & \ldots & \mathbf{x}_{0,N-1}^{N_{T}}\\\vdots & \ddots & \vdots & \ddots & \vdots\\ \mathbf{x}_{k,l}^{1} & \ldots & \mathbf{x}_{k,l}^{i} & \ldots & \mathbf{x}_{k,l}^{N_{t}}\\\vdots & \ddots & \vdots & \ddots & \vdots\\ \mathbf{x}_{M-1,N-1}^{1} & \ldots & \mathbf{x}_{M-1,N-1}^{i} & \ldots & \mathbf{x}_{M-1,N-1}^{N_{T}}\end{bmatrix} \tag{14} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""></p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span><span id="skip_info" class="notranslate">$X_{i}$</span> 是维度为 <span id="skip_info" class="notranslate">$M \times N$</span> 传输自 <span id="skip_info" class="notranslate">$i^{th}$</span> 发射天线。 <span id="skip_info" class="notranslate">$X_i$</span> 是通过收集所有元素形成的 <span id="skip_info" class="notranslate">$i^{th}$</span> 列 <span id="skip_info" class="notranslate">$\mathbf{X_{ESM}}$</span>.</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>正在从 <span id="skip_info" class="notranslate">$i^{th}$</span> 发射天线 <span id="skip_info" class="notranslate">$s_{i}$</span> 来自 <span id="skip_info" class="notranslate">$X_{i}$</span> 通过 ISSFT 单元和 OFDM 调制器模拟海森堡变换，如下所示 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} s_{i}=vec\left( F^{H}_{M}\left(F_{M}X_{i}F^{H}_{N}\right) \right)=\left(F^{H}_{N}\otimes I_{M}\right)x_{i} \tag{15} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$s_{i}$</span> 是 <span id="skip_info" class="notranslate">$MN\times 1$</span> 维列向量和 <span id="skip_info" class="notranslate">$vec(.)$</span> 是列向量运算。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>TD信号 <span id="skip_info" class="notranslate">$s_{i}$</span> 是从 <span id="skip_info" class="notranslate">$i^{th}$</span> 发射天线接收到的信号通过多径无线信道传播。 <span id="skip_info" class="notranslate">$j^{th}$</span> 接收天线 <span id="skip_info" class="notranslate">$i^{th}$</span> 发射天线定义为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} r_{j}=\breve{\mathbf{H}}_{ji}s_{i}+n_{j} \tag{16} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 在接收机中，每个接收天线接收到的 TD 信号通过 SFFT 和 OFDM 解调器转换为 DD 域，模拟 Wigner 变换。 <span id="skip_info" class="notranslate">$j^{th}$</span> 接收天线定义为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} y_{j}=\mathbf{H}_{j1}x_{1}+\mathbf{H}_{j2}x_{2}+\cdots+\mathbf{H}_{ji}x_{i}+\cdots+\mathbf{H}_{jN_{R}}x_{N_{R}}+w_{j} \tag{17} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 考虑所有接收天线的 DD 域接收信号如下所示 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \mathbf{y}_{ESM}=\mathbf{H}_{eff}\mathbf{x}_{ESM}+\mathbf{w}_{eff} \tag{18} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$\mathbf{y}_{ESM}=[y_{0},y_{1},\cdots,y_{N_{R}}]$</span>, <span id="skip_info" class="notranslate">$\mathbf{x}_{ESM}=[x_{0},x_{1},\cdots,x_{N_{T}}]$</span> 和 <span id="skip_info" class="notranslate">$w_{eff}$</span> 是有效噪声矢量。同时，我们有 <span id="skip_info" class="notranslate">$\mathbf{y}_{ESM},\mathbf{w}_{eff} \in {\mathbb{C}}^{N_{R}MN \times 1}$</span>, <span id="skip_info" class="notranslate">$\mathbf{x}_{ESM}\in {\mathbb{C}}^{N_{T}MN \times 1}$</span> 和 <span id="skip_info" class="notranslate">$\mathbf{H}_{eff} \in {\mathbb{C}}^{N_{R}MN \times N_{T}MN }$</span>. 有效通道矩阵 <span id="skip_info" class="notranslate">$\mathbf{H}_{eff}$</span> ESM-OTFS 在 DD 域中的性能为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \mathbf{H}_{eff}=\begin{bmatrix}\mathbf{H}_{11}&\mathbf{H}_{12}&\ldots&\mathbf{H}_{1N_{T}}\\\mathbf{H}_{21}&\mathbf{H}_{22}&\ldots&\mathbf{H}_{2N_{T}}\\\vdots&\vdots&\ddots&\vdots\\\mathbf{H}_{N_{R}1}&\mathbf{H}_{N_{R}2}&\cdots&\mathbf{H}_{N_{R}N_{T}}\end{bmatrix} \tag{19} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""></p> </div> </div> <div class="fj-pagetop"><a href="#top">页面顶部</a></div> </div> <div class="gt-block fj-sec" data-gt-block=""> <div> <h4 id="sec_3" class="gt-block headline" data-gt-block=""><span></span>3. ESM-OTFS 检测</h4> <div> <h5 id="sec_3_1" class="gt-block headline" data-gt-block=""><span></span>3.1 MMSE检测器</h5> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>为了降低检测复杂度，提出了一种结合MMSE均衡和最小欧氏距离检测的检测器来检测ESM-OTFS。首先估计发射信号 <span id="skip_info" class="notranslate">$\mathbf{\hat{x}}_{ESM}^{MMSE}$</span> 是使用基于 MMSE 的均衡器获得的。MMSE 均衡如下所示 </p> <div id="math_20" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \mathbf{\hat{x}}_{ESM}^{MMSE} =\left(\mathbf{H}^\mathbf{H}+\frac{I_{N_{T}MN}}{\rho_{snr}} \right)^{-1}\mathbf{H}\mathbf{y}_{ESM} \tag{20} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$I_{N_{T}MN}$</span> 是顺序的单位矩阵 <span id="skip_info" class="notranslate">$N_{T}MN\times N_{T}MN$</span> 和 <span id="skip_info" class="notranslate">$\rho_{snr}$</span> 是 DD 域中的平均 SNR。现在对每行应用最小欧几里德距离检测器 <span id="skip_info" class="notranslate">$\mathbf{\hat{X}}_{ESM}^{MMSE}$</span> 针对 ESM 星座矢量的所有可能组合 <span id="skip_info" class="notranslate">$\mathcal{C}_{ESM}$</span>.这可以表述如下 </p> <div id="math_21" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{align} \Big \{\mathbf{\hat{X}}^{\eta}_{ESM}\Big \}=& \underset{\mathbf{C}_{\mathbf{ESM}} \in \mathcal{C}_{\mathbf{ESM}}}{\arg\min} \left | \mathbf{\hat{X}}_{ESM}^{MMSE}(\eta)- \mathbf{C}_{\mathbf{\mathbf{ESM}}} \right |^{2}, \tag{21} \\ &1\leq \eta \leq MN, \nonumber \end{align}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$\hat{\mathbf{X}}_{ESM}^{MMSE}(\eta)$</span> 是 <span id="skip_info" class="notranslate">$\eta^{th}$</span> 矩阵的行 <span id="skip_info" class="notranslate">$\hat{\mathbf{X}}_{ESM}^{MMSE}$</span>然后将欧氏距离最小的ESM星座向量作为ESM-OTFS帧每个时隙的检测ESM-OTFS发射向量，经过均衡和检测后，解调后的ESM-OTFS帧 <span id="skip_info" class="notranslate">$\mathbf{\hat{X}}_{ESM} \in \mathbb{C}^{MN\times N_{T}}$</span> 可以以矩阵形式表示为 </p> <div id="math_22" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \mathbf{\hat{X}}_{ESM}=\begin{bmatrix}\mathbf{\hat{x}}_{0,0}^{1} & \ldots & \mathbf{\hat{x}}_{0,0}^{i} & \ldots & \mathbf{\hat{x}}_{0,0}^{N_{T}} \\ \mathbf{\hat{x}}_{0,1}^{1} & \ldots & \mathbf{\hat{x}}_{0,1}^{i} & \ldots & \mathbf{\hat{x}}_{0,1}^{N_{T}}\\ \vdots & \ddots & \vdots & \ddots & \vdots\\ \mathbf{\hat{x}}_{0,N-1}^{1} & \ldots & \mathbf{\hat{x}}_{0,N-1}^{i} & \ldots & \mathbf{\hat{x}}_{0,N-1}^{N_{T}}\\\vdots & \ddots & \vdots & \ddots & \vdots\\ \mathbf{\hat{x}}_{k,l}^{1} & \ldots & \mathbf{\hat{x}}_{k,l}^{i} & \ldots & \mathbf{\hat{x}}_{k,l}^{N_{t}}\\\vdots & \ddots & \vdots & \ddots & \vdots\\ \mathbf{\hat{x}}_{M-1,N-1}^{1} & \ldots & \mathbf{\hat{x}}_{M-1,N-1}^{i} & \ldots & \mathbf{\hat{x}}_{M-1,N-1}^{N_{T}}\end{bmatrix} \tag{22} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 每行 <span id="skip_info" class="notranslate">$\mathbf{\hat{X}}_{ESM}$</span> 表示每个 ESM-OTFS 传输向量的估计值 <span id="skip_info" class="notranslate">$MN$</span> ESM-OTFS 帧的时隙。现在对原始传输比特的估计 <span id="skip_info" class="notranslate">$\hat{b}$</span> 可以通过比较每一行来恢复 <span id="skip_info" class="notranslate">$\mathbf{\hat{X}}_{ESM}$</span> 使用查找表如表2所示。使用MMSE检测器检测ESM-OTFS所涉及的步骤总结在算法1中。</p> <div id="graphic_1" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/algo01.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/algo01.jpg" class="fj-fig-graphic-bpadzero"></a></td> </tr> </tbody> </table> </div> </div> <div> <h5 id="sec_3_2" class="gt-block headline" data-gt-block=""><span></span>3.2 基于变分贝叶斯推理的 ESM-OTFS 检测器 </h5> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>由于最大似然检测器的计算复杂度随着发射次数的增加而呈指数增长 <span id="skip_info" class="notranslate">$N_{T}$</span> 并收到 <span id="skip_info" class="notranslate">$N_{R}$</span> 天线，我们提出了一种基于 ESM-OTFS 发射帧稀疏性的新检测算法。在 ESM-OTFS 中，只有一个或两个发射天线同时辐射，其他天线保持静默。这导致形成数据传输矩阵，其中大多数条目为零，使矩阵稀疏。所提出的检测器背后的关键思想是使用变分贝叶斯学习对接收信号进行稀疏信号估计。因此，ESM-OTFS 信号检测问题可以重述为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} y=\mathbf{H}x+w, \tag{23} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$x$</span> 和 <span id="skip_info" class="notranslate">$y$</span> 发送和接收信号的维度 <span id="skip_info" class="notranslate">$N_{T}MN\times 1$</span> 和 <span id="skip_info" class="notranslate">$N_{R}MN\times 1$</span> 在DD域中， <span id="skip_info" class="notranslate">$\mathbf{H}$</span> 是维度为的有效 DD 域信道矩阵 <span id="skip_info" class="notranslate">$N_{R}MN\times N_{T}MN$</span> 和 <span id="skip_info" class="notranslate">$w$</span> 是均值和方差为零的高斯分布白噪声信号 <span id="skip_info" class="notranslate">$\gamma$</span>.</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>假设传输数据信号具有两层分层先验 <span id="skip_info" class="notranslate">$x$</span> 如[19]中提出的那样，这样它就能激发 <span id="skip_info" class="notranslate">$x$</span>。假设 <span id="skip_info" class="notranslate">$x$</span> 服从高斯分布，参数为 <span id="skip_info" class="notranslate">$\alpha=[\alpha_{1},\alpha_{2},\cdots,\alpha_{N_{T}MN}]$</span> 哪里 <span id="skip_info" class="notranslate">$\alpha_{i}$</span> 是方差参数的逆 <span id="skip_info" class="notranslate">$x_{i}$</span> 和 <span id="skip_info" class="notranslate">$x$</span> 给出为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} p(x/\alpha) = \prod_{i=1}^{N_{T}MN} p(x_i/\alpha_i) = \prod_{i=1}^{N_{T}MN} \mathcal{N}(0,\alpha_i^{-1}). \tag{24} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 此外，假设 Gamma 先验分布 <span id="skip_info" class="notranslate">$\alpha$</span> </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} p(\alpha)= \prod_{i=1}^{N_{T}MN} p(\alpha_i/a,b) = \prod_{i=1}^{N_{T}MN} \Gamma^{-1}(a) b^a \alpha_i^{a-1} e^{-b\alpha_i}. \tag{25} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 假设方差 <span id="skip_info" class="notranslate">$\gamma$</span> 白噪声信号 <span id="skip_info" class="notranslate">$w$</span> 是已知的，并且接收端可以访问完整的 DD 域信道状态信息 (CSI)。接收信号的似然分布 <span id="skip_info" class="notranslate">$y$</span> 如下所示 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} p(y/x) = (2\pi)^{-N_{R}MN/2} \gamma^{N_{R}MN/2} e^{\frac{-\gamma \left||y - \mathbf{H} x \right||^2}{2}}. \tag{26} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""></p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>接收信号的后验分布估计 <span id="skip_info" class="notranslate">$y$</span> 非常麻烦。为了解决这个问题，应用变分贝叶斯技术，并计算后验分布 <span id="skip_info" class="notranslate">$p(x/y,\alpha)$</span> 通过变分分布估计 <span id="skip_info" class="notranslate">$q(x,\alpha)$</span>。它可以表示为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} q(x,\alpha)= \prod_{i=1}^{N_{T}MN}q_{x_i}(x_i)\prod_{i=1}^{N_{T}MN}q_{\alpha_i}(\alpha_i). \tag{27} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""></p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>变分贝叶斯技术计算 <span id="skip_info" class="notranslate">$q(x,\alpha)$</span> 通过最小化变分分布之间的 Kullback-Leibler (KL) 距离 <span id="skip_info" class="notranslate">$q(x,\alpha)$</span> 以及真实的后验分布 <span id="skip_info" class="notranslate">$p(x,\alpha/y)$</span>. 之间的 KL 距离 <span id="skip_info" class="notranslate">$q(x,\alpha)$</span> 和 <span id="skip_info" class="notranslate">$p(x,\alpha/y)$</span> 表示为 <span id="skip_info" class="notranslate">$KLD_{VBI}$</span>. </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} KLD_{VBI}= KL\left(p(x,\alpha/y) || q(x,\alpha) \right). \tag{28} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""></p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>最小化 KL 距离相当于最大化证据下限 (ELBO)。为了进一步讨论这一点， <span id="skip_info" class="notranslate">$KLD_{VBI}$</span> 可以表示为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \begin{aligned} KLD_{VBI}&=-\int q(\theta) \ln \frac{p(\theta/y)}{q(\theta)} d\theta \\ &= -\int q(\theta) \ln \frac{p(y,\theta)}{p(y)q(\theta)} d\theta. \end{aligned} \tag{29} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""></p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>这进一步简化为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} KLD_{VBI}= \ln p(y)- \int q(\theta) \ln \frac{p(y,\theta)}{q(\theta)} d\theta, \tag{30} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$\theta=\left\{x,\alpha\right\}$</span> 并可以重新排列为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \ln p(y)=KLD_{VBI}+L(q). \tag{31} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 建立 <span id="skip_info" class="notranslate">$KLD_{VBI}$</span> 是距离， <span id="skip_info" class="notranslate">$KLD_{VBI}\geq 0$</span>. 这意味着 ELBO <span id="skip_info" class="notranslate">$L(q)$</span> 是下限 <span id="skip_info" class="notranslate">$\ln p(y)$</span>。据我们所知， <span id="skip_info" class="notranslate">$\ln y$</span> 是独立的 <span id="skip_info" class="notranslate">$q(\theta)$</span> 和最小化 <span id="skip_info" class="notranslate">$KLD_{VBI}$</span> 类似于最大化下限 <span id="skip_info" class="notranslate">$L(q)$</span>. ELBO 最大化结果如下表达式 </p> <div id="math_32" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \ln (q_i({\theta}_i)) = <\ln p(y, \theta)>_{k\neq i} + c_i, \tag{32} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$\theta\,=\,\left\{x,\alpha\right\}$</span> 和 <span id="skip_info" class="notranslate">$\theta_i$</span> 表示每个标量 <span id="skip_info" class="notranslate">$\theta$</span>。这里 <span id="skip_info" class="notranslate">$<>_{k\neq i}$</span> 表示分布期望的算子 <span id="skip_info" class="notranslate">$q_k$</span> 支持所有 <span id="skip_info" class="notranslate">$k\neq i$</span>. 联合概率分布 <span id="skip_info" class="notranslate">$p(y,\theta)$</span> 可以表示为 </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} p(y,\theta) = p(y/x,\alpha)p(x/\alpha)p(\alpha) \tag{33} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 现在的重点是找到一个迭代解决方案。为此， <span id="skip_info" class="notranslate">$\ln p(y,\theta)$</span> 可以扩展如下 </p> <div id="math_34" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \begin{aligned} \ln p(y,\theta) &= \frac{N_{R}MN}{2}\ln \gamma - \frac{\gamma}{2}\left\|y - \mathbf{H} x\right\|^2 \\ &\quad+ \sum_{i=1}^{N_{T}MN}\left(\frac{1}{2}\ln \alpha_i - \frac{\alpha_i}{2}x_i^2\right) \\ &\quad+ \sum_{i=1}^{N_{T}MN}\left((a-1)\ln \alpha_i+a\ln b - b\alpha_i\right) \\ &\quad+ \text{constants}. \end{aligned} \tag{34} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""></p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>现在利用（32）和（34），我们需要找到更新表达式 <span id="skip_info" class="notranslate">$\ln q_{x_i}(x_i)$</span> 和 <span id="skip_info" class="notranslate">$\ln q_{\alpha_i}(\alpha_i)\,$</span>. </p> <div id="math_35" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \begin{array}{l} \ln q_{x_i}(x_i) = \\ -\frac{\gamma}{2}\Big\{ <\left||y-\mathbf{H}_{\bar{i}}x_{\bar{i}}\right||^2>\,-\,(y-\mathbf{H}_{\bar{i}}<x_{\bar{i}}>)^{H}\mathbf{H}_ix_i\,-\,\\ x_i\mathbf{H}_i^H(y-\mathbf{H}_{\bar{i}}<x_{\bar{i}}>)\,+\,\left||\mathbf{H}_i\right||^2x_i^2 \Big\},-\,\frac{<\alpha_i>}{2}x_i^2 + c_{x_i} \\ = \, -\frac{1}{2\sigma^2_i}\left(x_i\, - \,\mu_i\right)^2 + c_{x_i}', \end{array} \tag{35} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""><span></span> 我们代表 <span id="skip_info" class="notranslate">$\mathbf{H}x$</span> as <span id="skip_info" class="notranslate">$\mathbf{H}x\,=\,\mathbf{H}_ix_i\,+\,\mathbf{H}_{\bar{i}}x_{\bar{i}}$</span> 哪里哪里 <span id="skip_info" class="notranslate">$\mathbf{H}_i$</span> 表示 <span id="skip_info" class="notranslate">$i^{th}$</span> 列 <span id="skip_info" class="notranslate">$\mathbf{H}$</span>,<span id="skip_info" class="notranslate">$\mathbf{H}_{\bar{i}}$</span> 通过去除 <span id="skip_info" class="notranslate">$i^{th}$</span> 列 <span id="skip_info" class="notranslate">$\mathbf{H}$</span>,<span id="skip_info" class="notranslate">$x_i$</span> 是 <span id="skip_info" class="notranslate">$i^{th}$</span> 的元素 <span id="skip_info" class="notranslate">$x$</span> 和 <span id="skip_info" class="notranslate">$x_{\bar{i}}$</span> 是通过去除 <span id="skip_info" class="notranslate">$i^{th}$</span> 的元素 <span id="skip_info" class="notranslate">$x$</span>. <span id="skip_info" class="notranslate">$c_{x_i}$</span> 和 <span id="skip_info" class="notranslate">$c_{x_i}'$</span> 是归一化常数。从 <span id="skip_info" class="notranslate">$(35)$</span>，我们可以理解 <span id="skip_info" class="notranslate">$\ln q_{x_i}(x_i)$</span> 本质上是二次函数，可以表示为高斯分布的随机变量。随后的高斯分布的均值和方差如下 </p> <div id="math_36" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \begin{array}{@{}l@{}} \sigma^2_i \, = \, \frac{1}{\gamma \left||\mathbf{H}\right||^2 \, + \, \alpha_i}, \,\,\, \\ <x_i> = \mu_i \, = \, \sigma^2_i \mathbf{H}^H\left(y\,-\,\mathbf{H}_{\bar{i}}<x_{\bar{i}}>\right)\gamma, \end{array} \tag{36} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$\mu_i$</span> 是点估计 <span id="skip_info" class="notranslate">$i^{th}$</span> 传输信号的元素 <span id="skip_info" class="notranslate">$x$</span>. 类似地 <span id="skip_info" class="notranslate">$\ln q_{\alpha_i}(\alpha_i)\,$</span> 可以表示如下 </p> <div id="math_37" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \begin{array}{@{}l@{}} \ln q_{\alpha_i}(\alpha_i) = (a-1+\frac{1}{2})\ln \alpha_i\,-\,\alpha_i\left(\frac{<x_i^2>}{2}\,+\,b\right)\,+\,c_{\alpha_i}, \\ q_{\alpha_i}(\alpha_i)\, \propto \, \alpha_i^{a+\frac{1}{2}-1}e^{-\alpha_i \left(\frac{<x_i^2>}{2}\,+\,b\right)}, \end{array} \tag{37} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$c_{\alpha_i}$</span> 是归一化常数。从 <span id="skip_info" class="notranslate">$(37)$</span>，我们可以得出一个结论，变分近似 <span id="skip_info" class="notranslate">$q_{\alpha_i}(\alpha_i)$</span> 服从 Gamma 分布。所得 Gamma pdf 的平均值如下 </p> <div id="math_38" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \begin{array}{@{}l@{}} <\alpha_i>\,=\, \frac{a+\frac{1}{2}}{\left(\frac{<x_i^2>}{2}\,+\,b\right)}, \,\,\, \mbox{where}\,\,\, <x_i^2> = \mu_i^2\,+\,\sigma^2_i. \end{array}\!\!\!\!\! \tag{38} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""></p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>现在，发射信号矩阵的均衡版本 <span id="skip_info" class="notranslate">$\mathbf{\hat{X}}_{ESM}^{VBI}$</span> 在 DD 域中，通过收集所有点估计来形成 <span id="skip_info" class="notranslate">$\mu_{i}$</span> 哪里 <span id="skip_info" class="notranslate">$i=1,2\cdots N_{T}MN$</span>再次，最小欧几里得距离检测器应用于每一行 <span id="skip_info" class="notranslate">$\mathbf{\hat{X}}_{ESM}^{VBI}$</span> 利用（21）可得 <span id="skip_info" class="notranslate">$\mathbf{\hat{X}}_{ESM}$</span> 如 (22) 所示。现在每一行 <span id="skip_info" class="notranslate">$\mathbf{\hat{X}}_{ESM}$</span> 使用表 2 所示的 ESM 映射规则进行解码，以检索原始传输比特的估计值。整个 ESM-OTFS 帧的检测以这种方式完成。使用 VBI 检测器检测 ESM-OTFS 所涉及的步骤总结在算法 2 中。</p> <div id="graphic_2" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/algo02.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/algo02.jpg" class="fj-fig-graphic-bpadzero"></a></td> </tr> </tbody> </table> </div> </div> </div> <div class="fj-pagetop"><a href="#top">页面顶部</a></div> </div> <div class="gt-block fj-sec" data-gt-block=""> <div> <h4 id="sec_4" class="gt-block headline" data-gt-block=""><span></span>4. 检测器的计算复杂度</h4> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>接收器的信号检测算法由两个不同的部分组成，这两个部分决定了其整体复杂度。第一部分是用于均衡的算法的计算复杂度，第二部分是解调算法的复杂度。MMSE 检测器利用（20）进行均衡，其计算复杂度为 <span id="skip_info" class="notranslate">$O(M^3N^3N_T^3)$</span> [21]。最小欧几里德距离检测器用于解调目的，其计算量为 <span id="skip_info" class="notranslate">$O(MN\mathbb{C})$</span>，其中 <span id="skip_info" class="notranslate">$\mathbb{C}$</span> 表示 ESM 星座的大小，如表 2 所示。另外还有一个搜索复杂度 <span id="skip_info" class="notranslate">$O(\mathbb{C})$</span> 用于解码位。</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>基于 VBI 的检测器不需要任何矩阵求逆运算来进行均衡操作。它的计算复杂度为 <span id="skip_info" class="notranslate">$O(M^2N^2N_T^2L)$</span> 哪里 <span id="skip_info" class="notranslate">$L$</span> 是算法收敛所需的迭代次数。由于基于 VBI 的检测器也使用基于欧几里德距离的检测器进行解调部分，因此与用于解调的 MMSE 检测器相比，它具有相同的计算复杂度。</p> </div> <div class="fj-pagetop"><a href="#top">页面顶部</a></div> </div> <div class="gt-block fj-sec" data-gt-block=""> <div> <h4 id="sec_5" class="gt-block headline" data-gt-block=""><span></span>5.频谱效率</h4> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>频谱效率 (SE) 主要被描述为给定带宽内的数据传输容量，可以表示为信息速率与占用的总带宽之间的比率。ESM-OTFS 帧的总时间跨度为 <span id="skip_info" class="notranslate">$NT$</span> 一帧占用的总带宽为 <span id="skip_info" class="notranslate">$M \Delta f$</span>。ESM-OTFS帧传输的位数为 <span id="skip_info" class="notranslate">$MNlog_2(\mathbb{C})$</span>。因此，我们可以将 OTFS-ESM 的 SE 表示如下 </p> <div id="math_39" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \begin{split} SE_{ESM-OTFS} & = \frac{MN \times log_2(\mathbb{C})}{NT \times M\Delta f} \\ & = log_2(\mathbb{C}), \end{split} \tag{39} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$T\Delta f=1$</span>OTFS-SM 和 OTFS-QSM [20] 系统的 SE 可以用以下相同的参数表示： </p> <div id="math_40" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \begin{aligned} & SE_{SM-OTFS} =log_{2}(M_{mod})+log_{2}(N_T) \\ & SE_{QSM-OTFS} =log_{2}(M_{mod})+2log_{2}(N_T), \end{aligned} \tag{40} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> 哪里 <span id="skip_info" class="notranslate">$M_{mod}$</span> 是所用调制字母表的大小。例如，考虑以 QPSK 作为主要调制的 ESM-OTFS 系统，并且 <span id="skip_info" class="notranslate">$N_T=2$</span>。与该系统配置相对应的ESM星座如表2所示，从中我们可以看出 <span id="skip_info" class="notranslate">$16$</span> 不同的星座向量。因此，ESM-OTFS 的频谱效率为 4 位/秒/赫兹，这也称为每信道比特使用率 (bpcu)。在相同设置下，SM-OTFS 和 QSM-OTFS 的 SE 分别为 3 和 4 位/秒/赫兹。</p> </div> <div class="fj-pagetop"><a href="#top">页面顶部</a></div> </div> <div class="gt-block fj-sec" data-gt-block=""> <div> <h4 id="sec_6" class="gt-block headline" data-gt-block=""><span></span>6. 模拟结果与讨论</h4> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>在本节中，我们讨论了在不同系统配置下 ESM-OTFS 与 SM-OTFS 和 QSM-OTFS 的误码率 (BER) 性能的仿真结果。假设接收器具有完美的信道状态信息 (CSI)，并且所有信道都具有瑞利衰落。主要模拟参数如表 3 所示。</p> <div id="table_3" class="fj-table-g"> <table> <tbody> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>表3</b>  模拟参数。</p></td> </tr> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/t03.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/t03.jpg" class="fj-table-graphic"></a></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>图 4 给出了 2 bpcu 的 ESM-OTFS、QSM-OTFS、SM-OTFS 和 SIMO-OTFS 的 BER 性能比较。每个方案中使用的星座图如图例所示，对于 ESM-OTFS，则标出了主星座图。MIMO 设置 <span id="skip_info" class="notranslate">$2\times 4$</span> 用于本次仿真。从图 2 可以看出，ESM-OTFS 在 BER 性能方面优于其他方案。在 BER 值为 <span id="skip_info" class="notranslate">$10^{-4}$</span>其中，ESM-OTFS 比 QSM-OTFS 高 2.1 dB，比 SM-OTFS 高 3 dB，比 SIMO-OTFS 高 5.3 dB。</p> <div id="fig_2" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f02.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f02.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>图。 2</b>  基于 MMSE 检测器的 ESM-OTFS、QSM-OTFS、SM-OTFS 和 SIMO-OTFS 系统的 BER 性能 <span id="skip_info" class="notranslate">$M=4$</span>, <span id="skip_info" class="notranslate">$N=4$</span> 为 4 位/秒/赫兹。</p></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>图 6 给出了 3 bpcu 的 ESM-OTFS、QSM-OTFS、SM-OTFS 和 SIMO-OTFS 的 BER 性能比较。 <span id="skip_info" class="notranslate">$4\times 4$</span> 用于本次模拟。在 BER 值为 <span id="skip_info" class="notranslate">$10^{-3}$</span>，ESM-OTFS 比 QSM-OTFS 好 2 <b>dB</b> SM-OTFS 升级至 3.8 <b>dB</b>.</p> <div id="fig_3" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f03.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f03.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>图。 3</b>  基于 MMSE 检测器的 ESM-OTFS、QSM-OTFS、SM-OTFS 和 SIMO-OTFS 系统的 BER 性能 <span id="skip_info" class="notranslate">$M=4$</span>, <span id="skip_info" class="notranslate">$N=4$</span> 为 6 位/秒/赫兹</p></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>图 4 描述了使用各种检测器时 8 bpcu 的 ESM-OTFS 的 BER 性能。MIMO 设置 <span id="skip_info" class="notranslate">$4\times 4$</span> 用于此模拟，并使用 16-QAM 作为主要调制。可以看出，基于 VBI 的检测器优于线性检测器。ESM-OTFS 检测器在值为 <span id="skip_info" class="notranslate">$10^{-2}$</span> 与使用 MMSE 检测器进行检测相比。</p> <div id="fig_4" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f04.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f04.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>图。 4</b>  使用 ZF、MMSE 和 VBI 检测器的 ESM-OTFS 的 BER 性能 <span id="skip_info" class="notranslate">$M=4$</span>, <span id="skip_info" class="notranslate">$N=4$</span> 为 8 位/秒/赫兹。</p></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>图 10 显示了使用各种检测器的 5 bpcu 的 ESM-OTFS 的 BER 性能。 <span id="skip_info" class="notranslate">$8\times 8$</span> 用于此仿真，并使用 16-QAM 作为主要调制。基于 VBI 的检测器比基于 MMSE 的检测器具有 7.8 dB 的增益。从图 4 和图 5 可以看出，随着传输数据矩阵变得更加稀疏，基于 VBI 的检测器的性能得到改善。</p> <div id="fig_5" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f05.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f05.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>图。 5</b>  使用 ZF、MMSE 和 VBI 检测器的 ESM-OTFS 的 BER 性能 <span id="skip_info" class="notranslate">$M=4$</span>, <span id="skip_info" class="notranslate">$N=4$</span> 为 10 位/秒/赫兹</p></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>ESM-OTFS 对多普勒频移具有很强的鲁棒性，多普勒频移在高移动环境中很普遍。图 6 和图 7 展示了 ESM-OTFS 在不同速度下的性能。图 6 和图 7 分别展示了 4 bpcu 和 6 bpcu 的 ESM-OTFS 的 BER 性能。从图中可以看出，从 30 公里/小时的正常速度到 500 公里/小时的极高速度，ESM-OTFS 的 BER 性能几乎保持不变。在更高的速度下，性能仅略有下降，我们可以估计 ESM-OTFS 对速度变化导致的多普勒频移具有很强的免疫力。</p> <div id="fig_6" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f06.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f06.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>图。 6</b>  不同速度下 ESM-OTFS 的 BER 性能 <span id="skip_info" class="notranslate">$M=16$</span>, <span id="skip_info" class="notranslate">$N=16$</span> 为 4 位/秒/赫兹。</p></td> </tr> </tbody> </table> </div> <div id="fig_7" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f07.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f07.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>图。 7</b>  不同速度下 ESM-OTFS 的 BER 性能 <span id="skip_info" class="notranslate">$M=16$</span>, <span id="skip_info" class="notranslate">$N=16$</span> 为 6 位/秒/赫兹。</p></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>第四部分讨论了所提出的 ESM-OTFS 探测器的计算复杂度。为了进一步说明，考虑一个 ESM-OTFS 系统 <span id="skip_info" class="notranslate">$M=4$</span>, <span id="skip_info" class="notranslate">$N=4$</span> 和 <span id="skip_info" class="notranslate">$N_T=2$</span>为了比较不同bpcu下的接收机复杂度，QPSK、16-QAM、64-QAM、256-QAM被用作主星座，bpcu分别为4、6、8和10。由于均衡算法的计算复杂度取决于 <span id="skip_info" class="notranslate">$M$</span>, <span id="skip_info" class="notranslate">$N$</span> 和 <span id="skip_info" class="notranslate">$N_T$</span>，bpcu 的四种情况下的计算复杂度保持不变。由于解调算法的计算复杂度为 <span id="skip_info" class="notranslate">$O(MN\mathbb{C})$</span>，乘法的计算量随着 <span id="skip_info" class="notranslate">$\mathbb{C}$</span>。我们知道，ESM-OTFS系统的bpcu是 <span id="skip_info" class="notranslate">$log_2(\mathbb{C})$</span>，并且检测器的计算复杂度随着bpcu的增加而增加。这在图8中突出显示。</p> <div id="fig_8" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f08.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/f08.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>图。 8</b>  ESM-OTFS 系统中检测器复杂性和 bpcu 之间的权衡。</p></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>随着调制阶数的增加，接收器必须执行更复杂的信号处理来区分间距很近的星座点，从而增加了计算负担。计算复杂度与 bpcu 的关系图（图 8）有效地捕捉了这种关系。随着 bpcu 的增加（从 QPSK 变为 256-QAM），接收器的计算复杂度也会增加，因为需要更精细的信号处理技术来准确解码高阶调制信号。这种权衡对于设计和优化特定应用场景的通信系统至关重要，需要在高数据速率（以及更高的 bpcu）需求与接收器复杂性、功耗和实时处理能力的限制之间取得平衡。</p> </div> <div class="fj-pagetop"><a href="#top">页面顶部</a></div> </div> <div class="gt-block fj-sec" data-gt-block=""> <div> <h4 id="sec_7" class="gt-block headline" data-gt-block=""><span></span>7.结论</h4> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>本文提出了一种适用于高多普勒频移无线通信环境的 ESM-OTFS 方案，提高了系统的可靠性和频谱效率。讨论了 ESM-OTFS 的系统模型和信号处理。提出了一种基于变分贝叶斯推理的新型检测器来检测 ESM-OTFS。通过仿真证明，与 SM-OTFS 和 QSM-OTFS 相比，ESM-OTFS 具有更好的 BER 性能。还验证了基于 VBI 的 ESM-OTFS 检测器优于线性检测器。</p> </div> <div class="fj-pagetop"><a href="#top">页面顶部</a></div> </div> <div id="sec-references" class="gt-block fj-sec" data-gt-block=""> <h4 id="references" class="gt-block headline" data-gt-block=""><span></span>参考文献</h4> <div id="skip_info" class="notranslate"> 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Hao, “Generalized spatial modulation based orthogonal time frequency space system,” 2021 IEEE 94th Vehicular Technology Conference (VTC2021-Fall), Norman, OK, USA, pp.1-5, 2021, doi: 10.1109/VTC2021-Fall52928.2021.9625452. <br><a target="_blank" href="https://doi.org/10.1109/vtc2021-fall52928.2021.9625452">CrossRef</a></p> </div> </div> <div class="fj-pagetop"><a href="#top">页面顶部</a></div> </div> <div id="sec-authors" class="fj-sec-authors"> <h4 id="authors" class="gt-block headline" data-gt-block=""><span></span>作者</h4> <div id="skip_info" class="notranslate"> <div class="fj-author"> <b><a href="https://zh-cn.global.ieice.org/en_transactions/Author/a_name=Anoop%20A"><span>Anoop A</span></a></b><br>  <span style="font-Size:15px;"><b>Indian Institute of Information Technology</b></span><br> <p class="fj-p-no-indent" data-gt-block=""><span></span>received BTech degree in electronics and communication engineering from National Institute of Technology, Calicut, India in 2010. He is currently an MS-PhD student in the Department of ECE at the Indian Institute of Information Technology (IIIT) Kottayam, Kerala, India. His research interests include OTFS modulation, OTFS-based index and spatial modulation schemes.</p> <div id="graphic_3" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/a1.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/a1.jpg" class="fj-bio-graphic"></a></td> </tr> </tbody> </table> </div> </div> <div class="fj-author"> <p class="fj-p-no-indent" data-gt-block=""><span></span><b>Christo K. Thomas</b></p> <p class="fj-p-no-indent" data-gt-block=""><span></span>received his BS in Electronics and Communication Engineering from National Institute of Technology, Calicut, India in year 2010, his MS in Telecommunication Engineering from Indian Institute of Science, Bangalore, India in year 2012, and his PhD from EURECOM, France in year 2020. He is currently a postdoctoral fellow at the Electrical and Computer Engineering Department at Virginia Tech. His research interests include semantic communications, statistical signal processing, and machine learning for wireless communications. From 2012 to 2014, he was a staff design engineer on 4G LTE with Broadcom communications, Bangalore, and from 2014 to 2017, he was a design engineer with Intel corporation, Bangalore. During November 2020 till June 2022, he was a staff engineer on 5G modems with wireless research and development division of Qualcomm Inc., Espoo, Finland. He was a recipient of the best student paper award at IEEE SPAWC 2018, Kalamata, Greece, and also received third prize for his team titled “Learned Chester” ML5G-PHY channel estimation challenge, as part of the ITU AI/ML in 5G challenge, conducted at NCSU, US, 2020.</p> <div id="graphic_4" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/a2.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/a2.jpg" class="fj-bio-graphic"></a></td> </tr> </tbody> </table> </div> </div> <div class="fj-author"> <b><a href="https://zh-cn.global.ieice.org/en_transactions/Author/a_name=Kala%20S"><span>Kala S</span></a></b><br>  <span style="font-Size:15px;"><b>Indian Institute of Information Technology</b></span><br> <p class="fj-p-no-indent" data-gt-block=""><span></span>(Senior Member, IEEE) received BTech degree in electronics and communication engineering from MG University, India in 2006 and MS (Engg) from CeNSE, Indian Institute of Science Bangalore (IISc), India in 2013. She received her PhD degree in Electronics Engineering from Cochin University of Science and Technology, India in 2020. She is currently an Assistant Professor in the Department of ECE at the Indian Institute of Information Technology (IIIT) Kottayam, Kerala, India. Her research interests include FPGA based system design, Wireless Communications, hardware acceleration of deep learning algorithms and DSP algorithms, neuromorphic architectures and hardware security.</p> <div id="graphic_5" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/a3.jpg"><img alt="" src="https://zh-cn.global.ieice.org/full_text/transcom/E107.B/11/E107.B_785/Graphics/a3.jpg" class="fj-bio-graphic"></a></td> </tr> </tbody> </table> </div> </div> </div> <div class="fj-pagetop"><a href="#top">页面顶部</a></div> </div> </div>   </div> <div style="border-bottom: solid 1px #ccc;"></div> <h4 id="Keyword">关键字</h4> <div> <p class="gt-block"> <a href="https://zh-cn.global.ieice.org/en_transactions/Keyword/keyword=enhanced%20spatial%20modulation%20%28ESM%29"><span class="TEXT-COL">增强空间调制（ESM）</span></a>,  <a href="https://zh-cn.global.ieice.org/en_transactions/Keyword/keyword=orthogonal%20time%20frequency%20space%20%28OTFS%29"><span class="TEXT-COL">正交时间频率空间（OTFS）</span></a>,  <a href="https://zh-cn.global.ieice.org/en_transactions/Keyword/keyword=variational%20Bayesian%20inference%20%28VBI%29"><span class="TEXT-COL">变分贝叶斯推理 (VBI)</span></a>,  <a href="https://zh-cn.global.ieice.org/en_transactions/Keyword/keyword=delay-Doppler%20%28DD%29"><span class="TEXT-COL">延迟多普勒（DD）</span></a>,  <a href="https://zh-cn.global.ieice.org/en_transactions/Keyword/keyword=bit%20error%20rate%20%28BER%29"><span class="TEXT-COL">误码率 (BER)</span></a> </p></div>  </section>  </div> <div class="right_box">   <section class="latest_issue"> <h4 id="skip_info" class="notranslate">Latest Issue</h4> <ul id="skip_info" class="notranslate"> <li class="a"><a href="https://zh-cn.global.ieice.org/en_transactions/fundamentals">IEICE Trans. Fundamentals</a></li> <li class="b"><a href="https://zh-cn.global.ieice.org/en_transactions/communications">IEICE Trans. Communications</a></li> <li class="c"><a href="https://zh-cn.global.ieice.org/en_transactions/electronics">IEICE Trans. Electronics</a></li> <li class="d"><a href="https://zh-cn.global.ieice.org/en_transactions/information">IEICE Trans. Inf. & Syst.</a></li> <li class="elex"><a href="https://zh-cn.global.ieice.org/en_publications/elex">IEICE Electronics Express</a></li> </ul> </section> </div> <div class="index_box"> <h4>内容</h4> <ul> <li><a href="#Summary">总结</a></li> <li> <ul> <li><a href="#sec_1">1. 引言 </a></li> <li><a href="#sec_2">2. 系统模型</a></li> <li><a href="#sec_3">3. ESM-OTFS 检测</a></li> <li><a href="#sec_4">4. 检测器的计算复杂度</a></li> <li><a href="#sec_5">5.频谱效率</a></li> <li><a href="#sec_6">6. 模拟结果与讨论</a></li> <li><a href="#sec_7">7.结论</a></li> </ul> </li> <li><a href="#references">参考文献</a></li> <li><a href="#authors">作者</a></li> <li><a href="#Keyword">关键字</a></li> </ul> </div> </div>  <div id="modal_copyright" class="modal js-modal"> <div class="modal-wrap"> <div class="modal__bg"></div> <div class="modal__content"> <div class="notranslate modal__inner" id="skip_info"> <h4>Copyrights notice of machine-translated contents</h4> <p>The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See <a href="https://www.ieice.org/eng/copyright/files/copyright.pdf" target="_blank">IEICE Provisions on Copyright</a> for details.</p> <p class="js-modal-close"><i class="fas fa-times"></i></p> </div> </div> </div> </div>   <form method="POST" action="/sns_mail" id="mailform" class="mailform" novalidate=""> <div id="modal_mail" class="modal js-modal"> <div class="modal-wrap"> <div class="modal__bg"></div> <div class="modal__content mail"> <div class="modal__inner"> <h4>电邮文件</h4> <p> </p><div class="row"> <div class="input-box"> <input type="text" name="yourname" id="yourname" value="" size="40" placeholder="收件人" class="form-text"> <div id="yourname" style="color: red;"></div> </div> </div> <p></p> <p> </p><div class="row"> <div class="input-box"> <input type="text" name="email" id="email" value="" size="40" placeholder="收件人电子邮件" class="form-text"> <div id="email" style="color: red;"></div> </div> </div> <p></p> <p> </p><div class="row"> <div class="input-box"> <textarea name="message" id="message" cols="40" rows="10" placeholder="留言信息" class="form-text">我很高兴与大家分享，我的最新研究论文《基于增强空间调制的正交时频空间系统》刚刚发表在 IEICE TRANSACTIONS 关于通信。这项工作探索了新的见解和实际意义，我相信您会发现它们很有价值。该论文有多种语言版本，因此您可以用自己喜欢的语言轻松阅读。如果您能与您所在国家的同事分享这篇文章，我将不胜感激，因为我希望它能激发进一步的讨论和合作！请在此处阅读：https://zh-cn。global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3206/_f </textarea> <div id="message" style="color: red;"></div> </div> </div> <p></p> <button type="submit" id="sendbutton">提交</button> <p class="js-modal-close"><i class="fas fa-times"></i></p> </div> </div> </div> </div> <input type="hidden" name="pid" value="e107-b_11_785" id="hidden"> <input type="hidden" name="request_uri" value="/en_transactions/communications/10.23919/transcom.2023EBP3206/_f" id="set_request_uri"><input type="hidden" name="site_url" value="https://zh-cn.global.ieice.org/" id="set_site_url"> </form>   <div id="modal_cite" class="modal js-modal"> <div class="modal-wrap"> <div class="modal__bg"></div> <div class="modal__content"> <div class="modal__inner"> <h4 id="skip_info" class="notranslate">Cite this</h4> <nav class="nav-tab"> <ul> <li class="notranslate tab is-active" id="skip_info">Plain Text</li> <li class="notranslate tab" id="skip_info">BibTeX</li> <li class="notranslate tab" id="skip_info">RIS</li> <li class="notranslate tab" id="skip_info">Refworks</li> </ul> </nav> <div class="copy_box"> <div class="box is-show"> <p class="gt-block btn" id="js-copy"><i class="fas fa-copy"></i>复制</p> <p class="notranslate copy-text" id="skip_info">Anoop A, Christo K. THOMAS, Kala S, "Enhanced Spatial Modulation Based Orthogonal Time Frequency Space System" in IEICE TRANSACTIONS on Communications, vol. E107-B, no. 11, pp. 785-796, November 2024, doi: <span class="TEXT-COL">10.23919/transcom.2023EBP3206</span>.<br> Abstract: <span class="TEXT-COL">In this paper, a novel Enhanced Spatial Modulation-based Orthogonal Time Frequency Space (ESM-OTFS) is proposed to maximize the benefits of enhanced spatial modulation (ESM) and orthogonal time frequency space (OTFS) transmission. The primary objective of this novel modulation is to enhance transmission reliability, meeting the demanding requirements of high transmission rates and rapid data transfer in future wireless communication systems. The paper initially outlines the system model and specific signal processing techniques employed in ESM-OTFS. Furthermore, a novel detector based on sparse signal estimation is presented specifically for ESM-OTFS. The sparse signal estimation is performed using a fully factorized posterior approximation using Variational Bayesian Inference that leads to a low complexity solution without any matrix inversions. Simulation results indicate that ESM-OTFS surpasses traditional spatial modulation-based OTFS, and the newly introduced detection algorithm outperforms other linear detection methods.</span><br> URL: https://global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3206/_f</p> </div> <div class="box"> <p class="gt-block btn" id="js-copy-BibTeX"><i class="fas fa-copy"></i>复制</p> <p class="notranslate copy-BibTeX" id="skip_info">@ARTICLE{e107-b_11_785,<br> author={Anoop A, Christo K. THOMAS, Kala S, },<br> journal={IEICE TRANSACTIONS on Communications}, <br> title={Enhanced Spatial Modulation Based Orthogonal Time Frequency Space System}, <br> year={2024},<br> volume={E107-B},<br> number={11},<br> pages={785-796},<br> abstract={<span class="TEXT-COL">In this paper, a novel Enhanced Spatial Modulation-based Orthogonal Time Frequency Space (ESM-OTFS) is proposed to maximize the benefits of enhanced spatial modulation (ESM) and orthogonal time frequency space (OTFS) transmission. The primary objective of this novel modulation is to enhance transmission reliability, meeting the demanding requirements of high transmission rates and rapid data transfer in future wireless communication systems. The paper initially outlines the system model and specific signal processing techniques employed in ESM-OTFS. Furthermore, a novel detector based on sparse signal estimation is presented specifically for ESM-OTFS. The sparse signal estimation is performed using a fully factorized posterior approximation using Variational Bayesian Inference that leads to a low complexity solution without any matrix inversions. Simulation results indicate that ESM-OTFS surpasses traditional spatial modulation-based OTFS, and the newly introduced detection algorithm outperforms other linear detection methods.</span>},<br> keywords={},<br> doi={<span class="TEXT-COL">10.23919/transcom.2023EBP3206</span>},<br> ISSN={<span class="TEXT-COL">1745-1345</span>},<br> month={November},}</p> </div> <div class="box"> <p class="gt-block btn" id="js-copy-RIS"><i class="fas fa-copy"></i>复制</p> <p class="notranslate copy-RIS" id="skip_info">TY - JOUR<br> TI - Enhanced Spatial Modulation Based Orthogonal Time Frequency Space System<br> T2 - IEICE TRANSACTIONS on Communications<br> SP - 785<br> EP - 796<br> AU - Anoop A<br> AU - Christo K. THOMAS<br> AU - Kala S<br> PY - 2024<br> DO - <span class="TEXT-COL">10.23919/transcom.2023EBP3206</span><br> JO - IEICE TRANSACTIONS on Communications<br> SN - <span class="TEXT-COL">1745-1345</span><br> VL - E107-B<br> IS - 11<br> JA - IEICE TRANSACTIONS on Communications<br> Y1 - November 2024<br> AB - <span class="TEXT-COL">In this paper, a novel Enhanced Spatial Modulation-based Orthogonal Time Frequency Space (ESM-OTFS) is proposed to maximize the benefits of enhanced spatial modulation (ESM) and orthogonal time frequency space (OTFS) transmission. The primary objective of this novel modulation is to enhance transmission reliability, meeting the demanding requirements of high transmission rates and rapid data transfer in future wireless communication systems. The paper initially outlines the system model and specific signal processing techniques employed in ESM-OTFS. Furthermore, a novel detector based on sparse signal estimation is presented specifically for ESM-OTFS. The sparse signal estimation is performed using a fully factorized posterior approximation using Variational Bayesian Inference that leads to a low complexity solution without any matrix inversions. Simulation results indicate that ESM-OTFS surpasses traditional spatial modulation-based OTFS, and the newly introduced detection algorithm outperforms other linear detection methods.</span><br> ER - </p> </div> <div class="box"> <p id="skip_info" class="notranslate"></p> </div> </div> <p class="js-modal-close"><i class="fas fa-times"></i></p> </div> </div> </div>  </div></section>   <section class="flyer_box"> <div class="inner"> <h3>单页<span>IEICE 已准备了多语种服务宣传单。请使用您本国语言的宣传单。</span></h3> <ul> <li><a href="/assets/pdf/English.pdf" target="_blank"> <figure><img src="https://global.ieice.org/assets/img/lang_english.png" alt="英语"></figure> <figcaption>英语</figcaption> </a></li> <li><a href="/assets/pdf/zh-cn.pdf" target="_blank"> <figure><img src="https://global.ieice.org/assets/img/lang_simplified_chinese.png" alt="简体中文"></figure> <figcaption>简体<br>中文</figcaption> </a></li> <li><a href="/assets/pdf/zh-tw.pdf" target="_blank"> <figure><img 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