OFDM同步算法之Minn算法

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OFDM经典同步算法之一Minn算法,里面附带Minn算法的经典文献,及MATLAB仿真验证代码
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内容介绍
<html xmlns="http://www.w3.org/1999/xhtml"><head><meta charset="utf-8"><meta name="generator" content="pdf2htmlEX"><meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/css/base.min.css"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/11847768/raw.css"><script src="https://csdnimg.cn/release/download_crawler_static/js/compatibility.min.js"></script><script src="https://csdnimg.cn/release/download_crawler_static/js/pdf2htmlEX.min.js"></script><script>try{pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({});}catch(e){}</script><title></title></head><body><div id="sidebar" style="display: none"><div id="outline"></div></div><div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://csdnimg.cn/release/download_crawler_static/11847768/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">242<span class="_ _0"> </span>IEEE<span class="_ _1"> </span>COMMUNCA<span class="_ _2"></span>TIONS<span class="_"> </span>LETTERS,<span class="_ _1"> </span>VOL.<span class="_"> </span>4,<span class="_ _1"> </span>NO.<span class="_ _1"> </span>7,<span class="_ _1"> </span>JUL<span class="_ _2"></span>Y<span class="_ _1"> </span>2000</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls0 ws0">On<span class="_"> </span>T<span class="_ _2"></span>iming<span class="_"> </span>Of<span class="_ _3"></span>fset<span class="_"> </span>Estimation<span class="_"> </span>for<span class="_ _4"> </span>OFDM<span class="_"> </span>Systems</div><div class="t m0 x3 h4 y3 ff1 fs2 fc0 sc0 ls0 ws0">H.<span class="_ _5"> </span>Minn,<span class="_ _5"> </span>M.<span class="_ _5"> </span>Zeng,<span class="_ _5"> </span>and<span class="_"> </span>V<span class="_ _6"></span>.<span class="_ _5"> </span>K.<span class="_ _5"> </span>Bharga<span class="_ _3"></span>v<span class="_ _3"></span>a<span class="ff2">,<span class="_ _5"> </span>F<span class="_ _2"></span>ellow<span class="_ _2"></span>,<span class="_ _5"> </span>IEEE</span></div><div class="t m0 x4 h5 y4 ff3 fs3 fc0 sc0 ls0 ws0">Abstract&#8212;<span class="ff4">T<span class="_ _2"></span>wo<span class="_"> </span>timing<span class="_"> </span>offset<span class="_"> </span>estimation<span class="_ _1"> </span>methods<span class="_ _1"> </span>f<span class="_ _3"></span>or<span class="_"> </span>orthogonal</span></div><div class="t m0 x1 h5 y5 ff4 fs3 fc0 sc0 ls0 ws0">frequency<span class="_ _1"> </span>division<span class="_ _1"> </span>multiplexing<span class="_"> </span>(OFDM)<span class="_ _1"> </span>systems<span class="_ _1"> </span>as<span class="_ _1"> </span>modif<span class="_ _3"></span>ications</div><div class="t m0 x1 h5 y6 ff4 fs3 fc0 sc0 ls0 ws0">to<span class="_ _1"> </span>Schmidl<span class="_ _1"> </span>and<span class="_ _1"> </span>Cox&#8217;s<span class="_ _7"> </span>method<span class="_ _7"> </span>[6]<span class="_"> </span>ar<span class="_ _3"></span>e<span class="_"> </span>pr<span class="_ _3"></span>esented.<span class="_ _1"> </span>The<span class="_ _7"> </span>performances</div><div class="t m0 x1 h5 y7 ff4 fs3 fc0 sc0 ls0 ws0">of<span class="_ _8"> </span>the<span class="_ _8"> </span>timing<span class="_ _8"> </span>offset<span class="_ _8"> </span>estimators<span class="_ _8"> </span>in<span class="_ _8"> </span>additive<span class="_ _8"> </span>white<span class="_ _8"> </span>Gaussian<span class="_ _8"> </span>noise</div><div class="t m0 x1 h5 y8 ff4 fs3 fc0 sc0 ls0 ws0">channel<span class="_ _9"> </span>and<span class="_ _9"> </span>intersymbol<span class="_ _9"> </span>interference<span class="_ _9"> </span>channel<span class="_ _9"> </span>ar<span class="_ _3"></span>e<span class="_ _9"> </span>compared</div><div class="t m0 x1 h5 y9 ff4 fs3 fc0 sc0 ls0 ws0">in<span class="_ _a"> </span>terms<span class="_ _a"> </span>of<span class="_ _a"> </span>estimator<span class="_ _a"> </span>variance<span class="_ _a"> </span>obtained<span class="_ _b"> </span>by<span class="_ _b"> </span>simulation.<span class="_ _a"> </span>Both</div><div class="t m0 x1 h5 ya ff4 fs3 fc0 sc0 ls0 ws0">proposed<span class="_ _8"> </span>methods<span class="_ _8"> </span>ha<span class="_ _3"></span>ve<span class="_ _8"> </span>significantly<span class="_ _8"> </span>smaller<span class="_ _8"> </span>estimator<span class="_ _8"> </span>variance</div><div class="t m0 x1 h5 yb ff4 fs3 fc0 sc0 ls0 ws0">in<span class="_ _c"> </span>both<span class="_ _c"> </span>channel<span class="_ _c"> </span>conditions.</div><div class="t m0 x5 h5 yc ff3 fs3 fc0 sc0 ls0 ws0">Index<span class="_"> </span>T<span class="_ _2"></span>erms&#8212;<span class="ff4">OFDM,<span class="_"> </span>sliding<span class="_ _c"> </span>window,<span class="_"> </span>timing<span class="_"> </span>offset<span class="_"> </span>estimation,</span></div><div class="t m0 x1 h5 yd ff4 fs3 fc0 sc0 ls0 ws0">timing<span class="_"> </span>synchronization,<span class="_ _c"> </span>training<span class="_"> </span>symbol.</div><div class="t m0 x6 h6 ye ff1 fs4 fc0 sc0 ls0 ws0">I.<span class="_ _b"> </span>I<span class="fs5">NTRODUCTION</span></div><div class="t m0 x1 h7 yf ff4 fs6 fc0 sc0 ls0 ws0">O</div><div class="t m0 x7 h6 y10 ff1 fs4 fc0 sc0 ls0 ws0">FDM<span class="_ _d"> </span>SYSTEMS<span class="_ _d"> </span>are<span class="_ _d"> </span>much<span class="_ _d"> </span>more<span class="_ _d"> </span>sensitiv<span class="_ _3"></span>e<span class="_ _d"> </span>to<span class="_ _d"> </span>synchro-</div><div class="t m0 x7 h6 y11 ff1 fs4 fc0 sc0 ls0 ws0">nization<span class="_ _7"> </span>errors<span class="_ _7"> </span>than<span class="_ _1"> </span>single<span class="_ _7"> </span>carrier<span class="_ _1"> </span>systems<span class="_ _7"> </span>[1],<span class="_ _1"> </span>[2].<span class="_ _7"> </span>Sev<span class="_ _3"></span>eral</div><div class="t m0 x1 h6 y12 ff1 fs4 fc0 sc0 ls0 ws0">approaches<span class="_"> </span>hav<span class="_ _3"></span>e<span class="_"> </span>been<span class="_"> </span>proposed<span class="_"> </span>to<span class="_"> </span>estimate<span class="_"> </span>time<span class="_"> </span>and<span class="_"> </span>frequency</div><div class="t m0 x1 h6 y13 ff1 fs4 fc0 sc0 ls0 ws0">offset<span class="_ _5"> </span>either<span class="_ _8"> </span>jointly<span class="_ _8"> </span>or<span class="_ _8"> </span>individually<span class="_ _2"></span>.<span class="_ _8"> </span>In<span class="_ _8"> </span>[3]<span class="_ _8"> </span>and<span class="_ _8"> </span>[4],<span class="_ _5"> </span>the<span class="_ _8"> </span>redun-</div><div class="t m0 x1 h6 y14 ff1 fs4 fc0 sc0 ls0 ws0">dancy<span class="_"> </span>of<span class="_"> </span>the<span class="_"> </span>signal<span class="_"> </span>due<span class="_"> </span>to<span class="_"> </span>cyclic<span class="_"> </span>prefix<span class="_"> </span>is<span class="_"> </span>used.<span class="_"> </span>Since<span class="_"> </span>guard<span class="_"> </span>in-</div><div class="t m0 x1 h6 y15 ff1 fs4 fc0 sc0 ls0 ws0">terval<span class="_ _7"> </span>is<span class="_ _1"> </span>usually<span class="_ _1"> </span>affected<span class="_ _7"> </span>by<span class="_ _1"> </span>ISI,<span class="_ _1"> </span>the<span class="_ _1"> </span>result<span class="_ _1"> </span>of<span class="_ _1"> </span>estimation<span class="_ _1"> </span>depends</div><div class="t m0 x1 h6 y16 ff1 fs4 fc0 sc0 ls0 ws0">on<span class="_ _8"> </span><span class="ff2">&#225;<span class="_ _8"> </span>priori<span class="_ _5"> </span></span>assumption<span class="_ _8"> </span>about<span class="_ _8"> </span>the<span class="_ _8"> </span>channel.<span class="_ _8"> </span>The<span class="_ _8"> </span>method<span class="_ _8"> </span>in<span class="_ _5"> </span>[5]</div><div class="t m0 x1 h6 y17 ff1 fs4 fc0 sc0 ls0 ws0">uses<span class="_"> </span>a<span class="_"> </span>longer<span class="_"> </span>guard<span class="_"> </span>interv<span class="_ _3"></span>al<span class="_"> </span>where<span class="_"> </span>ISI<span class="_"> </span>free<span class="_"> </span>part<span class="_"> </span>of<span class="_"> </span>the<span class="_"> </span>guard<span class="_ _1"> </span>in-</div><div class="t m0 x1 h6 y18 ff1 fs4 fc0 sc0 ls0 ws0">terval<span class="_ _1"> </span>is<span class="_"> </span>used<span class="_"> </span>for<span class="_"> </span>timing<span class="_"> </span>offset<span class="_ _1"> </span>estimation,<span class="_"> </span>and<span class="_"> </span>fails<span class="_"> </span>under<span class="_"> </span>some</div><div class="t m0 x1 h6 y19 ff1 fs4 fc0 sc0 ls0 ws0">channel<span class="_ _5"> </span>conditions.<span class="_ _c"> </span>T<span class="_ _2"></span>o<span class="_ _5"> </span>av<span class="_ _3"></span>oid<span class="_ _5"> </span>these<span class="_ _c"> </span>problems<span class="_ _5"> </span>in<span class="_ _5"> </span>timing<span class="_ _c"> </span>estima-</div><div class="t m0 x1 h6 y1a ff1 fs4 fc0 sc0 ls0 ws0">tion,<span class="_ _1"> </span>Schmidl<span class="_"> </span>and<span class="_ _1"> </span>Cox<span class="_"> </span>[6]<span class="_ _1"> </span>use<span class="_"> </span>a<span class="_ _1"> </span>training<span class="_"> </span>symbol<span class="_ _1"> </span>containing<span class="_"> </span>two</div><div class="t m0 x1 h6 y1b ff1 fs4 fc0 sc0 ls0 ws0">identical<span class="_ _c"> </span>halves.<span class="_ _c"> </span>But,<span class="_ _5"> </span>the<span class="_"> </span>timing<span class="_ _5"> </span>metric<span class="_"> </span>plateau<span class="_ _c"> </span>inherent<span class="_ _5"> </span>in<span class="_"> </span>this</div><div class="t m0 x1 h6 y1c ff1 fs4 fc0 sc0 ls0 ws0">method<span class="_ _8"> </span>causes<span class="_ _5"> </span>large<span class="_ _5"> </span>variance<span class="_ _5"> </span>of<span class="_ _8"> </span>the<span class="_ _5"> </span>timing<span class="_ _5"> </span>estimate.<span class="_ _8"> </span>Alterna-</div><div class="t m0 x1 h6 y1d ff1 fs4 fc0 sc0 ls0 ws0">tiv<span class="_ _3"></span>ely<span class="_ _2"></span>,<span class="_ _8"> </span>in<span class="_ _8"> </span>[7]<span class="_ _5"> </span>cyclic<span class="_ _5"> </span>prefix<span class="_ _5"> </span>and<span class="_ _8"> </span>pilot<span class="_ _8"> </span>symbols<span class="_ _5"> </span>used<span class="_ _8"> </span>for<span class="_ _5"> </span>channel</div><div class="t m0 x1 h6 y1e ff1 fs4 fc0 sc0 ls0 ws0">estimation<span class="_ _d"> </span>are<span class="_ _e"> </span>exploited<span class="_ _d"> </span>for<span class="_ _e"> </span>timing<span class="_ _d"> </span>estimation.<span class="_ _d"> </span>In<span class="_ _e"> </span>this<span class="_ _d"> </span>letter,</div><div class="t m0 x1 h6 y1f ff1 fs4 fc0 sc0 ls0 ws0">we<span class="_ _5"> </span>present<span class="_ _8"> </span>two<span class="_ _5"> </span>methods<span class="_ _5"> </span>as<span class="_ _8"> </span>modif<span class="_ _3"></span>ications<span class="_ _8"> </span>to<span class="_ _5"> </span>[6]<span class="_ _5"> </span>in<span class="_ _8"> </span>an<span class="_ _5"> </span>attempt</div><div class="t m0 x1 h6 y20 ff1 fs4 fc0 sc0 ls0 ws0">to<span class="_ _5"> </span>a<span class="_ _3"></span>void<span class="_ _5"> </span>timing<span class="_"> </span>metric<span class="_ _5"> </span>plateau.<span class="_ _5"> </span>Section<span class="_ _c"> </span>II<span class="_ _5"> </span>briefly<span class="_ _5"> </span>describes<span class="_ _5"> </span>the</div><div class="t m0 x1 h6 y21 ff1 fs4 fc0 sc0 ls0 ws0">timing<span class="_ _1"> </span>estimation<span class="_ _1"> </span>method<span class="_ _7"> </span>of<span class="_ _1"> </span>[6]<span class="_ _1"> </span>and<span class="_ _1"> </span>Section<span class="_ _1"> </span>III<span class="_ _1"> </span>presents<span class="_ _1"> </span>the<span class="_ _1"> </span>two</div><div class="t m0 x1 h6 y22 ff1 fs4 fc0 sc0 ls0 ws0">proposed<span class="_ _5"> </span>methods.<span class="_ _5"> </span>In<span class="_ _8"> </span>Section<span class="_ _5"> </span>IV<span class="_ _6"></span>,<span class="_ _5"> </span>the<span class="_ _5"> </span>performance<span class="_ _5"> </span>of<span class="_ _8"> </span>the<span class="_ _5"> </span>pro-</div><div class="t m0 x1 h6 y23 ff1 fs4 fc0 sc0 ls0 ws0">posed<span class="_"> </span>methods<span class="_ _5"> </span>and<span class="_"> </span>[6],<span class="_ _c"> </span>[7]<span class="_ _5"> </span>are<span class="_"> </span>compared<span class="_ _c"> </span>in<span class="_ _5"> </span>terms<span class="_"> </span>of<span class="_ _c"> </span>estimator</div><div class="t m0 x1 h6 y24 ff1 fs4 fc0 sc0 ls0 ws0">variance<span class="_"> </span>obtained<span class="_ _c"> </span>by<span class="_ _5"> </span>simulation.</div><div class="t m0 x8 h6 y25 ff1 fs4 fc0 sc0 ls0 ws0">II.<span class="_ _b"> </span>S</div><div class="t m0 x9 h6 y26 ff1 fs5 fc0 sc0 ls0 ws0">YSTEM<span class="_ _5"> </span><span class="fs4">D</span>ESCRIPTION</div><div class="t m0 xa h6 y27 ff1 fs4 fc0 sc0 ls0 ws0">The<span class="_ _8"> </span>samples<span class="_ _5"> </span>of<span class="_ _8"> </span>transmitted<span class="_ _8"> </span>baseband<span class="_ _8"> </span>OFDM<span class="_ _5"> </span>signal<span class="_ _8"> </span>can<span class="_ _8"> </span>be</div><div class="t m0 x1 h6 y28 ff1 fs4 fc0 sc0 ls0 ws0">giv<span class="_ _3"></span>en<span class="_ _5"> </span>by</div><div class="t m0 xb h6 y29 ff1 fs4 fc0 sc0 ls0 ws0">(1)</div><div class="t m0 x1 h6 y2a ff1 fs4 fc0 sc0 ls0 ws0">where</div><div class="t m0 xc h6 y2b ff1 fs4 fc0 sc0 ls0 ws0">is<span class="_ _d"> </span>modulated<span class="_ _e"> </span>data<span class="_ _d"> </span>on<span class="_ _d"> </span>the<span class="_ _f"> </span>th<span class="_ _d"> </span>subcarrier<span class="_ _3"></span>,<span class="_ _10"> </span>is<span class="_ _d"> </span>the</div><div class="t m0 x1 h6 y2c ff1 fs4 fc0 sc0 ls0 ws0">number<span class="_ _5"> </span>of<span class="_"> </span>inv<span class="_ _3"></span>erse<span class="_ _5"> </span>fast<span class="_"> </span>Fourier<span class="_ _5"> </span>transform<span class="_"> </span>(IFFT)<span class="_ _5"> </span>points,</div><div class="t m0 xd h8 y2d ff1 fs5 fc0 sc0 ls0 ws0">Manuscript<span class="_ _5"> </span>received<span class="_ _5"> </span>September<span class="_ _5"> </span>21,<span class="_ _8"> </span>1999.<span class="_ _5"> </span>This<span class="_ _5"> </span>work<span class="_ _5"> </span>was<span class="_ _5"> </span>supported<span class="_ _8"> </span>by<span class="_ _5"> </span>a</div><div class="t m0 x1 h8 y2e ff1 fs5 fc0 sc0 ls0 ws0">Strategic<span class="_ _c"> </span>Project<span class="_ _5"> </span>Grant<span class="_ _c"> </span>from<span class="_ _5"> </span>the<span class="_ _c"> </span>Natural<span class="_ _5"> </span>Sciences<span class="_ _c"> </span>and<span class="_ _c"> </span>Engineering<span class="_ _5"> </span>Research</div><div class="t m0 x1 h8 y2f ff1 fs5 fc0 sc0 ls0 ws0">Council<span class="_ _c"> </span>(NSERC)<span class="_ _11"> </span>of<span class="_ _11"> </span>Canada.<span class="_ _c"> </span>The<span class="_ _11"> </span>associate<span class="_ _c"> </span>editor<span class="_ _11"> </span>coordinating<span class="_ _c"> </span>the<span class="_ _11"> </span>review<span class="_ _11"> </span>of</div><div class="t m0 x1 h8 y30 ff1 fs5 fc0 sc0 ls0 ws0">this<span class="_"> </span>letter<span class="_ _11"> </span>and<span class="_"> </span>approving<span class="_"> </span>it<span class="_"> </span>for<span class="_ _11"> </span>publication<span class="_"> </span>was<span class="_"> </span>Dr.<span class="_"> </span>H.<span class="_"> </span>Sari.</div><div class="t m0 xd h8 y31 ff1 fs5 fc0 sc0 ls0 ws0">The<span class="_ _12"> </span>authors<span class="_ _12"> </span>are<span class="_ _12"> </span>with<span class="_ _12"> </span>the<span class="_ _12"> </span>Department<span class="_ _12"> </span>of<span class="_ _12"> </span>Electrical<span class="_ _12"> </span>and<span class="_ _12"> </span>Computer<span class="_ _12"></span>Engineering,</div><div class="t m0 x1 h8 y32 ff1 fs5 fc0 sc0 ls0 ws0">Univ<span class="_ _3"></span>ersity<span class="_ _1"> </span>of<span class="_ _11"> </span>V<span class="_ _3"></span>ictoria,<span class="_"> </span>V<span class="_ _3"></span>ictoria,<span class="_ _11"> </span>BC.,<span class="_"> </span>Canada<span class="_ _11"> </span>V8W<span class="_"> </span>3P6.</div><div class="t m0 xd h8 y33 ff1 fs5 fc0 sc0 ls0 ws0">Publisher<span class="_"> </span>Item<span class="_ _11"> </span>Identifier<span class="_"> </span>S<span class="_"> </span>1089-7798(00)05679-9.</div><div class="t m0 xe h6 y4 ff1 fs4 fc0 sc0 ls0 ws0">is<span class="_ _8"> </span>the<span class="_ _d"> </span>number<span class="_ _8"> </span>of<span class="_ _d"> </span>subcarriers,<span class="_ _13"> </span>is<span class="_ _8"> </span>the<span class="_ _d"> </span>number<span class="_ _8"> </span>of<span class="_ _d"> </span>guard</div><div class="t m0 xf h6 y34 ff1 fs4 fc0 sc0 ls0 ws0">samples,</div><div class="t m0 x10 h6 y35 ff1 fs4 fc0 sc0 ls0 ws0">,<span class="_ _d"> </span>and<span class="_ _8"> </span>the<span class="_ _d"> </span>sampling<span class="_ _d"> </span>period<span class="_ _d"> </span>is<span class="_ _14"> </span>with</div><div class="t m0 x11 h6 y36 ff1 fs4 fc0 sc0 ls0 ws0">being<span class="_ _5"> </span>subcarrier<span class="_ _5"> </span>spacing.<span class="_ _5"> </span>The<span class="_ _5"> </span>samples<span class="_ _5"> </span>at<span class="_ _5"> </span>the<span class="_ _8"> </span>recei<span class="_ _3"></span>ver<span class="_ _3"></span>,<span class="_ _5"> </span>if</div><div class="t m0 xf h6 y37 ff1 fs4 fc0 sc0 ls0 ws0">assuming<span class="_"> </span><span class="ff2">Nyquist<span class="_ _c"> </span></span>channel<span class="_ _c"> </span>and<span class="_ _c"> </span>perfect<span class="_ _5"> </span>timing,<span class="_"> </span>is</div><div class="t m0 x12 h6 y38 ff1 fs4 fc0 sc0 ls0 ws0">(2)</div><div class="t m0 xf h6 y39 ff1 fs4 fc0 sc0 ls0 ws0">where</div><div class="t m0 x13 h6 y3a ff1 fs4 fc0 sc0 ls0 ws0">is<span class="_ _8"> </span>the<span class="_ _8"> </span>carrier<span class="_ _8"> </span>frequency<span class="_ _8"> </span>offset<span class="_ _8"> </span>normalized<span class="_ _8"> </span>to<span class="_ _8"> </span>subcar-</div><div class="t m0 xf h6 y3b ff1 fs4 fc0 sc0 ls0 ws0">rier<span class="_"> </span>spacing,</div><div class="t m0 x14 h6 y3c ff1 fs4 fc0 sc0 ls0 ws0">is<span class="_"> </span>the<span class="_ _5"> </span>sample<span class="_"> </span>of<span class="_"> </span>zero<span class="_ _c"> </span>mean<span class="_ _5"> </span>comple<span class="_ _3"></span>x<span class="_ _c"> </span>A<span class="_ _2"></span>WGN</div><div class="t m0 xf h6 y3d ff1 fs4 fc0 sc0 ls0 ws0">process.<span class="_ _7"> </span>Including<span class="_ _1"> </span>a<span class="_ _1"> </span>timing<span class="_ _1"> </span>offset</div><div class="t m0 x15 h6 y3e ff1 fs4 fc0 sc0 ls0 ws0">,<span class="_ _7"> </span>the<span class="_ _1"> </span>received<span class="_ _7"> </span>sample<span class="_ _1"> </span>is<span class="_ _1"> </span>giv<span class="_ _3"></span>en</div><div class="t m0 xf h6 y3f ff1 fs4 fc0 sc0 ls0 ws0">by</div><div class="t m0 x16 h6 y40 ff1 fs4 fc0 sc0 ls0 ws0">.<span class="_ _1"> </span>The<span class="_"> </span>symbol<span class="_ _1"> </span>timing<span class="_"> </span>estimator<span class="_ _1"> </span>finds<span class="_ _1"> </span>the<span class="_ _1"> </span>start</div><div class="t m0 xf h6 y41 ff1 fs4 fc0 sc0 ls0 ws0">of<span class="_ _1"> </span>the<span class="_ _1"> </span>OFDM<span class="_ _1"> </span>symbol.<span class="_ _1"> </span>Let<span class="_ _1"> </span>the<span class="_ _1"> </span>training<span class="_ _1"> </span>symbol<span class="_ _1"> </span>(excluding<span class="_ _7"> </span>cyclic</div><div class="t m0 xf h6 y42 ff1 fs4 fc0 sc0 ls0 ws0">prefix)<span class="_ _1"> </span>contain<span class="_ _1"> </span>two<span class="_"> </span>identical<span class="_ _1"> </span>halves<span class="_ _1"> </span>in<span class="_"> </span>time<span class="_ _1"> </span>domain<span class="_ _1"> </span>each<span class="_"> </span>ha<span class="_ _3"></span>ving</div><div class="t m0 x17 h6 y43 ff1 fs4 fc0 sc0 ls0 ws0">samples.<span class="_"> </span>At<span class="_ _c"> </span>the<span class="_ _5"> </span>recei<span class="_ _3"></span>ver<span class="_"> </span>there<span class="_"> </span>will<span class="_"> </span>be<span class="_ _5"> </span>a<span class="_"> </span>phase<span class="_"> </span>differ-</div><div class="t m0 xf h6 y44 ff1 fs4 fc0 sc0 ls0 ws0">ence<span class="_ _1"> </span>between<span class="_ _1"> </span>the<span class="_ _1"> </span>samples<span class="_ _1"> </span>in<span class="_ _1"> </span>the<span class="_ _1"> </span>first<span class="_ _1"> </span>half<span class="_ _1"> </span>and<span class="_ _1"> </span>their<span class="_ _1"> </span>replica<span class="_ _1"> </span>in<span class="_ _1"> </span>the</div><div class="t m0 xf h6 y45 ff1 fs4 fc0 sc0 ls0 ws0">second<span class="_ _7"> </span>half<span class="_ _1"> </span>caused<span class="_ _1"> </span>by<span class="_ _1"> </span>the<span class="_ _1"> </span>carrier<span class="_ _7"> </span>frequency<span class="_ _1"> </span>offset.<span class="_ _7"> </span>T<span class="_ _3"></span>raining<span class="_ _1"> </span>data</div><div class="t m0 xf h6 y46 ff1 fs4 fc0 sc0 ls0 ws0">is<span class="_ _5"> </span>usually<span class="_ _c"> </span>a<span class="_ _5"> </span>PN<span class="_ _5"> </span>sequence.<span class="_ _c"> </span>Then<span class="_ _5"> </span>the<span class="_ _5"> </span>Schmidl<span class="_ _5"> </span>and<span class="_"> </span>Cox&#8217;s<span class="_ _5"> </span>timing</div><div class="t m0 xf h6 y47 ff1 fs4 fc0 sc0 ls0 ws0">estimator<span class="_ _1"> </span>takes<span class="_"> </span>as<span class="_ _1"> </span>the<span class="_"> </span>start<span class="_ _1"> </span>of<span class="_"> </span>the<span class="_ _1"> </span>symbol<span class="_"> </span>the<span class="_"> </span>maximum<span class="_ _1"> </span>point<span class="_"> </span>of</div><div class="t m0 xf h6 y48 ff1 fs4 fc0 sc0 ls0 ws0">the<span class="_ _c"> </span>timing<span class="_ _5"> </span>metric<span class="_ _c"> </span>given<span class="_"> </span>by</div><div class="t m0 x12 h6 y49 ff1 fs4 fc0 sc0 ls0 ws0">(3)</div><div class="t m0 xf h6 y4a ff1 fs4 fc0 sc0 ls0 ws0">where</div><div class="t m0 x18 h6 y4b ff1 fs4 fc0 sc0 ls0 ws0">is<span class="_ _5"> </span>a<span class="_ _5"> </span>time<span class="_ _5"> </span>index<span class="_ _5"> </span>corresponding<span class="_ _5"> </span>to<span class="_ _5"> </span>the<span class="_ _5"> </span>first<span class="_ _5"> </span>sample<span class="_ _5"> </span>in<span class="_ _5"> </span>a</div><div class="t m0 xf h6 y4c ff1 fs4 fc0 sc0 ls0 ws0">window<span class="_"> </span>of</div><div class="t m0 x19 h6 y4d ff1 fs4 fc0 sc0 ls0 ws0">samples<span class="_ _c"> </span>and</div><div class="t m0 x12 h6 y4e ff1 fs4 fc0 sc0 ls0 ws0">(4)</div><div class="t m0 xf h6 y4f ff1 fs4 fc0 sc0 ls0 ws0">and</div><div class="t m0 x12 h6 y50 ff1 fs4 fc0 sc0 ls0 ws0">(5)</div><div class="t m0 x1a h6 y51 ff1 fs4 fc0 sc0 ls0 ws0">The<span class="_"> </span>timing<span class="_"> </span>metric<span class="_ _5"> </span>reaches<span class="_"> </span>a<span class="_"> </span>plateau<span class="_"> </span>(see<span class="_"> </span>Fig.<span class="_ _5"> </span>1)<span class="_"> </span>which<span class="_"> </span>leads</div><div class="t m0 xf h6 y52 ff1 fs4 fc0 sc0 ls0 ws0">to<span class="_ _d"> </span>some<span class="_ _8"> </span>uncertainty<span class="_ _d"> </span>as<span class="_ _8"> </span>to<span class="_ _d"> </span>the<span class="_ _d"> </span>start<span class="_ _8"> </span>of<span class="_ _d"> </span>the<span class="_ _d"> </span>frame.<span class="_ _8"> </span>T<span class="_ _2"></span>o<span class="_ _d"> </span>alleviate</div><div class="t m0 xf h6 y53 ff1 fs4 fc0 sc0 ls0 ws0">this,<span class="_ _1"> </span>Schmidl<span class="_"> </span>and<span class="_ _1"> </span>Cox<span class="_"> </span>proposes<span class="_ _1"> </span>an<span class="_ _1"> </span>averaging<span class="_ _1"> </span>method<span class="_"> </span>where<span class="_ _1"> </span>the</div><div class="t m0 xf h6 y54 ff1 fs4 fc0 sc0 ls0 ws0">maximum<span class="_"> </span>point<span class="_ _5"> </span>is<span class="_"> </span>f<span class="_ _3"></span>irst<span class="_ _5"> </span>found<span class="_"> </span>and<span class="_"> </span>then<span class="_ _c"> </span>two<span class="_ _c"> </span>points<span class="_ _c"> </span>with<span class="_ _5"> </span>90%<span class="_"> </span>of</div><div class="t m0 xf h6 y55 ff1 fs4 fc0 sc0 ls0 ws0">the<span class="_"> </span>maximum<span class="_"> </span>value,<span class="_"> </span>one<span class="_"> </span>to<span class="_"> </span>the<span class="_"> </span>left<span class="_"> </span>and<span class="_"> </span>the<span class="_"> </span>other<span class="_"> </span>to<span class="_ _c"> </span>the<span class="_"> </span>right<span class="_ _c"> </span>of</div><div class="t m0 xf h6 y56 ff1 fs4 fc0 sc0 ls0 ws0">the<span class="_"> </span>maximum<span class="_ _c"> </span>point,<span class="_ _c"> </span>are<span class="_ _5"> </span>found.<span class="_"> </span>The<span class="_"> </span>timing<span class="_ _c"> </span>estimate<span class="_ _c"> </span>is<span class="_ _5"> </span>tak<span class="_ _3"></span>en<span class="_ _c"> </span>as</div><div class="t m0 xf h6 y57 ff1 fs4 fc0 sc0 ls0 ws0">the<span class="_ _c"> </span>average<span class="_"> </span>of<span class="_ _5"> </span>the<span class="_"> </span>two<span class="_"> </span>90%<span class="_ _5"> </span>points.</div><div class="t m0 x14 h6 y58 ff1 fs4 fc0 sc0 ls0 ws0">III.<span class="_ _b"> </span>P</div><div class="t m0 x1b h6 y59 ff1 fs5 fc0 sc0 ls0 ws0">R<span class="_ _3"></span>OPOSED<span class="_ _5"> </span><span class="fs4">M</span>ETHODS</div><div class="t m0 x1a h6 y5a ff1 fs4 fc0 sc0 ls0 ws0">In<span class="_"> </span>this<span class="_ _c"> </span>section,<span class="_ _5"> </span>we<span class="_"> </span>present<span class="_"> </span>two<span class="_ _c"> </span>methods<span class="_ _5"> </span>to<span class="_"> </span>reduce<span class="_"> </span>the<span class="_ _c"> </span>uncer-</div><div class="t m0 xf h6 y5b ff1 fs4 fc0 sc0 ls0 ws0">tainty<span class="_ _8"> </span>due<span class="_ _d"> </span>to<span class="_ _8"> </span>the<span class="_ _d"> </span>timing<span class="_ _8"> </span>metric<span class="_ _d"> </span>plateau<span class="_ _8"> </span>and<span class="_ _d"> </span>thus<span class="_ _8"> </span>improve<span class="_ _8"> </span>the</div><div class="t m0 xf h6 y5c ff1 fs4 fc0 sc0 ls0 ws0">timing<span class="_"> </span>of<span class="_ _3"></span>fset<span class="_ _1"> </span>estimation<span class="_"> </span>scheme<span class="_ _1"> </span>proposed<span class="_"> </span>by<span class="_ _1"> </span>Schmidl<span class="_"> </span>and<span class="_"> </span>Cox.</div><div class="t m0 xf h9 y5d ff2 fs4 fc0 sc0 ls0 ws0">A.<span class="_ _b"> </span>Sliding<span class="_ _5"> </span>W<span class="_ _2"></span>indow<span class="_ _c"> </span>Method</div><div class="t m0 x1a h6 y5e ff1 fs4 fc0 sc0 ls0 ws0">Firstly<span class="_ _2"></span>,<span class="_ _7"> </span>in<span class="_ _7"> </span>calculation<span class="_ _7"> </span>of<span class="_ _7"> </span>the<span class="_ _7"> </span>half<span class="_ _7"> </span>symbol<span class="_ _7"> </span>energy</div><div class="t m0 x1c h6 y5f ff1 fs4 fc0 sc0 ls0 ws0">,<span class="_ _12"> </span>all<span class="_ _7"> </span>sam-</div><div class="t m0 xf h6 y60 ff1 fs4 fc0 sc0 ls0 ws0">ples<span class="_"> </span>over<span class="_"> </span>one<span class="_ _5"> </span>symbol<span class="_"> </span>period<span class="_ _5"> </span>(excluding<span class="_"> </span>guard<span class="_"> </span>interval)<span class="_ _c"> </span>is<span class="_ _5"> </span>used</div><div class="t m0 xf h6 y61 ff1 fs4 fc0 sc0 ls0 ws0">instead<span class="_ _7"> </span>of<span class="_ _1"> </span>over<span class="_ _7"> </span>the<span class="_ _7"> </span>second<span class="_ _1"> </span>half<span class="_ _1"> </span>symbol<span class="_ _1"> </span>period.<span class="_ _1"> </span>Secondly<span class="_ _2"></span>,<span class="_ _1"> </span>instead</div><div class="t m0 x1d h8 y62 ff1 fs5 fc0 sc0 ls0 ws0">1089&#8211;7798/00$10.00<span class="_ _11"> </span>&#169;<span class="_ _11"> </span>2000<span class="_ _11"> </span>IEEE</div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div></body></html>
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