OFDM同步算法之SC算法

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OFDM经典同步算法之一SC算法,里面附带SC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/12190445/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/12190445/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">IEEE<span class="_ _0"> </span>TRANSACTIONS<span class="_ _0"> </span>ON<span class="_ _0"> </span>COMMUNICA<span class="_ _1"></span>TIONS,<span class="_ _0"> </span>VOL.<span class="_ _0"> </span>45,<span class="_ _0"> </span>NO.<span class="_ _0"> </span>12,<span class="_ _0"> </span>DECEMBER<span class="_ _0"> </span>1997<span class="_ _2"> </span>1613</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls0 ws0">Robust<span class="_ _3"> </span>Frequency<span class="_ _3"> </span>and<span class="_ _3"> </span>T<span class="_ _1"></span>iming</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls0 ws0">Synchronization<span class="_ _3"> </span>for<span class="_ _4"> </span>OFDM</div><div class="t m0 x4 h4 y4 ff1 fs2 fc0 sc0 ls0 ws0">T<span class="_ _5"></span>imothy<span class="_ _6"> </span>M.<span class="_ _6"> </span>Schmidl<span class="_ _6"> </span>and<span class="_ _6"> </span>Donald<span class="_ _6"> </span>C.<span class="_ _6"> </span>Cox,<span class="_ _6"> </span><span class="ff2 fs3">Fellow,<span class="_ _7"> </span>IEEE</span></div><div class="t m0 x5 h5 y5 ff3 fs4 fc0 sc0 ls0 ws0">Abstract<span class="_ _8"></span>&#8212;<span class="_"> </span><span class="ff4">A<span class="_ _6"> </span>rapid<span class="_ _6"> </span>synchronization<span class="_ _6"> </span>method<span class="_ _6"> </span>is<span class="_ _6"> </span>pr<span class="_ _5"></span>esented<span class="_ _6"> </span>for</span></div><div class="t m0 x1 h5 y6 ff4 fs4 fc0 sc0 ls0 ws0">an<span class="_ _9"> </span>orthogonal<span class="_ _9"> </span>frequency-division<span class="_ _7"> </span>multiplexing<span class="_ _9"> </span>(OFDM)<span class="_ _9"> </span>system</div><div class="t m0 x1 h5 y7 ff4 fs4 fc0 sc0 ls0 ws0">using<span class="_ _0"> </span>either<span class="_ _a"> </span>a<span class="_ _0"> </span>continuous<span class="_ _a"> </span>transmission<span class="_ _0"> </span>or<span class="_ _a"> </span>a<span class="_ _0"> </span>burst<span class="_ _a"> </span>operation<span class="_ _0"> </span>over</div><div class="t m0 x1 h5 y8 ff4 fs4 fc0 sc0 ls0 ws0">a<span class="_ _7"> </span>frequency-selective<span class="_ _7"> </span>channel.<span class="_ _9"> </span>The<span class="_ _7"> </span>presence<span class="_ _9"> </span>of<span class="_ _7"> </span>a<span class="_ _9"> </span>signal<span class="_ _7"> </span>can<span class="_ _9"> </span>be</div><div class="t m0 x1 h5 y9 ff4 fs4 fc0 sc0 ls0 ws0">detected<span class="_ _7"> </span>upon<span class="_ _7"> </span>the<span class="_ _9"> </span>r<span class="_ _5"></span>eceipt<span class="_ _7"> </span>of<span class="_ _9"> </span>just<span class="_ _7"> </span>one<span class="_ _7"> </span>training<span class="_ _7"> </span>sequence<span class="_ _9"> </span>of<span class="_ _7"> </span>two</div><div class="t m0 x1 h5 ya ff4 fs4 fc0 sc0 ls0 ws0">symbols.<span class="_ _0"> </span>The<span class="_ _a"> </span>start<span class="_ _0"> </span>of<span class="_ _a"> </span>the<span class="_ _0"> </span>frame<span class="_ _a"> </span>and<span class="_ _0"> </span>the<span class="_ _a"> </span>beginning<span class="_ _0"> </span>of<span class="_ _a"> </span>the<span class="_ _0"> </span>symbol</div><div class="t m0 x1 h5 yb ff4 fs4 fc0 sc0 ls0 ws0">can<span class="_ _0"> </span>be<span class="_ _0"> </span>found,<span class="_ _0"> </span>and<span class="_ _0"> </span>carrier<span class="_ _0"> </span>frequency<span class="_ _0"> </span>offsets<span class="_"> </span>of<span class="_ _a"> </span>many<span class="_ _0"> </span>subchannels</div><div class="t m0 x1 h5 yc ff4 fs4 fc0 sc0 ls0 ws0">spacings<span class="_ _b"> </span>can<span class="_ _b"> </span>be<span class="_ _b"> </span>corrected.<span class="_ _b"> </span>The<span class="_ _b"> </span>algorithms<span class="_ _b"> </span>operate<span class="_ _b"> </span>near<span class="_ _b"> </span>the</div><div class="t m0 x1 h5 yd ff4 fs4 fc0 sc0 ls0 ws0">Cram</div><div class="t m0 x6 h5 ye ff4 fs4 fc0 sc0 ls0 ws0">&#180;</div><div class="t m0 x6 h5 yd ff4 fs4 fc0 sc0 ls0 ws0">er&#8211;Rao<span class="_ _c"> </span>lower<span class="_ _c"> </span>bound<span class="_ _c"> </span>for<span class="_ _c"> </span>the<span class="_ _c"> </span>variance<span class="_ _c"> </span>of<span class="_ _c"> </span>the<span class="_ _c"> </span>frequency</div><div class="t m0 x1 h5 yf ff4 fs4 fc0 sc0 ls0 ws0">offset<span class="_"> </span>estimate,<span class="_"> </span>and<span class="_"> </span>the<span class="_ _d"> </span>inherent<span class="_"> </span>averaging<span class="_ _d"> </span>over<span class="_"> </span>many<span class="_"> </span>subcarriers</div><div class="t m0 x1 h5 y10 ff4 fs4 fc0 sc0 ls0 ws0">allows<span class="_ _a"> </span>acquisition<span class="_ _a"> </span>at<span class="_ _a"> </span>very<span class="_ _a"> </span>low<span class="_ _a"> </span>signal-to-noise<span class="_ _a"> </span>ratios<span class="_ _e"> </span>(SNR&#8217;s).</div><div class="t m0 x5 h5 y11 ff3 fs4 fc0 sc0 ls0 ws0">Index<span class="_ _a"> </span>T<span class="_ _1"></span>erms<span class="_ _8"></span>&#8212;<span class="_ _f"> </span><span class="ff4">Carrier<span class="_ _10"> </span>frequency,<span class="_ _10"> </span>orthogonal<span class="_ _11"> </span>frequency-</span></div><div class="t m0 x1 h5 y12 ff4 fs4 fc0 sc0 ls0 ws0">division<span class="_ _e"> </span>multiplexing,<span class="_ _e"> </span>symbol<span class="_ _e"> </span>timing<span class="_ _e"> </span>estimation.</div><div class="t m0 x7 h6 y13 ff1 fs3 fc0 sc0 ls0 ws0">I.<span class="_ _12"> </span>I<span class="fs5">NTRODUCTION</span></div><div class="t m0 x1 h7 y14 ff4 fs6 fc0 sc0 ls0 ws0">I</div><div class="t m0 x8 h6 y15 ff1 fs3 fc0 sc0 ls0 ws0">N<span class="_"> </span>AN<span class="_"> </span>orthogonal<span class="_"> </span>frequency-division<span class="_"> </span>multiplexing<span class="_"> </span>(OFDM)</div><div class="t m0 x8 h6 y16 ff1 fs3 fc0 sc0 ls0 ws0">system,<span class="_ _13"> </span>synchronization<span class="_ _13"> </span>at<span class="_ _13"> </span>the<span class="_ _13"> </span>receiver<span class="_ _13"> </span>is<span class="_ _13"> </span>one<span class="_ _13"> </span>important</div><div class="t m0 x1 h6 y17 ff1 fs3 fc0 sc0 ls0 ws0">step<span class="_ _7"> </span>that<span class="_ _9"> </span>must<span class="_ _7"> </span>be<span class="_ _9"> </span>performed.<span class="_ _7"> </span>This<span class="_ _7"> </span>paper<span class="_ _9"> </span>describes<span class="_ _7"> </span>a<span class="_ _7"> </span>method</div><div class="t m0 x1 h6 y18 ff1 fs3 fc0 sc0 ls0 ws0">to<span class="_ _9"> </span>acquire<span class="_ _7"> </span>synchronization<span class="_ _9"> </span>for<span class="_ _9"> </span>either<span class="_ _9"> </span>a<span class="_ _7"> </span>continuous<span class="_ _9"> </span>stream<span class="_ _9"> </span>of</div><div class="t m0 x1 h6 y19 ff1 fs3 fc0 sc0 ls0 ws0">data<span class="_ _13"> </span>as<span class="_ _13"> </span>in<span class="_ _c"> </span>a<span class="_ _13"> </span>broadcast<span class="_ _13"> </span>application<span class="_ _c"> </span>or<span class="_ _13"> </span>for<span class="_ _c"> </span>bursty<span class="_ _13"> </span>data<span class="_ _13"> </span>as<span class="_ _13"> </span>in</div><div class="t m0 x1 h6 y1a ff1 fs3 fc0 sc0 ls0 ws0">a<span class="_ _c"> </span>wireless<span class="_ _b"> </span>local<span class="_ _c"> </span>area<span class="_ _c"> </span>network<span class="_ _b"> </span>(WLAN).<span class="_ _c"> </span>In<span class="_ _b"> </span>both<span class="_ _c"> </span>cases<span class="_ _b"> </span>the</div><div class="t m0 x1 h6 y1b ff1 fs3 fc0 sc0 ls0 ws0">receiver<span class="_ _e"> </span>must<span class="_ _e"> </span>continuously<span class="_ _e"> </span>scan<span class="_ _14"> </span>for<span class="_ _e"> </span>incoming<span class="_ _e"> </span>data,<span class="_ _e"> </span>and<span class="_ _e"> </span>rapid</div><div class="t m0 x1 h6 y1c ff1 fs3 fc0 sc0 ls0 ws0">acquisition<span class="_"> </span>is<span class="_ _0"> </span>needed.<span class="_"> </span>The<span class="_ _0"> </span>ratio<span class="_"> </span>of<span class="_ _0"> </span>the<span class="_"> </span>number<span class="_ _0"> </span>of<span class="_"> </span>overhead<span class="_ _0"> </span>bits</div><div class="t m0 x1 h6 y1d ff1 fs3 fc0 sc0 ls0 ws0">for<span class="_"> </span>synchronization<span class="_ _d"> </span>to<span class="_"> </span>the<span class="_"> </span>number<span class="_ _d"> </span>of<span class="_"> </span>message<span class="_"> </span>bits<span class="_ _d"> </span>must<span class="_"> </span>be<span class="_ _d"> </span>kept</div><div class="t m0 x1 h6 y1e ff1 fs3 fc0 sc0 ls0 ws0">to<span class="_ _e"> </span>a<span class="_ _e"> </span>minimum,<span class="_ _e"> </span>and<span class="_ _e"> </span>low-complexity<span class="_ _14"> </span>algorithms<span class="_ _e"> </span>are<span class="_ _e"> </span>needed.</div><div class="t m0 x9 h6 y1f ff1 fs3 fc0 sc0 ls0 ws0">Synchronization<span class="_ _6"> </span>of<span class="_ _13"> </span>an<span class="_ _13"> </span>OFDM<span class="_ _6"> </span>signal<span class="_ _13"> </span>requires<span class="_ _13"> </span>&#64257;nding<span class="_ _6"> </span>the</div><div class="t m0 x1 h6 y20 ff1 fs3 fc0 sc0 ls0 ws0">symbol<span class="_ _13"> </span>timing<span class="_ _6"> </span>and<span class="_ _13"> </span>carrier<span class="_ _13"> </span>frequency<span class="_ _13"> </span>offset.<span class="_ _6"> </span>Symbol<span class="_ _13"> </span>timing</div><div class="t m0 x1 h6 y21 ff1 fs3 fc0 sc0 ls0 ws0">for<span class="_ _a"> </span>an<span class="_ _a"> </span>OFDM<span class="_ _a"> </span>signal<span class="_ _a"> </span>is<span class="_ _a"> </span>signi&#64257;cantly<span class="_ _a"> </span>different<span class="_ _0"> </span>than<span class="_ _a"> </span>for<span class="_ _a"> </span>a<span class="_ _a"> </span>single</div><div class="t m0 x1 h6 y22 ff1 fs3 fc0 sc0 ls0 ws0">carrier<span class="_ _13"> </span>signal<span class="_ _13"> </span>since<span class="_ _13"> </span>there<span class="_ _13"> </span>is<span class="_ _13"> </span>not<span class="_ _c"> </span>an<span class="_ _13"> </span>&#8220;eye<span class="_ _13"> </span>opening&#8221;<span class="_ _13"> </span>where<span class="_ _13"> </span>a</div><div class="t m0 x1 h6 y23 ff1 fs3 fc0 sc0 ls0 ws0">best<span class="_ _0"> </span>sampling<span class="_ _a"> </span>time<span class="_ _0"> </span>can<span class="_ _0"> </span>be<span class="_ _a"> </span>found.<span class="_ _0"> </span>Rather<span class="_ _0"> </span>there<span class="_ _a"> </span>are<span class="_ _0"> </span>hundreds<span class="_ _0"> </span>or</div><div class="t m0 x1 h6 y24 ff1 fs3 fc0 sc0 ls0 ws0">thousands<span class="_ _a"> </span>of<span class="_ _e"> </span>samples<span class="_ _a"> </span>per<span class="_ _e"> </span>OFDM<span class="_ _a"> </span>symbol<span class="_ _a"> </span>since<span class="_ _e"> </span>the<span class="_ _a"> </span>number<span class="_ _e"> </span>of</div><div class="t m0 x1 h6 y25 ff1 fs3 fc0 sc0 ls0 ws0">samples<span class="_"> </span>necessary<span class="_"> </span>is<span class="_"> </span>proportional<span class="_"> </span>to<span class="_ _d"> </span>the<span class="_"> </span>number<span class="_"> </span>of<span class="_"> </span>subcarriers.</div><div class="t m0 x1 h6 y26 ff1 fs3 fc0 sc0 ls0 ws0">Finding<span class="_ _12"> </span>the<span class="_ _15"> </span>symbol<span class="_ _12"> </span>timing<span class="_ _15"> </span>for<span class="_ _12"> </span>OFDM<span class="_ _15"> </span>means<span class="_ _12"> </span>&#64257;nding<span class="_ _15"> </span>an</div><div class="t m0 x1 h6 y27 ff1 fs3 fc0 sc0 ls0 ws0">estimate<span class="_ _6"> </span>of<span class="_ _6"> </span>where<span class="_ _9"> </span>the<span class="_ _6"> </span>symbol<span class="_ _6"> </span>starts.<span class="_ _6"> </span>There<span class="_ _6"> </span>is<span class="_ _6"> </span>usually<span class="_ _9"> </span>some</div><div class="t m0 x1 h6 y28 ff1 fs3 fc0 sc0 ls0 ws0">tolerance<span class="_ _13"> </span>for<span class="_ _c"> </span>symbol<span class="_ _13"> </span>timing<span class="_ _c"> </span>errors<span class="_ _13"> </span>when<span class="_ _c"> </span>a<span class="_ _13"> </span>cyclic<span class="_ _c"> </span>pre&#64257;x<span class="_ _13"> </span>is</div><div class="t m0 x1 h6 y29 ff1 fs3 fc0 sc0 ls0 ws0">used<span class="_ _b"> </span>to<span class="_ _c"> </span>extend<span class="_ _b"> </span>the<span class="_ _b"> </span>symbol.<span class="_ _b"> </span>Synchronization<span class="_ _c"> </span>of<span class="_ _b"> </span>the<span class="_ _b"> </span>carrier</div><div class="t m0 x1 h6 y2a ff1 fs3 fc0 sc0 ls0 ws0">frequency<span class="_ _e"> </span>at<span class="_ _14"> </span>the<span class="_ _14"> </span>receiver<span class="_ _14"> </span>must<span class="_ _e"> </span>be<span class="_ _14"> </span>performed<span class="_ _14"> </span>very<span class="_ _14"> </span>accurately,</div><div class="t m0 x1 h6 y2b ff1 fs3 fc0 sc0 ls0 ws0">or<span class="_ _0"> </span>there<span class="_ _a"> </span>will<span class="_ _0"> </span>be<span class="_ _0"> </span>loss<span class="_ _a"> </span>of<span class="_ _0"> </span>orthogonality<span class="_ _0"> </span>between<span class="_ _a"> </span>the<span class="_ _0"> </span>subsymbols.</div><div class="t m0 x1 h6 y2c ff1 fs3 fc0 sc0 ls0 ws0">OFDM<span class="_ _a"> </span>systems<span class="_ _e"> </span>are<span class="_ _e"> </span>very<span class="_ _e"> </span>sensitive<span class="_ _a"> </span>to<span class="_ _e"> </span>carrier<span class="_ _e"> </span>frequency<span class="_ _a"> </span>offsets</div><div class="t m0 x1 h6 y2d ff1 fs3 fc0 sc0 ls0 ws0">since<span class="_ _a"> </span>they<span class="_ _a"> </span>can<span class="_ _a"> </span>only<span class="_ _a"> </span>tolerate<span class="_ _0"> </span>offsets<span class="_ _a"> </span>which<span class="_ _a"> </span>are<span class="_ _a"> </span>a<span class="_ _a"> </span>fraction<span class="_ _a"> </span>of<span class="_ _a"> </span>the</div><div class="t m0 xa h8 y2e ff1 fs5 fc0 sc0 ls0 ws0">Paper<span class="_ _c"> </span>approved<span class="_ _c"> </span>by<span class="_ _13"> </span>M.<span class="_ _b"> </span>Luise,<span class="_ _13"> </span>the<span class="_ _c"> </span>Editor<span class="_ _c"> </span>for<span class="_ _c"> </span>Synchronization<span class="_ _c"> </span>of<span class="_ _c"> </span>the</div><div class="t m0 x1 h8 y2f ff1 fs5 fc0 sc0 ls0 ws0">IEEE<span class="_ _0"> </span>Communications<span class="_ _0"> </span>Society.<span class="_ _0"> </span>Manuscript<span class="_ _0"> </span>received<span class="_ _a"> </span>April<span class="_ _0"> </span>16,<span class="_ _0"> </span>1996;<span class="_ _0"> </span>revised</div><div class="t m0 x1 h8 y30 ff1 fs5 fc0 sc0 ls0 ws0">February<span class="_ _a"> </span>11,<span class="_ _a"> </span>1997.<span class="_ _e"> </span>This<span class="_ _a"> </span>work<span class="_ _a"> </span>was<span class="_ _e"> </span>supported<span class="_ _a"> </span>in<span class="_ _a"> </span>part<span class="_ _e"> </span>by<span class="_ _a"> </span>a<span class="_ _a"> </span>National<span class="_ _e"> </span>Science</div><div class="t m0 x1 h8 y31 ff1 fs5 fc0 sc0 ls0 ws0">Foundation<span class="_"> </span>Graduate<span class="_ _16"> </span>Fellowship.<span class="_"> </span>This<span class="_"> </span>work<span class="_ _16"> </span>was<span class="_"> </span>presented<span class="_ _16"> </span>in<span class="_"> </span>part<span class="_ _16"> </span>at<span class="_"> </span>the<span class="_ _16"> </span>IEEE</div><div class="t m0 x1 h8 y32 ff1 fs5 fc0 sc0 ls0 ws0">International<span class="_ _0"> </span>Conference<span class="_ _0"> </span>on<span class="_ _0"> </span>Communications<span class="_ _16"> </span>(ICC),<span class="_ _0"> </span>Dallas,<span class="_ _0"> </span>TX,<span class="_ _0"> </span>June<span class="_ _0"> </span>1996.</div><div class="t m0 xa h8 y33 ff1 fs5 fc0 sc0 ls0 ws0">T.<span class="_ _e"> </span>M.<span class="_ _e"> </span>Schmidl<span class="_ _e"> </span>is<span class="_ _e"> </span>with<span class="_ _e"> </span>DSP<span class="_ _e"> </span>Research<span class="_ _14"> </span>and<span class="_ _e"> </span>Development<span class="_ _e"> </span>Center<span class="_ _e"> </span>at<span class="_ _14"> </span>T<span class="_ _5"></span>exas</div><div class="t m0 x1 h8 y34 ff1 fs5 fc0 sc0 ls0 ws0">Instruments<span class="_ _0"> </span>Incorporated,<span class="_ _0"> </span>Dallas,<span class="_ _0"> </span>TX<span class="_ _16"> </span>75243<span class="_ _0"> </span>USA<span class="_ _0"> </span>(e-mail:<span class="_ _0"> </span>schmidl@ti.com).</div><div class="t m0 xa h8 y35 ff1 fs5 fc0 sc0 ls0 ws0">D.<span class="_ _b"> </span>C.<span class="_ _c"> </span>Cox<span class="_ _b"> </span>is<span class="_ _b"> </span>with<span class="_ _b"> </span>the<span class="_ _b"> </span>ST<span class="_ _1"></span>AR<span class="_ _b"> </span>Laboratory,<span class="_ _b"> </span>Department<span class="_ _b"> </span>of<span class="_ _b"> </span>Electrical</div><div class="t m0 x1 h8 y36 ff1 fs5 fc0 sc0 ls0 ws0">Engineering,<span class="_ _7"> </span>Stanford<span class="_ _14"> </span>University,<span class="_ _7"> </span>Stanford,<span class="_ _7"> </span>CA<span class="_ _7"> </span>94305-4055<span class="_ _7"> </span>USA<span class="_ _7"> </span>(e-mail:</div><div class="t m0 x1 h8 y37 ff1 fs5 fc0 sc0 ls0 ws0">dcox@nova.stanford.edu).</div><div class="t m0 xa h8 y38 ff1 fs5 fc0 sc0 ls0 ws0">Publisher<span class="_ _0"> </span>Item<span class="_ _0"> </span>Identi&#64257;er<span class="_ _0"> </span>S<span class="_ _16"> </span>0090-6778(97)09083-1.</div><div class="t m0 xb h6 y5 ff1 fs3 fc0 sc0 ls0 ws0">spacing<span class="_"> </span>between<span class="_ _a"> </span>the<span class="_ _0"> </span>subcarriers<span class="_ _0"> </span>without<span class="_ _0"> </span>a<span class="_ _0"> </span>large<span class="_ _0"> </span>degradation<span class="_ _0"> </span>in</div><div class="t m0 xb h6 y39 ff1 fs3 fc0 sc0 ls0 ws0">system<span class="_ _9"> </span>performance<span class="_ _9"> </span>[1].</div><div class="t m0 xc h6 y3a ff1 fs3 fc0 sc0 ls0 ws0">There<span class="_ _e"> </span>have<span class="_ _7"> </span>been<span class="_ _14"> </span>several<span class="_ _14"> </span>papers<span class="_ _14"> </span>on<span class="_ _14"> </span>the<span class="_ _14"> </span>subject<span class="_ _14"> </span>of<span class="_ _14"> </span>synchro-</div><div class="t m0 xb h6 y3b ff1 fs3 fc0 sc0 ls0 ws0">nization<span class="_"> </span>for<span class="_"> </span>OFDM<span class="_"> </span>in<span class="_"> </span>recent<span class="_"> </span>years.<span class="_"> </span>Moose<span class="_"> </span>gives<span class="_"> </span>the<span class="_"> </span>maximum</div><div class="t m0 xb h6 y3c ff1 fs3 fc0 sc0 ls0 ws0">likelihood<span class="_ _14"> </span>estimator<span class="_ _7"> </span>for<span class="_ _7"> </span>the<span class="_ _7"> </span>carrier<span class="_ _14"> </span>frequency<span class="_ _7"> </span>offset<span class="_ _14"> </span>which<span class="_ _7"> </span>is</div><div class="t m0 xb h6 y3d ff1 fs3 fc0 sc0 ls0 ws0">calculated<span class="_ _14"> </span>in<span class="_ _7"> </span>the<span class="_ _7"> </span>frequency<span class="_ _7"> </span>domain<span class="_ _7"> </span>after<span class="_ _7"> </span>taking<span class="_ _7"> </span>the<span class="_ _14"> </span>FFT<span class="_ _7"> </span>[2].</div><div class="t m0 xb h6 y3e ff1 fs3 fc0 sc0 ls0 ws0">He<span class="_ _0"> </span>assumes<span class="_ _0"> </span>that<span class="_ _a"> </span>the<span class="_ _0"> </span>symbol<span class="_ _0"> </span>timing<span class="_ _a"> </span>is<span class="_ _0"> </span>known,<span class="_ _0"> </span>so<span class="_ _a"> </span>he<span class="_ _0"> </span>just<span class="_ _0"> </span>has<span class="_ _a"> </span>to</div><div class="t m0 xb h6 y3f ff1 fs3 fc0 sc0 ls0 ws0">&#64257;nd<span class="_ _14"> </span>the<span class="_ _7"> </span>carrier<span class="_ _14"> </span>frequency<span class="_ _7"> </span>offset.<span class="_ _14"> </span>The<span class="_ _7"> </span>limit<span class="_ _7"> </span>of<span class="_ _14"> </span>the<span class="_ _7"> </span>acquisition</div><div class="t m0 xb h6 y40 ff1 fs3 fc0 sc0 ls0 ws0">range<span class="_ _7"> </span>for<span class="_ _7"> </span>the<span class="_ _7"> </span>carrier<span class="_ _9"> </span>frequency<span class="_ _7"> </span>offset<span class="_ _14"> </span>is</div><div class="t m0 xd h6 y41 ff1 fs3 fc0 sc0 ls0 ws0">the<span class="_ _7"> </span>subcarrier</div><div class="t m0 xb h6 y42 ff1 fs3 fc0 sc0 ls0 ws0">spacing.<span class="_ _0"> </span>He<span class="_ _0"> </span>also<span class="_ _0"> </span>describes<span class="_ _a"> </span>how<span class="_"> </span>to<span class="_ _0"> </span>increase<span class="_ _a"> </span>this<span class="_ _0"> </span>range<span class="_ _0"> </span>by<span class="_ _0"> </span>using</div><div class="t m0 xb h6 y43 ff1 fs3 fc0 sc0 ls0 ws0">shorter<span class="_ _9"> </span>training<span class="_ _7"> </span>symbols<span class="_ _9"> </span>to<span class="_ _9"> </span>&#64257;nd<span class="_ _7"> </span>the<span class="_ _9"> </span>carrier<span class="_ _9"> </span>frequency<span class="_ _9"> </span>of<span class="_ _5"></span>fset.</div><div class="t m0 xb h6 y44 ff1 fs3 fc0 sc0 ls0 ws0">For<span class="_ _9"> </span>example<span class="_ _6"> </span>shortening<span class="_ _9"> </span>the<span class="_ _9"> </span>training<span class="_ _6"> </span>symbols<span class="_ _9"> </span>by<span class="_ _9"> </span>a<span class="_ _6"> </span>factor<span class="_ _9"> </span>of</div><div class="t m0 xb h6 y45 ff1 fs3 fc0 sc0 ls0 ws0">two<span class="_ _14"> </span>would<span class="_ _14"> </span>double<span class="_ _14"> </span>the<span class="_ _7"> </span>range<span class="_ _14"> </span>of<span class="_ _14"> </span>carrier<span class="_ _7"> </span>frequency<span class="_ _14"> </span>acquisition.</div><div class="t m0 xb h6 y46 ff1 fs3 fc0 sc0 ls0 ws0">This<span class="_ _c"> </span>approach<span class="_ _c"> </span>will<span class="_ _c"> </span>work<span class="_ _c"> </span>to<span class="_ _c"> </span>a<span class="_ _b"> </span>point,<span class="_ _c"> </span>but<span class="_ _c"> </span>the<span class="_ _c"> </span>estimates<span class="_ _c"> </span>get</div><div class="t m0 xb h6 y47 ff1 fs3 fc0 sc0 ls0 ws0">worse<span class="_ _c"> </span>as<span class="_ _b"> </span>the<span class="_ _c"> </span>symbols<span class="_ _b"> </span>get<span class="_ _c"> </span>shorter<span class="_ _b"> </span>because<span class="_ _c"> </span>there<span class="_ _b"> </span>are<span class="_ _c"> </span>fewer</div><div class="t m0 xb h6 y48 ff1 fs3 fc0 sc0 ls0 ws0">samples<span class="_ _0"> </span>over<span class="_ _a"> </span>which<span class="_ _0"> </span>to<span class="_ _a"> </span>average,<span class="_ _a"> </span>and<span class="_ _0"> </span>the<span class="_ _a"> </span>training<span class="_ _0"> </span>symbols<span class="_ _a"> </span>need</div><div class="t m0 xb h6 y49 ff1 fs3 fc0 sc0 ls0 ws0">to<span class="_ _14"> </span>be<span class="_ _7"> </span>kept<span class="_ _7"> </span>longer<span class="_ _7"> </span>than<span class="_ _14"> </span>the<span class="_ _7"> </span>guard<span class="_ _7"> </span>interval<span class="_ _7"> </span>so<span class="_ _7"> </span>that<span class="_ _14"> </span>the<span class="_ _7"> </span>channel</div><div class="t m0 xb h6 y4a ff1 fs3 fc0 sc0 ls0 ws0">impulse<span class="_ _9"> </span>response<span class="_ _9"> </span>does<span class="_ _6"> </span>not<span class="_ _9"> </span>cause<span class="_ _9"> </span>distortion<span class="_ _6"> </span>when<span class="_ _9"> </span>estimating</div><div class="t m0 xb h6 y4b ff1 fs3 fc0 sc0 ls0 ws0">the<span class="_ _9"> </span>frequency<span class="_ _6"> </span>offset.</div><div class="t m0 xc h6 y4c ff1 fs3 fc0 sc0 ls0 ws0">Nogami<span class="_ _7"> </span>and<span class="_ _7"> </span>Nagashima<span class="_ _7"> </span>[4]<span class="_ _7"> </span>present<span class="_ _7"> </span>algorithms<span class="_ _9"> </span>to<span class="_ _7"> </span>&#64257;nd<span class="_ _7"> </span>the</div><div class="t m0 xb h6 y4d ff1 fs3 fc0 sc0 ls0 ws0">carrier<span class="_ _6"> </span>frequency<span class="_ _13"> </span>offset<span class="_ _6"> </span>and<span class="_ _13"> </span>sampling<span class="_ _13"> </span>rate<span class="_ _13"> </span>offset.<span class="_ _6"> </span>They<span class="_ _13"> </span>use</div><div class="t m0 xb h6 y4e ff1 fs3 fc0 sc0 ls0 ws0">a<span class="_ _9"> </span>null<span class="_ _6"> </span>symbol<span class="_ _6"> </span>where<span class="_ _6"> </span>nothing<span class="_ _9"> </span>is<span class="_ _6"> </span>transmitted<span class="_ _6"> </span>for<span class="_ _6"> </span>one<span class="_ _9"> </span>symbol</div><div class="t m0 xb h6 y4f ff1 fs3 fc0 sc0 ls0 ws0">period<span class="_ _14"> </span>so<span class="_ _14"> </span>that<span class="_ _7"> </span>the<span class="_ _14"> </span>drop<span class="_ _7"> </span>in<span class="_ _14"> </span>received<span class="_ _14"> </span>power<span class="_ _7"> </span>can<span class="_ _14"> </span>be<span class="_ _7"> </span>detected<span class="_ _14"> </span>to</div><div class="t m0 xb h6 y50 ff1 fs3 fc0 sc0 ls0 ws0">&#64257;nd<span class="_ _14"> </span>the<span class="_ _14"> </span>beginning<span class="_ _7"> </span>of<span class="_ _14"> </span>the<span class="_ _7"> </span>frame.<span class="_ _14"> </span>The<span class="_ _7"> </span>carrier<span class="_ _14"> </span>frequency<span class="_ _7"> </span>offset</div><div class="t m0 xb h6 y51 ff1 fs3 fc0 sc0 ls0 ws0">is<span class="_ _9"> </span>found<span class="_ _6"> </span>in<span class="_ _6"> </span>the<span class="_ _9"> </span>frequency<span class="_ _6"> </span>domain<span class="_ _9"> </span>after<span class="_ _6"> </span>applying<span class="_ _9"> </span>a<span class="_ _6"> </span>Hanning</div><div class="t m0 xb h6 y52 ff1 fs3 fc0 sc0 ls0 ws0">window<span class="_ _e"> </span>and<span class="_ _14"> </span>taking<span class="_ _14"> </span>the<span class="_ _e"> </span>FFT.<span class="_ _14"> </span>The<span class="_ _14"> </span>null<span class="_ _e"> </span>symbol<span class="_ _14"> </span>is<span class="_ _14"> </span>also<span class="_ _e"> </span>used<span class="_ _14"> </span>in</div><div class="t m0 xb h6 y53 ff1 fs3 fc0 sc0 ls0 ws0">[11].<span class="_ _0"> </span>This<span class="_ _0"> </span>extra<span class="_ _0"> </span>overhead<span class="_ _a"> </span>of<span class="_"> </span>using<span class="_ _0"> </span>a<span class="_ _a"> </span>null<span class="_ _0"> </span>symbol<span class="_ _0"> </span>is<span class="_ _0"> </span>avoided<span class="_ _0"> </span>by</div><div class="t m0 xb h6 y54 ff1 fs3 fc0 sc0 ls0 ws0">using<span class="_"> </span>the<span class="_"> </span>technique<span class="_"> </span>described<span class="_ _0"> </span>in<span class="_"> </span>this<span class="_ _0"> </span>paper.<span class="_"> </span>If<span class="_"> </span>instead<span class="_ _0"> </span>of<span class="_"> </span>a<span class="_ _0"> </span>con-</div><div class="t m0 xb h6 y55 ff1 fs3 fc0 sc0 ls0 ws0">tinuous<span class="_ _e"> </span>transmission<span class="_ _a"> </span>mode,<span class="_ _e"> </span>a<span class="_ _e"> </span>burst<span class="_ _e"> </span>mode<span class="_ _e"> </span>is<span class="_ _a"> </span>used,<span class="_ _e"> </span>it<span class="_ _e"> </span>would<span class="_ _e"> </span>be</div><div class="t m0 xb h6 y56 ff1 fs3 fc0 sc0 ls0 ws0">dif&#64257;cult<span class="_ _d"> </span>to<span class="_"> </span>use<span class="_ _d"> </span>a<span class="_"> </span>null<span class="_ _d"> </span>symbol<span class="_"> </span>since<span class="_ _d"> </span>there<span class="_"> </span>would<span class="_ _d"> </span>be<span class="_"> </span>no<span class="_ _d"> </span>difference</div><div class="t m0 xb h6 y57 ff1 fs3 fc0 sc0 ls0 ws0">between<span class="_ _e"> </span>the<span class="_ _e"> </span>null<span class="_ _e"> </span>symbol<span class="_ _e"> </span>and<span class="_ _e"> </span>the<span class="_ _e"> </span>idle<span class="_ _e"> </span>period<span class="_ _e"> </span>between<span class="_ _e"> </span>bursts.</div><div class="t m0 xc h6 y58 ff1 fs3 fc0 sc0 ls0 ws0">V<span class="_ _1"></span>an<span class="_ _e"> </span>de<span class="_ _e"> </span>Beek<span class="_ _14"> </span>[3]<span class="_ _14"> </span>describes<span class="_ _e"> </span>a<span class="_ _14"> </span>method<span class="_ _14"> </span>of<span class="_ _e"> </span>using<span class="_ _14"> </span>a<span class="_ _14"> </span>correlation</div><div class="t m0 xb h6 y59 ff1 fs3 fc0 sc0 ls0 ws0">with<span class="_"> </span>the<span class="_ _a"> </span>cyclic<span class="_"> </span>pre&#64257;x<span class="_ _0"> </span>to<span class="_ _0"> </span>&#64257;nd<span class="_ _0"> </span>the<span class="_ _0"> </span>symbol<span class="_ _0"> </span>timing.<span class="_ _0"> </span>If<span class="_ _0"> </span>this<span class="_ _0"> </span>method</div><div class="t m0 xb h6 y5a ff1 fs3 fc0 sc0 ls0 ws0">were<span class="_ _14"> </span>used<span class="_ _7"> </span>to<span class="_ _7"> </span>&#64257;nd<span class="_ _14"> </span>the<span class="_ _7"> </span>symbol<span class="_ _14"> </span>timing,<span class="_ _7"> </span>while<span class="_ _7"> </span>using<span class="_ _7"> </span>one<span class="_ _14"> </span>of<span class="_ _7"> </span>the</div><div class="t m0 xb h6 y5b ff1 fs3 fc0 sc0 ls0 ws0">previous<span class="_ _6"> </span>methods<span class="_ _6"> </span>to<span class="_ _6"> </span>&#64257;nd<span class="_ _6"> </span>the<span class="_ _6"> </span>carrier<span class="_ _13"> </span>frequency<span class="_ _6"> </span>offset,<span class="_ _6"> </span>there</div><div class="t m0 xb h6 y5c ff1 fs3 fc0 sc0 ls0 ws0">would<span class="_ _7"> </span>still<span class="_ _7"> </span>be<span class="_ _7"> </span>a<span class="_ _7"> </span>problem<span class="_ _7"> </span>of<span class="_ _9"> </span>&#64257;nding<span class="_ _14"> </span>the<span class="_ _7"> </span>start<span class="_ _9"> </span>of<span class="_ _14"> </span>the<span class="_ _9"> </span>frame<span class="_ _14"> </span>to</div><div class="t m0 xb h6 y5d ff1 fs3 fc0 sc0 ls0 ws0">know<span class="_ _14"> </span>where<span class="_ _7"> </span>the<span class="_ _14"> </span>training<span class="_ _7"> </span>symbols<span class="_ _14"> </span>are<span class="_ _7"> </span>located.</div><div class="t m0 xc h6 y5e ff1 fs3 fc0 sc0 ls0 ws0">Classen<span class="_ _9"> </span>introduces<span class="_ _9"> </span>a<span class="_ _6"> </span>method<span class="_ _9"> </span>which<span class="_ _6"> </span>jointly<span class="_ _9"> </span>&#64257;nds<span class="_ _9"> </span>both<span class="_ _9"> </span>the</div><div class="t m0 xb h6 y5f ff1 fs3 fc0 sc0 ls0 ws0">symbol<span class="_ _9"> </span>timing<span class="_ _9"> </span>and<span class="_ _9"> </span>carrier<span class="_ _6"> </span>frequency<span class="_ _9"> </span>offset<span class="_ _9"> </span>[5].<span class="_ _9"> </span>However,<span class="_ _9"> </span>it</div><div class="t m0 xb h6 y60 ff1 fs3 fc0 sc0 ls0 ws0">is<span class="_ _9"> </span>very<span class="_ _9"> </span>computationally<span class="_ _9"> </span>complex<span class="_ _9"> </span>because<span class="_ _6"> </span>it<span class="_ _9"> </span>uses<span class="_ _9"> </span>a<span class="_ _9"> </span>trial<span class="_ _6"> </span>and</div><div class="t m0 xb h6 y61 ff1 fs3 fc0 sc0 ls0 ws0">error<span class="_ _9"> </span>method<span class="_ _6"> </span>where<span class="_ _6"> </span>the<span class="_ _6"> </span>carrier<span class="_ _6"> </span>frequency<span class="_ _9"> </span>is<span class="_ _6"> </span>incremented<span class="_ _6"> </span>in</div><div class="t m0 xb h6 y62 ff1 fs3 fc0 sc0 ls0 ws0">small<span class="_ _14"> </span>steps<span class="_ _14"> </span>over<span class="_ _14"> </span>the<span class="_ _14"> </span>entire<span class="_ _7"> </span>acquisition<span class="_ _14"> </span>range<span class="_ _14"> </span>until<span class="_ _14"> </span>the<span class="_ _7"> </span>correct</div><div class="t m0 xb h6 y63 ff1 fs3 fc0 sc0 ls0 ws0">carrier<span class="_"> </span>frequency<span class="_ _d"> </span>is<span class="_"> </span>found.<span class="_ _d"> </span>It<span class="_"> </span>is<span class="_"> </span>impractical<span class="_ _d"> </span>to<span class="_"> </span>do<span class="_ _d"> </span>the<span class="_"> </span>exhaustive</div><div class="t m0 xb h6 y64 ff1 fs3 fc0 sc0 ls0 ws0">search<span class="_ _a"> </span>and<span class="_ _e"> </span>go<span class="_ _e"> </span>through<span class="_ _e"> </span>a<span class="_ _a"> </span>large<span class="_ _e"> </span>amount<span class="_ _a"> </span>of<span class="_ _e"> </span>computation<span class="_ _e"> </span>at<span class="_ _a"> </span>each</div><div class="t m0 xb h6 y65 ff1 fs3 fc0 sc0 ls0 ws0">possible<span class="_ _7"> </span>carrier<span class="_ _9"> </span>frequency<span class="_ _9"> </span>of<span class="_ _5"></span>fset.</div><div class="t m0 xc h6 y66 ff1 fs3 fc0 sc0 ls0 ws0">This<span class="_ _15"> </span>paper<span class="_ _15"> </span>introduces<span class="_ _15"> </span>some<span class="_ _15"> </span>modi&#64257;cations<span class="_ _15"> </span>of<span class="_ _15"> </span>Classen&#8217;s</div><div class="t m0 xb h6 y67 ff1 fs3 fc0 sc0 ls0 ws0">method<span class="_"> </span>which<span class="_"> </span>both<span class="_"> </span>greatly<span class="_"> </span>simplify<span class="_"> </span>the<span class="_"> </span>computation<span class="_"> </span>necessary</div><div class="t m0 xb h6 y68 ff1 fs3 fc0 sc0 ls0 ws0">for<span class="_ _7"> </span>synchronization<span class="_ _9"> </span>and<span class="_ _9"> </span>extend<span class="_ _9"> </span>the<span class="_ _9"> </span>range<span class="_ _7"> </span>for<span class="_ _9"> </span>the<span class="_ _9"> </span>acquisition</div><div class="t m0 xe h9 y69 ff1 fs5 fc0 sc0 ls0 ws0">0090&#8211;6778/97$10.00<span class="_ _14"> </span><span class="ff5">&#63721;<span class="_ _14"> </span></span>1997<span class="_ _14"> </span>IEEE</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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