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  • 2017-12-28 02:20
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Performance analysis for MIMO systems using zero forcing detector over fading channels
MIMO.rar
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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://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/6255768247503a0a93dc714a/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/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://static.pudn.com/prod/directory_preview_static/6255768247503a0a93dc714a/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Performance<span class="_ _0"> </span>analysis<span class="_ _0"> </span>for<span class="_ _0"> </span>MIMO<span class="_ _0"> </span>systems<span class="_ _0"> </span>using<span class="_ _0"> </span>zero</div><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls1 ws0">forcing<span class="_ _0"> </span>detector<span class="_ _0"> </span>over<span class="_ _0"> </span>fading<span class="_ _0"> </span>channels</div><div class="t m0 x1 h3 y3 ff2 fs1 fc0 sc0 ls2 ws0">R.<span class="_ _1"> </span>Xu<span class="_ _1"> </span>and<span class="_ _1"> </span>F.C.M.<span class="_ _1"> </span>Lau</div><div class="t m0 x2 h4 y4 ff3 fs1 fc0 sc0 ls3 ws0">Abstract:<span class="_ _2"> </span><span class="ff4 ls4">In<span class="_ _3"> </span>the<span class="_ _3"> </span>paper,<span class="_ _3"> </span>the<span class="_ _3"> </span>performance<span class="_ _3"> </span>of<span class="_ _3"> </span>multiple-input-multiple-output<span class="_ _3"> </span>(MIMO)<span class="_ _3"> </span>systems<span class="_ _3"> </span>using</span></div><div class="t m0 x2 h4 y5 ff4 fs1 fc0 sc0 ls5 ws0">a<span class="_ _1"> </span>zero<span class="_ _1"> </span>forcing<span class="_ _1"> </span>detector<span class="_ _1"> </span>is<span class="_ _1"> </span>studied<span class="_ _1"> </span>over<span class="_ _1"> </span>Rayleigh<span class="_ _1"> </span>and<span class="_ _1"> </span>Rice<span class="_ _1"> </span>fading<span class="_ _1"> </span>channels.<span class="_ _1"> </span>Approximation<span class="_ _1"> </span>to<span class="_ _1"> </span>the</div><div class="t m0 x2 h4 y6 ff4 fs1 fc0 sc0 ls4 ws0">distribution<span class="_ _1"> </span>of<span class="_ _4"> </span>non-central<span class="_ _1"> </span>complex<span class="_ _4"> </span>Wishart<span class="_ _4"> </span>dist<span class="ls6">ribution<span class="_ _1"> </span>is<span class="_ _4"> </span>used<span class="_ _1"> </span>to<span class="_ _4"> </span>derive<span class="_ _1"> </span>the<span class="_ _4"> </span>distribution<span class="_ _1"> </span>of<span class="_ _4"> </span>the</span></div><div class="t m0 x2 h4 y7 ff4 fs1 fc0 sc0 ls6 ws0">post-detection<span class="_ _5"> </span>signal-to-noise<span class="_ _5"> </span>(SNR)<span class="_ _5"> </span>ratio.<span class="_ _5"> </span>A<span class="_ _5"> </span>clos<span class="ls4">ed-form<span class="_ _5"> </span>expression<span class="_ _5"> </span>of<span class="_ _5"> </span>bit<span class="_ _5"> </span>error<span class="_ _5"> </span>rate<span class="_ _5"> </span>is<span class="_ _5"> </span>obtained<span class="_ _5"> </span>in</span></div><div class="t m0 x2 h4 y8 ff4 fs1 fc0 sc0 ls6 ws0">terms<span class="_ _5"> </span>of<span class="_ _5"> </span>t<span class="_"> </span>he<span class="_ _5"> </span>hypergeometric<span class="_ _5"> </span>and<span class="_ _6"> </span>Gamma<span class="_ _6"> </span>functions.<span class="_ _5"> </span>The<span class="_ _6"> </span>performance<span class="_ _5"> </span>of<span class="_ _5"> </span>MIMO<span class="_ _6"> </span>s<span class="_ _7"></span>ystems<span class="_ _6"> </span>under<span class="_ _5"> </span>the</div><div class="t m0 x2 h4 y9 ff4 fs1 fc0 sc0 ls6 ws0">scenario<span class="_ _6"> </span>that<span class="_ _5"> </span>the<span class="_ _5"> </span>individual<span class="_ _5"> </span>sub-channels<span class="_ _6"> </span>are<span class="_ _5"> </span>corre<span class="ls7">lated<span class="_ _5"> </span>is<span class="_ _5"> </span>also<span class="_ _5"> </span>investigated.<span class="_ _5"> </span>It<span class="_ _5"> </span>is<span class="_ _5"> </span>shown<span class="_ _5"> </span>that,<span class="_ _5"> </span>for<span class="_ _5"> </span>the</span></div><div class="t m0 x2 h4 ya ff4 fs1 fc0 sc0 ls3 ws0">exponential<span class="_ _6"> </span>correlation<span class="_ _5"> </span>channel<span class="_ _5"> </span>model,<span class="_ _5"> </span>an<span class="_ _5"> </span>increas<span class="ls2">e<span class="_ _5"> </span>in<span class="_ _5"> </span>channel<span class="_ _5"> </span>correlation<span class="_ _5"> </span>between<span class="_ _5"> </span>the<span class="_ _5"> </span>transmission</span></div><div class="t m0 x2 h4 yb ff4 fs1 fc0 sc0 ls8 ws0">paths<span class="_ _4"> </span>results<span class="_ _4"> </span>a<span class="_ _4"> </span>decrease<span class="_ _4"> </span>in<span class="_ _4"> </span>SNR<span class="_ _4"> </span>at<span class="_ _4"> </span>the<span class="_ _8"> </span>receiver.<span class="_ _4"> </span>It<span class="_ _4"> </span>is<span class="_ _4"> </span>concluded<span class="_ _4"> </span>that<span class="_ _4"> </span>with<span class="_ _4"> </span>the<span class="_ _4"> </span>same<span class="_ _4"> </span>SNR<span class="_ _4"> </span>at<span class="_ _8"> </span>the</div><div class="t m0 x2 h4 yc ff4 fs1 fc0 sc0 ls9 ws0">receiver,<span class="_ _6"> </span>the<span class="_ _5"> </span>performance<span class="_ _5"> </span>of<span class="_ _6"> </span>MIMO<span class="_ _5"> </span>systems<span class="_ _5"> </span>over<span class="_ _6"> </span><span class="lsa">a<span class="_ _5"> </span>Rice<span class="_ _6"> </span>f<span class="_ _7"></span>ading<span class="_ _6"> </span>channel<span class="_ _5"> </span>degrades<span class="_ _5"> </span>compared<span class="_ _5"> </span>to<span class="_ _6"> </span>that</span></div><div class="t m0 x2 h4 yd ff4 fs1 fc0 sc0 ls6 ws0">over<span class="_ _1"> </span>an<span class="_ _1"> </span>independent<span class="_ _1"> </span>and<span class="_ _1"> </span>identical<span class="_ _1"> </span>distri<span class="lsb">buted<span class="_ _1"> </span>(i.i.d.)<span class="_ _1"> </span>Raylei<span class="lsc">gh<span class="_ _1"> </span>fading<span class="_ _1"> </span>channel.</span></span></div><div class="t m0 x1 h5 ye ff1 fs1 fc0 sc0 lsd ws0">1<span class="_ _9"> </span>Introduction</div><div class="t m0 x1 h4 yf ff4 fs1 fc0 sc0 ls2 ws0">Multiple-input-multiple-out<span class="ls3">put<span class="_ _2"> </span>(<span class="_"> </span>MIMO)<span class="_ _2"> </span>systems<span class="_ _a"> </span>have<span class="_ _a"> </span>at-</span></div><div class="t m0 x1 h4 y10 ff4 fs1 fc0 sc0 ls3 ws0">tracted<span class="_ _6"> </span>a<span class="_ _5"> </span>lot<span class="_ _6"> </span>of<span class="_ _5"> </span>research<span class="_ _6"> </span>a<span class="_ _7"></span>ttention<span class="_ _6"> </span>in<span class="_ _5"> </span>the<span class="_ _6"> </span>past<span class="_ _5"> </span>decade<span class="_ _6"> </span>because</div><div class="t m0 x1 h4 y11 ff4 fs1 fc0 sc0 lse ws0">they<span class="_ _b"> </span>possess<span class="_ _b"> </span>the<span class="_ _b"> </span>ability<span class="_ _b"> </span>to<span class="_ _b"> </span>provide<span class="_ _b"> </span>high<span class="_ _b"> </span>speed<span class="_ _b"> </span>wireless</div><div class="t m0 x1 h4 y12 ff4 fs1 fc0 sc0 lse ws0">communications<span class="_ _4"> </span>over<span class="_ _4"> </span>a<span class="_ _4"> </span>multipath<span class="_ _4"> </span>environment<span class="_ _4"> </span><span class="fc1 lsf">[1,<span class="_ _4"> </span>2]</span><span class="ls10">.T<span class="_ _c"></span>h<span class="_ _c"></span>e</span></div><div class="t m0 x1 h4 y13 ff4 fs1 fc0 sc0 ls5 ws0">performance<span class="_ _4"> </span>of<span class="_ _4"> </span>the<span class="_ _4"> </span>MIMO<span class="_ _8"> </span>systems<span class="_ _4"> </span>is<span class="_ _4"> </span>very<span class="_ _8"> </span>much<span class="_ _4"> </span>affected</div><div class="t m0 x1 h4 y14 ff4 fs1 fc0 sc0 lsc ws0">by<span class="_ _5"> </span>the<span class="_ _3"> </span>characteristics<span class="_ _5"> </span>of<span class="_ _5"> </span>the<span class="_ _3"> </span>radio<span class="_ _5"> </span>propagation<span class="_ _3"> </span>channel.<span class="_ _5"> </span>For</div><div class="t m0 x1 h4 y15 ff4 fs1 fc0 sc0 ls6 ws0">example,<span class="_ _a"> </span>the<span class="_ _a"> </span>correlation<span class="_ _a"> </span>between<span class="_ _a"> </span>the<span class="_ _a"> </span>sub-channels<span class="_ _a"> </span>in<span class="_ _a"> </span>the</div><div class="t m0 x1 h4 y16 ff4 fs1 fc0 sc0 ls6 ws0">propagation<span class="_ _b"> </span>channel<span class="_ _b"> </span>limits<span class="_ _b"> </span>the<span class="_ _b"> </span>capacity<span class="_ _b"> </span>of<span class="_ _b"> </span>the<span class="_ _b"> </span>MIMO</div><div class="t m0 x1 h4 y17 ff4 fs1 fc0 sc0 ls11 ws0">architecture.<span class="_ _1"> </span>In<span class="_ _1"> </span><span class="fc1 ls12">[3<span class="_"> </span>]</span><span class="ls6">,<span class="_ _3"> </span>the<span class="_ _1"> </span>effect<span class="_ _3"> </span>of<span class="_ _1"> </span>a<span class="_ _3"> </span>fading<span class="_ _3"> </span>correlation<span class="_ _1"> </span>on<span class="_ _3"> </span>the</span></div><div class="t m0 x1 h4 y18 ff4 fs1 fc0 sc0 ls13 ws0">capacity<span class="_ _5"> </span>of<span class="_ _3"> </span>the<span class="_ _5"> </span>MIMO<span class="_ _5"> </span>architecture<span class="_ _3"> </span>has<span class="_ _5"> </span>been<span class="_ _5"> </span>investigated<span class="_ _5"> </span>in</div><div class="t m0 x1 h4 y19 ff4 fs1 fc0 sc0 lse ws0">detail<span class="_ _a"> </span>based<span class="_ _a"> </span>on<span class="_ _a"> </span>an<span class="_ _a"> </span>exponential<span class="_ _a"> </span>correlation<span class="_ _8"> </span>matrix.<span class="_ _a"> </span>It<span class="_ _a"> </span>has</div><div class="t m0 x1 h4 y1a ff4 fs1 fc0 sc0 lsc ws0">been<span class="_ _8"> </span>shown<span class="_ _a"> </span>that<span class="_ _4"> </span>a<span class="_ _7"></span>n<span class="_ _8"> </span>increase<span class="_ _a"> </span>i<span class="ls3">n<span class="_ _8"> </span>the<span class="_ _8"> </span>correlation<span class="_ _8"> </span>will<span class="_ _a"> </span>result</span></div><div class="t m0 x1 h4 y1b ff4 fs1 fc0 sc0 ls14 ws0">in<span class="_ _b"> </span>a<span class="_ _d"> </span>decrease<span class="_ _d"> </span>in<span class="_ _b"> </span>capacity.<span class="_ _d"> </span>In<span class="_ _b"> </span>the<span class="_ _b"> </span>worst<span class="_ _d"> </span>case<span class="_ _b"> </span>when<span class="_ _d"> </span>the</div><div class="t m0 x1 h4 y1c ff4 fs1 fc0 sc0 ls6 ws0">correlation<span class="_ _3"> </span>coef&#64257;cient<span class="_ _3"> </span>equals<span class="_ _3"> </span>to<span class="_ _1"> </span>unity,<span class="_ _3"> </span>no<span class="_ _3"> </span>advantage<span class="_ _3"> </span>will<span class="_ _1"> </span>be</div><div class="t m0 x1 h4 y1d ff4 fs1 fc0 sc0 ls6 ws0">provided<span class="_ _0"> </span>by<span class="_ _0"> </span>the<span class="_ _0"> </span>MIMO<span class="_ _0"> </span>architecture.<span class="_ _0"> </span>The<span class="_ _0"> </span>exponential</div><div class="t m0 x1 h4 y1e ff4 fs1 fc0 sc0 ls9 ws0">correlation<span class="_ _d"> </span>matrix,<span class="_ _b"> </span>which<span class="_ _d"> </span>has<span class="_ _b"> </span>been<span class="_ _d"> </span>successfully<span class="_ _d"> </span>used<span class="_ _b"> </span>in</div><div class="t m0 x1 h4 y1f ff4 fs1 fc0 sc0 ls5 ws0">many<span class="_ _1"> </span>communication<span class="_ _1"> </span>problem<span class="ls15">s,<span class="_ _4"> </span>will<span class="_ _1"> </span>be<span class="_ _1"> </span>used<span class="_ _1"> </span>to<span class="_ _1"> </span>model<span class="_ _4"> </span>the</span></div><div class="t m0 x1 h4 y20 ff4 fs1 fc0 sc0 ls3 ws0">correlation<span class="_ _e"> </span>between<span class="_ _e"> </span>sub-<span class="ls6">channels<span class="_ _e"> </span>in<span class="_ _e"> </span>this<span class="_ _e"> </span>paper.<span class="_ _e"> </span>An</span></div><div class="t m0 x1 h4 y21 ff4 fs1 fc0 sc0 ls3 ws0">analytical<span class="_ _1"> </span>formula<span class="_ _1"> </span>will<span class="_ _1"> </span>then<span class="_ _3"> </span>be<span class="_ _1"> </span>derived<span class="_ _1"> </span>for<span class="_ _1"> </span>the<span class="_ _1"> </span>degradation</div><div class="t m0 x1 h4 y22 ff4 fs1 fc0 sc0 ls2 ws0">of<span class="_ _2"> </span>signal-to-noise<span class="_ _d"> </span>(SNR)<span class="_ _2"> </span>ratio<span class="_ _2"> </span>based<span class="_ _d"> </span>on<span class="_ _2"> </span>the<span class="_ _2"> </span>exponential</div><div class="t m0 x1 h4 y23 ff4 fs1 fc0 sc0 lse ws0">correlation<span class="_ _1"> </span>coef&#64257;cients.<span class="_ _4"> </span>Finally,<span class="_ _1"> </span>we<span class="_ _4"> </span>will<span class="_ _1"> </span>show<span class="_ _4"> </span>that,<span class="_ _1"> </span>for<span class="_ _4"> </span>this</div><div class="t m0 x1 h4 y24 ff4 fs1 fc0 sc0 lse ws0">model,<span class="_ _3"> </span>an<span class="_ _3"> </span>increase<span class="_ _3"> </span>in<span class="_ _3"> </span>correlation<span class="_ _5"> </span>is<span class="_ _3"> </span>equivalent<span class="_ _3"> </span>to<span class="_ _3"> </span>a<span class="_ _3"> </span>decrease</div><div class="t m0 x1 h4 y25 ff4 fs1 fc0 sc0 lse ws0">in<span class="_ _1"> </span>the<span class="_ _1"> </span>SNR<span class="_ _1"> </span>under<span class="_ _1"> </span>some<span class="_ _1"> </span>realistic<span class="_ _1"> </span>conditions.</div><div class="t m0 x3 h4 y26 ff4 fs1 fc0 sc0 lse ws0">Although<span class="_ _d"> </span>Rayleigh<span class="_ _d"> </span>and<span class="_ _2"> </span>Rice<span class="_ _d"> </span>fading<span class="_ _d"> </span>channels<span class="_ _d"> </span>are<span class="_ _d"> </span>the</div><div class="t m0 x1 h4 y27 ff4 fs1 fc0 sc0 lsc ws0">most<span class="_ _a"> </span>popular<span class="_ _2"> </span>models<span class="_ _a"> </span>for<span class="_ _2"> </span>wireless<span class="_ _a"> </span>channels,<span class="_ _a"> </span>much<span class="_ _2"> </span>of<span class="_ _a"> </span>the</div><div class="t m0 x1 h4 y28 ff4 fs1 fc0 sc0 ls16 ws0">research<span class="_ _8"> </span>on<span class="_ _4"> </span>the<span class="_ _8"> </span>performance<span class="_ _8"> </span>of<span class="_ _8"> </span>MIMO<span class="_ _8"> </span>systems<span class="_ _4"> </span>has<span class="_ _8"> </span>been</div><div class="t m0 x1 h4 y29 ff4 fs1 fc0 sc0 ls17 ws0">f<span class="_ _f"></span>o<span class="_ _f"></span>c<span class="_ _f"></span>u<span class="_ _f"></span>s<span class="_ _f"></span>e<span class="_ _f"></span>do<span class="_ _f"></span>nR<span class="_ _f"></span>a<span class="_ _f"></span>y<span class="_ _10"></span>l<span class="_ _f"></span>e<span class="_ _10"></span>i<span class="_ _f"></span>g<span class="_ _f"></span>hf<span class="_ _f"></span>a<span class="_ _f"></span>d<span class="_ _f"></span>i<span class="_ _f"></span>n<span class="_ _f"></span>gc<span class="_ _f"></span>h<span class="_ _10"></span>a<span class="_ _f"></span>n<span class="_ _f"></span>n<span class="_ _f"></span>e<span class="_ _f"></span>l<span class="_ _f"></span>s<span class="fc1 ls18">[4&#8211;6]</span><span class="ls19">.O<span class="_ _10"></span>n<span class="_ _f"></span>eo<span class="_ _f"></span>ft<span class="_ _f"></span>h<span class="_ _f"></span>ef<span class="_ _10"></span>e<span class="_ _f"></span>w</span></div><div class="t m0 x1 h4 y2a ff4 fs1 fc0 sc0 ls6 ws0">MIMO<span class="_ _6"> </span>systems<span class="_ _5"> </span>that<span class="_ _6"> </span>has<span class="_ _6"> </span>been<span class="_ _6"> </span>evaluated<span class="_ _5"> </span>under<span class="_ _6"> </span>a<span class="_ _6"> </span>Rice<span class="_ _5"> </span>fading</div><div class="t m0 x1 h4 y2b ff4 fs1 fc0 sc0 ls8 ws0">channel<span class="_ _4"> </span>is<span class="_ _1"> </span>the<span class="_ _4"> </span>Alamouti<span class="_ _4"> </span>scheme<span class="_ _1"> </span><span class="fc1 lsf">[7,<span class="_ _4"> </span>8]</span><span class="ls1a">.I<span class="_ _10"></span>n<span class="fc1 lsf">[9]</span><span class="ls1b">,<span class="_ _4"> </span>the<span class="_ _4"> </span>bit<span class="_ _1"> </span>error</span></span></div><div class="t m0 x1 h4 y2c ff4 fs1 fc0 sc0 ls5 ws0">rate<span class="_ _b"> </span>(BER)<span class="_ _d"> </span>performance<span class="_ _b"> </span>of<span class="_ _d"> </span>MIMO<span class="_ _b"> </span>systems<span class="_ _b"> </span>using<span class="_ _d"> </span>zero</div><div class="t m0 x1 h4 y2d ff4 fs1 fc0 sc0 ls4 ws0">forcing<span class="_ _a"> </span>(ZF)<span class="_ _a"> </span>detectors<span class="_ _a"> </span>in<span class="_ _a"> </span>both<span class="_ _a"> </span>Rayleigh<span class="_ _a"> </span>and<span class="_ _a"> </span>Rice<span class="_ _2"> </span>fading</div><div class="t m0 x1 h4 y2e ff4 fs1 fc0 sc0 lse ws0">channels<span class="_ _5"> </span>was<span class="_ _5"> </span>evaluated<span class="_ _5"> </span>by<span class="_ _5"> </span>simul<span class="lsc">ations.<span class="_ _5"> </span>Results<span class="_ _5"> </span>showed<span class="_ _5"> </span>that</span></div><div class="t m0 x4 h4 y2f ff4 fs1 fc0 sc0 lse ws0">provided<span class="_ _8"> </span>that<span class="_ _a"> </span>the<span class="_ _4"> </span>signal<span class="_ _a"> </span>power<span class="_ _4"> </span>from<span class="_ _a"> </span>the<span class="_ _8"> </span>non-line-of-sight</div><div class="t m0 x4 h4 y30 ff4 fs1 fc0 sc0 ls2 ws0">components<span class="_ _b"> </span>remains<span class="_ _d"> </span>the<span class="_ _b"> </span>same,<span class="_ _b"> </span>the<span class="_ _b"> </span>performance<span class="_ _d"> </span>of<span class="_ _b"> </span>the</div><div class="t m0 x4 h4 y31 ff4 fs1 fc0 sc0 ls3 ws0">MIMO<span class="_ _2"> </span>system<span class="_ _2"> </span>in<span class="_ _2"> </span>Rayleigh<span class="_ _2"> </span>and<span class="_ _d"> </span>Rice<span class="_ _2"> </span>fading<span class="_ _2"> </span>channels<span class="_ _2"> </span>is</div><div class="t m0 x4 h4 y32 ff4 fs1 fc0 sc0 ls2 ws0">almost<span class="_ _8"> </span>the<span class="_ _4"> </span>same.<span class="_ _a"> </span>In<span class="_ _4"> </span>this<span class="_ _8"> </span>paper,<span class="_ _8"> </span>we<span class="_ _8"> </span>investigate<span class="_ _8"> </span>the<span class="_ _8"> </span>perfor-</div><div class="t m0 x4 h4 y33 ff4 fs1 fc0 sc0 ls16 ws0">mance<span class="_ _1"> </span>of<span class="_ _4"> </span>the<span class="_ _1"> </span>MIMO<span class="_ _1"> </span>systems<span class="_ _4"> </span><span class="fc1 ls6">[10]<span class="_ _1"> </span><span class="fc0">over<span class="_ _1"> </span>Rayleigh<span class="_ _4"> </span>and<span class="_ _1"> </span>Rice</span></span></div><div class="t m0 x4 h4 y34 ff4 fs1 fc0 sc0 ls1c ws0">fading<span class="_ _5"> </span>channels.<span class="_ _5"> </span>Ass<span class="_ _7"></span><span class="ls1b">uming<span class="_ _5"> </span>ZF<span class="_ _5"> </span>detectors<span class="_ _3"> </span><span class="fc1 ls6">[11]<span class="_ _5"> </span></span><span class="ls1d">are<span class="_ _5"> </span>used<span class="_ _5"> </span>at<span class="_ _5"> </span>the</span></span></div><div class="t m0 x4 h4 y35 ff4 fs1 fc0 sc0 ls4 ws0">receiver,<span class="_ _b"> </span>a<span class="_ _d"> </span>closed-form<span class="_ _b"> </span>expression<span class="_ _b"> </span>of<span class="_ _d"> </span>the<span class="_ _b"> </span>bit<span class="_ _b"> </span>error<span class="_ _d"> </span>rate</div><div class="t m0 x4 h4 y36 ff4 fs1 fc0 sc0 lse ws0">(BER)<span class="_ _11"> </span>is<span class="_ _11"> </span>derived<span class="_ _11"> </span>in<span class="_ _11"> </span>terms<span class="_ _11"> </span>of<span class="_ _11"> </span>the<span class="_ _11"> </span>hypergeometric<span class="_ _11"> </span>and</div><div class="t m0 x4 h4 y37 ff4 fs1 fc0 sc0 lse ws0">Gamma<span class="_ _d"> </span>functions.<span class="_ _2"> </span>The<span class="_ _d"> </span>performance<span class="_ _d"> </span>degradatio<span class="_"> </span>n<span class="_ _d"> </span>of<span class="_ _2"> </span>the</div><div class="t m0 x4 h4 y38 ff4 fs1 fc0 sc0 ls1c ws0">system<span class="_ _4"> </span>over<span class="_ _4"> </span>a<span class="_ _4"> </span>Rice<span class="_ _4"> </span>fading<span class="_ _8"> </span>channel<span class="_ _4"> </span>compared<span class="_ _4"> </span>to<span class="_ _4"> </span>that<span class="_ _4"> </span>over</div><div class="t m0 x4 h4 y39 ff4 fs1 fc0 sc0 ls5 ws0">an<span class="_ _2"> </span>independent<span class="_ _2"> </span>and<span class="_ _2"> </span>identical<span class="_ _2"> </span>di<span class="ls1e">stributed<span class="_ _a"> </span>(i.i.d.)<span class="_ _2"> </span>Rayleigh</span></div><div class="t m0 x4 h4 y3a ff4 fs1 fc0 sc0 ls2 ws0">fading<span class="_ _a"> </span>channel<span class="_ _a"> </span>is<span class="_ _a"> </span>also<span class="_ _a"> </span>evaluated<span class="_ _a"> </span>assuming<span class="_ _a"> </span>identical<span class="_ _a"> </span>SNR</div><div class="t m0 x4 h4 y3b ff4 fs1 fc0 sc0 ls2 ws0">at<span class="_ _1"> </span>the<span class="_ _1"> </span>receiver.</div><div class="t m0 x5 h4 y3c ff4 fs1 fc0 sc0 ls2 ws0">Before<span class="_ _1"> </span>proceeding<span class="_ _1"> </span>further,<span class="_ _1"> </span>we<span class="_ _4"> </span>&#64257;rst<span class="_ _1"> </span>describe<span class="_ _1"> </span>the<span class="_ _4"> </span>notation</div><div class="t m0 x4 h4 y3d ff4 fs1 fc0 sc0 lse ws0">used<span class="_ _3"> </span>in<span class="_ _3"> </span>this<span class="_ _3"> </span>paper.<span class="_ _3"> </span>All<span class="_ _5"> </span>vectors<span class="_ _3"> </span>and<span class="_ _3"> </span>matrices<span class="_ _3"> </span>are<span class="_ _3"> </span>in<span class="_ _3"> </span>boldface.</div><div class="t m0 x4 h6 y3e ff5 fs1 fc0 sc0 ls1f ws0">j<span class="ff6">x</span>j<span class="_ _1"> </span><span class="ff4 ls4">represents<span class="_ _3"> </span>the<span class="_ _1"> </span>norm<span class="_ _1"> </span>value<span class="_ _3"> </span>of<span class="_ _1"> </span>complex<span class="_ _1"> </span>number<span class="_ _1"> </span></span><span class="ff7">x<span class="_ _5"> </span><span class="ff4 ls8">and<span class="_ _1"> </span></span>x</span></div><div class="t m1 x6 h7 y3f ff4 fs2 fc0 sc0 ls1f ws0">*</div><div class="t m0 x4 h8 y40 ff4 fs1 fc0 sc0 ls3 ws0">represents<span class="_ _a"> </span>the<span class="_ _a"> </span>complex<span class="_ _2"> </span>conjugate<span class="_ _a"> </span>of<span class="_ _a"> </span><span class="ff7 ls1f">x<span class="_ _12"></span><span class="ff4">.<span class="_ _a"> </span><span class="ff8">I</span></span></span></div><div class="t m1 x7 h9 y41 ff7 fs2 fc0 sc0 ls1f ws0">m</div><div class="t m0 x8 h4 y40 ff4 fs1 fc0 sc0 lsf ws0">is<span class="_ _a"> </span>the<span class="_ _2"> </span>identity</div><div class="t m0 x4 h6 y42 ff4 fs1 fc0 sc0 ls20 ws0">matrix<span class="_ _8"> </span>of<span class="_ _a"> </span>size<span class="_ _a"> </span><span class="ff7 ls1f">m<span class="_ _13"></span><span class="ff5">&#58881;<span class="_ _14"></span></span>m<span class="ff4">.<span class="_ _4"> </span><span class="ff8">X</span></span></span></div><div class="t m1 x9 h9 y43 ff7 fs2 fc0 sc0 ls1f ws0">H</div><div class="t m0 xa h4 y44 ff4 fs1 fc0 sc0 ls21 ws0">denotes<span class="_ _a"> </span>the<span class="_ _8"> </span>complex<span class="_ _a"> </span>conjugate</div><div class="t m0 x4 h4 y45 ff4 fs1 fc0 sc0 ls2 ws0">transpose<span class="_ _5"> </span>of<span class="_ _3"> </span><span class="ff8 ls1f">X<span class="_ _6"> </span></span><span class="ls8">and<span class="_ _3"> </span><span class="ff8 ls1f">X</span></span></div><div class="t m1 xb h9 y46 ff7 fs2 fc0 sc0 ls1f ws0">T</div><div class="t m0 xc h4 y47 ff4 fs1 fc0 sc0 ls21 ws0">is<span class="_ _5"> </span>the<span class="_ _3"> </span>transpose<span class="_ _3"> </span>of<span class="_ _5"> </span><span class="ff8 ls1f">X</span><span class="ls22">.[<span class="_ _15"></span><span class="ff8 ls1f">X<span class="_ _12"></span><span class="ff4">]</span></span></span></div><div class="t m1 xd h9 y48 ff7 fs2 fc0 sc0 ls23 ws0">ij</div><div class="t m0 xe h4 y47 ff4 fs1 fc0 sc0 ls24 ws0">represents</div><div class="t m0 x4 h6 y49 ff4 fs1 fc0 sc0 ls25 ws0">the<span class="_ _4"> </span><span class="ff5 ls1f">&#240;<span class="ff6">i<span class="ff9">;<span class="_ _14"> </span></span>j</span>&#222;</span><span class="ls6">th<span class="_ _8"> </span>element<span class="_ _8"> </span>of<span class="_ _8"> </span><span class="ff8 ls1f">X<span class="_ _4"> </span></span><span class="ls5">while<span class="_ _8"> </span><span class="ff8 ls1f">X</span></span></span></div><div class="t m1 xf ha y4a ff5 fs2 fc0 sc0 ls1f ws0">&#58882;<span class="ff4">1</span></div><div class="t m0 x10 h4 y4b ff4 fs1 fc0 sc0 ls1b ws0">represents<span class="_ _4"> </span>the<span class="_ _8"> </span>inverse</div><div class="t m0 x4 h6 y4c ff4 fs1 fc0 sc0 lsf ws0">of<span class="_ _4"> </span>square<span class="_ _8"> </span>matrix<span class="_ _8"> </span><span class="ff8 ls1f">X<span class="_ _12"></span><span class="ff4 ls26">.E<span class="_ _c"></span>[<span class="_ _16"></span><span class="ff5 ls1f">&#58883;<span class="_ _14"></span><span class="ff4 ls2">]<span class="_ _4"> </span>is<span class="_ _8"> </span>the<span class="_ _4"> </span>expectation<span class="_ _8"> </span>operator.<span class="_ _4"> </span>The</span></span></span></span></div><div class="t m0 x4 h4 y4d ff4 fs1 fc0 sc0 ls8 ws0">operator<span class="_ _11"> </span>det<span class="_ _14"> </span>(<span class="ff8 ls1f">X<span class="_ _13"> </span></span><span class="ls4">)<span class="_ _11"> </span>stands<span class="_ _11"> </span>for<span class="_ _11"> </span>the<span class="_ _11"> </span>determinant<span class="_ _b"> </span>of<span class="_ _11"> </span>square</span></div><div class="t m0 x4 h4 y4e ff4 fs1 fc0 sc0 ls27 ws0">matrix<span class="_ _1"> </span><span class="ff8 ls1f">X<span class="_ _12"></span><span class="ff4">.</span></span></div><div class="t m0 x4 h5 y4f ff1 fs1 fc0 sc0 ls28 ws0">2<span class="_ _9"> </span>System<span class="_ _1"> </span>overview</div><div class="t m0 x4 h8 y50 ff4 fs1 fc0 sc0 ls13 ws0">We<span class="_ _4"> </span>consider<span class="_ _4"> </span>a<span class="_ _4"> </span>MIMO<span class="_ _4"> </span>systems<span class="_ _4"> </span>(<span class="ff7 ls1f">t<span class="_ _12"></span><span class="ff4">,<span class="_ _14"> </span><span class="ff7">r<span class="_ _12"></span><span class="ff4 ls29">)w<span class="_ _c"></span>h<span class="_ _c"></span>e<span class="_ _c"></span>r<span class="_ _c"></span>e<span class="ff7 ls1f">t<span class="_ _4"> </span></span><span class="ls2a">and<span class="_ _4"> </span><span class="ff7 ls1f">r<span class="_ _1"> </span></span><span class="lsc">denote</span></span></span></span></span></span></div><div class="t m0 x4 h4 y51 ff4 fs1 fc0 sc0 ls13 ws0">the<span class="_ _4"> </span>number<span class="_ _1"> </span>of<span class="_ _4"> </span>transmit<span class="_ _1"> </span>and<span class="_ _4"> </span>receive<span class="_ _4"> </span>antennas,<span class="_ _1"> </span>respectively.</div><div class="t m0 x4 hb y52 ff4 fs1 fc0 sc0 ls2b ws0">We<span class="_ _1"> </span>always<span class="_ _3"> </span>assume<span class="_ _1"> </span><span class="ff7 ls1f">r<span class="_ _13"> </span><span class="ffa">Z<span class="_ _14"> </span></span>t<span class="_ _12"></span><span class="ff4 ls2">.<span class="_ _1"> </span>The<span class="_ _3"> </span>incoming<span class="_ _1"> </span>data<span class="_ _1"> </span>stream<span class="_ _1"> </span>is<span class="_ _3"> </span>&#64257;rst</span></span></div><div class="t m0 x4 h8 y53 ff4 fs1 fc0 sc0 ls2c ws0">split<span class="_ _3"> </span>into<span class="_ _3"> </span><span class="ff7 ls1f">t<span class="_ _3"> </span></span><span class="ls6">data<span class="_ _3"> </span>sub-streams<span class="_ _3"> </span>with<span class="_ _3"> </span>the<span class="_ _3"> </span>same<span class="_ _1"> </span>symbol<span class="_ _3"> </span>rate<span class="_ _3"> </span>1/<span class="ff7 ls1f">T</span></span></div><div class="t m0 x4 h8 y54 ff4 fs1 fc0 sc0 ls1f ws0">(<span class="_ _12"></span><span class="ff7">T<span class="_ _3"> </span><span class="ff4 ls3">is<span class="_ _1"> </span>the<span class="_ _1"> </span>symbol<span class="_ _3"> </span>period),<span class="_ _1"> </span>which<span class="_ _1"> </span>are<span class="_ _1"> </span>independently<span class="_ _1"> </span>encoded</span></span></div><div class="t m0 x4 h4 y55 ff4 fs1 fc0 sc0 ls3 ws0">and<span class="_ _b"> </span>modulated.<span class="_ _b"> </span>We<span class="_ _d"> </span>assume<span class="_ _b"> </span>that<span class="_ _b"> </span>the<span class="_ _d"> </span>same<span class="_ _b"> </span>modulation</div><div class="t m0 x4 h8 y56 ff4 fs1 fc0 sc0 ls5 ws0">scheme<span class="_ _2"> </span><span class="ff7 ls1f">V<span class="_ _2"> </span></span><span class="ls2">is<span class="_ _2"> </span>used<span class="_ _d"> </span>for<span class="_ _2"> </span>each<span class="_ _2"> </span>data<span class="_ _d"> </span>s<span class="_"> </span>ub-stream<span class="_ _2"> </span>and<span class="_ _d"> </span>all<span class="_ _2"> </span>the</span></div><div class="t m0 x4 h8 y57 ff4 fs1 fc0 sc0 ls2d ws0">transmitters<span class="_ _d"> </span>(1<span class="_ _b"> </span>to<span class="_ _b"> </span><span class="ff7 ls1f">t<span class="_ _12"></span><span class="ff4 ls2e">)<span class="_ _b"> </span>are<span class="_ _b"> </span>operating<span class="_ _b"> </span>at<span class="_ _b"> </span>the<span class="_ _b"> </span>same<span class="_ _b"> </span>carrier</span></span></div><div class="t m0 x4 h4 y58 ff4 fs1 fc0 sc0 ls2e ws0">frequency.<span class="_ _1"> </span>Also,<span class="_ _1"> </span>data<span class="_ _4"> </span>transmi<span class="ls2f">ssion<span class="_ _1"> </span>is<span class="_ _4"> </span>organised<span class="_ _1"> </span>into<span class="_ _1"> </span>bursts</span></div><div class="t m0 x4 h8 y59 ff4 fs1 fc0 sc0 ls6 ws0">of<span class="_ _11"> </span><span class="ff7 ls1f">L<span class="_ _b"> </span></span><span class="lsc">symbols<span class="_ _11"> </span>and<span class="_ _b"> </span>the<span class="_ _11"> </span>modulated<span class="_ _11"> </span>signals<span class="_ _11"> </span>are<span class="_ _11"> </span>radiated</span></div><div class="t m0 x4 h4 y5a ff4 fs1 fc0 sc0 ls6 ws0">through<span class="_ _1"> </span>the<span class="_ _1"> </span>respective<span class="_ _1"> </span>antennas.</div><div class="t m0 x5 h4 y5b ff4 fs1 fc0 sc0 ls2e ws0">Consider<span class="_ _17"> </span>the<span class="_ _17"> </span>structure<span class="_ _17"> </span>of<span class="_ _17"> </span>the<span class="_ _17"> </span>equivalent<span class="_ _17"> </span>baseband</div><div class="t m0 x4 h4 y5c ff4 fs1 fc0 sc0 ls13 ws0">systems<span class="_ _18"> </span>of<span class="_ _18"> </span>a<span class="_ _18"> </span>single-user<span class="_ _18"> </span>link.<span class="_ _18"> </span>We<span class="_ _18"> </span>assume<span class="_ _18"> </span>th<span class="_"> </span>at<span class="_ _18"> </span>the</div><div class="t m0 x4 h4 y5d ff4 fs1 fc0 sc0 ls9 ws0">transmitted<span class="_ _2"> </span>signals<span class="_ _2"> </span><span class="ls1c">encounter<span class="_ _2"> </span>&#64258;at<span class="_ _2"> </span>fading<span class="_ _2"> </span>before<span class="_ _2"> </span>reaching</span></div><div class="t m0 x4 h4 y5e ff4 fs1 fc0 sc0 ls2 ws0">the<span class="_ _1"> </span>receiving<span class="_ _3"> </span>antennas.<span class="_ _1"> </span>Denote<span class="_ _1"> </span>the<span class="_ _3"> </span>impulse<span class="_ _1"> </span>response<span class="_ _1"> </span>of<span class="_ _1"> </span>the</div><div class="t m0 x4 h6 y5f ff4 fs1 fc0 sc0 ls1d ws0">channel<span class="_ _5"> </span>between<span class="_ _3"> </span>the<span class="_ _3"> </span><span class="ff7 ls1f">j<span class="_ _13"> </span></span><span class="ls30">th<span class="_ _3"> </span><span class="ff5 ls1f">&#240;<span class="_ _14"></span><span class="ff6">j<span class="_ _a"> </span></span>&#188;<span class="_ _a"> </span><span class="ff4">1<span class="ff9">;<span class="_ _14"> </span></span>2<span class="ff9">;<span class="_ _14"> </span><span class="ffb ls31">...<span class="_ _7"></span></span>;<span class="_ _14"> </span><span class="ff6">t</span></span></span>&#222;<span class="_ _3"> </span></span><span class="ls3">transmit<span class="_ _3"> </span>antenna</span></span></div><div class="t m0 x1 hc y60 ff4 fs3 fc0 sc0 ls32 ws0">E-mail:<span class="_ _6"> </span>xurt@eie.polyu.edu.hk</div><div class="t m0 x1 hc y61 ff4 fs3 fc0 sc0 ls33 ws0">The<span class="_ _b"> </span>authors<span class="_ _d"> </span>are<span class="_ _b"> </span>with<span class="_ _b"> </span>the<span class="_ _d"> </span>Department<span class="_ _b"> </span>of<span class="_ _d"> </span>Electronic<span class="_ _b"> </span>and<span class="_ _b"> </span>Information</div><div class="t m0 x1 hc y62 ff4 fs3 fc0 sc0 ls34 ws0">Engineering,<span class="_ _6"> </span>The<span class="_ _5"> </span>Hong<span class="_ _5"> </span>Kong<span class="_ _5"> </span>Polytechnic<span class="_ _6"> </span>University,<span class="_ _5"> </span>Hong<span class="_ _5"> </span>Kong,<span class="_ _5"> </span>China</div><div class="t m0 x1 hc y63 ffc fs3 fc0 sc0 ls1f ws0">r<span class="_ _6"> </span><span class="ff4 ls35">IEE,<span class="_ _5"> </span>2006</span></div><div class="t m0 x1 hd y64 ff7 fs3 fc0 sc0 ls36 ws0">IEE<span class="_ _6"> </span>Proceedings<span class="_ _5"> </span><span class="ff4 ls37">online<span class="_ _5"> </span>no.<span class="_ _5"> </span>20045281</span></div><div class="t m0 x1 hc y65 ff4 fs3 fc0 sc0 ls35 ws0">doi:10.1049/ip-com:20045281</div><div class="t m0 x1 hc y66 ff4 fs3 fc0 sc0 ls37 ws0">Paper<span class="_ _14"> </span>&#64257;rst<span class="_ _14"> </span>recei<span class="_"> </span>ved<span class="_ _14"> </span>6th<span class="_ _14"> </span>November<span class="_ _14"> </span>2004<span class="_ _14"> </span>and<span class="_ _14"> </span>in<span class="_ _19"> </span>&#64257;nal<span class="_ _14"> </span>revise<span class="_"> </span>d<span class="_ _14"> </span>form<span class="_ _14"> </span>28th<span class="_ _14"> </span>April<span class="_ _14"> </span>2005</div><div class="t m0 x1 he y67 ff4 fs4 fc0 sc0 ls38 ws0">74<span class="_ _1a"> </span><span class="ff7 fs3 ls37">IEE<span class="_ _5"> </span>Proc.-Commun.,<span class="_ _6"> </span>Vol.<span class="_ _5"> </span>153,<span class="_ _5"> </span>No.<span class="_ _5"> </span>1,<span class="_ _5"> </span>February<span class="_ _6"> </span>2006</span></div><div class="d m2"></div><div class="d m2"></div><div class="d m2"></div><div class="d m2"></div><div class="d m2"></div><div class="d m2"></div><div class="d m2"></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div> </body> </html>
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