<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/11532111/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/11532111/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Published<span class="_ _0"> </span>in<span class="_ _0"> </span>IET<span class="_ _0"> </span>Communications</div><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">Received<span class="_ _0"> </span>on<span class="_ _0"> </span>20th<span class="_ _0"> </span>February<span class="_ _0"> </span>2008</div><div class="t m0 x1 h2 y3 ff1 fs0 fc0 sc0 ls0 ws0">Revised<span class="_ _0"> </span>on<span class="_ _0"> </span>2nd<span class="_ _0"> </span>June<span class="_ _0"> </span>2008</div><div class="t m0 x1 h2 y4 ff1 fs0 fc0 sc0 ls0 ws0">doi:<span class="_ _1"> </span>10.1049/iet<span class="_ _2"></span>-com:20080110</div><div class="t m0 x2 h3 y5 ff1 fs1 fc0 sc0 ls0 ws0">ISSN<span class="_ _3"> </span>1751-8628</div><div class="t m0 x3 h4 y6 ff2 fs2 fc0 sc0 ls0 ws0">P<span class="_ _2"></span>erformance<span class="_ _4"> </span>of<span class="_ _4"> </span>zer<span class="_ _2"></span>o-f<span class="_ _2"></span>or<span class="_ _2"></span>cing<span class="_ _4"> </span>det<span class="_ _2"></span>ector<span class="_ _2"></span>s<span class="_ _4"> </span>over</div><div class="t m0 x3 h4 y7 ff2 fs2 fc0 sc0 ls1 ws0">MIMO<span class="_ _4"> </span>flat<span class="_ _2"></span>-correlat<span class="_ _2"></span>ed<span class="_ _4"> </span>Ricean<span class="_ _4"> </span>fading<span class="_ _4"> </span>channels</div><div class="t m0 x3 h5 y8 ff3 fs3 fc0 sc0 ls0 ws0">H.A.<span class="_ _5"> </span>Abou<span class="_ _5"> </span>Saleh<span class="_ _6"> </span>W<span class="_ _7"></span>.<span class="_ _5"> </span>Hamouda</div><div class="t m0 x3 h6 y9 ff3 fs1 fc0 sc0 ls0 ws0">Department<span class="_ _3"> </span>of<span class="_ _3"> </span>Electrical<span class="_ _3"> </span>and<span class="_ _3"> </span>Computer<span class="_ _3"> </span>Engineering,<span class="_ _3"> </span>Concordia<span class="_ _3"> </span>University<span class="_ _2"></span>,<span class="_ _3"> </span>Montre</div><div class="t m0 x4 h6 ya ff3 fs1 fc0 sc0 ls0 ws0">´</div><div class="t m0 x5 h6 y9 ff3 fs1 fc0 sc0 ls0 ws0">al,<span class="_ _3"> </span>Quebec,<span class="_ _3"> </span>Canada<span class="_ _3"> </span>H3G<span class="_ _3"> </span>1M8</div><div class="t m0 x3 h6 yb ff3 fs1 fc0 sc0 ls0 ws0">E-mail:<span class="_ _3"> </span>hamouda@ece.concordia.ca</div><div class="t m0 x3 h7 yc ff2 fs4 fc0 sc0 ls0 ws0">Ab<span class="_ _8"></span>strac<span class="_ _8"></span>t:<span class="_ _9"> </span><span class="ff1">Th<span class="_ _8"></span>e<span class="_ _9"> </span>bit<span class="_ _9"> </span>error<span class="_ _9"> </span>rate<span class="_ _9"> </span>(B<span class="_ _8"></span>ER<span class="_ _8"></span>)<span class="_ _9"> </span>perfor<span class="_ _8"></span>m<span class="_ _8"></span>an<span class="_ _8"></span>ce<span class="_ _9"> </span>of<span class="_ _9"> </span>the<span class="_ _9"> </span>zero-<span class="_ _8"></span>forc<span class="_ _8"></span>in<span class="_"> </span>g<span class="_ _9"> </span>(Z<span class="_ _8"></span>F)<span class="_ _9"> </span>rec<span class="_ _8"></span>ei<span class="_ _8"></span>ve<span class="_ _8"></span>r<span class="_ _a"> </span>ove<span class="_ _8"></span>r<span class="_ _a"> </span>t<span class="_ _8"></span>ran<span class="_ _8"></span>sm<span class="_ _8"></span>it-c<span class="_ _8"></span>or<span class="_ _8"></span>re<span class="_ _8"></span>la<span class="_ _8"></span>ted<span class="_ _a"> </span>fl<span class="_ _8"></span>a<span class="_"> </span>t</span></div><div class="t m0 x3 h7 yd ff1 fs4 fc0 sc0 ls0 ws0">Ricean<span class="_ _a"> </span>fading<span class="_ _a"> </span>channels<span class="_ _a"> </span>is<span class="_ _a"> </span>investigated.<span class="_ _a"> </span>In<span class="_ _a"> </span>particular<span class="_ _b"></span>,<span class="_ _a"> </span>f<span class="_ _2"></span>or<span class="_ _a"> </span>a<span class="_ _3"> </span>multi<span class="_ _8"></span>ple-inp<span class="_ _8"></span>ut<span class="_ _a"> </span>multiple-o<span class="_ _8"></span>utput<span class="_ _a"> </span>(MI<span class="_"> </span>MO)<span class="_ _a"> </span>ch<span class="_ _8"></span>annel<span class="_ _a"> </span>with</div><div class="t m0 x3 h7 ye ff3 fs4 fc0 sc0 ls0 ws0">M<span class="_ _a"> </span><span class="ff1">transmit<span class="_ _3"> </span>and<span class="_ _a"> </span></span>N<span class="_ _a"> </span><span class="ff1">receive<span class="_ _3"> </span>antennas,<span class="_ _a"> </span>an<span class="_ _a"> </span>approximation<span class="_ _a"> </span>f<span class="_ _2"></span>or<span class="_ _a"> </span>the<span class="_ _3"> </span>average<span class="_ _a"> </span>BER<span class="_ _3"> </span>of<span class="_ _a"> </span>each<span class="_ _a"> </span>substr<span class="_ _2"></span>eam<span class="_ _a"> </span>is<span class="_ _3"> </span>der<span class="_ _8"></span>ived.<span class="_ _c"> </span>Then</span></div><div class="t m0 x3 h7 yf ff1 fs4 fc0 sc0 ls0 ws0">the<span class="_ _a"> </span>s<span class="_ _2"></span>ystem<span class="_ _3"> </span>performance<span class="_ _a"> </span>in<span class="_ _3"> </span>receive-correlated<span class="_ _a"> </span>flat<span class="_ _3"> </span>Ricean<span class="_ _a"> </span>fading<span class="_ _3"> </span>channels<span class="_ _a"> </span>is<span class="_ _a"> </span>addressed.<span class="_ _3"> </span>In<span class="_ _a"> </span>this<span class="_ _d"> </span>case,<span class="_ _d"> </span>it<span class="_ _d"> </span>is<span class="_ _d"> </span>shown</div><div class="t m0 x3 h7 y10 ff1 fs4 fc0 sc0 ls2 ws0">that<span class="_ _d"> </span>the<span class="_ _a"> </span>performance,<span class="_ _d"> </span>when<span class="_ _a"> </span><span class="ff3 ls0">N<span class="_ _c"> </span><span class="ff4">¼<span class="_ _3"> </span></span>M</span><span class="ls3">,<span class="_ _a"> </span>is<span class="_ _a"> </span>the<span class="_ _a"> </span>same<span class="_ _d"> </span>as<span class="_ _a"> </span>that<span class="_ _a"> </span>of<span class="_ _a"> </span>transmit<span class="_ _2"></span>-correlat<span class="_ _2"></span>ed<span class="_ _a"> </span>flat<span class="_ _a"> </span>Ricean<span class="_ _a"> </span>fading<span class="_ _d"> </span>channels.</span></div><div class="t m0 x3 h7 y11 ff1 fs4 fc0 sc0 ls4 ws0">A<span class="_ _a"> </span>closed-form<span class="_ _d"> </span>expression<span class="_ _a"> </span>for<span class="_ _d"> </span>the<span class="_ _a"> </span>optimum<span class="_ _9"> </span>transmit<span class="_ _d"> </span>correlation<span class="_ _a"> </span>coefficient,<span class="_ _a"> </span>which<span class="_ _a"> </span>achieves<span class="_ _a"> </span>the<span class="_ _9"> </span>maximum</div><div class="t m0 x3 h7 y12 ff1 fs4 fc0 sc0 ls5 ws0">capacity<span class="_ _e"> </span>(i.e.<span class="_ _e"> </span>uncorrelat<span class="_ _2"></span>ed<span class="_ _e"> </span>case),<span class="_ _e"> </span>is<span class="_ _e"> </span>also<span class="_ _e"> </span>derived.<span class="_ _e"> </span>As<span class="_ _e"> </span><span class="ls6">a<span class="_ _e"> </span>r<span class="_ _2"></span>esult,<span class="_ _e"> </span>a<span class="_ _e"> </span>significant<span class="_ _9"> </span>c<span class="_"> </span>apacity<span class="_ _e"> </span>g<span class="_ _2"></span>ain<span class="_ _e"> </span>is<span class="_ _e"> </span>achieved<span class="_ _e"> </span>by</span></div><div class="t m0 x3 h7 y13 ff1 fs4 fc0 sc0 ls7 ws0">exploiting<span class="_ _e"> </span>the<span class="_ _f"> </span>knowledge<span class="_ _f"> </span>of<span class="_ _f"> </span>the<span class="_ _e"> </span>Ricean<span class="_ _f"> </span>channel.<span class="_ _f"> </span>Extensive<span class="_ _10"> </span>simulations<span class="_ _10"> </span>are<span class="_ _f"> </span>present<span class="_ _2"></span>ed<span class="_ _10"> </span>to<span class="_ _f"> </span>validate<span class="_ _10"> </span>and</div><div class="t m0 x3 h7 y14 ff1 fs4 fc0 sc0 ls0 ws0">demonstrat<span class="_ _2"></span>e<span class="_ _d"> </span>the<span class="_ _d"> </span>performance<span class="_ _d"> </span>gain<span class="_ _d"> </span>with<span class="_ _d"> </span>differ<span class="_ _2"></span>ent<span class="_ _d"> </span>system<span class="_ _3"> </span>parameters.</div><div class="t m0 x3 h8 y15 ff2 fs5 fc0 sc0 ls8 ws0">1<span class="_ _11"> </span>Introduction</div><div class="t m0 x3 h9 y16 ff5 fs1 fc0 sc0 ls9 ws0">Multiple-input<span class="_ _3"> </span>multiple-output<span class="_ _a"> </span>(MIMO)<span class="_ _d"> </span>spatial<span class="_ _d"> </span>multiplexing</div><div class="t m0 x3 h9 y17 ff5 fs1 fc0 sc0 ls0 ws0">systems<span class="_ _0"> </span>have<span class="_ _c"> </span>recently<span class="_ _c"> </span>received<span class="_ _c"> </span>significant<span class="_ _3"> </span>attention<span class="_ _c"> </span>owing<span class="_ _c"> </span>to</div><div class="t m0 x3 h9 y18 ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _f"> </span>extraordinary<span class="_ _f"> </span>high<span class="_ _f"> </span>spectral<span class="_ _f"> </span>efficiency<span class="_ _f"> </span>they<span class="_ _f"> </span>provide<span class="_ _10"> </span>in</div><div class="t m0 x3 h9 y19 ff5 fs1 fc0 sc0 ls0 ws0">wireless<span class="_ _12"> </span>communication<span class="_ _12"> </span>systems<span class="_ _12"> </span><span class="fc1">[1,<span class="_ _12"> </span>2]</span>.<span class="_ _12"> </span>However,<span class="_ _12"> </span>some</div><div class="t m0 x3 ha y1a ff5 fs1 fc0 sc0 ls0 ws0">impairments,<span class="_ _f"> </span>such<span class="_ _f"> </span>as<span class="_ _f"> </span>correlation,<span class="_ _f"> </span>at<span class="_ _f"> </span>the<span class="_ _f"> </span>transmit<span class="_ _f"> </span>and<span class="ff6">/</span>or</div><div class="t m0 x3 h9 y1b ff5 fs1 fc0 sc0 ls0 ws0">receive<span class="_ _3"> </span>antennas<span class="_ _a"> </span>may<span class="_ _d"> </span>lead<span class="_ _d"> </span>to<span class="_ _d"> </span>substantial<span class="_ _d"> </span>degradation<span class="_ _d"> </span>in<span class="_ _d"> </span>the</div><div class="t m0 x3 h9 y1c ff5 fs1 fc0 sc0 ls0 ws0">system<span class="_ _c"> </span>performance.<span class="_ _3"> </span>Many<span class="_ _c"> </span>detectors<span class="_ _3"> </span>have<span class="_ _c"> </span>been<span class="_ _3"> </span>proposed<span class="_ _3"> </span>to</div><div class="t m0 x3 h9 y1d ff5 fs1 fc0 sc0 ls0 ws0">overcome<span class="_ _13"> </span>the<span class="_ _14"> </span>effect<span class="_ _14"> </span>of<span class="_ _13"> </span>fading<span class="_ _14"> </span>and<span class="_ _14"> </span>spatial<span class="_ _14"> </span>correlation,</div><div class="t m0 x3 h9 y1e ff5 fs1 fc0 sc0 ls0 ws0">resulting<span class="_ _9"> </span>in<span class="_ _e"> </span>a<span class="_ _9"> </span>significant<span class="_ _e"> </span>gain<span class="_ _9"> </span>in<span class="_ _e"> </span>sy<span class="_ _2"></span>stem<span class="_ _9"> </span>capacity<span class="_ _15"> </span><span class="fc1">[3]</span><span class="lsa">.I<span class="_ _16"></span>ti<span class="_ _16"></span>s</span></div><div class="t m0 x3 h9 y1f ff5 fs1 fc0 sc0 ls0 ws0">well-known<span class="_ _15"> </span>that<span class="_ _10"> </span>spatial<span class="_ _e"> </span>multiplexing<span class="_ _e"> </span>systems<span class="_ _15"> </span>that<span class="_ _e"> </span>em<span class="_ _8"></span>ploy</div><div class="t m0 x3 h9 y20 ff5 fs1 fc0 sc0 ls0 ws0">linear<span class="_ _0"> </span>receivers,<span class="_ _0"> </span>either<span class="_ _0"> </span>zero-forcing<span class="_ _0"> </span>(ZF<span class="_ _8"></span>)<span class="_ _0"> </span>or<span class="_ _0"> </span>minimu<span class="_ _8"></span>m<span class="_ _0"> </span>mean-</div><div class="t m0 x3 h9 y21 ff5 fs1 fc0 sc0 ls0 ws0">square<span class="_ _d"> </span>error<span class="_ _a"> </span>(MMSE),<span class="_ _a"> </span>are<span class="_ _a"> </span>practically<span class="_ _d"> </span>important<span class="_ _a"> </span>because<span class="_ _a"> </span>of</div><div class="t m0 x3 h9 y22 ff5 fs1 fc0 sc0 ls0 ws0">their<span class="_ _5"> </span>minimal<span class="_ _5"> </span>complexity<span class="_ _5"> </span>requirements.<span class="_ _5"> </span>Ho<span class="_ _2"></span>wever,<span class="_ _5"> </span>these</div><div class="t m0 x3 h9 y23 ff5 fs1 fc0 sc0 ls0 ws0">detectors<span class="_ _3"> </span>result<span class="_ _3"> </span>in<span class="_ _d"> </span>a<span class="_ _3"> </span>loss<span class="_ _3"> </span>in<span class="_ _d"> </span>the<span class="_ _3"> </span>diversity<span class="_ _3"> </span>gai<span class="_ _8"></span>n<span class="_ _3"> </span>relative<span class="_ _3"> </span>to<span class="_ _3"> </span>the</div><div class="t m0 x3 h9 y24 ff5 fs1 fc0 sc0 ls0 ws0">maximum-likelihood<span class="_ _5"> </span>(ML)<span class="_ _13"> </span>receiver.<span class="_ _5"> </span>For<span class="_ _5"> </span>instance,<span class="_ _5"> </span>in<span class="_ _13"> </span>a</div><div class="t m0 x3 h9 y25 ff5 fs1 fc0 sc0 ls0 ws0">system<span class="_ _17"> </span>with<span class="_ _0"> </span><span class="ff7">M<span class="_ _17"> </span></span>transmit<span class="_ _0"> </span>and<span class="_ _17"> </span><span class="ff7">N<span class="_ _0"> </span></span>receive<span class="_ _17"> </span>antenna<span class="_ _8"></span>s,<span class="_ _0"> </span>ZF<span class="_ _17"> </span>receivers</div><div class="t m0 x3 hb y26 ff5 fs1 fc0 sc0 ls0 ws0">achieve<span class="_ _d"> </span>a<span class="_ _a"> </span>diversity<span class="_ _a"> </span>order<span class="_ _a"> </span>of<span class="_ _a"> </span><span class="ff7">N<span class="_ _d"> </span><span class="ff8"><span class="_ _0"> </span></span>M<span class="_ _c"> </span><span class="ff8">þ<span class="_ _17"> </span></span></span>1,<span class="_ _a"> </span>whereas<span class="_ _a"> </span>the<span class="_ _a"> </span>more</div><div class="t m0 x3 h9 y27 ff5 fs1 fc0 sc0 ls0 ws0">complex<span class="_ _17"> </span>ML<span class="_ _0"> </span>detectors<span class="_ _17"> </span>achieve<span class="_ _17"> </span>a<span class="_ _0"> </span>diversity<span class="_ _17"> </span>order<span class="_ _17"> </span>of<span class="_ _0"> </span><span class="ff7">N<span class="_ _17"> </span></span><span class="fc1">[3]</span>.</div><div class="t m0 x6 h9 y28 ff5 fs1 fc0 sc0 ls0 ws0">In<span class="_ _f"> </span><span class="fc1">[4]</span>,<span class="_ _18"> </span>the<span class="_ _f"> </span>authors<span class="_ _18"> </span>study<span class="_ _f"> </span>the<span class="_ _f"> </span>perfo<span class="_ _8"></span>rmance<span class="_ _f"> </span>of<span class="_ _18"> </span>the<span class="_ _f"> </span>ZF</div><div class="t m0 x3 h9 y29 ff5 fs1 fc0 sc0 ls0 ws0">receiver<span class="_ _19"> </span>in<span class="_ _19"> </span>Rayleigh<span class="_ _1a"> </span>fading<span class="_ _19"> </span>channels<span class="_ _1a"> </span>with<span class="_ _1a"> </span>transmit</div><div class="t m0 x3 h9 y2a ff5 fs1 fc0 sc0 ls0 ws0">correlation.<span class="_ _10"> </span>On<span class="_ _10"> </span>the<span class="_ _10"> </span>basis<span class="_ _f"> </span>of<span class="_ _10"> </span>Wishart<span class="_ _10"> </span>matrix<span class="_ _10"> </span>analysis,<span class="_ _10"> </span>the</div><div class="t m0 x3 h9 y2b ff5 fs1 fc0 sc0 ls0 ws0">authors<span class="_ _3"> </span>show<span class="_ _c"> </span>that<span class="_ _3"> </span>the<span class="_ _3"> </span>ZF<span class="_ _3"> </span>detector<span class="_ _3"> </span>decomposes<span class="_ _c"> </span>the<span class="_ _3"> </span>MIMO</div><div class="t m0 x3 hb y2c ff5 fs1 fc0 sc0 ls0 ws0">system<span class="_ _9"> </span>into<span class="_ _e"> </span><span class="ff7">M<span class="_ _15"> </span></span>parallel<span class="_ _e"> </span>streams<span class="_ _15"> </span>with<span class="_ _15"> </span><span class="ff7">N<span class="_ _d"> </span><span class="ff8"><span class="_ _0"> </span></span>M<span class="_ _c"> </span><span class="ff8">þ<span class="_ _17"> </span></span></span>1<span class="_ _e"> </span>diversity</div><div class="t m0 x7 h9 y2d ff5 fs1 fc0 sc0 ls0 ws0">order.<span class="_ _10"> </span>In<span class="_ _f"> </span><span class="fc1">[5]</span>,<span class="_ _10"> </span>the<span class="_ _f"> </span>capacity<span class="_ _10"> </span>of<span class="_ _10"> </span>MIMO<span class="_ _f"> </span>Ricean<span class="_ _f"> </span>distributed</div><div class="t m0 x7 h9 y2e ff5 fs1 fc0 sc0 ls0 ws0">channels<span class="_ _10"> </span>is<span class="_ _10"> </span>investigated.<span class="_ _10"> </span>In<span class="_ _10"> </span>particula<span class="_ _8"></span>r,<span class="_ _10"> </span>the<span class="_ _10"> </span>authors<span class="_ _f"> </span>in<span class="_ _10"> </span><span class="fc1">[5]</span></div><div class="t m0 x7 h9 y2f ff5 fs1 fc0 sc0 ls0 ws0">show<span class="_ _d"> </span>that<span class="_ _d"> </span>as<span class="_ _d"> </span>the<span class="_ _d"> </span>line-of-sight<span class="_ _9"> </span>(LOS)<span class="_ _3"> </span>compo<span class="_ _8"></span>nent<span class="_ _d"> </span>increases,</div><div class="t m0 x7 h9 y30 ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _14"> </span>MIMO<span class="_ _14"> </span>system<span class="_ _13"> </span>capacity<span class="_ _14"> </span>decreases,<span class="_ _14"> </span>even<span class="_ _14"> </span>for<span class="_ _14"> </span>large</div><div class="t m0 x7 h9 y31 ff5 fs1 fc0 sc0 ls0 ws0">number<span class="_ _e"> </span>of<span class="_ _e"> </span>transmit<span class="_ _e"> </span>antennas.<span class="_ _10"> </span>In<span class="_ _e"> </span><span class="fc1">[6]</span>,<span class="_ _e"> </span>the<span class="_ _10"> </span>performance<span class="_ _e"> </span>of</div><div class="t m0 x7 h9 y32 ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _18"> </span>ZF<span class="_ _18"> </span>receiv<span class="_ _2"></span>er<span class="_ _18"> </span>is<span class="_ _18"> </span>inves<span class="_ _2"></span>tigated<span class="_ _18"> </span>ov<span class="_ _2"></span>er<span class="_ _18"> </span>independent<span class="_ _18"> </span>Ricean</div><div class="t m0 x7 h9 y33 ff5 fs1 fc0 sc0 ls0 ws0">fading<span class="_ _3"> </span>channels<span class="_ _3"> </span>where<span class="_ _3"> </span>an<span class="_ _d"> </span>approximation<span class="_ _3"> </span>for<span class="_ _3"> </span>the<span class="_ _3"> </span>average<span class="_ _3"> </span>bit</div><div class="t m0 x7 h9 y34 ff5 fs1 fc0 sc0 ls0 ws0">error<span class="_ _f"> </span>rate<span class="_ _10"> </span>(BER)<span class="_ _18"> </span>is<span class="_ _f"> </span>given.<span class="_ _f"> </span>Note<span class="_ _f"> </span>that<span class="_ _f"> </span>the<span class="_ _f"> </span>authors<span class="_ _f"> </span>in<span class="_ _18"> </span><span class="fc1">[6]</span></div><div class="t m0 x7 h9 y35 ff5 fs1 fc0 sc0 ls0 ws0">assume<span class="_ _d"> </span>that<span class="_ _d"> </span>the<span class="_ _a"> </span>subchannels<span class="_ _a"> </span>fade<span class="_ _a"> </span>independently.<span class="_ _d"> </span>However,</div><div class="t m0 x7 h9 y36 ff5 fs1 fc0 sc0 ls0 ws0">in<span class="_ _18"> </span>re<span class="_ _2"></span>al<span class="_ _18"> </span>propagation<span class="_ _f"> </span>environments,<span class="_ _18"> </span>fading<span class="_ _f"> </span>signals<span class="_ _18"> </span>are<span class="_ _f"> </span>not</div><div class="t m0 x7 h9 y37 ff5 fs1 fc0 sc0 ls0 ws0">independent,<span class="_ _e"> </span>where<span class="_ _15"> </span>measurement<span class="_ _e"> </span>results<span class="_ _15"> </span>indicate<span class="_ _e"> </span>that<span class="_ _15"> </span>the</div><div class="t m0 x7 h9 y38 ff5 fs1 fc0 sc0 ls0 ws0">channels<span class="_ _5"> </span>suffer<span class="_ _12"> </span>from<span class="_ _5"> </span>correla<span class="_ _2"></span>tion<span class="_ _12"> </span><span class="fc1">[7<span class="_ _1"></span>–<span class="_ _1b"></span>9]</span>.<span class="_ _5"> </span>The<span class="_ _12"> </span>impact<span class="_ _5"> </span>of</div><div class="t m0 x7 h9 y39 ff5 fs1 fc0 sc0 ls0 ws0">correlation<span class="_ _15"> </span>on<span class="_ _15"> </span>the<span class="_ _e"> </span>capacity<span class="_ _15"> </span>of<span class="_ _e"> </span>multiple-antenna<span class="_ _e"> </span>systems<span class="_ _9"> </span>is</div><div class="t m0 x7 h9 y3a ff5 fs1 fc0 sc0 ls0 ws0">investigated<span class="_ _3"> </span>in<span class="_ _d"> </span><span class="fc1">[10]</span>.<span class="_ _a"> </span>In<span class="_ _d"> </span>that,<span class="_ _d"> </span>the<span class="_ _d"> </span>authors<span class="_ _a"> </span>in<span class="_ _d"> </span><span class="fc1">[10]<span class="_ _d"> </span></span>show<span class="_ _d"> </span>that</div><div class="t m0 x7 h9 y3b ff5 fs1 fc0 sc0 ls0 ws0">an<span class="_ _3"> </span>increase<span class="_ _d"> </span>in<span class="_ _d"> </span>the<span class="_ _d"> </span>correlation<span class="_ _3"> </span>coefficients<span class="_ _d"> </span>results<span class="_ _d"> </span>in<span class="_ _3"> </span>capacity</div><div class="t m0 x7 h9 y3c ff5 fs1 fc0 sc0 ls0 ws0">decrease,<span class="_ _d"> </span>and<span class="_ _d"> </span>when<span class="_ _a"> </span>the<span class="_ _d"> </span>correlation<span class="_ _d"> </span>coefficients<span class="_ _a"> </span>are<span class="_ _d"> </span>equal<span class="_ _d"> </span>to</div><div class="t m0 x7 h9 y3d ff5 fs1 fc0 sc0 ls0 ws0">unity,<span class="_ _c"> </span>no<span class="_ _3"> </span>advantage<span class="_ _3"> </span>is<span class="_ _c"> </span>provided<span class="_ _3"> </span>by<span class="_ _c"> </span>the<span class="_ _3"> </span>MIMO<span class="_ _3"> </span>architecture.</div><div class="t m0 x7 h9 y3e ff5 fs1 fc0 sc0 ls0 ws0">Hence,<span class="_ _c"> </span>correlation<span class="_ _c"> </span>can<span class="_ _3"> </span>potentially<span class="_ _3"> </span>lead<span class="_ _c"> </span>to<span class="_ _c"> </span>a<span class="_ _3"> </span>reduction<span class="_ _c"> </span>in<span class="_ _c"> </span>the</div><div class="t m0 x7 h9 y3f ff5 fs1 fc0 sc0 ls0 ws0">MIMO<span class="_ _3"> </span>system<span class="_ _3"> </span>capacity.<span class="_ _c"> </span>Therefore<span class="_ _3"> </span>the<span class="_ _3"> </span>independe<span class="_ _8"></span>nt<span class="_ _3"> </span>Ricean</div><div class="t m0 x7 h9 y40 ff5 fs1 fc0 sc0 ls0 ws0">fading<span class="_ _5"> </span>model<span class="_ _12"> </span>assumed<span class="_ _5"> </span>in<span class="_ _5"> </span><span class="fc1">[6]<span class="_ _12"> </span></span>is<span class="_ _5"> </span>not<span class="_ _5"> </span>ideal<span class="_ _12"> </span>in<span class="_ _5"> </span>practice,</div><div class="t m0 x7 h9 y41 ff5 fs1 fc0 sc0 ls0 ws0">especially<span class="_ _15"> </span>for<span class="_ _15"> </span>systems<span class="_ _9"> </span>that<span class="_ _15"> </span>have<span class="_ _15"> </span>poor<span class="_ _15"> </span>scattering<span class="_ _e"> </span>conditions</div><div class="t m0 x7 ha y42 ff5 fs1 fc0 sc0 ls0 ws0">and<span class="ff6">/</span>or<span class="_ _14"> </span>insufficient<span class="_ _13"> </span>spacing<span class="_ _14"> </span>between<span class="_ _13"> </span>adjacent<span class="_ _14"> </span>antennas.</div><div class="t m0 x7 h9 y43 ff5 fs1 fc0 sc0 ls0 ws0">A<span class="_ _14"> </span>widely<span class="_ _14"> </span>accepted<span class="_ _1c"> </span>mathematical<span class="_ _14"> </span>model<span class="_ _1c"> </span>for<span class="_ _1c"> </span>corre<span class="_ _2"></span>lated</div><div class="t m0 x7 h9 y44 ff5 fs1 fc0 sc0 ls0 ws0">fading<span class="_ _10"> </span>channels<span class="_ _f"> </span>is<span class="_ _10"> </span>presented<span class="_ _10"> </span>in<span class="_ _f"> </span><span class="fc1">[11<span class="_ _1b"></span>–<span class="_ _1b"></span>14]</span>.<span class="_ _10"> </span>Their<span class="_ _10"> </span>comm<span class="_ _8"></span>on</div><div class="t m0 x7 h9 y45 ff5 fs1 fc0 sc0 ls0 ws0">approach<span class="_ _d"> </span>is<span class="_ _a"> </span>to<span class="_ _9"> </span>model<span class="_ _9"> </span>the<span class="_ _a"> </span>correlation<span class="_ _a"> </span>at<span class="_ _a"> </span>the<span class="_ _a"> </span>receiver<span class="_ _a"> </span>and<span class="_ _a"> </span>at</div><div class="t m0 x7 h9 y46 ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _13"> </span>transmitter<span class="_ _13"> </span>independently,<span class="_ _13"> </span>neglecting<span class="_ _14"> </span>the<span class="_ _13"> </span>statistical</div><div class="t m0 x8 h3 y47 ff1 fs1 fc0 sc0 ls0 ws0">10<span class="_ _1d"> </span><span class="ff3">IET<span class="_ _3"> </span>Commun.</span>,<span class="_ _3"> </span>2009,<span class="_ _0"> </span>V<span class="_ _2"></span>ol.<span class="_ _3"> </span>3,<span class="_ _3"> </span>Iss.<span class="_ _3"> </span>1,<span class="_ _3"> </span>pp.<span class="_ _3"> </span>10<span class="_ _1b"></span>–<span class="_ _1b"></span>16</div><div class="t m0 x8 hc y48 ff9 fs6 fc0 sc0 ls0 ws0">&</div><div class="t m0 x9 h3 y49 ff1 fs1 fc0 sc0 ls0 ws0">The<span class="_ _3"> </span>Institution<span class="_ _3"> </span>of<span class="_ _3"> </span>Engineering<span class="_ _3"> </span>and<span class="_ _3"> </span>T<span class="_ _b"></span>echnology<span class="_ _3"> </span>2009<span class="_ _1e"> </span>doi:<span class="_ _1f"> </span>10.1049/iet-com:20080110</div><div class="t m0 x8 hd y4a ff2 fs7 fc0 sc0 ls0 ws0">www<span class="_ _b"></span>.ietdl.or<span class="_ _2"></span>g</div><div class="t m0 xa he y4b ffa fs8 fc0 sc0 ls0 ws0">Authorized licensed use limited to: Shantou University. Downloaded on June 24, 2009 at 03:15 from IEEE Xplore. Restrictions apply.</div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div></body></html>
<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://csdnimg.cn/release/download_crawler_static/11532111/bg2.jpg"><div class="t m0 x3 h9 y4c ff5 fs1 fc0 sc0 ls0 ws0">interdependence<span class="_ _19"> </span>of<span class="_ _19"> </span>both<span class="_ _20"> </span>links.<span class="_ _20"> </span>Thus,<span class="_ _19"> </span>correlation<span class="_ _20"> </span>is</div><div class="t m0 x3 h9 y4d ff5 fs1 fc0 sc0 ls0 ws0">determined<span class="_ _15"> </span>as<span class="_ _9"> </span>the<span class="_ _15"> </span>product<span class="_ _15"> </span>of<span class="_ _9"> </span>a<span class="_ _15"> </span>receive-side<span class="_ _9"> </span>and<span class="_ _15"> </span>transmit-</div><div class="t m0 x3 h9 y4e ff5 fs1 fc0 sc0 ls0 ws0">side<span class="_ _18"> </span>components.<span class="_ _12"> </span>This<span class="_ _f"> </span>allows<span class="_ _18"> </span>one<span class="_ _12"> </span>to<span class="_ _f"> </span>write<span class="_ _12"> </span>the<span class="_ _18"> </span>channel</div><div class="t m0 x3 h9 y4f ff5 fs1 fc0 sc0 ls0 ws0">matrix<span class="_ _f"> </span>in<span class="_ _f"> </span>a<span class="_ _f"> </span>simple<span class="_ _f"> </span>format<span class="_ _f"> </span>on<span class="_ _f"> </span>the<span class="_ _f"> </span>basis<span class="_ _18"> </span>of<span class="_ _10"> </span>two<span class="_ _18"> </span>constant</div><div class="t m0 x3 h9 y50 ff5 fs1 fc0 sc0 ls0 ws0">correlation<span class="_ _10"> </span>matrices<span class="_ _10"> </span>plus<span class="_ _f"> </span>an<span class="_ _f"> </span>inner<span class="_ _f"> </span>matrix<span class="_ _10"> </span>of<span class="_ _f"> </span>independent</div><div class="t m0 x3 h9 y51 ff5 fs1 fc0 sc0 ls0 ws0">and<span class="_ _21"> </span>identically<span class="_ _21"> </span>distributed<span class="_ _21"> </span>(i.i.d.)<span class="_ _21"> </span>circularly<span class="_ _21"> </span>symmetric</div><div class="t m0 x3 h9 y52 ff5 fs1 fc0 sc0 ls0 ws0">complex<span class="_ _c"> </span>Gaussian<span class="_ _c"> </span>random<span class="_ _3"> </span>variables.</div><div class="t m0 x6 h9 y53 ff5 fs1 fc0 sc0 ls0 ws0">Motivated<span class="_ _c"> </span>by<span class="_ _c"> </span>the<span class="_ _c"> </span>observations<span class="_ _c"> </span>given<span class="_ _c"> </span>earlier,<span class="_ _c"> </span>in<span class="_ _c"> </span>this<span class="_ _3"> </span>paper,</div><div class="t m0 x3 h9 y54 ff5 fs1 fc0 sc0 ls0 ws0">we<span class="_ _c"> </span>study<span class="_ _3"> </span>the<span class="_ _3"> </span>performance<span class="_ _3"> </span>of<span class="_ _3"> </span>the<span class="_ _3"> </span>ZF<span class="_ _3"> </span>receiver<span class="_ _c"> </span>over<span class="_ _3"> </span>transmit-</div><div class="t m0 x3 h9 y55 ff5 fs1 fc0 sc0 ls0 ws0">correlated<span class="_ _3"> </span>flat<span class="_ _a"> </span>Ricean<span class="_ _d"> </span>fading<span class="_ _a"> </span>channels.<span class="_ _a"> </span>This<span class="_ _d"> </span>channel<span class="_ _a"> </span>model</div><div class="t m0 x3 h9 y56 ff5 fs1 fc0 sc0 ls0 ws0">is<span class="_ _4"> </span>known<span class="_ _4"> </span>to<span class="_ _4"> </span>be<span class="_ _4"> </span>an<span class="_ _22"> </span>appropriate<span class="_ _21"> </span>mo<span class="_"> </span>del<span class="_ _22"> </span>for<span class="_ _4"> </span>wireless</div><div class="t m0 x3 h9 y57 ff5 fs1 fc0 sc0 ls0 ws0">propagation<span class="_ _12"> </span>environments.<span class="_ _12"> </span>Note<span class="_ _5"> </span>that,<span class="_ _12"> </span>in<span class="_ _12"> </span>our<span class="_ _5"> </span>work,<span class="_ _12"> </span>we</div><div class="t m0 x3 h9 y58 ff5 fs1 fc0 sc0 ls0 ws0">constrain<span class="_ _a"> </span>our<span class="_ _a"> </span>analysis<span class="_ _a"> </span>to<span class="_ _9"> </span>the<span class="_ _9"> </span>exponential<span class="_ _a"> </span>correlation<span class="_ _9"> </span>model</div><div class="t m0 x3 h9 y59 ff5 fs1 fc1 sc0 ls0 ws0">[15]<span class="fc0">.<span class="_ _15"> </span>This<span class="_ _e"> </span>model<span class="_ _15"> </span>is<span class="_ _e"> </span>physically<span class="_ _15"> </span>realistic<span class="_ _15"> </span>because<span class="_ _15"> </span>correlation</span></div><div class="t m0 x3 h9 y5a ff5 fs1 fc0 sc0 ls0 ws0">decreases<span class="_ _15"> </span>with<span class="_ _15"> </span>increasing<span class="_ _15"> </span>distances<span class="_ _15"> </span>between<span class="_ _15"> </span>antennas.<span class="_ _15"> </span>We</div><div class="t m0 x3 h9 y5b ff5 fs1 fc0 sc0 ls0 ws0">derive<span class="_ _1c"> </span>an<span class="_ _1c"> </span>approximation<span class="_ _1c"> </span>for<span class="_ _1c"> </span>the<span class="_ _1c"> </span>aver<span class="_ _2"></span>age<span class="_ _1c"> </span>BER<span class="_ _1c"> </span>when</div><div class="t m0 x3 h9 y5c ff5 fs1 fc0 sc0 ls0 ws0">quadratur<span class="_ _2"></span>e<span class="_ _15"> </span>phase-shift<span class="_ _15"> </span>keying<span class="_ _9"> </span>(QPSK)<span class="_ _15"> </span>modulation<span class="_ _9"> </span>is<span class="_ _15"> </span>used</div><div class="t m0 x3 h9 y5d ff5 fs1 fc0 sc0 ls0 ws0">with<span class="_ _a"> </span>each<span class="_ _9"> </span>transmitted<span class="_ _a"> </span>substream.<span class="_ _a"> </span>Moreover,<span class="_ _a"> </span>we<span class="_ _a"> </span>investigate</div><div class="t m0 x3 h9 y5e ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _18"> </span>system<span class="_ _18"> </span>performance<span class="_ _12"> </span>in<span class="_ _18"> </span>receive-correlated<span class="_ _18"> </span>flat<span class="_ _18"> </span>Ricean</div><div class="t m0 x3 h9 y5f ff5 fs1 fc0 sc0 ls0 ws0">fading<span class="_ _1c"> </span>channels.<span class="_ _1c"> </span>In<span class="_ _1c"> </span>this<span class="_ _1c"> </span>case,<span class="_ _1c"> </span>it<span class="_ _1c"> </span>is<span class="_ _1c"> </span>shown<span class="_ _23"> </span>that<span class="_ _23"> </span>the</div><div class="t m0 x3 h9 y60 ff5 fs1 fc0 sc0 ls0 ws0">performance,<span class="_ _21"> </span>when<span class="_ _1c"> </span><span class="ff7">N<span class="_ _0"> </span><span class="ff4">¼<span class="_ _c"> </span></span>M</span>,<span class="_ _1c"> </span>is<span class="_ _1c"> </span>the<span class="_ _21"> </span>same<span class="_ _21"> </span>as<span class="_ _23"> </span>that<span class="_ _21"> </span>of</div><div class="t m0 x3 h9 y61 ff5 fs1 fc0 sc0 ls0 ws0">transmit-correlated<span class="_ _3"> </span>flat<span class="_ _3"> </span>Ricean<span class="_ _d"> </span>fading<span class="_ _d"> </span>channel<span class="_ _8"></span>s.<span class="_ _3"> </span>We<span class="_ _d"> </span>further</div><div class="t m0 x3 h9 y62 ff5 fs1 fc0 sc0 ls0 ws0">derive<span class="_ _c"> </span>a<span class="_ _c"> </span>closed-form<span class="_ _3"> </span>expr<span class="_ _2"></span>ession<span class="_ _c"> </span>for<span class="_ _3"> </span>the<span class="_ _c"> </span>optimum<span class="_ _3"> </span>correlation</div><div class="t m0 x3 h9 y63 ff5 fs1 fc0 sc0 ls0 ws0">coefficient<span class="_ _c"> </span>that<span class="_ _c"> </span>maximis<span class="_ _8"></span>es<span class="_ _c"> </span>the<span class="_ _c"> </span>system<span class="_ _c"> </span>capacity.</div><div class="t m0 x6 h9 y64 ff5 fs1 fc0 sc0 ls0 ws0">The<span class="_ _0"> </span>remainder<span class="_ _17"> </span>of<span class="_ _17"> </span>the<span class="_ _0"> </span>paper<span class="_ _0"> </span>is<span class="_ _17"> </span>organised<span class="_ _0"> </span>as<span class="_ _17"> </span>follows.<span class="_ _0"> </span>Sys<span class="_ _2"></span>tem</div><div class="t m0 x3 h9 y65 ff5 fs1 fc0 sc0 ls0 ws0">model<span class="_ _17"> </span>is<span class="_ _0"> </span>introduced<span class="_ _17"> </span>in<span class="_ _17"> </span>Section<span class="_ _17"> </span>2.<span class="_ _17"> </span>The<span class="_ _0"> </span>performance<span class="_ _17"> </span>analysis<span class="_ _17"> </span>is</div><div class="t m0 x3 h9 y66 ff5 fs1 fc0 sc0 ls0 ws0">presented<span class="_ _c"> </span>in<span class="_ _c"> </span>Section<span class="_ _c"> </span>3.<span class="_ _c"> </span>Section<span class="_ _3"> </span>4<span class="_ _c"> </span>presents<span class="_ _c"> </span>simulation<span class="_ _c"> </span>results</div><div class="t m0 x3 h9 y67 ff5 fs1 fc0 sc0 ls0 ws0">to<span class="_ _12"> </span>assess<span class="_ _12"> </span>the<span class="_ _12"> </span>accuracy<span class="_ _24"> </span>of<span class="_ _12"> </span>our<span class="_ _12"> </span>analytical<span class="_ _12"> </span>results.<span class="_ _12"> </span>Finally,</div><div class="t m0 x3 h9 y68 ff5 fs1 fc0 sc0 ls0 ws0">conclusions<span class="_ _c"> </span>are<span class="_ _c"> </span>given<span class="_ _c"> </span>in<span class="_ _3"> </span>Section<span class="_ _c"> </span>5.</div><div class="t m0 x3 h8 y69 ff2 fs5 fc0 sc0 ls0 ws0">2<span class="_ _11"> </span>Sys<span class="_ _2"></span>tem<span class="_ _10"> </span>model</div><div class="t m0 x3 h9 y6a ff5 fs1 fc0 sc0 ls0 ws0">We<span class="_ _c"> </span>consider<span class="_ _3"> </span>a<span class="_ _c"> </span>communication<span class="_ _3"> </span>sy<span class="_ _2"></span>stem<span class="_ _c"> </span>with<span class="_ _3"> </span><span class="ff7">M<span class="_ _3"> </span></span>transmit<span class="_ _c"> </span>and</div><div class="t m0 x3 hb y6b ff7 fs1 fc0 sc0 ls0 ws0">N<span class="_ _18"> </span><span class="ff5">(</span>N<span class="_ _0"> </span><span class="ff8"><span class="_ _0"> </span></span>M<span class="_ _1b"></span><span class="ff5">)<span class="_ _18"> </span>receive<span class="_ _f"> </span>antennas<span class="_ _18"> </span>in<span class="_ _18"> </span>a<span class="_ _f"> </span>correlated<span class="_ _f"> </span>Ricea<span class="_ _8"></span>n<span class="_ _f"> </span>flat</span></div><div class="t m0 x3 h9 y6c ff5 fs1 fc0 sc0 ls0 ws0">fading<span class="_ _e"> </span>channel.<span class="_ _e"> </span>The<span class="_ _10"> </span>incoming<span class="_ _e"> </span>data<span class="_ _e"> </span>are<span class="_ _e"> </span>fed<span class="_ _e"> </span>into<span class="_ _10"> </span>a<span class="_ _e"> </span>spatial</div><div class="t m0 x3 h9 y6d ff5 fs1 fc0 sc0 ls0 ws0">multiplexer<span class="_ _f"> </span>(serial-to-pa<span class="_ _8"></span>rallel<span class="_ _18"> </span>converter)<span class="_ _f"> </span>that<span class="_ _18"> </span>converts<span class="_ _f"> </span>the</div><div class="t m0 x3 h9 y6e ff5 fs1 fc0 sc0 ls0 ws0">input<span class="_ _a"> </span>data<span class="_ _a"> </span>stream<span class="_ _a"> </span>into<span class="_ _9"> </span><span class="ff7">M<span class="_ _a"> </span></span>independent<span class="_ _9"> </span>parallel<span class="_ _a"> </span>substreams.</div><div class="t m0 x3 h9 y6f ff5 fs1 fc0 sc0 ls0 ws0">Next,<span class="_ _3"> </span>the<span class="_ _3"> </span>substreams<span class="_ _c"> </span>are<span class="_ _3"> </span>independently<span class="_ _3"> </span>mapped<span class="_ _3"> </span>to<span class="_ _3"> </span>produce</div><div class="t m0 x3 h9 y70 ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _9"> </span><span class="ff7">M</span>-dimensional<span class="_ _15"> </span>symbol<span class="_ _9"> </span>vector<span class="_ _9"> </span><span class="ffb">x</span>.<span class="_ _15"> </span>We<span class="_ _a"> </span>also<span class="_ _15"> </span>assume<span class="_ _9"> </span>that</div><div class="t m0 x3 h9 y71 ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _21"> </span>transmitted<span class="_ _4"> </span>substreams<span class="_ _21"> </span>have<span class="_ _21"> </span>uniform<span class="_ _4"> </span>power,<span class="_ _21"> </span>i.e.</div><div class="t m0 x3 hb y72 ffb fs1 fc0 sc0 ls0 ws0">x<span class="_ _0"> </span><span class="ffc">[<span class="_ _c"> </span><span class="ff8">C</span></span></div><div class="t m0 xb hf y73 ff7 fs9 fc0 sc0 ls0 ws0">M<span class="_ _25"></span><span class="ff8"><span class="ff5">1</span></span></div><div class="t m0 xc h9 y74 ff5 fs1 fc0 sc0 ls0 ws0">has<span class="_ _d"> </span>covariance<span class="_ _a"> </span>matrix<span class="_ _a"> </span><span class="ffd">E<span class="_ _a"> </span><span class="ffb lsb">xx</span></span></div><div class="t m0 xd h10 y73 ff7 fs9 fc0 sc0 ls0 ws0">H</div><div class="t m0 xe h11 y75 ffe fs1 fc0 sc0 lsc ws0"></div><div class="t m0 xf hb y76 ff8 fs1 fc0 sc0 ls0 ws0">¼</div><div class="t m1 x10 h12 y74 fff fsa fc0 sc0 ls0 ws0">s</div><div class="t m0 x11 h13 y73 ff5 fs9 fc0 sc0 ls0 ws0">2</div><div class="t m0 x12 h10 y77 ff7 fs9 fc0 sc0 ls0 ws0">x</div><div class="t m0 x13 h14 y74 ffb fs1 fc0 sc0 ls0 ws0">I</div><div class="t m0 x14 h10 y78 ff7 fs9 fc0 sc0 ls0 ws0">M</div><div class="t m0 x15 h9 y74 ff5 fs1 fc0 sc0 ls0 ws0">,<span class="_ _d"> </span>where</div><div class="t m0 x3 hb y79 ffd fs1 fc0 sc0 ls0 ws0">E<span class="_ _0"> </span><span class="ff8"><span class="_ _26"></span><span class="lsd">½<span class="_ _1"></span><span class="ff5 ls0">stands<span class="_ _15"> </span>for<span class="_ _9"> </span>expectation,<span class="_ _14"> </span><span class="ff8"><span class="_ _27"></span><span class="lse">ðÞ</span></span></span></span></span></div><div class="t m0 x16 h10 y7a ff7 fs9 fc0 sc0 ls0 ws0">H</div><div class="t m0 x17 h9 y7b ff5 fs1 fc0 sc0 ls0 ws0">is<span class="_ _9"> </span>the<span class="_ _9"> </span>conjugate<span class="_ _15"> </span>transpose</div><div class="t m0 x3 h9 y7c ff5 fs1 fc0 sc0 ls0 ws0">and<span class="_ _a"> </span><span class="ffb">I</span></div><div class="t m0 xb h10 y7d ff7 fs9 fc0 sc0 ls0 ws0">M</div><div class="t m0 x18 h9 y7e ff5 fs1 fc0 sc0 ls0 ws0">denotes<span class="_ _a"> </span>an<span class="_ _9"> </span>identity<span class="_ _a"> </span>matrix<span class="_ _a"> </span>with<span class="_ _9"> </span>dimension<span class="_ _9"> </span><span class="ff7">M</span><span class="lsf">.A<span class="_ _28"></span>t</span></div><div class="t m0 x3 h9 y7f ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _24"> </span>receiver<span class="_ _18"> </span>end,<span class="_ _12"> </span>we<span class="_ _24"> </span>have<span class="_ _18"> </span>a<span class="_ _24"> </span>ZF<span class="_ _12"> </span>receiver.<span class="_ _24"> </span>The<span class="_ _24"> </span>sampled</div><div class="t m0 x3 h9 y80 ff5 fs1 fc0 sc0 ls0 ws0">received<span class="_ _c"> </span>baseband<span class="_ _c"> </span>signal<span class="_ _3"> </span>is<span class="_ _c"> </span>given<span class="_ _c"> </span>by</div><div class="t m0 x19 hb y81 ffb fs1 fc0 sc0 ls0 ws0">y<span class="_ _0"> </span><span class="ff8">¼<span class="_ _c"> </span></span><span class="ls10">Hx<span class="_ _2"></span><span class="ff8 ls0">þ<span class="_ _17"></span><span class="ffb">n<span class="_ _29"> </span><span class="ff5">(1)</span></span></span></span></div><div class="t m0 x3 hb y82 ff5 fs1 fc0 sc0 ls0 ws0">where<span class="_ _15"> </span><span class="ffb">y<span class="_ _0"> </span><span class="ffc">[<span class="_ _c"> </span><span class="ff8">C</span></span></span></div><div class="t m0 x1a hf y83 ff7 fs9 fc0 sc0 ls0 ws0">N<span class="_ _1b"> </span><span class="ff8"><span class="ff5">1</span></span></div><div class="t m0 x1b hb y84 ff5 fs1 fc0 sc0 ls0 ws0">is<span class="_ _9"> </span>the<span class="_ _e"> </span>received<span class="_ _9"> </span>signal,<span class="_ _e"> </span><span class="ffb">H<span class="_ _d"> </span><span class="ffc">[<span class="_ _c"> </span><span class="ff8">C</span></span></span></div><div class="t m0 x1c hf y83 ff7 fs9 fc0 sc0 ls0 ws0">N<span class="_ _1b"> </span><span class="ff8"></span>M</div><div class="t m0 x1d h9 y84 ff5 fs1 fc0 sc0 ls0 ws0">is<span class="_ _9"> </span>the</div><div class="t m0 x3 h9 y85 ff5 fs1 fc0 sc0 ls0 ws0">spatially<span class="_ _23"> </span>correlated<span class="_ _14"> </span>Ricean<span class="_ _1c"> </span>flat<span class="_ _23"> </span>fading<span class="_ _23"> </span>channel<span class="_ _23"> </span>matrix.</div><div class="t m0 x3 h9 y86 ff5 fs1 fc0 sc0 ls0 ws0">Throughout<span class="_ _21"> </span>the<span class="_ _1c"> </span>paper,<span class="_ _21"> </span>we<span class="_ _21"> </span>assume<span class="_ _21"> </span>that<span class="_ _21"> </span>the<span class="_ _1c"> </span>receiver</div><div class="t m0 x3 h9 y87 ff5 fs1 fc0 sc0 ls0 ws0">perfectly<span class="_ _15"> </span>knows<span class="_ _9"> </span>the<span class="_ _15"> </span>channel<span class="_ _15"> </span>matrix<span class="_ _15"> </span><span class="ffb">H</span>.<span class="_ _15"> </span>The<span class="_ _15"> </span>latter<span class="_ _9"> </span>consists</div><div class="t m0 x3 h9 y88 ff5 fs1 fc0 sc0 ls0 ws0">of<span class="_ _15"> </span>Gaussian<span class="_ _9"> </span>random<span class="_ _15"> </span>variables<span class="_ _15"> </span>with<span class="_ _15"> </span>non-zero<span class="_ _15"> </span>mean</div><div class="t m1 x1e h12 y89 fff fsa fc0 sc0 ls0 ws0">m</div><div class="t m0 x1f h9 y89 ff5 fs1 fc0 sc0 ls0 ws0">and</div><div class="t m0 x3 h9 y8a ff5 fs1 fc0 sc0 ls0 ws0">unit<span class="_ _5"> </span>variance,<span class="_ _12"> </span>i.e.<span class="_ _5"> </span><span class="ff7">h</span></div><div class="t m0 x20 h13 y8b ff7 fs9 fc0 sc0 ls0 ws0">i<span class="ff5">,<span class="_"> </span><span class="ff10">;</span></span>j</div><div class="t m0 x21 hb y8c ff11 fs1 fc0 sc0 ls0 ws0"><span class="_ _0"> </span><span class="ff8">CN</span></div><div class="t m1 x22 h12 y8c fff fsa fc0 sc0 ls0 ws0">m</div><div class="t m0 x17 hb y8c ff5 fs1 fc0 sc0 ls11 ws0">,1<span class="_ _2a"></span><span class="ff8 ls12">ðÞ<span class="_ _2b"></span><span class="ff5 ls0">for<span class="_ _5"> </span><span class="ff7">i<span class="_ _c"> </span><span class="ff8">¼<span class="_ _0"> </span></span></span>1,<span class="_ _c"> </span>2,<span class="_ _3"> </span><span class="ff10 ls13">...<span class="_"> </span></span>,<span class="_ _0"> </span><span class="ff7">N<span class="_ _1f"> </span></span>,</span></span></div><div class="t m0 x3 hb y8d ff7 fs1 fc0 sc0 ls0 ws0">j<span class="_ _3"> </span><span class="ff8">¼<span class="_ _c"> </span><span class="ff5">1,<span class="_ _0"> </span>2,<span class="_ _3"> </span><span class="ff10 ls14">...<span class="_"> </span></span>,<span class="_ _0"> </span></span></span>M<span class="_ _1b"></span><span class="ff5">.<span class="_ _13"> </span>The<span class="_ _13"> </span>receiver<span class="_ _13"> </span>noise<span class="_ _13"> </span><span class="ffb">n<span class="_ _c"> </span><span class="ff11"><span class="_ _0"> </span><span class="ff8">CN<span class="_ _18"> </span></span></span></span>0,<span class="_ _c"> </span></span>N</div><div class="t m0 x23 h13 y8e ff5 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 x24 h14 y8f ffb fs1 fc0 sc0 ls0 ws0">I</div><div class="t m0 x25 h10 y8e ff7 fs9 fc0 sc0 ls0 ws0">N</div><div class="t m0 x26 h11 y90 ffe fs1 fc0 sc0 ls15 ws0"></div><div class="t m0 x3 h9 y91 ff5 fs1 fc0 sc0 ls0 ws0">consists<span class="_ _5"> </span>of<span class="_ _5"> </span>independent<span class="_ _5"> </span>circularly<span class="_ _5"> </span>symmetric<span class="_ _5"> </span>zero-mean</div><div class="t m0 x7 h9 y92 ff5 fs1 fc0 sc0 ls0 ws0">complex<span class="_ _c"> </span>Gaussian<span class="_ _3"> </span>entries<span class="_ _3"> </span>of<span class="_ _c"> </span>variance<span class="_ _3"> </span><span class="ff7">N</span></div><div class="t m0 x27 h13 y93 ff5 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 x28 h9 y4c ff5 fs1 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span>where<span class="_ _3"> </span><span class="ffb">I</span></div><div class="t m0 x29 h10 y93 ff7 fs9 fc0 sc0 ls0 ws0">N</div><div class="t m0 x2a h9 y4c ff5 fs1 fc0 sc0 ls0 ws0">denotes</div><div class="t m0 x7 h9 y4d ff5 fs1 fc0 sc0 ls0 ws0">an<span class="_ _c"> </span>identity<span class="_ _3"> </span>matrix<span class="_ _c"> </span>of<span class="_ _c"> </span>size<span class="_ _c"> </span><span class="ff7">N</span>.</div><div class="t m0 x2b h9 y4f ff5 fs1 fc0 sc0 ls0 ws0">For<span class="_ _a"> </span>the<span class="_ _a"> </span>sake<span class="_ _a"> </span>of<span class="_ _9"> </span>simplicity,<span class="_ _a"> </span>we<span class="_ _a"> </span>assume<span class="_ _9"> </span>the<span class="_ _a"> </span>receiver<span class="_ _a"> </span>to<span class="_ _a"> </span>be</div><div class="t m0 x7 h9 y50 ff5 fs1 fc0 sc0 ls0 ws0">located<span class="_ _18"> </span>at<span class="_ _18"> </span>a<span class="_ _18"> </span>richly-scattered<span class="_ _18"> </span>propagation<span class="_ _18"> </span>environment<span class="_ _18"> </span>so</div><div class="t m0 x7 h9 y51 ff5 fs1 fc0 sc0 ls0 ws0">that<span class="_ _c"> </span>the<span class="_ _3"> </span>fading<span class="_ _3"> </span>at<span class="_ _c"> </span>the<span class="_ _3"> </span>receiver<span class="_ _c"> </span>is<span class="_ _3"> </span>spatially<span class="_ _3"> </span>uncorrelated<span class="_ _c"> </span>while</div><div class="t m0 x7 h9 y52 ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _9"> </span>transmitter<span class="_ _15"> </span>is<span class="_ _9"> </span>located<span class="_ _15"> </span>at<span class="_ _9"> </span>a<span class="_ _9"> </span>high<span class="_ _15"> </span>altitude,<span class="_ _15"> </span>and<span class="_ _9"> </span>therefore</div><div class="t m0 x7 h9 y94 ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _24"> </span>fading<span class="_ _12"> </span>is<span class="_ _12"> </span>only<span class="_ _12"> </span>transmit<span class="_ _24"> </span>correlated.<span class="_ _12"> </span>This<span class="_ _24"> </span>scenario<span class="_ _12"> </span>is</div><div class="t m0 x7 h9 y53 ff5 fs1 fc0 sc0 ls0 ws0">typical<span class="_ _d"> </span>in<span class="_ _3"> </span>the<span class="_ _d"> </span>down-link<span class="_ _d"> </span>channel<span class="_ _d"> </span>in<span class="_ _d"> </span>mobi<span class="_ _8"></span>le<span class="_ _3"> </span>communication</div><div class="t m0 x7 h9 y54 ff5 fs1 fc0 sc0 ls0 ws0">systems.<span class="_ _18"> </span>Accor<span class="_ _8"></span>dingly,<span class="_ _24"> </span>the<span class="_ _12"> </span>elements<span class="_ _12"> </span>of<span class="_ _12"> </span>each<span class="_ _24"> </span>row<span class="_ _24"> </span>of<span class="_ _12"> </span>the</div><div class="t m0 x7 h9 y55 ff5 fs1 fc0 sc0 ls0 ws0">channel<span class="_ _9"> </span>matrix<span class="_ _a"> </span><span class="ffb">H<span class="_ _9"> </span></span>are<span class="_ _9"> </span>correlated<span class="_ _a"> </span>and<span class="_ _9"> </span>for<span class="_ _9"> </span>each<span class="_ _a"> </span>row,<span class="_ _a"> </span>we<span class="_ _9"> </span>can</div><div class="t m0 x7 h9 y56 ff5 fs1 fc0 sc0 ls0 ws0">write</div><div class="t m0 x2c h14 y95 ffb fs1 fc0 sc0 ls0 ws0">R</div><div class="t m0 x2d h10 y96 ff7 fs9 fc0 sc0 ls0 ws0">Tx</div><div class="t m0 x2e hb y97 ff8 fs1 fc0 sc0 ls0 ws0">¼<span class="_ _0"> </span><span class="ffd">E<span class="_ _a"> </span><span class="ffb">h</span></span></div><div class="t m0 x2f h10 y98 ff7 fs9 fc0 sc0 ls0 ws0">H</div><div class="t m0 x2f h10 y99 ff7 fs9 fc0 sc0 ls0 ws0">i</div><div class="t m0 x30 h14 y97 ffb fs1 fc0 sc0 ls0 ws0">h</div><div class="t m0 x31 h10 y96 ff7 fs9 fc0 sc0 ls0 ws0">i</div><div class="t m0 x32 h11 y9a ffe fs1 fc0 sc0 ls16 ws0"></div><div class="t m0 x33 hb y9b ff5 fs1 fc0 sc0 ls0 ws0">,<span class="_ _2c"> </span>for<span class="_ _1a"> </span><span class="ff7">i<span class="_ _3"> </span><span class="ff8">¼<span class="_ _0"> </span></span></span>1,<span class="_ _c"> </span>2,<span class="_ _3"> </span><span class="ff10 ls14">...<span class="_ _1"> </span></span>,<span class="_ _c"> </span><span class="ff7">N<span class="_ _2d"> </span></span>(2)</div><div class="t m0 x7 h9 y9c ff5 fs1 fc0 sc0 ls17 ws0">where<span class="_ _21"> </span><span class="ffb ls0">R</span></div><div class="t m0 x34 h10 y9d ff7 fs9 fc0 sc0 ls18 ws0">Tx</div><div class="t m0 x35 h9 y9e ff5 fs1 fc0 sc0 ls19 ws0">and<span class="_ _21"> </span><span class="ffb ls0">h</span></div><div class="t m0 x36 h10 y9d ff7 fs9 fc0 sc0 ls0 ws0">i</div><div class="t m0 x37 hb y9e ff5 fs1 fc0 sc0 ls1a ws0">are<span class="_ _21"> </span>the<span class="_ _21"> </span><span class="ff7 ls0">M<span class="_ _3"> </span><span class="ff8"><span class="_ _17"> </span></span>M<span class="_ _20"> </span></span><span class="ls1b">transmit<span class="_ _21"> </span>no<span class="_"> </span>n-</span></div><div class="t m0 x7 h9 y9f ff5 fs1 fc0 sc0 ls1c ws0">negativ<span class="_ _2"></span>e<span class="_ _4"> </span>semi-definite<span class="_ _22"> </span>(Hermitian)<span class="_ _4"> </span>correla<span class="_ _2"></span>tion<span class="_ _4"> </span>matrix</div><div class="t m0 x7 h9 ya0 ff5 fs1 fc0 sc0 ls1d ws0">and<span class="_ _9"> </span>the<span class="_ _9"> </span><span class="ff7 ls0">i<span class="ff5">th<span class="_ _15"> </span>row<span class="_ _15"> </span>of<span class="_ _15"> </span><span class="ffb">H</span>,<span class="_ _9"> </span>re<span class="_ _8"></span>sp<span class="_ _8"></span>ect<span class="_ _8"></span>ive<span class="_ _8"></span>ly.<span class="_ _15"> </span>Not<span class="_ _8"></span>e<span class="_ _9"> </span>t<span class="_ _8"></span>hat<span class="_ _15"> </span>the<span class="_ _15"> </span>f<span class="_ _8"></span>orm<span class="_ _8"></span>er</span></span></div><div class="t m0 x7 h9 ya1 ff5 fs1 fc0 sc0 ls1e ws0">can<span class="_ _2e"> </span>be<span class="_ _2e"> </span>represented<span class="_ _2f"> </span>as<span class="_ _2e"> </span><span class="ffb ls0">R</span></div><div class="t m0 x38 h10 ya2 ff7 fs9 fc0 sc0 ls18 ws0">Tx</div><div class="t m0 x39 hb ya3 ff8 fs1 fc0 sc0 ls0 ws0">¼<span class="_ _0"> </span><span class="ffb">R</span></div><div class="t m0 x3a h13 ya4 ff5 fs9 fc0 sc0 ls0 ws0">1<span class="ff12">=</span>2</div><div class="t m0 x3a h10 ya5 ff7 fs9 fc0 sc0 ls18 ws0">Tx</div><div class="t m0 x3b h14 ya3 ffb fs1 fc0 sc0 ls0 ws0">R</div><div class="t m0 x3c h13 ya4 ff7 fs9 fc0 sc0 ls0 ws0">H<span class="_ _25"> </span><span class="ff12">=<span class="_"> </span><span class="ff5">2</span></span></div><div class="t m0 x3c h10 ya5 ff7 fs9 fc0 sc0 ls18 ws0">Tx</div><div class="t m0 x3d h9 ya3 ff5 fs1 fc0 sc0 ls1f ws0">(Cholesky</div><div class="t m0 x7 h9 ya6 ff5 fs1 fc0 sc0 ls20 ws0">factorisation).</div><div class="t m0 x2b h9 ya7 ff5 fs1 fc0 sc0 ls0 ws0">The<span class="_ _5"> </span>Ricean<span class="_ _5"> </span>channel<span class="_ _13"> </span>matrix<span class="_ _5"> </span><span class="ffb">H<span class="_ _5"> </span></span>is<span class="_ _5"> </span>composed<span class="_ _5"> </span>of<span class="_ _5"> </span>two</div><div class="t m0 x7 h9 ya8 ff5 fs1 fc0 sc0 ls0 ws0">components:<span class="_ _21"> </span>the<span class="_ _4"> </span>LOS<span class="_ _21"> </span>component<span class="_ _22"> </span>(deterministic<span class="_ _21"> </span>and</div><div class="t m0 x7 h9 ya9 ff5 fs1 fc0 sc0 ls0 ws0">constant)<span class="_ _1c"> </span>and<span class="_ _1c"> </span>a<span class="_ _1c"> </span>componen<span class="_ _8"></span>t<span class="_ _1c"> </span>resulting<span class="_ _1c"> </span>from<span class="_ _1c"> </span>multipath</div><div class="t m0 x7 h9 yaa ff5 fs1 fc0 sc0 ls0 ws0">propagation<span class="_ _3"> </span>(randomly<span class="_ _3"> </span>varying).<span class="_ _3"> </span>Hence,<span class="_ _3"> </span>the<span class="_ _d"> </span>channel<span class="_ _3"> </span>matrix</div><div class="t m0 x7 h9 yab ffb fs1 fc0 sc0 ls0 ws0">H<span class="ff5">,<span class="_ _24"> </span>which<span class="_ _12"> </span>contain<span class="_ _8"></span>s<span class="_ _24"> </span>transmit<span class="_ _12"> </span>antenna<span class="_ _24"> </span>correlation<span class="_ _12"> </span>but<span class="_ _12"> </span>no</span></div><div class="t m0 x7 h9 yac ff5 fs1 fc0 sc0 ls0 ws0">receive<span class="_ _c"> </span>correlation<span class="_ _c"> </span><span class="fc1">[16]</span>,<span class="_ _c"> </span>is<span class="_ _c"> </span>given<span class="_ _c"> </span>by</div><div class="t m0 x5 hb yad ffb fs1 fc0 sc0 ls0 ws0">H<span class="_ _d"> </span><span class="ff8">¼</span></div><div class="t m0 x3e h15 yae ff10 fs1 fc0 sc0 ls0 ws0"></div><div class="t m0 x37 h14 yad ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 x3f h10 yaf ff7 fs9 fc0 sc0 ls0 ws0">w</div><div class="t m0 x40 h14 yb0 ffb fs1 fc0 sc0 ls0 ws0">R</div><div class="t m0 x41 h13 yb1 ff5 fs9 fc0 sc0 ls0 ws0">1<span class="ff12">=</span>2</div><div class="t m0 x41 h10 yb2 ff7 fs9 fc0 sc0 ls0 ws0">Tx</div><div class="t m0 x42 hb yb0 ff8 fs1 fc0 sc0 ls0 ws0">þ</div><div class="t m0 x43 h15 yb3 ff10 fs1 fc0 sc0 ls0 ws0"></div><div class="t m0 x44 h14 yb0 ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 x45 h13 yaf ff5 fs9 fc0 sc0 ls0 ws0">LOS</div><div class="t m0 x46 h9 yb0 ff5 fs1 fc0 sc0 ls0 ws0">(3)</div><div class="t m0 x7 h9 yb4 ff5 fs1 fc0 sc0 ls0 ws0">where</div><div class="t m0 x47 h15 yb5 ff10 fs1 fc0 sc0 ls0 ws0"></div><div class="t m0 x48 h14 yb6 ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 x49 h10 yb7 ff7 fs9 fc0 sc0 ls0 ws0">w</div><div class="t m0 x4a hb yb8 ff8 fs1 fc0 sc0 ls0 ws0">¼</div><div class="t m0 x4b h11 yb9 ffe fs1 fc0 sc0 ls0 ws0">ffiffiffiffiffiffiffiffiffiffiffi</div><div class="t m0 x4c h9 yba ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m1 x4b h12 ybb fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x4d hb ybb ff8 fs1 fc0 sc0 ls0 ws0">þ<span class="_ _17"> </span><span class="ff5">1</span></div><div class="t m0 x4e h11 ybc ffe fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 x5 h14 ybd ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 x4f h10 yb7 ff7 fs9 fc0 sc0 ls0 ws0">w</div><div class="t m0 x3e h9 yb8 ff5 fs1 fc0 sc0 ls0 ws0">and</div><div class="t m0 x38 h15 ybe ff10 fs1 fc0 sc0 ls0 ws0"></div><div class="t m0 x50 h14 yb8 ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 x42 h13 yb7 ff5 fs9 fc0 sc0 ls0 ws0">LOS</div><div class="t m0 x51 hb yb8 ff8 fs1 fc0 sc0 ls0 ws0">¼</div><div class="t m0 x52 h11 ybf ffe fs1 fc0 sc0 ls0 ws0">ffiffiffiffiffiffiffiffiffiffiffi</div><div class="t m1 x53 h12 yba fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m1 x52 h12 yc0 fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x54 hb ybb ff8 fs1 fc0 sc0 ls0 ws0">þ<span class="_ _17"> </span><span class="ff5">1</span></div><div class="t m0 x55 h11 yc1 ffe fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 x56 h14 ybd ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 x57 h13 yb7 ff5 fs9 fc0 sc0 ls0 ws0">LOS</div><div class="t m0 x46 h9 yb8 ff5 fs1 fc0 sc0 ls0 ws0">(4)</div><div class="t m0 x7 hb yc2 ff5 fs1 fc0 sc0 ls0 ws0">The<span class="_ _0"> </span><span class="ff7">N<span class="_ _3"> </span><span class="ff8"><span class="_ _17"> </span></span>M<span class="_ _3"> </span></span>matrix<span class="_ _0"> </span><span class="ffb">H</span></div><div class="t m0 x58 h10 yc3 ff7 fs9 fc0 sc0 ls0 ws0">w</div><div class="t m0 x59 h9 yc4 ff5 fs1 fc0 sc0 ls0 ws0">consists<span class="_ _17"> </span>of<span class="_ _3"> </span>i.i.d.<span class="_ _0"> </span>circularly<span class="_ _17"> </span>symmetric</div><div class="t m0 x7 h9 yc5 ff5 fs1 fc0 sc0 ls0 ws0">Gaussian<span class="_ _14"> </span>random<span class="_ _23"> </span>variables<span class="_ _14"> </span>with<span class="_ _23"> </span>zero<span class="_ _14"> </span>mean<span class="_ _23"> </span>and<span class="_ _23"> </span>unit</div><div class="t m0 x7 hb yc6 ff5 fs1 fc0 sc0 ls0 ws0">variance<span class="_ _a"> </span><span class="ff11"><span class="_ _c"> </span><span class="ff8">CN<span class="_ _10"> </span></span></span>0,<span class="_ _c"> </span>1<span class="_ _30"></span><span class="ff8 ls21">ðÞ<span class="_ _31"></span><span class="ff12 ls0">:</span></span></div><div class="t m0 x5a h15 yc7 ff10 fs1 fc0 sc0 ls0 ws0"></div><div class="t m0 x5b h14 yc6 ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 x59 h13 yc8 ff5 fs9 fc0 sc0 ls0 ws0">LOS</div><div class="t m0 x5c hb yc9 ff13 fs1 fc0 sc0 ls0 ws0">W<span class="_ _0"> </span><span class="ffd">E<span class="_ _c"> </span><span class="ffb">H<span class="_ _32"></span><span class="ff8 ls22">½<span class="_ _26"></span><span class="ff5 ls0">represents<span class="_ _a"> </span>the<span class="_ _9"> </span>channel</span></span></span></span></div><div class="t m0 x7 h9 yca ff5 fs1 fc0 sc0 ls0 ws0">mean<span class="_ _a"> </span>and</div><div class="t m1 x2d h12 ycb fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x5d h9 ycb ff5 fs1 fc0 sc0 ls0 ws0">defines<span class="_ _d"> </span>the<span class="_ _9"> </span>Ricean<span class="_ _a"> </span>factor,<span class="_ _a"> </span>which<span class="_ _a"> </span>indicates<span class="_ _a"> </span>the</div><div class="t m0 x7 h9 ycc ff5 fs1 fc0 sc0 ls0 ws0">strength<span class="_ _9"> </span>of<span class="_ _15"> </span>the<span class="_ _e"> </span>L<span class="_ _2"></span>OS<span class="_ _15"> </span>component<span class="_ _15"> </span>relative<span class="_ _9"> </span>to<span class="_ _e"> </span>the<span class="_ _15"> </span>multipath</div><div class="t m0 x7 h9 ycd ff5 fs1 fc0 sc0 ls0 ws0">component.<span class="_ _13"> </span>Following<span class="_ _13"> </span>the<span class="_ _13"> </span>definition<span class="_ _14"> </span>in<span class="_ _13"> </span><span class="fc1">[17]</span>,<span class="_ _14"> </span>we<span class="_ _13"> </span>can</div><div class="t m0 x7 h9 yce ff5 fs1 fc0 sc0 ls0 ws0">readily<span class="_ _c"> </span>see<span class="_ _c"> </span>that</div><div class="t m1 x5 h12 ycf fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x5e hb ycf ff8 fs1 fc0 sc0 ls0 ws0">¼</div><div class="t m0 x5f hb yd0 ff8 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x60 h15 yd1 ff10 fs1 fc0 sc0 ls0 ws0"></div><div class="t m0 x61 h14 yd0 ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 x50 h13 yd2 ff5 fs9 fc0 sc0 ls0 ws0">LOS</div><div class="t m0 x62 hb yd0 ff8 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x43 h13 yd3 ff5 fs9 fc0 sc0 ls0 ws0">2</div><div class="t m0 x63 hb yd4 ffd fs1 fc0 sc0 ls0 ws0">E<span class="_ _e"> </span><span class="ff8">k<span class="ffb">H<span class="_ _3"> </span></span></span></div><div class="t m0 x64 h15 yd5 ff10 fs1 fc0 sc0 ls0 ws0"></div><div class="t m0 x65 h14 yd4 ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 x66 h13 yd6 ff5 fs9 fc0 sc0 ls0 ws0">LOS</div><div class="t m0 x67 hb yd4 ff8 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x27 h13 yd7 ff5 fs9 fc0 sc0 ls0 ws0">2</div><div class="t m0 x59 h11 yd8 ffe fs1 fc0 sc0 ls23 ws0">hi</div><div class="t m0 x46 h9 yd9 ff5 fs1 fc0 sc0 ls0 ws0">(5)</div><div class="t m0 x7 hb yda ff5 fs1 fc0 sc0 ls0 ws0">where<span class="_ _3"> </span><span class="ff8 ls24">k<span class="_ _33"></span><span class="lse">ðÞ<span class="_ _34"></span>k<span class="_ _25"></span><span class="ff5 ls0">denotes<span class="_ _3"> </span>Frobenius<span class="_ _3"> </span>norm.<span class="_ _3"> </span>Moreover,<span class="_ _c"> </span>we<span class="_ _3"> </span>assume</span></span></span></div><div class="t m0 x7 h9 ydb ff5 fs1 fc0 sc0 ls0 ws0">that<span class="_ _10"> </span>the<span class="_ _f"> </span>transmitter<span class="_ _f"> </span>and<span class="_ _f"> </span>receiver<span class="_ _10"> </span>are<span class="_ _10"> </span>positioned<span class="_ _f"> </span>far<span class="_ _f"> </span>from</div><div class="t m0 x7 h9 ydc ff5 fs1 fc0 sc0 ls0 ws0">each<span class="_ _18"> </span>other,<span class="_ _12"> </span>which<span class="_ _24"> </span>is<span class="_ _24"> </span>always<span class="_ _18"> </span>the<span class="_ _24"> </span>case<span class="_ _24"> </span>in<span class="_ _24"> </span>many<span class="_ _24"> </span>practical</div><div class="t m0 x7 h9 ydd ff5 fs1 fc0 sc0 ls0 ws0">applications<span class="_ _20"> </span><span class="fc1">[5]</span>.<span class="_ _19"> </span>Consequently,<span class="_ _20"> </span>the<span class="_ _20"> </span>channe<span class="_ _8"></span>l<span class="_ _20"> </span>can<span class="_ _19"> </span>be</div><div class="t m0 x7 h9 yde ff5 fs1 fc0 sc0 ls0 ws0">approximated<span class="_ _c"> </span>by</div><div class="t m0 x68 hb ydf ffb fs1 fc0 sc0 ls0 ws0">H<span class="_ _d"> </span><span class="ff8">¼</span></div><div class="t m0 x69 h11 ye0 ffe fs1 fc0 sc0 ls0 ws0">ffiffiffiffiffiffiffiffiffiffiffi</div><div class="t m0 x5 h9 ye1 ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m1 x69 h12 ye2 fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x5 hb ye2 ff8 fs1 fc0 sc0 ls0 ws0">þ<span class="_ _17"> </span><span class="ff5">1</span></div><div class="t m0 x35 h11 ye3 ffe fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 x58 h14 ye4 ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 x3e h10 ye5 ff7 fs9 fc0 sc0 ls0 ws0">w</div><div class="t m0 x6a h14 ye6 ffb fs1 fc0 sc0 ls0 ws0">R</div><div class="t m0 x6b h13 ye7 ff5 fs9 fc0 sc0 ls0 ws0">1<span class="ff12">=</span>2</div><div class="t m0 x6b h10 ye8 ff7 fs9 fc0 sc0 ls0 ws0">Tx</div><div class="t m0 x6c hb ye6 ff8 fs1 fc0 sc0 ls0 ws0">þ</div><div class="t m0 x44 h11 ye9 ffe fs1 fc0 sc0 ls0 ws0">ffiffiffiffiffiffiffiffiffiffiffi</div><div class="t m1 x45 h12 ye1 fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m1 x44 h12 yea fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x6d hb ye2 ff8 fs1 fc0 sc0 ls0 ws0">þ<span class="_ _17"> </span><span class="ff5">1</span></div><div class="t m0 x6e h11 yeb ffe fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 x3b h9 ye4 ff5 fs1 fc0 sc0 ls0 ws0">e</div><div class="t m0 x6f h10 yec ff7 fs9 fc0 sc0 ls0 ws0">j</div><div class="t m2 x70 h16 yec fff fsb fc0 sc0 ls0 ws0">u</div><div class="t m0 x71 h17 ye6 fff fs1 fc0 sc0 ls0 ws0">C</div><div class="t m0 x72 h13 ye5 ff7 fs9 fc0 sc0 ls0 ws0">N<span class="_ _1b"> </span><span class="ff5">,</span>M</div><div class="t m0 x46 h9 ye6 ff5 fs1 fc0 sc0 ls0 ws0">(6)</div><div class="t m0 x7 h17 yed ff5 fs1 fc0 sc0 ls0 ws0">wher<span class="_ _2"></span>e<span class="_ _10"> </span><span class="fff">C</span></div><div class="t m0 x2c h13 y8e ff7 fs9 fc0 sc0 ls0 ws0">N<span class="_ _1b"> </span><span class="ff5">,</span>M</div><div class="t m0 x4c hb y8f ff5 fs1 fc0 sc0 ls0 ws0">deno<span class="_ _2"></span>tes<span class="_ _10"> </span>the<span class="_ _10"> </span><span class="ff7">N<span class="_ _d"> </span><span class="ff8"><span class="_ _0"> </span></span>M<span class="_ _24"> </span></span>matrix<span class="_ _e"> </span>of<span class="_ _f"> </span>all<span class="_ _f"> </span>1’s.<span class="_ _10"> </span>It<span class="_ _f"> </span>is</div><div class="t m0 x7 h9 yee ff5 fs1 fc0 sc0 ls0 ws0">rea<span class="_ _2"></span>so<span class="_ _2"></span>nabl<span class="_ _2"></span>e<span class="_ _0"> </span>to<span class="_ _0"> </span>co<span class="_ _2"></span>nsid<span class="_ _2"></span>er</div><div class="t m1 x5b h12 yef fff fsa fc0 sc0 ls0 ws0">u</div><div class="t m0 x37 hb yef ff8 fs1 fc0 sc0 ls0 ws0">¼<span class="_ _0"> </span><span class="ff14">+</span></div><div class="t m1 x73 h12 yef fff fsa fc0 sc0 ls0 ws0">p</div><div class="t m0 x74 h9 yef ff12 fs1 fc0 sc0 ls0 ws0">=<span class="ff5">4,<span class="_ _0"> </span>with<span class="_ _17"> </span>e</span></div><div class="t m0 x2 h10 yf0 ff7 fs9 fc0 sc0 ls0 ws0">j</div><div class="t m2 x75 h16 yf0 fff fsb fc0 sc0 ls0 ws0">u</div><div class="t m0 x76 hb yef ff8 fs1 fc0 sc0 ls0 ws0">¼<span class="_ _5"> </span><span class="ff5">(1<span class="_ _17"> </span></span>þ<span class="_ _0"> </span><span class="ff7">j<span class="_ _8"></span><span class="ff5">)<span class="ff12">=</span></span></span></div><div class="t m0 x77 h11 yf1 ffe fs1 fc0 sc0 ls0 ws0">ffiffi<span class="_ _35"></span>ffi</div><div class="t m0 x77 h9 yef ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x78 hb yf1 ff8 fs1 fc0 sc0 ls0 ws0">p</div><div class="t m0 x79 h11 yf2 ffe fs1 fc0 sc0 ls25 ws0"></div><div class="t m0 x7a h9 yf3 ff5 fs1 fc0 sc0 ls0 ws0">,</div><div class="t m0 x8 h3 yf4 ff3 fs1 fc0 sc0 ls0 ws0">IET<span class="_ _c"> </span>Commun.<span class="_ _8"></span><span class="ff1">,<span class="_ _3"> </span>2009,<span class="_ _0"> </span>Vol.<span class="_ _c"> </span>3,<span class="_ _3"> </span>Iss.<span class="_ _3"> </span>1,<span class="_ _3"> </span>pp.<span class="_ _3"> </span>10<span class="_ _1b"></span>–<span class="_ _1b"> </span>16<span class="_ _1d"> </span>11</span></div><div class="t m0 x8 h3 yf5 ff1 fs1 fc0 sc0 ls0 ws0">doi:<span class="_ _1f"> </span>10.1049/iet-com:20080110</div><div class="t m0 x7b hc y48 ff9 fs6 fc0 sc0 ls0 ws0">&</div><div class="t m0 x7c h3 y49 ff1 fs1 fc0 sc0 ls0 ws0">The<span class="_ _3"> </span>Institution<span class="_ _3"> </span>of<span class="_ _3"> </span>Engineering<span class="_ _3"> </span>and<span class="_ _3"> </span>T<span class="_ _b"></span>echnology<span class="_ _3"> </span>2009</div><div class="t m0 x6d hd y4a ff2 fs7 fc0 sc0 ls0 ws0">www<span class="_ _b"></span>.ietdl.or<span class="_ _2"></span>g</div><div class="t m0 xa he y4b ffa fs8 fc0 sc0 ls0 ws0">Authorized licensed use limited to: Shantou University. Downloaded on June 24, 2009 at 03:15 from IEEE Xplore. Restrictions apply.</div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://csdnimg.cn/release/download_crawler_static/11532111/bg3.jpg"><div class="t m0 x3 h9 y4c ff5 fs1 fc0 sc0 ls0 ws0">whic<span class="_ _2"></span>h<span class="_ _18"> </span>indi<span class="_ _2"></span>ca<span class="_ _2"></span>tes<span class="_ _18"> </span>a<span class="_ _2"></span>n<span class="_ _18"> </span>equal<span class="_ _f"> </span>powe<span class="_ _2"></span>r<span class="_ _18"> </span>of<span class="_ _18"> </span>L<span class="_ _2"></span>O<span class="_ _2"></span>S<span class="_ _18"> </span>compon<span class="_ _2"></span>ent<span class="_ _f"> </span>per</div><div class="t m0 x3 hb y4d ff5 fs1 fc0 sc0 ls0 ws0">dime<span class="_ _2"></span>nsio<span class="_ _2"></span>n<span class="_ _20"> </span>of<span class="_ _19"> </span>the<span class="_ _20"> </span><span class="ffb">H<span class="_ _19"> </span></span>entrie<span class="_ _2"></span>s<span class="_ _20"> </span><span class="fc1">[5]</span><span class="ls26">.H<span class="_ _33"></span>e<span class="_ _36"></span>n<span class="_ _33"></span>c<span class="_ _36"></span>e<span class="_ _33"></span>,<span class="ffb ls0">H<span class="_ _d"> </span><span class="ff11"><span class="_ _c"> </span><span class="ff8">CN</span></span></span></span></div><div class="t m0 x7d h9 y4e ffb fs1 fc0 sc0 ls0 ws0">M<span class="_ _25"></span><span class="ff5">,<span class="_ _c"> </span></span>I</div><div class="t m0 xb h10 yf6 ff7 fs9 fc0 sc0 ls0 ws0">N</div><div class="t m0 x7e hb yf7 ff8 fs1 fc0 sc0 ls0 ws0"><span class="fff">S</span></div><div class="t m0 x3 h11 yf8 ffe fs1 fc0 sc0 ls27 ws0"></div><div class="t m0 x7f hb yf7 ff5 fs1 fc0 sc0 ls0 ws0">wit<span class="_ _2"></span>h<span class="_ _c"> </span><span class="ffb">M<span class="_ _d"> </span><span class="ff8">¼<span class="_ _c"> </span><span class="ffd">E</span></span></span>{<span class="ffb">H<span class="_ _1b"></span></span>}<span class="_ _c"> </span><span class="ff8">¼</span></div><div class="t m0 x80 h11 yf9 ffe fs1 fc0 sc0 ls0 ws0">ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi</div><div class="t m1 x80 h12 yf7 fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x81 h9 yf7 ff12 fs1 fc0 sc0 ls0 ws0">=<span class="ff5">(</span></div><div class="t m1 xd h12 yf7 fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x82 hb yf7 ff8 fs1 fc0 sc0 ls0 ws0">þ<span class="_ _17"> </span><span class="ff5">1)</span></div><div class="t m0 x83 h11 yf9 ffe fs1 fc0 sc0 ls0 ws0">p</div><div class="t m0 x84 hb yf7 ff5 fs1 fc0 sc0 ls0 ws0">(1<span class="_ _17"> </span><span class="ff8">þ<span class="_ _0"> </span><span class="ff7">j<span class="_ _8"></span></span></span>)<span class="ff12">=</span></div><div class="t m0 x25 h11 yfa ffe fs1 fc0 sc0 ls0 ws0">ffiffi<span class="_ _35"></span>ffi</div><div class="t m0 x25 h9 yf7 ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x23 hb yfa ff8 fs1 fc0 sc0 ls0 ws0">p</div><div class="t m0 x85 h11 yfb ffe fs1 fc0 sc0 ls25 ws0"></div><div class="t m0 x86 h17 yfc fff fs1 fc0 sc0 ls0 ws0">C</div><div class="t m0 x6 h13 yfd ff7 fs9 fc0 sc0 ls0 ws0">N<span class="_ _1b"> </span><span class="ff5">,</span>M</div><div class="t m0 x87 hb yfe ff5 fs1 fc0 sc0 ls0 ws0">,<span class="_ _0"> </span><span class="fff">S<span class="_ _c"> </span><span class="ff8">¼<span class="_ _0"> </span><span class="ffb">R</span></span></span></div><div class="t m0 x88 h10 yfd ff7 fs9 fc0 sc0 ls28 ws0">Tx</div><div class="t m0 x89 h14 yfe ffb fs1 fc0 sc0 ls0 ws0">I</div><div class="t m0 x8a h10 yfd ff7 fs9 fc0 sc0 ls0 ws0">M</div><div class="t m0 x8b hb yfe ff5 fs1 fc0 sc0 ls0 ws0">is<span class="_ _15"> </span>the<span class="_ _e"> </span>cova<span class="_ _2"></span>ria<span class="_ _2"></span>nce<span class="_ _e"> </span>mat<span class="_ _2"></span>rix<span class="_ _15"> </span>of<span class="_ _10"> </span><span class="ffb">H<span class="_ _e"> </span></span>and<span class="_ _e"> </span><span class="ff8"></span></div><div class="t m0 x3 h9 yff ff5 fs1 fc0 sc0 ls0 ws0">deno<span class="_ _2"></span>tes<span class="_ _17"> </span>the<span class="_ _17"> </span>Kron<span class="_ _2"></span>eck<span class="_ _2"></span>er<span class="_ _17"> </span>pro<span class="_ _2"></span>duct<span class="_ _17"> </span>of<span class="_ _0"> </span>ma<span class="_ _2"></span>t<span class="_ _2"></span>rice<span class="_ _2"></span>s.</div><div class="t m0 x6 h9 y100 ff5 fs1 fc0 sc0 ls0 ws0">As<span class="_ _0"> </span>previously<span class="_ _0"> </span>disclosed,<span class="_ _0"> </span>we<span class="_ _0"> </span>constrain<span class="_ _0"> </span>our<span class="_ _0"> </span>discussion<span class="_ _0"> </span>to<span class="_ _0"> </span>the</div><div class="t m0 x3 h9 y101 ff5 fs1 fc0 sc0 ls0 ws0">exponential<span class="_ _4"> </span>correlation<span class="_ _22"> </span>model<span class="_ _4"> </span><span class="fc1">[15]</span>.<span class="_ _22"> </span>For<span class="_ _4"> </span>this<span class="_ _22"> </span>model,</div><div class="t m0 x3 h9 y102 ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _24"> </span>entries<span class="_ _12"> </span>of<span class="_ _12"> </span>the<span class="_ _24"> </span>transmit<span class="_ _12"> </span>correlation<span class="_ _24"> </span>matrix,<span class="_ _24"> </span><span class="ffb">R</span></div><div class="t m0 x8c h10 y103 ff7 fs9 fc0 sc0 ls0 ws0">Tx</div><div class="t m0 x8d h9 y104 ff5 fs1 fc0 sc0 ls29 ws0">,a<span class="_ _27"></span>r<span class="_ _37"></span>e</div><div class="t m0 x3 h9 y105 ff5 fs1 fc0 sc0 ls0 ws0">given<span class="_ _c"> </span>by</div><div class="t m0 x8e h18 y106 ff7 fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 x8f h13 y107 ff7 fs9 fc0 sc0 ls0 ws0">i<span class="ff5">,<span class="_ _17"> </span></span>j</div><div class="t m0 x1b hb y108 ff8 fs1 fc0 sc0 ls0 ws0">¼</div><div class="t m0 x90 h18 y109 ff7 fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 x91 hf y10a ff7 fs9 fc0 sc0 ls0 ws0">j<span class="_ _8"></span><span class="ff8"></span>i</div><div class="t m0 x92 hb y10b ff5 fs1 fc0 sc0 ls0 ws0">,<span class="_ _2c"> </span><span class="ff7">i<span class="_ _c"> </span><span class="ff8"><span class="_ _c"> </span></span>j</span></div><div class="t m0 x90 h18 y10c ff7 fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 x91 hf y10d ff8 fs9 fc0 sc0 ls0 ws0"></div><div class="t m0 x91 h13 y10e ff7 fs9 fc0 sc0 ls0 ws0">j<span class="_ _8"></span><span class="ff5">,</span>i</div><div class="t m0 x93 hb y10f ff5 fs1 fc0 sc0 ls0 ws0">,<span class="_ _38"> </span><span class="ff7">i<span class="_ _c"> </span><span class="ff15">.<span class="_ _c"> </span></span>j<span class="_ _8"></span></span>,<span class="_ _2c"> </span><span class="ff8">j<span class="ff7">r<span class="_ _25"></span></span><span class="ls2a">j</span></span>1</div><div class="t m0 x94 h11 y110 ffe fs1 fc0 sc0 ls0 ws0"></div><div class="t m0 x95 h9 y111 ff5 fs1 fc0 sc0 ls0 ws0">(7)</div><div class="t m0 x3 hb y112 ff5 fs1 fc0 sc0 ls0 ws0">where<span class="_ _1c"> </span><span class="ff8"><span class="_ _27"></span><span class="lse">ðÞ</span></span></div><div class="t m0 x96 hf y113 ff8 fs9 fc0 sc0 ls0 ws0"></div><div class="t m0 x97 h9 y114 ff5 fs1 fc0 sc0 ls0 ws0">denotes<span class="_ _e"> </span>complex<span class="_ _e"> </span>conjugate<span class="_ _e"> </span>and<span class="_ _e"> </span><span class="ff7">r</span></div><div class="t m0 x98 h10 y115 ff7 fs9 fc0 sc0 ls0 ws0">ij</div><div class="t m0 x84 hb y114 ff5 fs1 fc0 sc0 ls0 ws0">,<span class="_ _15"> </span>the<span class="_ _21"> </span><span class="ff7">i</span>,<span class="_ _c"> </span><span class="ff7">j<span class="_ _39"></span><span class="ff8 ls2b">ðÞ<span class="_ _3a"></span><span class="ff5 ls0">th</span></span></span></div><div class="t m0 x3 h9 y116 ff5 fs1 fc0 sc0 ls0 ws0">entry<span class="_ _9"> </span>of<span class="_ _e"> </span><span class="ffb">R</span></div><div class="t m0 x99 h10 y117 ff7 fs9 fc0 sc0 ls0 ws0">Tx</div><div class="t m0 x8e hb y118 ff5 fs1 fc0 sc0 ls0 ws0">with<span class="_ _15"> </span><span class="ff7">i<span class="_ _c"> </span><span class="ff8">¼<span class="_ _c"> </span></span></span>1,<span class="_ _0"> </span>2,<span class="_ _3"> </span><span class="ff10 ls13">...<span class="_"> </span></span>,<span class="_ _c"> </span><span class="ff7">M<span class="_ _f"> </span></span>and<span class="_ _15"> </span><span class="ff7">j<span class="_ _3"> </span><span class="ff8">¼<span class="_ _c"> </span></span></span>1,<span class="_ _0"> </span>2,<span class="_ _3"> </span><span class="ff10 ls13">...<span class="_"> </span></span>,<span class="_ _c"> </span><span class="ff7">M<span class="_ _25"></span></span>,</div><div class="t m0 x3 h9 y119 ff5 fs1 fc0 sc0 ls0 ws0">is<span class="_ _14"> </span>the<span class="_ _14"> </span>complex<span class="_ _14"> </span>correlation<span class="_ _14"> </span>coefficient<span class="_ _23"> </span>of<span class="_ _14"> </span>neighbouring</div><div class="t m0 x3 h9 y11a ff5 fs1 fc0 sc0 ls0 ws0">transmit<span class="_ _3"> </span>branches.<span class="_ _d"> </span>On<span class="_ _a"> </span>the<span class="_ _d"> </span>basis<span class="_ _d"> </span>of<span class="_ _a"> </span>(7),<span class="_ _d"> </span>we<span class="_ _3"> </span>write<span class="_ _a"> </span><span class="ffb">R</span></div><div class="t m0 x9a h10 y11b ff7 fs9 fc0 sc0 ls0 ws0">Tx</div><div class="t m0 x9b h9 y11c ff5 fs1 fc0 sc0 ls0 ws0">in<span class="_ _d"> </span>its</div><div class="t m0 x3 h9 y11d ff5 fs1 fc0 sc0 ls0 ws0">matrix<span class="_ _c"> </span>form<span class="_ _c"> </span>as</div><div class="t m0 x9c h14 y11e ffb fs1 fc0 sc0 ls0 ws0">R</div><div class="t m0 x99 h10 y11f ff7 fs9 fc0 sc0 ls0 ws0">Tx</div><div class="t m0 x7f hb y120 ff8 fs1 fc0 sc0 ls0 ws0">¼</div><div class="t m0 x9d h9 y121 ff5 fs1 fc0 sc0 ls0 ws0">1<span class="_ _3b"> </span><span class="ff7 ls2c">rr</span></div><div class="t m0 x9e h13 y122 ff5 fs9 fc0 sc0 ls0 ws0">2</div><div class="t m0 x9f h18 y123 ff10 fs1 fc0 sc0 ls13 ws0">...<span class="_ _21"> </span><span class="ff7 ls0">r</span></div><div class="t m0 xa0 hf y122 ff7 fs9 fc0 sc0 ls0 ws0">M<span class="_ _25"></span><span class="ff8"><span class="ff5">1</span></span></div><div class="t m0 xa1 h18 y124 ff7 fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 x20 hf y125 ff8 fs9 fc0 sc0 ls0 ws0"></div><div class="t m0 xa2 h9 y124 ff5 fs1 fc0 sc0 ls0 ws0">1<span class="_ _3c"> </span><span class="ff7">r</span></div><div class="t m0 xa3 h15 y126 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xa4 h15 y124 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 x9f h15 y127 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xa5 h15 y128 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xa5 h15 y129 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xa5 h15 y12a ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xa6 h18 y12b ff7 fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 x9d hf y12c ff8 fs9 fc0 sc0 ls0 ws0"></div><div class="t m0 xa7 h13 y12d ff5 fs9 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa8 h18 y12e ff7 fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 xa9 hf y12c ff8 fs9 fc0 sc0 ls0 ws0"></div><div class="t m0 x83 h9 y12e ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m0 xa3 h15 y12f ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xa4 h15 y12e ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 x9f h15 y130 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xaa h18 y12e ff7 fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 x98 h13 y12c ff5 fs9 fc0 sc0 ls0 ws0">2</div><div class="t m0 x8b h15 y131 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 x8b h15 y132 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 x8b h15 y133 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xab h15 y134 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xac h15 y135 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xad h15 y136 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xae h15 y137 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xaf h15 y138 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xb0 h15 y139 ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xa3 h15 y13a ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xa4 h15 y13b ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 x9f h15 y13c ff10 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xb1 h18 y13b ff7 fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 xb2 h18 y13d ff7 fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 xb3 hf y13e ff8 fs9 fc0 sc0 ls0 ws0"></div><div class="t m0 xa1 hf y13f ff7 fs9 fc0 sc0 ls0 ws0">M<span class="_ _25"></span><span class="ff8"><span class="ff5">1</span></span></div><div class="t m0 xad h18 y140 ff10 fs1 fc0 sc0 ls13 ws0">...<span class="_ _21"> </span><span class="ff7 ls0">r</span></div><div class="t m0 x17 hf y13e ff8 fs9 fc0 sc0 ls0 ws0"></div><div class="t m0 xaf h13 y13f ff5 fs9 fc0 sc0 ls0 ws0">2</div><div class="t m0 xb4 h18 y140 ff7 fs1 fc0 sc0 ls0 ws0">r</div><div class="t m0 xb5 hf y13e ff8 fs9 fc0 sc0 ls0 ws0"></div><div class="t m0 xb1 h9 y140 ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m0 xb6 h11 y141 ffe fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 xb6 h11 y142 ffe fs1 fc0 sc0 ls0 ws0">6</div><div class="t m0 xb6 h11 y143 ffe fs1 fc0 sc0 ls0 ws0">6</div><div class="t m0 xb6 h11 y144 ffe fs1 fc0 sc0 ls0 ws0">6</div><div class="t m0 xb6 h11 y145 ffe fs1 fc0 sc0 ls0 ws0">6</div><div class="t m0 xb6 h11 y146 ffe fs1 fc0 sc0 ls0 ws0">6</div><div class="t m0 xb6 h11 y147 ffe fs1 fc0 sc0 ls0 ws0">6</div><div class="t m0 xb6 h11 y148 ffe fs1 fc0 sc0 ls0 ws0">6</div><div class="t m0 xb6 h11 y149 ffe fs1 fc0 sc0 ls0 ws0">6</div><div class="t m0 xb6 h11 y14a ffe fs1 fc0 sc0 ls0 ws0">4</div><div class="t m0 xb7 h11 y14b ffe fs1 fc0 sc0 ls0 ws0">3</div><div class="t m0 xb7 h11 y14c ffe fs1 fc0 sc0 ls0 ws0">7</div><div class="t m0 xb7 h11 y14d ffe fs1 fc0 sc0 ls0 ws0">7</div><div class="t m0 xb7 h11 y14e ffe fs1 fc0 sc0 ls0 ws0">7</div><div class="t m0 xb7 h11 y14f ffe fs1 fc0 sc0 ls0 ws0">7</div><div class="t m0 xb7 h11 y150 ffe fs1 fc0 sc0 ls0 ws0">7</div><div class="t m0 xb7 h11 y151 ffe fs1 fc0 sc0 ls0 ws0">7</div><div class="t m0 xb7 h11 y152 ffe fs1 fc0 sc0 ls0 ws0">7</div><div class="t m0 xb7 h11 y153 ffe fs1 fc0 sc0 ls0 ws0">7</div><div class="t m0 xb7 h11 y154 ffe fs1 fc0 sc0 ls0 ws0">5</div><div class="t m0 x95 h9 y155 ff5 fs1 fc0 sc0 ls0 ws0">(8)</div><div class="t m0 x3 h9 y156 ff5 fs1 fc0 sc0 ls0 ws0">Obviously,<span class="_ _c"> </span>this<span class="_ _c"> </span>model<span class="_ _3"> </span>is<span class="_ _c"> </span>physically<span class="_ _c"> </span>realistic<span class="_ _c"> </span>in<span class="_ _c"> </span>the<span class="_ _c"> </span>sense<span class="_ _c"> </span>that</div><div class="t m0 x3 h9 y157 ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _17"> </span>correlation<span class="_ _17"> </span>decreases<span class="_ _17"> </span>with<span class="_ _17"> </span>increasing<span class="_ _17"> </span>the<span class="_ _17"> </span>distance<span class="_ _17"> </span>between</div><div class="t m0 x3 h9 y158 ff5 fs1 fc0 sc0 ls0 ws0">transmit<span class="_ _c"> </span>antennas.</div><div class="t m0 x3 h8 y159 ff2 fs5 fc0 sc0 ls0 ws0">3<span class="_ _11"> </span>Perf<span class="_ _2"></span>ormance<span class="_ _f"> </span>analysis</div><div class="t m0 x3 h19 y15a ff3 fsc fc0 sc0 ls0 ws0">3.1<span class="_ _3d"> </span>BER<span class="_ _15"> </span>of<span class="_ _e"> </span>ZF<span class="_ _15"> </span>receiver<span class="_ _10"> </span>over<span class="_ _15"> </span>correlated</div><div class="t m0 x3 h19 y15b ff3 fsc fc0 sc0 ls0 ws0">ricean<span class="_ _e"> </span>channels</div><div class="t m0 x3 h9 y15c ff5 fs1 fc0 sc0 ls0 ws0">In<span class="_ _c"> </span>this<span class="_ _c"> </span>subsection,<span class="_ _c"> </span>the<span class="_ _c"> </span>main<span class="_ _3"> </span>focus<span class="_ _c"> </span>is<span class="_ _c"> </span>on<span class="_ _c"> </span>deriving<span class="_ _c"> </span>the<span class="_ _c"> </span>average</div><div class="t m0 x3 h9 y15d ff5 fs1 fc0 sc0 ls0 ws0">BER<span class="_ _13"> </span>performance<span class="_ _5"> </span>for<span class="_ _13"> </span>the<span class="_ _13"> </span>ZF<span class="_ _5"> </span>detector<span class="_ _13"> </span>ov<span class="_ _2"></span>er<span class="_ _13"> </span>transmit-</div><div class="t m0 x3 h9 y15e ff5 fs1 fc0 sc0 ls0 ws0">correlated<span class="_ _19"> </span>flat<span class="_ _19"> </span>Ricean<span class="_ _1a"> </span>fading<span class="_ _1a"> </span>channels<span class="_ _1a"> </span>with<span class="_ _1a"> </span>QPSK</div><div class="t m0 x3 h9 y15f ff5 fs1 fc0 sc0 ls0 ws0">modulation.</div><div class="t m0 x6 h9 y160 ff5 fs1 fc0 sc0 ls2d ws0">The<span class="_ _17"> </span>performance<span class="_ _0"> </span>of<span class="_ _17"> </span>spatial<span class="_ _17"> </span>multiplexing<span class="_ _17"> </span>with<span class="_ _17"> </span>linear<span class="_ _0"> </span>detectors</div><div class="t m0 x3 h9 y161 ff5 fs1 fc0 sc0 ls2e ws0">is<span class="_ _18"> </span>a<span class="_ _18"> </span>function<span class="_ _24"> </span>of<span class="_ _24"> </span>the<span class="_ _18"> </span>effective<span class="_ _18"> </span>signal-to-noise<span class="_ _24"> </span>ratio<span class="_ _18"> </span>(SNR),</div><div class="t m0 x3 h9 y162 ff5 fs1 fc0 sc0 ls2f ws0">denoted<span class="_ _9"> </span>by</div><div class="t m1 xb8 h12 y163 fff fsa fc0 sc0 ls0 ws0">g</div><div class="t m0 xb9 h10 y164 ff7 fs9 fc0 sc0 ls0 ws0">k</div><div class="t m0 xba hb y163 ff5 fs1 fc0 sc0 lsf ws0">,f<span class="_ _16"></span>o<span class="_ _28"></span>re<span class="_ _16"></span>a<span class="_ _16"></span>c<span class="_ _28"></span>hs<span class="_ _16"></span>t<span class="_ _16"></span>r<span class="_ _28"></span>e<span class="_ _16"></span>a<span class="_ _16"></span>mw<span class="_ _28"></span>i<span class="_ _16"></span>t<span class="_ _28"></span>h<span class="ff7 ls0">k<span class="_ _0"> </span><span class="ff8">¼<span class="_ _c"> </span><span class="ff5">1,<span class="_ _0"> </span>2,<span class="_ _3"> </span><span class="ff10 ls30">...<span class="_ _17"> </span></span>,<span class="_ _1f"> </span></span></span>M<span class="_ _25"></span></span>,a<span class="_ _28"></span>f<span class="_ _16"></span>t<span class="_ _16"></span>e<span class="_ _28"></span>r</div><div class="t m0 x3 h9 y165 ff5 fs1 fc0 sc0 ls31 ws0">linear<span class="_ _a"> </span>processing.<span class="_ _9"> </span>From<span class="_ _9"> </span><span class="fc1 ls32">[3]</span><span class="ls33">,<span class="_ _9"> </span>the<span class="_ _9"> </span>post-processing<span class="_ _9"> </span>SNR<span class="_ _a"> </span>of<span class="_ _9"> </span>the</span></div><div class="t m0 x3 h9 y166 ff7 fs1 fc0 sc0 ls0 ws0">k<span class="ff5 ls34">th<span class="_ _c"> </span>str<span class="_"> </span>eam<span class="_ _c"> </span>for<span class="_ _c"> </span>the<span class="_ _c"> </span>ZF<span class="_ _c"> </span>receiver<span class="_ _c"> </span>is<span class="_ _c"> </span>given<span class="_ _c"> </span>by</span></div><div class="t m1 xbb h12 y167 fff fsa fc0 sc0 ls0 ws0">g</div><div class="t m0 xbc h10 y168 ff7 fs9 fc0 sc0 ls0 ws0">k</div><div class="t m0 x21 hb y167 ff8 fs1 fc0 sc0 ls0 ws0">¼</div><div class="t m1 x22 h12 y169 fff fsa fc0 sc0 ls0 ws0">g</div><div class="t m0 xbd h13 y16a ff5 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 xab h14 y16b ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 xbe h10 y16c ff7 fs9 fc0 sc0 ls0 ws0">H</div><div class="t m0 xb0 h14 y16b ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 xad h11 y16d ffe fs1 fc0 sc0 ls35 ws0"></div><div class="t m0 xbf hf y16e ff8 fs9 fc0 sc0 ls0 ws0"><span class="ff5">1</span></div><div class="t m0 xbf h10 y16f ff7 fs9 fc0 sc0 ls36 ws0">kk</div><div class="t m0 x95 h9 y167 ff5 fs1 fc0 sc0 ls0 ws0">(9)</div><div class="t m0 x3 h9 y170 ff5 fs1 fc0 sc0 ls37 ws0">where</div><div class="t m1 xc0 h12 y8c fff fsa fc0 sc0 ls0 ws0">g</div><div class="t m0 x7e h13 y8b ff5 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 xc1 hb y8c ff8 fs1 fc0 sc0 ls0 ws0">¼</div><div class="t m1 xc2 h12 y8c fff fsa fc0 sc0 ls0 ws0">s</div><div class="t m0 xba h13 y171 ff5 fs9 fc0 sc0 ls0 ws0">2</div><div class="t m0 x8e h10 y8b ff7 fs9 fc0 sc0 ls0 ws0">x</div><div class="t m0 xc3 h18 y8c ff12 fs1 fc0 sc0 ls0 ws0">=<span class="ff7">N</span></div><div class="t m0 xb2 h13 y8b ff5 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 xa1 h9 y8c ff5 fs1 fc0 sc0 ls2e ws0">is<span class="_ _15"> </span>the<span class="_ _15"> </span>average<span class="_ _15"> </span>normalised<span class="_ _15"> </span>SNR<span class="_ _15"> </span>at<span class="_ _e"> </span>each</div><div class="t m0 x3 h9 y8d ff5 fs1 fc0 sc0 ls38 ws0">receiv<span class="_"> </span>e<span class="_ _10"> </span>antenna,<span class="_ _10"> </span>and<span class="_ _4"> </span><span class="ffb ls0">H</span></div><div class="t m0 x93 h10 y172 ff7 fs9 fc0 sc0 ls0 ws0">H</div><div class="t m0 xc4 h14 y8f ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 xbb h11 y173 ffe fs1 fc0 sc0 ls35 ws0"></div><div class="t m0 xc5 hf y174 ff8 fs9 fc0 sc0 ls0 ws0"><span class="ff5">1</span></div><div class="t m0 xc5 h10 y175 ff7 fs9 fc0 sc0 ls39 ws0">kk</div><div class="t m0 x9e hb y8f ff5 fs1 fc0 sc0 ls3a ws0">is<span class="_ _10"> </span>the<span class="_ _21"> </span><span class="ff7 ls0">k<span class="ff5">,<span class="_ _c"> </span></span>k<span class="_ _3e"></span><span class="ff8 ls3b">ðÞ<span class="_ _3f"></span><span class="ff5 ls3c">th<span class="_ _10"> </span>element<span class="_ _f"> </span>of</span></span></span></div><div class="t m0 x3 h9 yee ff5 fs1 fc0 sc0 ls3d ws0">matrix<span class="_ _13"> </span><span class="ffb ls0">H</span></div><div class="t m0 xc6 h10 yf0 ff7 fs9 fc0 sc0 ls0 ws0">H</div><div class="t m0 xc7 h14 yef ffb fs1 fc0 sc0 ls0 ws0">H</div><div class="t m0 xc0 h11 y176 ffe fs1 fc0 sc0 ls35 ws0"></div><div class="t m0 xc3 hf y177 ff8 fs9 fc0 sc0 ls0 ws0"><span class="ff5">1</span></div><div class="t m0 x1b h9 yef ff5 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 x2b h9 y178 ff5 fs1 fc0 sc0 ls0 ws0">Now<span class="_ _c"> </span>if<span class="_ _c"> </span>we<span class="_ _c"> </span>define</div><div class="t m0 x37 hb y179 ffb fs1 fc0 sc0 ls0 ws0">W<span class="_ _15"> </span><span class="ff8">¼<span class="_ _0"> </span></span>H</div><div class="t m0 x38 h10 y17a ff7 fs9 fc0 sc0 ls0 ws0">H</div><div class="t m0 x6e h9 y17b ffb fs1 fc0 sc0 ls0 ws0">H<span class="_ _40"> </span><span class="ff5">(10)</span></div><div class="t m0 x7 hb y17c ff5 fs1 fc0 sc0 ls0 ws0">then<span class="_ _e"> </span><span class="ffb">W<span class="_ _e"> </span></span>is<span class="_ _10"> </span>always<span class="_ _15"> </span>an<span class="_ _e"> </span><span class="ff7">M<span class="_ _3"> </span><span class="ff8"><span class="_ _17"> </span></span>M<span class="_ _18"> </span></span>square<span class="_ _10"> </span>matrix.<span class="_ _e"> </span>It<span class="_ _e"> </span>is<span class="_ _10"> </span>known</div><div class="t m0 x7 h9 y17d ff5 fs1 fc0 sc0 ls0 ws0">that<span class="_ _15"> </span>when<span class="_ _15"> </span><span class="ffb">H<span class="_ _18"> </span></span>is<span class="_ _9"> </span>a<span class="_ _15"> </span>complex<span class="_ _15"> </span>normal<span class="_"> </span>ly<span class="_ _e"> </span>distributed<span class="_ _15"> </span>matrix<span class="_ _15"> </span>as</div><div class="t m0 x7 h9 y17e ff5 fs1 fc0 sc0 ls0 ws0">described<span class="_ _3"> </span>earlier,<span class="_ _3"> </span>the<span class="_ _3"> </span>distribution<span class="_ _3"> </span>of<span class="_ _c"> </span><span class="ffb">W<span class="_ _3"> </span></span>is<span class="_ _3"> </span>given<span class="_ _c"> </span>by<span class="_ _3"> </span>the<span class="_ _3"> </span>non-</div><div class="t m0 x7 h9 y17f ff5 fs1 fc0 sc0 ls0 ws0">central<span class="_ _18"> </span>Wishart<span class="_ _24"> </span>distribution<span class="_ _24"> </span><span class="fc1">[18,<span class="_ _12"> </span>19]</span>.<span class="_ _24"> </span>Here<span class="_ _18"> </span>we<span class="_ _24"> </span>use<span class="_ _24"> </span>the</div><div class="t m0 x7 hb y180 ff5 fs1 fc0 sc0 ls0 ws0">shorthand<span class="_ _15"> </span>notation<span class="_ _e"> </span><span class="ffb">W<span class="_ _15"> </span><span class="ff11"><span class="_ _0"> </span><span class="ff8">CW</span></span></span></div><div class="t m0 xc8 h10 y181 ff7 fs9 fc0 sc0 ls0 ws0">M</div><div class="t m0 xc9 h9 y182 ff7 fs1 fc0 sc0 ls0 ws0">N<span class="_ _1"> </span><span class="ff5">,</span></div><div class="t m1 x43 h1a y182 ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 xca hb y182 ff8 fs1 fc0 sc0 ls3e ws0">ðÞ<span class="_ _41"></span><span class="ff5 ls0">to<span class="_ _15"> </span>denote<span class="_ _e"> </span>a<span class="_ _15"> </span>central</span></div><div class="t m0 x7 h9 y183 ff5 fs1 fc0 sc0 ls0 ws0">Wishart<span class="_ _c"> </span>distribution,<span class="_ _3"> </span>which<span class="_ _c"> </span>results<span class="_ _c"> </span>when<span class="_ _3"> </span>the<span class="_ _c"> </span>elements<span class="_ _3"> </span>of<span class="_ _c"> </span><span class="ffb">H</span></div><div class="t m0 x7 h9 y184 ff5 fs1 fc0 sc0 ls0 ws0">are<span class="_ _a"> </span>zero-mean<span class="_ _9"> </span>Gaussian<span class="_ _15"> </span>random<span class="_ _a"> </span>variables,<span class="_ _15"> </span>with<span class="_ _9"> </span><span class="ff7">N<span class="_ _9"> </span></span>degrees</div><div class="t m0 x7 h9 y185 ff5 fs1 fc0 sc0 ls0 ws0">of<span class="_ _21"> </span>freedom<span class="_ _21"> </span>(sample<span class="_ _21"> </span>size),<span class="_ _21"> </span>and</div><div class="t m1 xcb h1a y186 ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 xcc h9 y186 ff5 fs1 fc0 sc0 ls0 ws0">is<span class="_ _21"> </span>the<span class="_ _21"> </span>Hermitian</div><div class="t m0 x7 h9 y187 ff5 fs1 fc0 sc0 ls0 ws0">covariance<span class="_ _d"> </span>matrix<span class="_ _d"> </span>of<span class="_ _a"> </span>the<span class="_ _a"> </span>columns<span class="_ _d"> </span>(assumed<span class="_ _a"> </span>to<span class="_ _a"> </span>be<span class="_ _a"> </span>the<span class="_ _d"> </span>same</div><div class="t m0 x7 h9 y188 ff5 fs1 fc0 sc0 ls0 ws0">for<span class="_ _10"> </span>all<span class="_ _f"> </span>columns<span class="_ _8"></span>).<span class="_ _f"> </span>The<span class="_ _f"> </span>subscript<span class="_ _f"> </span><span class="ff7">M<span class="_ _f"> </span></span>explicitly<span class="_ _f"> </span>denotes<span class="_ _f"> </span>the</div><div class="t m0 x7 hb y189 ff5 fs1 fc0 sc0 ls0 ws0">sample<span class="_ _f"> </span>matrix.<span class="_ _f"> </span>Also,<span class="_ _f"> </span>the<span class="_ _f"> </span>shorthand<span class="_ _f"> </span>notation<span class="_ _f"> </span><span class="ffb">W<span class="_ _15"> </span><span class="ff11"><span class="_ _c"> </span><span class="ff8">CW</span></span></span></div><div class="t m0 xcd h10 y18a ff7 fs9 fc0 sc0 ls0 ws0">M</div><div class="t m0 xce h9 y18b ff7 fs1 fc0 sc0 ls0 ws0">N<span class="_ _1"> </span><span class="ff5">,</span></div><div class="t m1 xcf h1a y18b ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 xd0 h9 y18b ff5 fs1 fc0 sc0 ls0 ws0">,</div><div class="t m1 x7b h1a y18b ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 x34 hf y18c ff8 fs9 fc0 sc0 ls0 ws0"><span class="ff5">1</span></div><div class="t m0 xd1 h14 y18b ffb fs1 fc0 sc0 ls3f ws0">MM</div><div class="t m0 xd2 h10 y18d ff7 fs9 fc0 sc0 ls0 ws0">H</div><div class="t m0 x7 h11 y18e ffe fs1 fc0 sc0 ls40 ws0"></div><div class="t m0 x31 h9 y18f ff5 fs1 fc0 sc0 ls0 ws0">denotes<span class="_ _21"> </span>the<span class="_ _4"> </span>non-ce<span class="_ _8"></span>ntral<span class="_ _21"> </span>Wishart</div><div class="t m0 x7 h9 y190 ff5 fs1 fc0 sc0 ls0 ws0">distribution<span class="_ _c"> </span>with<span class="_ _3"> </span><span class="ff7">N<span class="_ _3"> </span></span>degrees<span class="_ _3"> </span>of<span class="_ _3"> </span>freedom,<span class="_ _c"> </span>which<span class="_ _3"> </span>results<span class="_ _3"> </span>when</div><div class="t m0 x7 h9 y191 ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _18"> </span>elemen<span class="_ _8"></span>ts<span class="_ _18"> </span>of<span class="_ _24"> </span><span class="ffb">H<span class="_ _18"> </span></span>are<span class="_ _24"> </span>Gaussian<span class="_ _24"> </span>random<span class="_ _18"> </span>variable<span class="_ _8"></span>s<span class="_ _18"> </span>with</div><div class="t m0 x7 hb y192 ffb fs1 fc0 sc0 ls0 ws0">M<span class="_ _3"> </span><span class="ff8">¼<span class="_ _c"> </span><span class="ffd">E<span class="_ _0"> </span></span></span>H<span class="_ _32"></span><span class="ff8 ls22">½<span class="_ _27"></span><span class="ff17 ls0">=<span class="_ _0"> </span><span class="ff5">0,<span class="_ _c"> </span>where<span class="_ _c"> </span>0<span class="_ _3"> </span>denotes<span class="_ _c"> </span>a<span class="_ _c"> </span>zero<span class="_ _c"> </span>matrix.</span></span></span></div><div class="t m0 x2b h9 y193 ff5 fs1 fc0 sc0 ls0 ws0">Here<span class="_ _17"> </span>we<span class="_ _17"> </span>approximate<span class="_ _0"> </span>the<span class="_ _17"> </span>non-central<span class="_ _0"> </span>Wis<span class="_ _2"></span>hart<span class="_ _17"> </span>distribution</div><div class="t m0 x7 hb y194 ffb fs1 fc0 sc0 ls0 ws0">W<span class="_ _15"> </span><span class="ff11"><span class="_ _0"> </span><span class="ff8">CW</span></span></div><div class="t m0 x34 h10 y195 ff7 fs9 fc0 sc0 ls0 ws0">M</div><div class="t m0 xd3 h9 y196 ff7 fs1 fc0 sc0 ls0 ws0">N<span class="_ _1"> </span><span class="ff5">,</span></div><div class="t m1 xd4 h1a y196 ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 x5 h9 y196 ff5 fs1 fc0 sc0 ls0 ws0">,</div><div class="t m1 xd5 h1a y196 ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 xd6 hf y197 ff8 fs9 fc0 sc0 ls0 ws0"><span class="ff5">1</span></div><div class="t m0 x59 h14 y196 ffb fs1 fc0 sc0 ls41 ws0">MM</div><div class="t m0 x60 h10 y198 ff7 fs9 fc0 sc0 ls0 ws0">H</div><div class="t m0 xd7 h11 y199 ffe fs1 fc0 sc0 ls40 ws0"></div><div class="t m0 x62 h9 y19a ff5 fs1 fc0 sc0 ls0 ws0">by<span class="_ _22"> </span>a<span class="_ _20"> </span>central<span class="_ _20"> </span>Wishart</div><div class="t m0 x7 h9 y19b ff5 fs1 fc0 sc0 ls0 ws0">distribution<span class="_ _15"> </span><span class="ffb">W</span></div><div class="t m0 xd8 hf y19c ff8 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 xd4 hb y19d ff11 fs1 fc0 sc0 ls0 ws0"><span class="_ _0"> </span><span class="ff8">CW</span></div><div class="t m0 x63 h10 y19e ff7 fs9 fc0 sc0 ls0 ws0">M</div><div class="t m0 xd9 h9 y19d ff7 fs1 fc0 sc0 ls0 ws0">N<span class="_ _1"> </span><span class="ff5">,</span></div><div class="t m1 xda h1a y19d ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 x38 hb y19d ff8 fs1 fc0 sc0 ls42 ws0">þð<span class="_ _7"></span><span class="ff5 ls0">1<span class="ff12">=<span class="ff7">N<span class="_ _1"> </span><span class="ff8">Þ<span class="_ _1f"></span><span class="ffb">M</span></span></span></span></span></div><div class="t m0 x6f h10 y19c ff7 fs9 fc0 sc0 ls0 ws0">H</div><div class="t m0 xdb h14 y19d ffb fs1 fc0 sc0 ls0 ws0">M</div><div class="t m0 xdc h11 y19f ffe fs1 fc0 sc0 ls43 ws0"></div><div class="t m0 xdd h9 y19d ff5 fs1 fc0 sc0 ls0 ws0">as<span class="_ _15"> </span>in<span class="_ _15"> </span><span class="fc1">[6]<span class="_ _8"></span></span>.</div><div class="t m0 x7 h9 y1a0 ff5 fs1 fc0 sc0 ls0 ws0">This<span class="_ _15"> </span>tech<span class="_ _8"></span>nique<span class="_ _e"> </span>represents<span class="_ _e"> </span>a<span class="_ _e"> </span>non-central<span class="_ _10"> </span>complex<span class="_ _15"> </span>Wishart</div><div class="t m0 x7 h9 y1a1 ff5 fs1 fc0 sc0 ls0 ws0">distribution<span class="_ _f"> </span>by<span class="_ _f"> </span>normal<span class="_ _f"> </span>vectors<span class="_ _18"> </span><span class="fc1">[20]</span>.<span class="_ _f"> </span>Note<span class="_ _f"> </span>that<span class="_ _f"> </span>the<span class="_ _f"> </span>first-</div><div class="t m0 x7 hb y1a2 ff5 fs1 fc0 sc0 ls0 ws0">order<span class="_ _e"> </span>moment<span class="_ _10"> </span>of<span class="_ _10"> </span><span class="ffb">W<span class="_ _15"> </span><span class="ff11"><span class="_ _0"> </span><span class="ff8">CW</span></span></span></div><div class="t m0 x61 h10 y1a3 ff7 fs9 fc0 sc0 ls0 ws0">M</div><div class="t m0 x65 h9 y1a4 ff7 fs1 fc0 sc0 ls0 ws0">N<span class="_ _1"> </span><span class="ff5">,</span></div><div class="t m1 xde h1a y1a4 ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 xdf h9 y1a4 ff5 fs1 fc0 sc0 ls0 ws0">,</div><div class="t m1 x3a h1a y1a4 ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 x28 hf y13e ff8 fs9 fc0 sc0 ls0 ws0"><span class="ff5">1</span></div><div class="t m0 x6f h14 y1a4 ffb fs1 fc0 sc0 ls41 ws0">MM</div><div class="t m0 xe0 h10 y1a5 ff7 fs9 fc0 sc0 ls0 ws0">H</div><div class="t m0 x74 h11 y1a6 ffe fs1 fc0 sc0 ls40 ws0"></div><div class="t m0 xe1 h9 y1a7 ff5 fs1 fc0 sc0 ls0 ws0">and<span class="_ _e"> </span>of</div><div class="t m0 x7 h9 y1a8 ff5 fs1 fc0 sc0 ls0 ws0">the<span class="_ _18"> </span>approximation<span class="_ _f"> </span><span class="ffb">W</span></div><div class="t m0 x5a hf y1a9 ff8 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 xdc h9 y1aa ff5 fs1 fc0 sc0 ls0 ws0">are<span class="_ _18"> </span>identical,<span class="_ _18"> </span>whereas<span class="_ _f"> </span>the<span class="_ _18"> </span>second</div><div class="t m0 x7 h9 y1ab ff5 fs1 fc0 sc0 ls0 ws0">order<span class="_ _21"> </span>moment<span class="_ _4"> </span>differs<span class="_ _21"> </span>by<span class="_ _21"> </span>(1<span class="ff12">=<span class="_"> </span><span class="ff7">N<span class="_ _1f"> </span></span></span>)<span class="_ _1f"> </span><span class="ffb">M</span></div><div class="t m0 x27 h10 y1ac ff7 fs9 fc0 sc0 ls0 ws0">H</div><div class="t m0 x3b h9 y1ad ffb fs1 fc0 sc0 ls0 ws0">M<span class="_ _25"></span><span class="ff5">.<span class="_ _21"> </span>Hence,<span class="_ _21"> </span>this</span></div><div class="t m0 x7 h9 y1ae ff5 fs1 fc0 sc0 ls0 ws0">justifies<span class="_ _18"> </span>the<span class="_ _24"> </span>approximation.<span class="_ _24"> </span>In<span class="_ _24"> </span>this<span class="_ _24"> </span>case,<span class="_ _24"> </span>the<span class="_ _24"> </span>probability</div><div class="t m0 x7 h9 y1af ff5 fs1 fc0 sc0 ls0 ws0">density<span class="_ _24"> </span>function<span class="_ _12"> </span>(PDF)<span class="_ _12"> </span>of<span class="_ _24"> </span>the<span class="_ _12"> </span>post-processing<span class="_ _24"> </span>SNR<span class="_ _24"> </span>of</div><div class="t m0 x7 h9 y1b0 ff5 fs1 fc0 sc0 ls0 ws0">each<span class="_ _c"> </span>stream<span class="_ _c"> </span><span class="fc1">[6]<span class="_ _c"> </span></span>is<span class="_ _c"> </span>given<span class="_ _3"> </span>by</div><div class="t m0 xe2 h18 y1b1 ff7 fs1 fc0 sc0 ls0 ws0">f</div><div class="t m1 xe3 h12 y1b2 fff fsa fc0 sc0 ls0 ws0">g</div><div class="t m0 xe4 h10 y1b3 ff7 fs9 fc0 sc0 ls0 ws0">k</div><div class="t m0 xe5 h11 y1b4 ffe fs1 fc0 sc0 ls44 ws0"></div><div class="t m0 xe6 hb y1b5 ff8 fs1 fc0 sc0 ls0 ws0">¼</div><div class="t m1 x5d h1a y1b6 ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 xd8 hf y1b7 ff8 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 x4b h11 y1b8 ffe fs1 fc0 sc0 ls45 ws0"></div><div class="t m0 xd4 hf y1b9 ff8 fs9 fc0 sc0 ls0 ws0"><span class="ff5">1</span></div><div class="t m0 xd4 h10 y1ba ff7 fs9 fc0 sc0 ls0 ws0">kk</div><div class="t m0 x2d h11 y1bb ffe fs1 fc0 sc0 ls46 ws0"></div><div class="t m0 x4f h9 y1bc ff5 fs1 fc0 sc0 ls0 ws0">e</div><div class="t m0 xe7 hf y1bd ff8 fs9 fc0 sc0 ls0 ws0"></div><div class="t m1 x37 h12 y1bd fff fsa fc0 sc0 ls0 ws0">g</div><div class="t m0 xe8 h10 y1be ff7 fs9 fc0 sc0 ls0 ws0">k</div><div class="t m0 x3f h1b y1bd ff12 fs1 fc0 sc0 ls0 ws0">=</div><div class="t m1 x5f h12 y1bd fff fsa fc0 sc0 ls0 ws0">g</div><div class="t m0 xe9 h13 y1be ff5 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 x63 hb y1bf ff8 fs1 fc0 sc0 ls47 ws0">ðÞ</div><div class="t m2 x38 h1c y1bd ff16 fsb fc0 sc0 ls0 ws0">S</div><div class="t m0 xc9 h1d y1c0 ff8 fsd fc0 sc0 ls0 ws0">0</div><div class="t m0 x50 hb y1bf ff8 fs1 fc0 sc0 ls48 ws0">½</div><div class="t m0 x66 h1d y1c1 ff8 fsd fc0 sc0 ls0 ws0"><span class="ff5">1</span></div><div class="t m0 x66 h1e y1c2 ff7 fsd fc0 sc0 ls49 ws0">kk</div><div class="t m1 x4c h12 y1c3 fff fsa fc0 sc0 ls0 ws0">g</div><div class="t m0 xea h13 y1c4 ff5 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 x4 hb y1c3 fff fs1 fc0 sc0 ls0 ws0">G<span class="_ _3"> </span><span class="ff7">N<span class="_ _d"> </span><span class="ff8"><span class="_ _17"> </span></span>M<span class="_ _3"> </span><span class="ff8">þ<span class="_ _17"> </span><span class="ff5">1<span class="_ _42"></span><span class="ff8 ls4a">ðÞ</span></span></span></span></div><div class="t m1 xeb h12 y1c5 fff fsa fc0 sc0 ls0 ws0">g</div><div class="t m0 x75 h10 y1c6 ff7 fs9 fc0 sc0 ls0 ws0">k</div><div class="t m1 xeb h12 y1c3 fff fsa fc0 sc0 ls0 ws0">g</div><div class="t m0 x75 h13 y1c4 ff5 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 x67 h11 y1c7 ffe fs1 fc0 sc0 ls4b ws0"></div><div class="t m1 x79 h1a y1b2 ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 x72 hf y1c8 ff8 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 xec h11 y1b4 ffe fs1 fc0 sc0 ls45 ws0"></div><div class="t m0 xed hf y1c9 ff8 fs9 fc0 sc0 ls0 ws0"><span class="ff5">1</span></div><div class="t m0 xed h10 y1ca ff7 fs9 fc0 sc0 ls0 ws0">kk</div><div class="t m0 x43 h11 y1c7 ffe fs1 fc0 sc0 ls4c ws0"></div><div class="t m0 xe1 hf y1cb ff7 fs9 fc0 sc0 ls0 ws0">N<span class="_ _1b"> </span><span class="ff8"></span>M</div><div class="t m0 xee h9 y1cc ff5 fs1 fc0 sc0 ls0 ws0">(11)</div><div class="t m0 x7 hb y1cd ff5 fs1 fc0 sc0 ls0 ws0">with<span class="_ _a"> </span><span class="ff7">k<span class="_ _c"> </span><span class="ff8">¼<span class="_ _0"> </span></span></span>1,<span class="_ _c"> </span>2,<span class="_ _c"> </span><span class="ff10 ls13">...<span class="_"> </span></span>,<span class="_ _1f"> </span><span class="ff7">M<span class="_ _1b"></span></span>,<span class="_ _c"> </span><span class="fff">G<span class="_ _a"> </span></span>denotes<span class="_ _a"> </span>the<span class="_ _a"> </span>gamma<span class="_ _a"> </span>function<span class="_ _9"> </span>and</div><div class="t m1 xef h1a y1ce ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 xf0 hf y1cf ff8 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 x7 h11 y1d0 ffe fs1 fc0 sc0 ls45 ws0"></div><div class="t m0 xe3 hf y1d1 ff8 fs9 fc0 sc0 ls0 ws0"><span class="ff5">1</span></div><div class="t m0 xe3 h10 y1d2 ff7 fs9 fc0 sc0 ls0 ws0">kk</div><div class="t m0 xf1 h9 y1ce ff5 fs1 fc0 sc0 ls0 ws0">is<span class="_ _c"> </span>the<span class="_ _5"> </span><span class="ff7">k</span>,<span class="_ _0"> </span><span class="ff7">k</span></div><div class="t m0 xf2 hb y1d3 ff8 fs1 fc0 sc0 ls3b ws0">ðÞ</div><div class="t m0 xf3 h9 y1ce ff5 fs1 fc0 sc0 ls0 ws0">th<span class="_ _c"> </span>element<span class="_ _c"> </span>of<span class="_ _3"> </span>the<span class="_ _c"> </span>matrix</div><div class="t m1 xec h1a y1ce ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 xf4 hf y1cf ff8 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 x70 h11 y1d0 ffe fs1 fc0 sc0 ls45 ws0"></div><div class="t m0 x56 hf y1d1 ff8 fs9 fc0 sc0 ls0 ws0"><span class="ff5">1</span></div><div class="t m0 x57 h9 y1ce ff5 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 x2b h9 y1d4 ff5 fs1 fc0 sc0 ls0 ws0">From<span class="_ _c"> </span>(11),<span class="_ _3"> </span>one<span class="_ _3"> </span>can<span class="_ _3"> </span>see<span class="_ _c"> </span>that<span class="_ _3"> </span>in<span class="_ _c"> </span>order<span class="_ _3"> </span>to<span class="_ _3"> </span>determine<span class="_ _3"> </span>all<span class="_ _c"> </span>the</div><div class="t m0 x7 h9 y1d5 ff5 fs1 fc0 sc0 ls0 ws0">parameters<span class="_ _5"> </span>of<span class="_ _5"> </span>the<span class="_ _5"> </span>central</div><div class="t m1 x73 h12 y1d6 fff fsa fc0 sc0 ls0 ws0">x</div><div class="t m3 xf5 h1f y1d7 ff5 fse fc0 sc0 ls0 ws0">2</div><div class="t m0 xc9 h9 y1d6 ff5 fs1 fc0 sc0 ls0 ws0">PDF<span class="_ _5"> </span>of</div><div class="t m1 x6f h12 y1d6 fff fsa fc0 sc0 ls0 ws0">g</div><div class="t m0 xec h10 y1d8 ff7 fs9 fc0 sc0 ls0 ws0">k</div><div class="t m0 xdb h9 y1d6 ff5 fs1 fc0 sc0 ls0 ws0">,<span class="_ _5"> </span>one<span class="_ _5"> </span>has<span class="_ _5"> </span>to</div><div class="t m0 x7 h9 y1d9 ff5 fs1 fc0 sc0 ls0 ws0">determine</div><div class="t m1 xf6 h1a y1da ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 x2e hf y1db ff8 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 x2d h11 y1dc ffe fs1 fc0 sc0 ls45 ws0"></div><div class="t m0 xf7 hf y1dd ff8 fs9 fc0 sc0 ls0 ws0"><span class="ff5">1</span></div><div class="t m0 xf7 h10 y1de ff7 fs9 fc0 sc0 ls0 ws0">kk</div><div class="t m0 xf8 h9 y1da ff5 fs1 fc0 sc0 ls0 ws0">.<span class="_ _9"> </span>Now<span class="_ _9"> </span>the<span class="_ _9"> </span>covariance<span class="_ _9"> </span>matrix,<span class="_ _9"> </span>denoted<span class="_ _9"> </span>by</div><div class="t m1 x7 h1a y1df ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 xf9 hf y1e0 ff8 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 x2b h9 y1df ff5 fs1 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span>can<span class="_ _c"> </span>be<span class="_ _c"> </span>written<span class="_ _3"> </span>as</div><div class="t m1 x2b h1a y1e1 ff16 fsa fc0 sc0 ls0 ws0">S</div><div class="t m0 xe3 hf y1e2 ff8 fs9 fc0 sc0 ls0 ws0">0</div><div class="t m0 x49 hb y1e1 ff8 fs1 fc0 sc0 ls0 ws0">¼</div><div class="t m0 xfa h9 y1e3 ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m1 xe6 h12 y1e4 fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x4e hb y1e4 ff8 fs1 fc0 sc0 ls0 ws0">þ<span class="_ _17"> </span><span class="ff5">1</span></div><div class="t m0 xfb h14 y1e5 ffb fs1 fc0 sc0 ls0 ws0">R</div><div class="t m0 xd4 h10 y1e6 ff7 fs9 fc0 sc0 ls0 ws0">Tx</div><div class="t m0 xfc hb y1e1 ff8 fs1 fc0 sc0 ls0 ws0">þ</div><div class="t m1 xfd h12 y1e3 fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m1 xfe h12 y1e7 fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x31 hb y1e4 ff8 fs1 fc0 sc0 ls0 ws0">þ<span class="_ _17"> </span><span class="ff5">1</span></div><div class="t m0 x41 h9 y1e3 ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m0 x60 h18 y1e7 ff7 fs1 fc0 sc0 ls0 ws0">N</div><div class="t m0 x6b h11 y1e8 ffe fs1 fc0 sc0 ls4d ws0"></div><div class="t m0 xff h9 y1e9 ff7 fs1 fc0 sc0 ls0 ws0">N<span class="_ _c"> </span><span class="ff5">e</span></div><div class="t m0 x3a h9 y1ea ff7 fs9 fc0 sc0 ls0 ws0">j<span class="_ _8"></span><span class="ff5 fs1">(</span></div><div class="t m1 x55 h12 y1ea fff fsa fc0 sc0 ls0 ws0">p</div><div class="t m0 x3b h9 y1ea ff12 fs1 fc0 sc0 ls0 ws0">=<span class="ff5">4)</span></div><div class="t m0 x100 h11 y1eb ffe fs1 fc0 sc0 ls4e ws0"></div><div class="t m0 x101 h17 y1ec fff fs1 fc0 sc0 ls0 ws0">C</div><div class="t m0 xed h13 y1e6 ff7 fs9 fc0 sc0 ls0 ws0">M<span class="_ _25"></span><span class="ff5">,</span>M</div><div class="t m0 xee h9 y1e1 ff5 fs1 fc0 sc0 ls0 ws0">(12)</div><div class="t m0 x7 h9 y1ed ff5 fs1 fc0 sc0 ls0 ws0">Let<span class="_ _15"> </span>us<span class="_ _15"> </span>define</div><div class="t m1 x102 h12 y1ee fff fsa fc0 sc0 ls0 ws0">j</div><div class="t m0 x103 hb y1ee ff8 fs1 fc0 sc0 ls0 ws0">¼</div><div class="t m1 x104 h12 y1ee fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x4f h9 y1ee ff12 fs1 fc0 sc0 ls0 ws0">=<span class="ff5">(</span></div><div class="t m1 x5a h12 y1ee fff fsa fc0 sc0 ls0 ws0">k</div><div class="t m0 x3e hb y1ee ff8 fs1 fc0 sc0 ls0 ws0">þ<span class="_ _17"> </span><span class="ff5">1)<span class="_ _15"> </span>and<span class="_ _15"> </span>consider<span class="_ _e"> </span>the<span class="_ _15"> </span>exponential</span></div><div class="t m0 x7 h9 y1ef ff5 fs1 fc0 sc0 ls0 ws0">transmit<span class="_ _d"> </span>correlation<span class="_ _d"> </span>matrix<span class="_ _d"> </span><span class="ffb">R</span></div><div class="t m0 x60 h10 y1f0 ff7 fs9 fc0 sc0 ls0 ws0">Tx</div><div class="t m0 x64 h9 y1f1 ff5 fs1 fc0 sc0 ls0 ws0">as<span class="_ _d"> </span>stated<span class="_ _d"> </span>earlier.<span class="_ _a"> </span>To<span class="_ _d"> </span>obtain</div><div class="t m0 x7 h9 y1f2 ff5 fs1 fc0 sc0 ls0 ws0">a<span class="_ _15"> </span>closed-form<span class="_ _e"> </span>expression<span class="_ _15"> </span>for<span class="_ _15"> </span>the<span class="_ _e"> </span>BER<span class="_ _15"> </span>of<span class="_ _e"> </span>each<span class="_ _15"> </span>substream,</div><div class="t m0 x7 h9 y1f3 ff5 fs1 fc0 sc0 ls0 ws0">we<span class="_ _e"> </span>have<span class="_ _e"> </span>to<span class="_ _10"> </span>transform<span class="_ _e"> </span>the<span class="_ _10"> </span>matrix<span class="_ _e"> </span>in<span class="_ _10"> </span>(12)<span class="_ _10"> </span>into<span class="_ _10"> </span>a<span class="_ _e"> </span>lower<span class="_ _e"> </span>or</div><div class="t m0 x7 h9 y1f4 ff5 fs1 fc0 sc0 ls0 ws0">upper<span class="_ _14"> </span>diagonal<span class="_ _14"> </span>matrix.<span class="_ _23"> </span>To<span class="_ _14"> </span>do<span class="_ _14"> </span>this,<span class="_ _14"> </span>we<span class="_ _14"> </span>perform<span class="_ _23"> </span>row</div><div class="t m0 x8 h3 y1f5 ff1 fs1 fc0 sc0 ls0 ws0">12<span class="_ _1d"> </span><span class="ff3">IET<span class="_ _3"> </span>Commun.</span>,<span class="_ _3"> </span>2009,<span class="_ _0"> </span>V<span class="_ _2"></span>ol.<span class="_ _3"> </span>3,<span class="_ _3"> </span>Iss.<span class="_ _3"> </span>1,<span class="_ _3"> </span>pp.<span class="_ _3"> </span>10<span class="_ _1b"></span>–<span class="_ _1b"></span>16</div><div class="t m0 x8 hc y48 ff9 fs6 fc0 sc0 ls0 ws0">&</div><div class="t m0 x9 h3 y49 ff1 fs1 fc0 sc0 ls0 ws0">The<span class="_ _3"> </span>Institution<span class="_ _3"> </span>of<span class="_ _3"> </span>Engineering<span class="_ _3"> </span>and<span class="_ _3"> </span>T<span class="_ _b"></span>echnology<span class="_ _3"> </span>2009<span class="_ _1e"> </span>doi:<span class="_ _1f"> </span>10.1049/iet-com:20080110</div><div class="t m0 x8 hd y4a ff2 fs7 fc0 sc0 ls0 ws0">www<span class="_ _b"></span>.ietdl.or<span class="_ _2"></span>g</div><div class="t m0 xa he y4b ffa fs8 fc0 sc0 ls0 ws0">Authorized licensed use limited to: Shantou University. Downloaded on June 24, 2009 at 03:15 from IEEE Xplore. Restrictions apply.</div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
MIMO_detection
