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detection processes for MIMO systems
younis2013.rar
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内容介绍
<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/624fb73e6caf596192eded7d/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/624fb73e6caf596192eded7d/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">IEEE<span class="_ _0"> </span>TRANSACTIONS<span class="_ _0"> </span>ON<span class="_ _0"> </span>COMMUNICA<span class="_ _1"></span>TIONS,<span class="_ _0"> </span>V<span class="_ _2"></span>OL.<span class="_ _0"> </span>61,<span class="_ _0"> </span>NO.<span class="_ _0"> </span>7,<span class="_ _0"> </span>JUL<span class="_ _1"></span>Y<span class="_ _0"> </span>2013<span class="_ _3"> </span><span class="ls1">2805</span></div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls2 ws0">Generalised<span class="_ _4"> </span>Sphere<span class="_ _4"> </span>Decoding<span class="_ _5"> </span>for</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls3 ws0">Spatial<span class="_ _4"> </span>Modulation</div><div class="t m0 x4 h4 y4 ff1 fs2 fc0 sc0 ls4 ws0">Abdelhamid<span class="_ _6"> </span>Y<span class="_ _7"></span>ounis,<span class="_ _6"> </span>Sinan<span class="_ _6"> </span>Sinanovi<span class="_ _8"></span>&#180;<span class="_ _9"></span><span class="ls5">c,<span class="_ _6"> </span>Marco<span class="_ _6"> </span>Di<span class="_ _a"> </span>Renzo,<span class="_ _6"> </span>Raed<span class="_ _6"> </span>Mesleh,<span class="_ _6"> </span>and<span class="_ _6"> </span>Harald<span class="_ _6"> </span>Haas</span></div><div class="t m0 x5 h5 y5 ff2 fs3 fc0 sc0 ls6 ws0">Abstract<span class="ff3 ls7">&#8212;In<span class="_ _b"> </span>this<span class="_ _b"> </span>pa<span class="_ _2"></span>per<span class="_ _1"></span>,<span class="_ _b"> </span>Spher<span class="_ _2"></span>e<span class="_ _b"> </span>Dec<span class="_ _2"></span>oding<span class="_ _b"> </span>(SD)<span class="_ _b"> </span>a<span class="_ _2"></span>lgorithms<span class="_ _c"> </span>f<span class="_ _2"></span>or</span></div><div class="t m0 x1 h5 y6 ff3 fs3 fc0 sc0 ls8 ws0">Spatial<span class="_ _b"> </span>Modulatio<span class="_ _2"></span>n<span class="_ _6"> </span>(SM)<span class="_ _c"> </span>are<span class="_ _b"> </span>deve<span class="_ _2"></span>loped<span class="_ _6"> </span>to<span class="_ _b"> </span>reduce<span class="_ _b"> </span>the<span class="_ _b"> </span>computa-</div><div class="t m0 x1 h5 y7 ff3 fs3 fc0 sc0 ls9 ws0">tional<span class="_ _6"> </span>complexity<span class="_ _6"> </span>of<span class="_ _6"> </span>Maximu<span class="_ _8"></span>m&#8211;Likelih<span class="_ _8"></span>ood<span class="_ _b"> </span>(M<span class="_ _8"></span>L)<span class="_ _b"> </span>det<span class="_ _8"></span>ectors.<span class="_ _6"> </span>T<span class="_ _1"></span>wo</div><div class="t m0 x1 h5 y8 ff3 fs3 fc0 sc0 ls8 ws0">SDs<span class="_ _6"> </span>speci&#64257;c<span class="_ _2"></span>ally<span class="_ _6"> </span>desig<span class="_ _2"></span>ned<span class="_ _6"> </span>for<span class="_ _6"> </span>SM<span class="_ _6"> </span>ar<span class="_ _2"></span>e<span class="_ _6"> </span>propos<span class="_ _2"></span>ed<span class="_ _6"> </span>and<span class="_ _6"> </span>analyse<span class="_ _2"></span>d<span class="_ _6"> </span>in</div><div class="t m0 x1 h5 y9 ff3 fs3 fc0 sc0 lsa ws0">terms<span class="_ _6"> </span>of<span class="_ _6"> </span>Bit<span class="_ _6"> </span>Err<span class="_ _2"></span>or<span class="_ _6"> </span>Ratio<span class="_ _6"> </span>(BER)<span class="_ _6"> </span>and<span class="_ _6"> </span>com<span class="_ _2"></span>putational<span class="_ _6"> </span>comple<span class="_ _2"></span>xity<span class="_ _1"></span>.</div><div class="t m0 x1 h5 ya ff3 fs3 fc0 sc0 lsb ws0">Using<span class="_ _b"> </span>Monte<span class="_ _6"> </span>Carlo<span class="_ _c"> </span>simulations<span class="_ _b"> </span>and<span class="_ _6"> </span>mathema<span class="_ _2"></span>tical<span class="_ _6"> </span>analy<span class="_ _2"></span>sis,<span class="_ _6"> </span>it<span class="_ _b"> </span>is</div><div class="t m0 x1 h5 yb ff3 fs3 fc0 sc0 lsc ws0">shown<span class="_ _c"> </span>that<span class="_ _c"> </span>by<span class="_ _b"> </span>care<span class="_ _2"></span>fully<span class="_ _b"> </span>choosing<span class="_ _c"> </span>the<span class="_ _c"> </span>initial<span class="_ _c"> </span>radius<span class="_ _b"> </span>the<span class="_ _c"> </span>propos<span class="_ _2"></span>ed</div><div class="t m0 x1 h5 yc ff3 fs3 fc0 sc0 lsc ws0">spher<span class="_ _2"></span>e<span class="_ _c"> </span>decode<span class="_ _2"></span>r<span class="_ _c"> </span>algorithm<span class="_ _2"></span>s<span class="_ _b"> </span>offer<span class="_ _0"> </span>the<span class="_ _c"> </span>same<span class="_ _c"> </span>BER<span class="_ _c"> </span>as<span class="_ _c"> </span>ML<span class="_ _0"> </span>detection,</div><div class="t m0 x1 h5 yd ff3 fs3 fc0 sc0 lsd ws0">with<span class="_ _6"> </span>a<span class="_ _6"> </span>signi&#64257;c<span class="_ _2"></span>ant<span class="_ _6"> </span>r<span class="_ _2"></span>eduction<span class="_ _6"> </span>in<span class="_ _b"> </span>the<span class="_ _6"> </span>computatio<span class="_ _2"></span>nal<span class="_ _6"> </span>comple<span class="_ _2"></span>xity<span class="_ _1"></span>.<span class="_ _6"> </span>A</div><div class="t m0 x1 h5 ye ff3 fs3 fc0 sc0 lse ws0">tight<span class="_ _c"> </span>closed<span class="_ _0"> </span>form<span class="_ _0"> </span>expression<span class="_ _c"> </span>f<span class="_ _2"></span>or<span class="_ _c"> </span>the<span class="_ _0"> </span>BER<span class="_ _0"> </span>p<span class="_ _8"></span>erformance<span class="_ _0"> </span>of<span class="_ _c"> </span>SM&#8211;SD</div><div class="t m0 x1 h5 yf ff3 fs3 fc0 sc0 ls7 ws0">is<span class="_ _c"> </span>der<span class="_ _2"></span>ived<span class="_ _0"> </span>in<span class="_ _c"> </span>the<span class="_ _c"> </span>pape<span class="_ _2"></span>r<span class="_ _1"></span>,<span class="_ _c"> </span>alo<span class="_ _2"></span>ng<span class="_ _c"> </span>with<span class="_ _c"> </span>an<span class="_ _0"> </span>algorithm<span class="_ _c"> </span>f<span class="_ _2"></span>or<span class="_ _c"> </span>choo<span class="_ _2"></span>sing<span class="_ _c"> </span>the</div><div class="t m0 x1 h5 y10 ff3 fs3 fc0 sc0 lsa ws0">initial<span class="_ _d"> </span>radius<span class="_"> </span>which<span class="_ _d"> </span>pr<span class="_ _2"></span>ovides<span class="_"> </span>ne<span class="_ _2"></span>ar<span class="_"> </span>to<span class="_"> </span>optim<span class="_ _2"></span>um<span class="_"> </span>perfo<span class="_ _2"></span>rmance.<span class="_"> </span>Also,</div><div class="t m0 x1 h5 y11 ff3 fs3 fc0 sc0 lsf ws0">it<span class="_ _c"> </span>is<span class="_ _c"> </span>shown<span class="_ _c"> </span>that<span class="_ _c"> </span>none<span class="_ _c"> </span>of<span class="_ _c"> </span>the<span class="_ _c"> </span>proposed<span class="_ _c"> </span>SDs<span class="_ _c"> </span>are<span class="_ _c"> </span>always<span class="_ _c"> </span>su<span class="_ _8"></span>perior<span class="_ _c"> </span>to</div><div class="t m0 x1 h5 y12 ff3 fs3 fc0 sc0 ls8 ws0">the<span class="_ _c"> </span>others<span class="_ _2"></span>,<span class="_ _c"> </span>but<span class="_ _c"> </span>the<span class="_ _0"> </span>best<span class="_ _c"> </span>SD<span class="_ _c"> </span>to<span class="_ _c"> </span>use<span class="_ _c"> </span>depends<span class="_"> </span>on<span class="_ _c"> </span>the<span class="_ _c"> </span>targe<span class="_ _2"></span>t<span class="_ _b"> </span>spectra<span class="_ _2"></span>l</div><div class="t m0 x1 h5 y13 ff3 fs3 fc0 sc0 ls4 ws0">ef&#64257;cienc<span class="_ _2"></span>y<span class="_ _1"></span>.<span class="_"> </span>The<span class="_ _0"> </span>computatio<span class="_ _2"></span>nal<span class="_"> </span>complexity<span class="_"> </span>trade&#8211;<span class="_ _2"></span>off<span class="_"> </span>offered<span class="_"> </span>by<span class="_"> </span>the</div><div class="t m0 x1 h5 y14 ff3 fs3 fc0 sc0 ls10 ws0">pro<span class="_ _2"></span>posed<span class="_ _b"> </span>solutions<span class="_ _c"> </span>is<span class="_ _c"> </span>studied<span class="_ _c"> </span>via<span class="_ _b"> </span>analys<span class="_ _2"></span>is<span class="_ _b"> </span>and<span class="_ _b"> </span>simulation,<span class="_ _c"> </span>and<span class="_ _c"> </span>is</div><div class="t m0 x1 h5 y15 ff3 fs3 fc0 sc0 ls11 ws0">sho<span class="_ _2"></span>wn<span class="_ _b"> </span>to<span class="_ _c"> </span>va<span class="_ _2"></span>lidate<span class="_ _c"> </span>our<span class="_ _b"> </span>&#64257;ndings.<span class="_ _c"> </span>Finally<span class="_ _1"></span>,<span class="_ _c"> </span>the<span class="_ _c"> </span>perf<span class="_ _2"></span>orma<span class="_ _2"></span>nce<span class="_ _b"> </span>of<span class="_ _c"> </span>SM&#8211;</div><div class="t m0 x1 h5 y16 ff3 fs3 fc0 sc0 ls12 ws0">SDs<span class="_ _b"> </span>are<span class="_ _6"> </span>co<span class="_ _2"></span>mpare<span class="_ _2"></span>d<span class="_ _6"> </span>to<span class="_ _6"> </span>Spatial<span class="_ _b"> </span>Multiplexing<span class="_ _c"> </span>(SMX)<span class="_ _b"> </span>applying<span class="_ _b"> </span>ML</div><div class="t m0 x1 h5 y17 ff3 fs3 fc0 sc0 ls13 ws0">decode<span class="_ _2"></span>r<span class="_ _b"> </span>and<span class="_ _c"> </span>applying<span class="_ _0"> </span>SD.<span class="_ _c"> </span>It<span class="_ _b"> </span>is<span class="_ _c"> </span>shown<span class="_ _c"> </span>that<span class="_ _c"> </span>f<span class="_ _2"></span>or<span class="_ _c"> </span>the<span class="_ _b"> </span>sam<span class="_ _2"></span>e<span class="_ _b"> </span>spectral</div><div class="t m0 x1 h6 y18 ff3 fs3 fc0 sc0 ls4 ws0">ef&#64257;cienc<span class="_ _2"></span>y<span class="_ _2"></span>,<span class="_ _e"> </span>SM&#8211;SD<span class="_ _e"> </span>offer<span class="_ _2"></span>s<span class="_ _f"> </span>up<span class="_ _e"> </span>to<span class="_ _e"> </span><span class="ff4 ls14">84%<span class="_ _f"> </span></span><span class="lsa">reduc<span class="_ _2"></span>tion<span class="_ _e"> </span>in<span class="_ _e"> </span>complexity</span></div><div class="t m0 x1 h6 y19 ff3 fs3 fc0 sc0 ls15 ws0">compared<span class="_ _0"> </span>to<span class="_ _c"> </span>SMX&#8211;S<span class="_ _8"></span>D,<span class="_ _0"> </span>with<span class="_ _c"> </span>up<span class="_ _0"> </span>t<span class="_ _8"></span>o<span class="_ _0"> </span><span class="ff4 ls16">1<span class="_ _c"> </span></span><span class="ls10">dB<span class="_"> </span>better<span class="_ _c"> </span>BER<span class="_"> </span>perfo<span class="_ _2"></span>rmance</span></div><div class="t m0 x1 h5 y1a ff3 fs3 fc0 sc0 ls17 ws0">than<span class="_ _b"> </span>SMX&#8211;ML<span class="_ _b"> </span>deco<span class="_ _2"></span>der<span class="_ _1"></span>.</div><div class="t m0 x5 h5 y1b ff2 fs3 fc0 sc0 ls18 ws0">Index<span class="_ _10"> </span>T<span class="_ _1"></span>erms<span class="ff3 ls19">&#8212;Multiple-input-multiple-o<span class="_ _2"></span>utput<span class="_ _11"> </span>(MIMO)<span class="_ _12"> </span>sys-</span></div><div class="t m0 x1 h5 y1c ff3 fs3 fc0 sc0 lsd ws0">tems,<span class="_ _11"> </span>spatial<span class="_ _11"> </span>modulation<span class="_ _11"> </span>(SM),<span class="_ _11"> </span>spatial<span class="_ _11"> </span>multiplexing<span class="_ _11"> </span>(SMX),</div><div class="t m0 x1 h5 y1d ff3 fs3 fc0 sc0 ls1a ws0">spher<span class="_ _2"></span>e<span class="_ _b"> </span>decoding<span class="_ _b"> </span>(SD),<span class="_ _b"> </span>larg<span class="_ _2"></span>e<span class="_ _6"> </span>scal<span class="_ _2"></span>e<span class="_ _6"> </span>MIMO.</div><div class="t m0 x6 h7 y1e ff1 fs4 fc0 sc0 ls1b ws0">I.<span class="_ _e"> </span>I<span class="fs5 ls1c">NTR<span class="_ _2"></span>ODUCTION</span></div><div class="t m0 x1 h8 y1f ff3 fs6 fc0 sc0 ls16 ws0">M</div><div class="t m0 x7 h7 y20 ff1 fs4 fc0 sc0 ls1d ws0">UL<span class="_ _1"></span>TIPLE&#8211;input<span class="_ _b"> </span>multiple&#8211;output<span class="_ _b"> </span>(MIMO)<span class="_ _6"> </span>systems<span class="_ _6"> </span>of-</div><div class="t m0 x7 h7 y21 ff1 fs4 fc0 sc0 ls1e ws0">fer<span class="_ _b"> </span>a<span class="_ _b"> </span>signi&#64257;cant<span class="_ _c"> </span>increase<span class="_ _b"> </span>in<span class="_ _b"> </span>spectral<span class="_ _b"> </span>ef&#64257;<span class="_ _2"></span>ciency<span class="_ _c"> </span>in<span class="_ _b"> </span>com-</div><div class="t m0 x1 h7 y22 ff1 fs4 fc0 sc0 ls1f ws0">parison<span class="_ _b"> </span>to<span class="_ _6"> </span>single<span class="_ _6"> </span>antenna<span class="_ _b"> </span>systems<span class="_ _6"> </span>[1].<span class="_ _6"> </span>An<span class="_ _6"> </span>example<span class="_ _b"> </span>is<span class="_ _6"> </span>Spatial</div><div class="t m0 x1 h7 y23 ff1 fs4 fc0 sc0 ls20 ws0">Multiplexing<span class="_ _c"> </span>(SMX)<span class="_ _c"> </span>[2]<span class="_ _8"></span>,<span class="_ _c"> </span>which<span class="_ _c"> </span>transmits<span class="_ _c"> </span>simu<span class="_ _8"></span>ltaneously<span class="_ _c"> </span>over</div><div class="t m0 x1 h7 y24 ff1 fs4 fc0 sc0 ls21 ws0">all<span class="_ _e"> </span>the<span class="_ _e"> </span>transmit<span class="_ _e"> </span>antennas.<span class="_ _e"> </span>This<span class="_ _e"> </span>method<span class="_ _e"> </span>achiev<span class="_ _2"></span>es<span class="_ _e"> </span>a<span class="_ _e"> </span>spectral</div><div class="t m0 x1 h7 y25 ff1 fs4 fc0 sc0 ls22 ws0">ef&#64257;<span class="_ _2"></span>ciency<span class="_ _b"> </span>that<span class="_ _6"> </span>increases<span class="_ _b"> </span>linearly<span class="_ _6"> </span>wit<span class="_ _2"></span>h<span class="_ _6"> </span>the<span class="_ _6"> </span>number<span class="_ _b"> </span>of<span class="_ _6"> </span>transmit</div><div class="t m0 x1 h7 y26 ff1 fs4 fc0 sc0 ls1f ws0">antennas.<span class="_ _c"> </span>Ho<span class="_ _2"></span>wev<span class="_ _2"></span>er<span class="_ _2"></span>,<span class="_ _c"> </span>these<span class="_ _b"> </span>systems<span class="_ _c"> </span>cannot<span class="_ _c"> </span>cope<span class="_ _c"> </span>with<span class="_ _b"> </span>the<span class="_ _b"> </span>expo-</div><div class="t m0 x1 h7 y27 ff1 fs4 fc0 sc0 ls21 ws0">nential<span class="_ _6"> </span>increase<span class="_ _a"> </span>of<span class="_ _6"> </span>wireless<span class="_ _a"> </span>data<span class="_ _a"> </span>traf&#64257;c,<span class="_ _6"> </span>and<span class="_ _6"> </span>a<span class="_ _13"> </span>larger<span class="_ _6"> </span>number</div><div class="t m0 x8 h9 y28 ff1 fs5 fc0 sc0 ls23 ws0">Manuscript<span class="_ _c"> </span>recei<span class="_ _2"></span>ved<span class="_ _c"> </span>July<span class="_ _0"> </span>29,<span class="_ _0"> </span>2012;<span class="_ _0"> </span>revised<span class="_ _0"> </span>December<span class="_ _c"> </span>24,<span class="_ _0"> </span>2012.<span class="_ _0"> </span>Th<span class="_ _8"></span>e<span class="_ _0"> </span>editor</div><div class="t m0 x1 h9 y29 ff1 fs5 fc0 sc0 ls24 ws0">coordinating<span class="_ _c"> </span>the<span class="_ _c"> </span>re<span class="_ _2"></span>view<span class="_ _0"> </span>of<span class="_ _c"> </span>this<span class="_ _0"> </span>paper<span class="_ _c"> </span>a<span class="ls23">nd<span class="_ _0"> </span>approving<span class="_ _c"> </span>it<span class="_ _0"> </span>for<span class="_ _c"> </span>publication<span class="_ _c"> </span>was<span class="_ _0"> </span>G.</span></div><div class="t m0 x1 h9 y2a ff1 fs5 fc0 sc0 ls25 ws0">Bauch.</div><div class="t m0 x8 h9 y2b ff1 fs5 fc0 sc0 ls26 ws0">This<span class="_ _0"> </span>work<span class="_"> </span>was<span class="_ _0"> </span>presented<span class="_ _0"> </span>in<span class="_"> </span>part<span class="_ _0"> </span>at<span class="_ _0"> </span>IEEE<span class="_"> </span>GL<span class="_ _8"></span>OBECOM<span class="_"> </span>2010,<span class="_ _0"> </span>Miami,<span class="_ _0"> </span>USA,</div><div class="t m0 x1 h9 y2c ff1 fs5 fc0 sc0 ls27 ws0">and<span class="_ _c"> </span>IEEE<span class="_ _c"> </span>ICC<span class="_ _c"> </span>2011,<span class="_ _b"> </span>Kyoto,<span class="_ _c"> </span>Japan.</div><div class="t m0 x8 h9 y2d ff1 fs5 fc0 sc0 ls28 ws0">A.<span class="_ _a"> </span>Y<span class="_ _1"></span>ounis<span class="_ _6"> </span>and<span class="_ _a"> </span>H.<span class="_ _a"> </span>Haas<span class="_ _a"> </span>are<span class="_ _a"> </span>with<span class="_ _a"> </span>The<span class="_ _a"> </span>University<span class="_ _a"> </span>of<span class="_ _a"> </span>Edinburgh,<span class="_ _6"> </span>College</div><div class="t m0 x1 h9 y2e ff1 fs5 fc0 sc0 ls29 ws0">of<span class="_ _c"> </span>Science<span class="_ _b"> </span>and<span class="_ _c"> </span>E<span class="_ _8"></span>ngineering,<span class="_ _b"> </span>Institute<span class="_ _b"> </span>for<span class="_ _b"> </span>Digital<span class="_ _b"> </span>Comm<span class="_ _8"></span>unications,<span class="_ _b"> </span>Joint<span class="_ _b"> </span>Re-</div><div class="t m0 x1 h9 y2f ff1 fs5 fc0 sc0 ls29 ws0">search<span class="_ _c"> </span>Institute<span class="_ _b"> </span>for<span class="_ _c"> </span>Signal<span class="_ _0"> </span>and<span class="_ _c"> </span>Im<span class="_ _8"></span>age<span class="_ _0"> </span>Proces<span class="_ _8"></span>sing,<span class="_ _c"> </span>King&#8217;<span class="_ _2"></span>s<span class="_ _c"> </span>Buildings,<span class="_ _c"> </span>May&#64257;<span class="_ _8"></span>eld</div><div class="t m0 x1 ha y30 ff1 fs5 fc0 sc0 ls2a ws0">Road,<span class="_ _c"> </span>Edinburgh,<span class="_ _c"> </span>EH<span class="_ _8"></span>9<span class="_ _c"> </span>3JL,<span class="_ _c"> </span>UK<span class="_ _c"> </span>(e-mail:<span class="_ _c"> </span><span class="ff5 ls16">{</span><span class="ls2b">a.<span class="_ _8"></span>younis,<span class="_ _c"> </span>h.haas<span class="_ _8"></span><span class="ff5 ls16">}</span><span class="ls24">@ed.ac.uk).</span></span></div><div class="t m0 x8 h9 y31 ff1 fs5 fc0 sc0 ls15 ws0">S.<span class="_"> </span>Sinanovi<span class="_ _8"></span>&#180;<span class="_ _14"></span><span class="ls2c">c<span class="_ _0"> </span>is<span class="_"> </span>with<span class="_"> </span>Glasgow<span class="_"> </span>Caledonian<span class="_ _0"> </span>University<span class="_ _1"></span>,<span class="_ _0"> </span>School<span class="_ _0"> </span>of<span class="_"> </span>Engineering</span></div><div class="t m0 x1 h9 y32 ff1 fs5 fc0 sc0 ls2d ws0">and<span class="_"> </span>Built<span class="_ _0"> </span>Environment,<span class="_"> </span>George<span class="_ _0"> </span>Moore<span class="_"> </span>B<span class="ls2e">uilding,<span class="_ _0"> </span>Cowcaddens<span class="_ _0"> </span>Road,<span class="_"> </span>Glasgow<span class="_ _2"></span>,</span></div><div class="t m0 x1 h9 y33 ff1 fs5 fc0 sc0 ls2f ws0">G4<span class="_ _c"> </span>0B<span class="_ _2"></span>A,<span class="_ _c"> </span>UK<span class="_ _c"> </span>(e-mail:<span class="_ _c"> </span>sinan.<span class="ls2e">sinanovic@gcu.ac.uk).</span></div><div class="t m0 x8 h9 y34 ff1 fs5 fc0 sc0 ls30 ws0">M.<span class="_ _15"> </span>Di<span class="_ _15"> </span>Renzo<span class="_ _15"> </span>is<span class="_ _15"> </span>with<span class="_ _15"> </span>the<span class="_ _e"> </span>Laborator<span class="ls2d">y<span class="_ _e"> </span>of<span class="_ _15"> </span>Signals<span class="_ _15"> </span>and<span class="_ _e"> </span>System<span class="_ _8"></span>s<span class="_ _15"> </span>(L2S),</span></div><div class="t m0 x1 h9 y35 ff1 fs5 fc0 sc0 ls31 ws0">French<span class="_ _16"> </span>National<span class="_ _16"> </span>Center<span class="_ _16"> </span>for<span class="_ _17"> </span>Scienti&#64257;c<span class="_ _16"> </span>Research<span class="_ _16"> </span>(<span class="_ _8"></span>CNRS),</div><div class="t m0 x9 h9 y36 ff1 fs5 fc0 sc0 ls16 ws0">&#180;</div><div class="t m0 xa h9 y35 ff1 fs5 fc0 sc0 ls17 ws0">Ecol<span class="_ _2"></span>e</div><div class="t m0 x1 h9 y37 ff1 fs5 fc0 sc0 ls32 ws0">Sup<span class="_ _8"></span>&#180;<span class="_ _14"></span><span class="ls33">erieure<span class="_ _15"> </span>d&#8217;</span></div><div class="t m0 xb h9 y38 ff1 fs5 fc0 sc0 ls16 ws0">&#180;</div><div class="t m0 xc h9 y37 ff1 fs5 fc0 sc0 ls34 ws0">Electricit<span class="_ _18"></span>&#180;<span class="_ _14"></span><span class="ls35">e(<span class="_ _19"></span>S<span class="_ _19"></span>U<span class="_ _19"></span>P</span></div><div class="t m0 xd h9 y38 ff1 fs5 fc0 sc0 ls16 ws0">&#180;</div><div class="t m0 xe h9 y37 ff1 fs5 fc0 sc0 ls36 ws0">ELEC),<span class="_ _13"> </span>Univ<span class="_ _2"></span>ersit<span class="_ _2"></span>y<span class="_ _15"> </span>of<span class="_ _15"> </span>Pa<span class="_ _2"></span>ris&#8211;Sud<span class="_ _15"> </span>XI<span class="_ _13"> </span>(UPS),</div><div class="t m0 x1 h9 y39 ff1 fs5 fc0 sc0 ls30 ws0">3<span class="_ _1a"> </span>rue<span class="_ _1a"> </span>J<span class="_ _8"></span>oliot&#8211;Curie,<span class="_ _5"> </span>91192<span class="_ _1a"> </span>Gif&#8211;s<span class="_ _8"></span>ur&#8211;Yv<span class="_ _2"></span>ette<span class="_ _5"> </span>(Paris),<span class="_ _5"> </span>France<span class="_ _1a"> </span>(e-m<span class="_ _8"></span>ail:</div><div class="t m0 x1 h9 y3a ff1 fs5 fc0 sc0 ls37 ws0">marco.direnzo@lss.supelec<span class="_ _2"></span>.fr).</div><div class="t m0 x8 h9 y3b ff1 fs5 fc0 sc0 ls38 ws0">R.<span class="_ _e"> </span>Mesleh<span class="_ _e"> </span>is<span class="_ _e"> </span>with<span class="_ _e"> </span>the<span class="_ _e"> </span>Electrical<span class="_ _f"> </span>Engineer<span class="_ _8"></span>ing<span class="_ _e"> </span>D<span class="_ _8"></span>epartment<span class="_ _e"> </span>and<span class="_ _e"> </span>SN<span class="_ _8"></span>CS</div><div class="t m0 x1 h9 y3c ff1 fs5 fc0 sc0 ls28 ws0">research<span class="_ _6"> </span>center,<span class="_ _6"> </span>University<span class="_ _6"> </span>of<span class="_ _6"> </span>T<span class="_ _2"></span>abuk,<span class="_ _6"> </span>P<span class="_ _1"></span>.O.Box:<span class="_ _b"> </span>71491<span class="_ _6"> </span>T<span class="_ _2"></span>abuk,<span class="_ _6"> </span>Saudi<span class="_ _6"> </span>Arabia</div><div class="t m0 x1 h9 y3d ff1 fs5 fc0 sc0 ls39 ws0">(e-mail:<span class="_ _c"> </span>rmesleh.sncs@ut.edu.sa).</div><div class="t m0 x8 h9 y3e ff1 fs5 fc0 sc0 ls27 ws0">Digital<span class="_ _b"> </span>Object<span class="_ _c"> </span>Identi&#64257;er<span class="_ _b"> </span>10.1109/T<span class="_ _8"></span>COMM.2013.061013.120547</div><div class="t m0 xf h7 y5 ff1 fs4 fc0 sc0 ls3a ws0">of<span class="_ _6"> </span>transmit<span class="_ _b"> </span>antennas<span class="_ _b"> </span>(large<span class="_ _b"> </span>scale<span class="_ _6"> </span>MIMO)<span class="_ _b"> </span>should<span class="_ _b"> </span>be<span class="_ _6"> </span>used<span class="_ _6"> </span>[3].</div><div class="t m0 xf h7 y3f ff1 fs4 fc0 sc0 ls3b ws0">Large<span class="_ _c"> </span>scale<span class="_ _c"> </span>MIMO<span class="_ _b"> </span>studied<span class="_ _c"> </span>in<span class="_ _b"> </span>[4]&#8211;[6],<span class="_"> </span>offers<span class="_ _c"> </span>higher<span class="_ _c"> </span>data<span class="_ _c"> </span>rates</div><div class="t m0 xf h7 y40 ff1 fs4 fc0 sc0 ls3c ws0">and<span class="_ _f"> </span>better<span class="_ _e"> </span>bit<span class="_ _f"> </span>error<span class="_ _f"> </span>rate<span class="_ _f"> </span>(BE<span class="ls3d">R)<span class="_ _e"> </span>performance.Howev<span class="_ _2"></span>er<span class="_ _2"></span>,<span class="_ _15"> </span>this</span></div><div class="t m0 xf h7 y41 ff1 fs4 fc0 sc0 ls3e ws0">comes<span class="_ _b"> </span>at<span class="_ _6"> </span>the<span class="_ _6"> </span>e<span class="_ _2"></span>xpense<span class="_ _b"> </span>of<span class="_ _6"> </span>an<span class="_ _6"> </span>increase<span class="_ _b"> </span>in:</div><div class="t m0 x10 h7 y42 ff1 fs4 fc0 sc0 ls3f ws0">1)<span class="_ _11"> </span>Comput<span class="_ _2"></span>ational<span class="_ _15"> </span>complexity:<span class="_ _15"> </span>A<span class="_ _f"> </span>SMX<span class="_ _e"> </span>maximum<span class="_ _e"> </span>likeli-</div><div class="t m0 x11 h7 y43 ff1 fs4 fc0 sc0 ls40 ws0">hood<span class="_ _6"> </span>(ML)<span class="_ _b"> </span>optimum<span class="_ _b"> </span>receiver<span class="_ _b"> </span>searches<span class="_ _b"> </span>across<span class="_ _6"> </span>all<span class="_ _6"> </span>possi<span class="_ _2"></span>-</div><div class="t m0 x11 h7 y44 ff1 fs4 fc0 sc0 ls41 ws0">ble<span class="_ _b"> </span>combinations,<span class="_ _c"> </span>and<span class="_ _b"> </span>tries<span class="_ _b"> </span>to<span class="_ _6"> </span>resolv<span class="_ _2"></span>e<span class="_ _b"> </span>the<span class="_ _6"> </span>inter<span class="_ _2"></span>&#8211;channel</div><div class="t m0 x11 h7 y45 ff1 fs4 fc0 sc0 ls42 ws0">interferen<span class="_ _8"></span>ce<span class="_ _13"> </span>(ICI)<span class="_ _15"> </span>caused<span class="_ _13"> </span>b<span class="_ _8"></span>y<span class="_ _1b"> </span>transmitting<span class="_ _1b"> </span>fro<span class="_ _8"></span>m<span class="_ _13"> </span>all<span class="_ _1b"> </span>an<span class="_ _8"></span>-</div><div class="t m0 x11 h7 y46 ff1 fs4 fc0 sc0 ls43 ws0">tennas<span class="_ _13"> </span>simultaneousl<span class="_ _2"></span>y<span class="_ _2"></span>,<span class="_ _a"> </span>on<span class="_ _1b"> </span>the<span class="_ _1b"> </span>same<span class="_ _13"> </span>frequency<span class="_ _1"></span>.<span class="_ _13"> </span>Sphere</div><div class="t m0 x11 h7 y47 ff1 fs4 fc0 sc0 ls44 ws0">decoder<span class="_"> </span>(SD)<span class="_ _c"> </span>was<span class="_ _c"> </span>proposed<span class="_ _c"> </span>to<span class="_ _c"> </span>reduce<span class="_ _c"> </span>the<span class="_"> </span>complexity<span class="_"> </span>of</div><div class="t m0 x11 h7 y48 ff1 fs4 fc0 sc0 ls45 ws0">the<span class="_"> </span>SMX&#8211;<span class="_ _8"></span>ML<span class="_"> </span>algorith<span class="_ _8"></span>m<span class="_"> </span>while<span class="_"> </span>retain<span class="_ _8"></span>ing<span class="_"> </span>a<span class="_ _c"> </span>near<span class="_"> </span>optim<span class="_ _8"></span>um</div><div class="t m0 x11 h7 y49 ff1 fs4 fc0 sc0 ls3e ws0">performance<span class="_ _13"> </span>[7],<span class="_ _1b"> </span>[8].<span class="_ _1b"> </span>The<span class="_ _1b"> </span>SD<span class="_ _1b"> </span>reduces<span class="_ _1b"> </span>the<span class="_ _1b"> </span>complexity</div><div class="t m0 x11 h7 y4a ff1 fs4 fc0 sc0 ls46 ws0">of<span class="_ _a"> </span>the<span class="_ _6"> </span>M<span class="_ _8"></span>L<span class="_ _a"> </span>decoder<span class="_ _6"> </span>b<span class="_ _8"></span>y<span class="_ _6"> </span>limitin<span class="_ _8"></span>g<span class="_ _6"> </span>the<span class="_ _a"> </span>nu<span class="_ _8"></span>mber<span class="_ _6"> </span>of<span class="_ _a"> </span>possib<span class="_ _8"></span>le</div><div class="t m0 x11 h7 y4b ff1 fs4 fc0 sc0 ls3f ws0">combinations<span class="_ _2"></span>.<span class="_ _a"> </span>Only<span class="_ _a"> </span>those<span class="_ _13"> </span>combinations<span class="_ _6"> </span>that<span class="_ _13"> </span>lie<span class="_ _a"> </span>within</div><div class="t m0 x11 h7 y4c ff1 fs4 fc0 sc0 ls47 ws0">a<span class="_ _a"> </span>sphere<span class="_ _a"> </span>centred<span class="_ _a"> </span>at<span class="_ _a"> </span>the<span class="_ _a"> </span>r<span class="_ _8"></span>ecei<span class="_ _2"></span>ved<span class="_ _a"> </span>signal<span class="_ _a"> </span>are<span class="_ _a"> </span>considered.</div><div class="t m0 x11 h7 y4d ff1 fs4 fc0 sc0 ls3a ws0">Ho<span class="_ _2"></span>weve<span class="_ _2"></span>r,<span class="_ _d"> </span>ev<span class="_ _2"></span>en<span class="_"> </span>though<span class="_"> </span>SMX<span class="_ _2"></span>&#8211;SD<span class="_"> </span>offers<span class="_ _d"> </span>a<span class="_"> </span>large<span class="_"> </span>reduct<span class="_ _2"></span>ion</div><div class="t m0 x11 h7 y4e ff1 fs4 fc0 sc0 ls48 ws0">in<span class="_ _c"> </span>co<span class="_ _8"></span>mplexity<span class="_"> </span>co<span class="_ _8"></span>mpared<span class="_ _c"> </span>to<span class="_ _c"> </span>SMX&#8211;ML,<span class="_ _c"> </span>it<span class="_ _b"> </span>still<span class="_ _c"> </span>h<span class="_ _8"></span>as<span class="_ _c"> </span>a<span class="_ _c"> </span>high</div><div class="t m0 x11 h7 y4f ff1 fs4 fc0 sc0 ls16 ws0">complexity<span class="_ _f"> </span>which<span class="_ _e"> </span>in<span class="_ _8"></span>creases<span class="_ _f"> </span>with<span class="_ _f"> </span>the<span class="_ _f"> </span>incr<span class="_ _8"></span>ease<span class="_ _e"> </span>of<span class="_ _f"> </span>th<span class="_ _8"></span>e</div><div class="t m0 x11 h7 y50 ff1 fs4 fc0 sc0 ls1f ws0">number<span class="_ _b"> </span>of<span class="_ _6"> </span>transmi<span class="_ _2"></span>t<span class="_ _6"> </span>antennas<span class="_ _2"></span>.</div><div class="t m0 x10 h7 y51 ff1 fs4 fc0 sc0 ls48 ws0">2)<span class="_ _11"> </span>Hardware<span class="_ _f"> </span>complexity:<span class="_ _f"> </span>In<span class="_ _f"> </span>SMX<span class="_ _f"> </span>th<span class="_ _8"></span>e<span class="_ _f"> </span>numbe<span class="_ _8"></span>r<span class="_ _e"> </span>o<span class="_ _8"></span>f<span class="_ _e"> </span>rad<span class="_ _8"></span>io</div><div class="t m0 x11 h7 y52 ff1 fs4 fc0 sc0 ls1f ws0">frequency<span class="_ _d"> </span>(RF)<span class="_"> </span>chains<span class="_ _d"> </span>is<span class="_"> </span>equal<span class="_"> </span>to<span class="_ _0"> </span>the<span class="_ _0"> </span>number<span class="_ _d"> </span>of<span class="_"> </span>transmit</div><div class="t m0 x11 h7 y53 ff1 fs4 fc0 sc0 ls3d ws0">antennas.<span class="_ _11"> </span>From<span class="_ _11"> </span>[9],<span class="_ _11"> </span>RF<span class="_ _11"> </span>chains<span class="_ _11"> </span>are<span class="_ _11"> </span>circuits<span class="_ _11"> </span>that<span class="_ _11"> </span>do</div><div class="t m0 x11 h7 y54 ff1 fs4 fc0 sc0 ls41 ws0">not<span class="_ _e"> </span>follo<span class="_ _2"></span>w<span class="_ _e"> </span>Moore&#8217;<span class="_ _2"></span>s<span class="_ _e"> </span>law<span class="_ _e"> </span>in<span class="_ _e"> </span>progressi<span class="_ _2"></span>ve<span class="_ _15"> </span>improvement.</div><div class="t m0 x11 h7 y55 ff1 fs4 fc0 sc0 ls49 ws0">Therefore,<span class="_ _a"> </span>increasing<span class="_ _a"> </span>the<span class="_ _a"> </span>number<span class="_ _a"> </span>of<span class="_ _13"> </span>transmit<span class="_ _13"> </span>antennas</div><div class="t m0 x11 h7 y56 ff1 fs4 fc0 sc0 ls4a ws0">and<span class="_ _15"> </span>consequently<span class="_ _1b"> </span>the<span class="_ _15"> </span>number<span class="_ _15"> </span>of<span class="_ _1b"> </span>RF<span class="_ _e"> </span>chains<span class="_ _15"> </span>increases</div><div class="t m0 x11 h7 y57 ff1 fs4 fc0 sc0 ls4b ws0">signi&#64257;cantly<span class="_ _d"> </span>the<span class="_"> </span>cost<span class="_ _d"> </span>of<span class="_"> </span>real<span class="_ _d"> </span>sy<span class="ls4c">stem<span class="_"> </span>implementation<span class="_"> </span>[10].</span></div><div class="t m0 x10 h7 y58 ff1 fs4 fc0 sc0 ls44 ws0">3)<span class="_ _11"> </span>Energy<span class="_ _b"> </span>consumption:<span class="_ _b"> </span>RF<span class="_ _6"> </span>chains<span class="_ _6"> </span>contain<span class="_ _6"> </span>Power<span class="_ _6"> </span>Ampli<span class="_ _2"></span>-</div><div class="t m0 x11 hb y59 ff1 fs4 fc0 sc0 ls3e ws0">&#64257;ers<span class="_"> </span>(P<span class="_ _7"></span>As)<span class="_"> </span>whi<span class="_ _2"></span>ch<span class="_"> </span>are<span class="_ _0"> </span>respons<span class="_ _2"></span>ible<span class="_ _d"> </span>for<span class="_"> </span><span class="ff6 ls4d">50</span><span class="ls16">&#8211;<span class="ff6 ls4d">80%<span class="_ _d"> </span></span><span class="ls4e">of<span class="_"> </span>the<span class="_ _d"> </span>total</span></span></div><div class="t m0 x11 h7 y5a ff1 fs4 fc0 sc0 ls4f ws0">power<span class="_ _13"> </span>consump<span class="_ _8"></span>tion<span class="_ _a"> </span>in<span class="_ _1b"> </span>the<span class="_ _1b"> </span>tran<span class="_ _8"></span>smitter<span class="_ _13"> </span>[11<span class="_ _8"></span>].<span class="_ _13"> </span>Ther<span class="_ _8"></span>efore,</div><div class="t m0 x11 h7 y5b ff1 fs4 fc0 sc0 ls50 ws0">increasing<span class="_"> </span>the<span class="_"> </span>number<span class="_"> </span>of<span class="_"> </span>RF<span class="_ _c"> </span>chains<span class="_"> </span>results<span class="_"> </span>in<span class="_"> </span>a<span class="_ _c"> </span>decrease</div><div class="t m0 x11 h7 y5c ff1 fs4 fc0 sc0 ls4a ws0">in<span class="_ _6"> </span>the<span class="_ _b"> </span>energy<span class="_ _b"> </span>ef&#64257;ci<span class="_ _2"></span>ency<span class="_ _b"> </span>[10].</div><div class="t m0 xf h7 y5d ff1 fs4 fc0 sc0 ls51 ws0">Thus,<span class="_ _a"> </span>SMX<span class="_ _13"> </span>may<span class="_ _13"> </span>not<span class="_ _13"> </span>always<span class="_ _a"> </span>be<span class="_ _13"> </span>feasible<span class="_ _13"> </span>and<span class="_ _13"> </span>a<span class="_ _13"> </span>more<span class="_ _13"> </span>energy</div><div class="t m0 xf h7 y5e ff1 fs4 fc0 sc0 ls1f ws0">ef&#64257;<span class="_ _2"></span>cient<span class="_ _b"> </span>and<span class="_ _6"> </span>lo<span class="_ _2"></span>w<span class="_ _6"> </span>complexit<span class="_ _2"></span>y<span class="_ _b"> </span>solution<span class="_ _b"> </span>should<span class="_ _b"> </span>be<span class="_ _6"> </span>considered.</div><div class="t m0 x10 h7 y5f ff1 fs4 fc0 sc0 ls43 ws0">Spatial<span class="_ _12"> </span>Modulat<span class="_ _2"></span>ion<span class="_ _12"> </span>(SM)<span class="_ _12"> </span>i<span class="_ _2"></span>s<span class="_ _12"> </span>a<span class="_ _12"> </span>transmission<span class="_ _12"> </span>t<span class="_ _2"></span>echnology</div><div class="t m0 xf h7 y60 ff1 fs4 fc0 sc0 ls3b ws0">proposed<span class="_ _15"> </span>for<span class="_ _e"> </span>MIMO<span class="_ _f"> </span>wireless<span class="_ _15"> </span>systems.<span class="_ _e"> </span>It<span class="_ _f"> </span>aims<span class="_ _e"> </span>to<span class="_ _f"> </span>increase</div><div class="t m0 xf hb y61 ff1 fs4 fc0 sc0 ls52 ws0">the<span class="_ _6"> </span>spectral<span class="_ _6"> </span>ef&#64257;cienc<span class="_ _2"></span>y<span class="_ _2"></span>,<span class="_ _b"> </span><span class="ff6 ls16">(<span class="ff7">m</span>)</span><span class="ls3f">,<span class="_ _a"> </span>of<span class="_ _6"> </span>single&#8211;antenna<span class="_ _b"> </span>systems<span class="_ _6"> </span>whil<span class="_ _2"></span>e</span></div><div class="t m0 xf h7 y62 ff1 fs4 fc0 sc0 ls53 ws0">a<span class="_ _2"></span>voiding<span class="_ _b"> </span>ICI<span class="_ _6"> </span>[12].<span class="_ _6"> </span>This<span class="_ _6"> </span>is<span class="_ _6"> </span>attained<span class="_ _b"> </span>through<span class="_ _6"> </span>the<span class="_ _6"> </span>adoption<span class="_ _b"> </span>of<span class="_ _6"> </span>a</div><div class="t m0 xf h7 y63 ff1 fs4 fc0 sc0 ls4e ws0">ne<span class="_ _2"></span>w<span class="_ _1b"> </span>m<span class="_ _8"></span>odulation<span class="_ _a"> </span>and<span class="_ _1b"> </span>coding<span class="_ _1b"> </span>scheme,<span class="_ _1b"> </span>which<span class="_ _1b"> </span>foresees:<span class="_ _13"> </span>i)<span class="_ _15"> </span>the</div><div class="t m0 xf h7 y64 ff1 fs4 fc0 sc0 ls4b ws0">acti<span class="_ _2"></span>vation,<span class="_ _e"> </span>at<span class="_ _f"> </span>each<span class="_ _f"> </span>time<span class="_ _f"> </span>instan<span class="ls47">ce,<span class="_ _e"> </span>of<span class="_ _f"> </span>a<span class="_ _f"> </span>single<span class="_ _e"> </span>antenna<span class="_ _f"> </span>that</span></div><div class="t m0 xf h7 y65 ff1 fs4 fc0 sc0 ls46 ws0">transmits<span class="_ _1c"> </span>a<span class="_ _f"> </span>g<span class="_ _8"></span>i<span class="_ _2"></span>ven<span class="_ _f"> </span>data<span class="_ _f"> </span>sy<span class="_ _8"></span>mbol<span class="_ _f"> </span>(<span class="_ _8"></span><span class="ff8 ls42">constellation<span class="_ _f"> </span>symbol</span><span class="ls51">),<span class="_ _f"> </span>and</span></div><div class="t m0 xf h7 y66 ff1 fs4 fc0 sc0 ls1 ws0">ii)<span class="_ _b"> </span>the<span class="_ _b"> </span>exploitation<span class="_ _c"> </span>of<span class="_ _b"> </span>the<span class="_ _b"> </span>sp<span class="_ _8"></span>atial<span class="_ _c"> </span>positio<span class="_ _8"></span>n<span class="_ _c"> </span>(in<span class="_ _8"></span>dex)<span class="_ _c"> </span>of<span class="_ _c"> </span>th<span class="_ _8"></span>e<span class="_ _c"> </span>active</div><div class="t m0 xf h7 y67 ff1 fs4 fc0 sc0 ls3e ws0">antenna<span class="_"> </span>as<span class="_"> </span>an<span class="_"> </span>additional<span class="_ _0"> </span>dimens<span class="_ _2"></span>ion<span class="_"> </span>for<span class="_"> </span>data<span class="_"> </span>transmis<span class="_ _2"></span>sion<span class="_"> </span>(<span class="ff8 ls4d">spa-</span></div><div class="t m0 xf h7 y68 ff8 fs4 fc0 sc0 ls42 ws0">tial<span class="_ _0"> </span>symbol<span class="ff1 ls54">)<span class="_"> </span>[13].<span class="_ _d"> </span>Both<span class="_ _0"> </span>t<span class="_ _2"></span>he<span class="_"> </span><span class="ff8 ls42">constellation<span class="_ _0"> </span>symbol<span class="_ _0"> </span></span><span class="ls3f">and<span class="_ _d"> </span>the<span class="_"> </span><span class="ff8 ls55">spatial</span></span></span></div><div class="t m0 xf h7 y69 ff8 fs4 fc0 sc0 ls4d ws0">symbol<span class="_ _c"> </span><span class="ff1 ls22">depend<span class="_ _c"> </span>on<span class="_ _c"> </span>the<span class="_ _b"> </span>incoming<span class="_ _c"> </span>data<span class="_ _c"> </span>bits.<span class="_ _b"> </span>An<span class="_ _c"> </span>overall<span class="_"> </span>increase</span></div><div class="t m0 xf h7 y6a ff1 fs4 fc0 sc0 ls4e ws0">by<span class="_"> </span>the<span class="_"> </span>bas<span class="_ _2"></span>e&#8211;two<span class="_"> </span>logari<span class="_ _2"></span>thm<span class="_"> </span>of<span class="_"> </span>the<span class="_ _d"> </span>number<span class="_"> </span>of<span class="_"> </span>transmi<span class="_ _2"></span>t&#8211;antennas</div><div class="t m0 xf h7 y6b ff1 fs4 fc0 sc0 ls4c ws0">of<span class="_ _6"> </span>the<span class="_ _a"> </span>spectral<span class="_ _6"> </span>ef&#64257;ciency<span class="_ _b"> </span>is<span class="_ _a"> </span>achiev<span class="_ _2"></span>ed.<span class="_ _6"> </span>This<span class="_ _6"> </span>lim<span class="_ _8"></span>its<span class="_ _6"> </span>the<span class="_ _6"> </span>num<span class="_ _8"></span>ber</div><div class="t m0 xf h7 y6c ff1 fs4 fc0 sc0 ls3a ws0">of<span class="_ _c"> </span>transmit<span class="_"> </span>antennas<span class="_"> </span>to<span class="_ _c"> </span>be<span class="_"> </span>a<span class="_ _c"> </span>power<span class="_"> </span>of<span class="_ _c"> </span>two<span class="_ _c"> </span>unless<span class="_"> </span>fractional<span class="_"> </span>bit</div><div class="t m0 xf h7 y6d ff1 fs4 fc0 sc0 ls3a ws0">encoding<span class="_"> </span>SM<span class="_ _c"> </span>(FBE&#8211;SM)<span class="_"> </span>[14],<span class="_"> </span>o<span class="_ _8"></span>r<span class="_"> </span>generalised<span class="_"> </span>SM<span class="_ _c"> </span>(GSM)<span class="_ _c"> </span>[15]</div><div class="t m0 x12 h9 y6e ff1 fs5 fc0 sc0 ls56 ws0">0090-6778/13$31.00</div><div class="t m0 x13 h9 y6f ff1 fs5 fc0 sc0 ls16 ws0">c</div><div class="t m0 x14 ha y6e ff5 fs5 fc0 sc0 ls16 ws0">&#58882;<span class="_ _c"> </span><span class="ff1 ls57">2013<span class="_ _c"> </span>IEEE</span></div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>
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