Training-Signal-Design-for-Correlated-MassiveMIMO

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Maasive MIMO systems the most emerging technology
Training-Signal-Design-for-Correlated-MassiveMIMO
  • Training Signal Design for Correlated MassiveMIMO Channel Estimation.pdf
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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/624f870674bc5c0105423c8d/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/624f870674bc5c0105423c8d/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">IEEE<span class="_ _0"> </span>TRANSA<span class="_ _1"></span>CTIONS<span class="_ _0"> </span>ON<span class="_ _0"> </span>WIRELESS<span class="_ _0"> </span>COMMUNICA<span class="_ _2"></span><span class="ls1">TIONS,<span class="_ _0"> </span>VOL.<span class="_ _0"> </span>16,<span class="_ _0"> </span>NO.<span class="_ _3"> </span>2,<span class="_ _0"> </span>FEBRU<span class="_ _1"></span>AR<span class="_ _1"></span>Y<span class="_ _0"> </span>2017<span class="_ _4"> </span>1135</span></div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls2 ws0">T<span class="_ _2"></span>raining<span class="_ _5"> </span>Signal<span class="_ _5"> </span>Design<span class="_ _5"> </span>for<span class="_ _5"> </span>Correlated<span class="_ _5"> </span>Massi<span class="_ _2"></span>ve</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls3 ws0">MIMO<span class="_ _5"> </span>Channel<span class="_ _5"> </span>Estimation</div><div class="t m0 x4 h4 y4 ff1 fs2 fc0 sc0 ls4 ws0">Mojtab<span class="_ _6"></span>a<span class="_ _7"> </span>Soltan<span class="_ _6"></span>alia<span class="_ _6"></span>n,<span class="_ _7"> </span><span class="ff2 ls5">Member<span class="_ _8"></span>,<span class="_ _7"> </span>I<span class="_ _1"></span>EEE,<span class="_ _7"> </span><span class="ff1 ls6">Mohammad<span class="_ _9"> </span>Mahdi<span class="_ _9"> </span>Naghsh,<span class="_ _9"> </span></span>Member<span class="_ _8"></span>,<span class="_ _9"> </span>IEEE,<span class="_ _9"> </span><span class="ff1 ls7">Na&#64257;seh<span class="_ _9"> </span>Shariati<span class="_ _1"></span>,</span></span></div><div class="t m0 x5 h4 y5 ff1 fs2 fc0 sc0 ls8 ws0">Petre<span class="_ _a"> </span>Stoic<span class="_ _6"></span>a,<span class="_ _7"> </span><span class="ff2 ls5">F<span class="_ _2"></span>ellow<span class="_ _8"></span>,<span class="_ _7"> </span>IEEE,<span class="_ _7"> </span><span class="ff1 ls9">and<span class="_ _9"> </span>Babak<span class="_ _7"> </span>Hassibi</span></span></div><div class="t m0 x6 h5 y6 ff3 fs3 fc0 sc0 lsa ws0">Abstract<span class="_ _6"></span><span class="ff4 lsb">&#8212;<span class="_ _b"></span>In<span class="_ _a"> </span>this<span class="_ _7"> </span>paper<span class="_ _8"></span>,<span class="_ _a"> </span>we<span class="_ _a"> </span>propo<span class="_ _1"></span>se<span class="_ _7"> </span>a<span class="_ _a"> </span>new<span class="_ _a"> </span>appro<span class="_ _1"></span>ach<span class="_ _7"> </span>to<span class="_ _a"> </span>the</span></div><div class="t m0 x1 h5 y7 ff4 fs3 fc0 sc0 lsc ws0">design<span class="_ _a"> </span>of<span class="_ _c"> </span>traini<span class="_ _6"></span>ng<span class="_ _a"> </span>sequen<span class="_ _6"></span>ces<span class="_ _a"> </span>that<span class="_ _a"> </span>can<span class="_ _c"> </span>be<span class="_ _a"> </span>u<span class="_ _6"></span>sed<span class="_ _a"> </span>for<span class="_ _7"> </span>an<span class="_ _c"> </span>accurate</div><div class="t m0 x1 h5 y8 ff4 fs3 fc0 sc0 lsd ws0">estima<span class="_ _1"></span>tion<span class="_ _a"> </span>of<span class="_ _a"> </span>multi-input<span class="_ _7"> </span>multi-output<span class="_ _7"> </span>channels.<span class="_ _7"> </span>The<span class="_ _a"> </span>proposed</div><div class="t m0 x1 h5 y9 ff4 fs3 fc0 sc0 lse ws0">method<span class="_ _3"> </span>is<span class="_ _d"> </span>particula<span class="_ _1"></span>rly<span class="_ _e"> </span>instrumenta<span class="_ _1"></span>l<span class="_ _e"> </span>in<span class="_ _e"> </span>training<span class="_ _e"> </span>sequence<span class="_ _3"> </span>designs</div><div class="t m0 x1 h5 ya ff4 fs3 fc0 sc0 lsf ws0">that<span class="_ _c"> </span>deal<span class="_ _c"> </span>with<span class="_ _c"> </span>three<span class="_ _a"> </span>key<span class="_ _c"> </span>chall<span class="_ _6"></span>enges:<span class="_ _c"> </span>1)<span class="_ _c"> </span>arbitrary<span class="_ _c"> </span>chan<span class="_ _6"></span>nel<span class="_ _c"> </span>and</div><div class="t m0 x1 h5 yb ff4 fs3 fc0 sc0 ls10 ws0">noise<span class="_ _9"> </span>statistic<span class="_ _1"></span>s<span class="_ _9"> </span>that<span class="_ _9"> </span>do<span class="_ _9"> </span>not<span class="_ _9"> </span>follo<span class="_ _1"></span>w<span class="_ _9"> </span>speci&#64257;c<span class="_ _9"> </span>models,<span class="_ _9"> </span>2<span class="_ _1"></span>)<span class="_ _9"> </span>limitations</div><div class="t m0 x1 h5 yc ff4 fs3 fc0 sc0 ls11 ws0">on<span class="_ _9"> </span>the<span class="_ _9"> </span>properties<span class="_ _9"> </span>of<span class="_ _9"> </span>the<span class="_ _9"> </span>transmi<span class="_ _6"></span>t<span class="_ _9"> </span>signals,<span class="_ _9"> </span>inclu<span class="_ _6"></span>ding<span class="_ _9"> </span>total<span class="_ _9"> </span>power<span class="_ _2"></span>,</div><div class="t m0 x1 h5 yd ff4 fs3 fc0 sc0 ls12 ws0">per<span class="_ _1"></span>-a<span class="_ _1"></span>ntenna<span class="_"> </span>po<span class="_ _1"></span>wer<span class="_ _8"></span>,<span class="_"> </span>ha<span class="_ _1"></span>ving<span class="_ _0"> </span>a<span class="_ _f"> </span>consta<span class="_ _1"></span>nt-modulus,<span class="_ _f"> </span>discr<span class="_ _1"></span>ete-pha<span class="_ _1"></span>se,<span class="_"> </span>o<span class="_ _1"></span>r</div><div class="t m0 x1 h5 ye ff4 fs3 fc0 sc0 ls13 ws0">low<span class="_ _10"> </span>peak-to-av<span class="_ _1"></span>erage-power<span class="_ _9"> </span>ratio,<span class="_ _10"> </span>an<span class="_ _6"></span>d<span class="_ _10"> </span>3)<span class="_ _10"> </span>sign<span class="_ _6"></span>al<span class="_ _d"> </span>d<span class="_ _6"></span>esign<span class="_ _10"> </span>for<span class="_ _d"> </span>l<span class="_ _6"></span>arge-</div><div class="t m0 x1 h5 yf ff4 fs3 fc0 sc0 ls14 ws0">scale<span class="_ _e"> </span>or<span class="_ _e"> </span>massive<span class="_ _e"> </span>anten<span class="_ _6"></span>na<span class="_ _e"> </span>arrays.<span class="_ _e"> </span>S<span class="_ _6"></span>everal<span class="_ _3"> </span>nu<span class="_ _6"></span>merical<span class="_ _3"> </span>e<span class="_ _6"></span>xamples<span class="_ _d"> </span>are</div><div class="t m0 x1 h5 y10 ff4 fs3 fc0 sc0 lsc ws0">provided<span class="_ _10"> </span>to<span class="_ _10"> </span>exami<span class="_ _6"></span>ne<span class="_ _10"> </span>th<span class="_ _6"></span>e<span class="_ _10"> </span>proposed<span class="_ _10"> </span>met<span class="_ _6"></span>hod.</div><div class="t m0 x6 h5 y11 ff3 fs3 fc0 sc0 ls15 ws0">Index<span class="_ _c"> </span>T<span class="_ _2"></span>erms<span class="ff4 ls16">&#8212;<span class="_ _b"></span>Channe<span class="_ _1"></span>l<span class="_ _a"> </span>estima<span class="_ _1"></span>tion,<span class="_ _a"> </span>massi<span class="_ _1"></span>v<span class="_ _1"></span>e<span class="_ _c"> </span>MIMO,<span class="_ _a"> </span>peak-to-</span></div><div class="t m0 x1 h5 y12 ff4 fs3 fc0 sc0 ls17 ws0">a<span class="_ _1"></span>ve<span class="_ _1"></span>rage-po<span class="_ _1"></span>wer<span class="_ _10"> </span>ratio<span class="_ _10"> </span>(P<span class="_ _2"></span>AR),<span class="_ _10"> </span>signal<span class="_ _d"> </span>design,<span class="_ _d"> </span>training<span class="_ _d"> </span>sequence.</div><div class="t m0 x7 h6 y13 ff1 fs4 fc0 sc0 ls18 ws0">I.<span class="_ _11"> </span>I<span class="fs5 ls19">NTR<span class="_ _1"></span>ODUCTION</span></div><div class="t m0 x1 h7 y14 ff4 fs6 fc0 sc0 ls1a ws0">A</div><div class="t m0 x8 h6 y15 ff1 fs4 fc0 sc0 ls1b ws0">CCUR<span class="_ _1"></span>A<span class="_ _8"></span>TE<span class="_ _12"> </span>knowledge<span class="_ _13"> </span>of<span class="_ _12"> </span>multi-input<span class="_ _13"> </span>multi-output</div><div class="t m0 x8 h6 y16 ff1 fs4 fc0 sc0 ls1c ws0">(MIMO)<span class="_"> </span>channel<span class="_ _0"> </span>state<span class="_"> </span>informati<span class="_ _1"></span>on<span class="_"> </span>(CS<span class="_ _1"></span>I)<span class="_"> </span>plays<span class="_"> </span>an<span class="_"> </span>impor<span class="_ _1"></span>-</div><div class="t m0 x1 h6 y17 ff1 fs4 fc0 sc0 ls1d ws0">tant<span class="_ _e"> </span>role<span class="_ _e"> </span>in<span class="_ _e"> </span>exp<span class="_ _6"></span>loiting<span class="_"> </span>the<span class="_ _d"> </span>full<span class="_ _e"> </span>poten<span class="_ _6"></span>tial<span class="_"> </span>of<span class="_ _e"> </span>MIMO<span class="_ _e"> </span>c<span class="_ _6"></span>ommun<span class="_ _6"></span>ica-</div><div class="t m0 x1 h6 y18 ff1 fs4 fc0 sc0 ls1e ws0">tion<span class="_ _e"> </span>systems.<span class="_ _e"> </span>A<span class="_ _10"> </span>practical<span class="_ _e"> </span>way<span class="_ _d"> </span>to<span class="_ _d"> </span>acquire<span class="_ _d"> </span>instantaneous<span class="_"> </span>CSI<span class="_ _d"> </span>of</div><div class="t m0 x1 h6 y19 ff1 fs4 fc0 sc0 ls1e ws0">the<span class="_"> </span>MIMO<span class="_"> </span>channel<span class="_"> </span>is<span class="_ _e"> </span>training-based<span class="_ _f"> </span>channel<span class="_"> </span>estimation<span class="_"> </span>which</div><div class="t m0 x1 h6 y1a ff1 fs4 fc0 sc0 ls1f ws0">relies<span class="_ _11"> </span>on<span class="_ _11"> </span>transmitting<span class="_ _c"> </span>a<span class="_ _6"></span>n<span class="_ _11"> </span><span class="ff2 ls20">ap<span class="_ _14"></span>r<span class="_ _14"></span>i<span class="_ _14"></span>o<span class="_ _15"></span>r<span class="_ _14"></span>i<span class="ff1 ls1c">known<span class="_ _c"> </span>sequence,<span class="_ _c"> </span>namely</span></span></div><div class="t m0 x1 h6 y1b ff1 fs4 fc0 sc0 ls1a ws0">a<span class="_ _a"> </span><span class="ff2 ls21">training<span class="_ _7"> </span><span class="ff1">or<span class="_ _c"> </span></span><span class="ls22">pilot<span class="_ _11"> </span></span></span><span class="ls23">sequence,<span class="_ _7"> </span>to<span class="_ _c"> </span>the<span class="_ _a"> </span>receiver<span class="_ _1"></span>,<span class="_ _9"> </span>and<span class="_ _c"> </span>estimating</span></div><div class="t m0 x1 h6 y1c ff1 fs4 fc0 sc0 ls24 ws0">the<span class="_ _a"> </span>instantaneous<span class="_ _7"> </span>channel<span class="_ _a"> </span>coef<span class="_ _1"></span>&#64257;cients<span class="_ _7"> </span>based<span class="_ _a"> </span>o<span class="_ _6"></span>n<span class="_ _a"> </span>the<span class="_ _a"> </span>recei<span class="_ _1"></span>ved</div><div class="t m0 x1 h6 y1d ff1 fs4 fc0 sc0 ls25 ws0">signal<span class="_ _9"> </span>[1]&#8211;<span class="_ _6"></span>[13]<span class="_ _6"></span>.<span class="_ _d"> </span>This<span class="_ _9"> </span>c<span class="_ _6"></span>hannel<span class="_ _9"> </span>estimation<span class="_ _9"> </span>scheme<span class="_ _9"> </span>is<span class="_ _9"> </span>illustrated</div><div class="t m0 x1 h6 y1e ff1 fs4 fc0 sc0 ls21 ws0">in<span class="_ _10"> </span>Fig.<span class="_ _10"> </span>1.</div><div class="t m0 x6 h6 y1f ff1 fs4 fc0 sc0 ls26 ws0">Massi<span class="_ _1"></span>ve<span class="_ _16"> </span>MIMO<span class="_ _16"> </span>is<span class="_ _17"> </span>an<span class="_ _16"> </span>emerging<span class="_ _16"> </span>technol<span class="_ _1"></span>ogical<span class="_ _16"> </span>concept</div><div class="t m0 x1 h6 y20 ff1 fs4 fc0 sc0 ls27 ws0">in<span class="_ _18"> </span>communications<span class="_ _19"> </span>where<span class="_ _18"> </span>a<span class="_ _18"> </span>large<span class="_ _19"> </span>number<span class="_ _18"> </span>of<span class="_ _18"> </span>antennas<span class="_ _18"> </span>is</div><div class="t m0 x9 h8 y21 ff1 fs5 fc0 sc0 ls28 ws0">Manuscript<span class="_ _c"> </span>received<span class="_ _c"> </span>October<span class="_ _c"> </span>13,<span class="_ _c"> </span>2015;<span class="_ _c"> </span>revised<span class="_ _a"> </span>February<span class="_ _11"> </span>27,<span class="_ _a"> </span>2016<span class="_ _c"> </span>and</div><div class="t m0 x1 h8 y22 ff1 fs5 fc0 sc0 ls29 ws0">September<span class="_ _19"> </span>3,<span class="_ _1a"> </span>2016;<span class="_ _1a"> </span>accepted<span class="_ _19"> </span>November<span class="_ _1a"> </span>28,<span class="_ _19"> </span>2016.<span class="_ _11"> </span>D<span class="_ _6"></span>ate<span class="_ _1a"> </span>of<span class="_ _1a"> </span>publication</div><div class="t m0 x1 h8 y23 ff1 fs5 fc0 sc0 ls28 ws0">December<span class="_ _a"> </span>14,<span class="_ _9"> </span>2016;<span class="_ _a"> </span>date<span class="_ _7"> </span>of<span class="_ _7"> </span>current<span class="_ _a"> </span>version<span class="_ _9"> </span>F<span class="_ _6"></span>ebruary<span class="_ _7"> </span>9,<span class="_ _7"> </span>2017.<span class="_ _7"> </span>T<span class="_ _6"></span>his<span class="_ _7"> </span>work</div><div class="t m0 x1 h8 y24 ff1 fs5 fc0 sc0 ls2a ws0">was<span class="_ _7"> </span>s<span class="_ _6"></span>upported<span class="_ _a"> </span>in<span class="_ _a"> </span>part<span class="_ _a"> </span>by<span class="_ _a"> </span>the<span class="_ _a"> </span>European<span class="_ _a"> </span>Research<span class="_ _c"> </span>Council,<span class="_ _a"> </span>in<span class="_ _a"> </span>part<span class="_ _a"> </span>by<span class="_ _a"> </span>the</div><div class="t m0 x1 h8 y25 ff1 fs5 fc0 sc0 ls2b ws0">Swedish<span class="_ _d"> </span>Research<span class="_ _10"> </span>Council,<span class="_ _d"> </span>in<span class="_ _d"> </span>part<span class="_ _d"> </span>by<span class="_ _d"> </span>the<span class="_ _d"> </span>U.S.<span class="_ _d"> </span>National<span class="_ _10"> </span>Science<span class="_ _10"> </span>Foundation</div><div class="t m0 x1 h8 y26 ff1 fs5 fc0 sc0 ls2c ws0">under<span class="_ _10"> </span>Grant<span class="_ _9"> </span>CNS-0932428,<span class="_ _9"> </span>Grant<span class="_ _9"> </span>CCF-1018927,<span class="_ _7"> </span>Grant<span class="_ _10"> </span>CCF-1423663,<span class="_ _7"> </span>and</div><div class="t m0 x1 h8 y27 ff1 fs5 fc0 sc0 ls2d ws0">Grant<span class="_ _10"> </span>CCF-1409204,<span class="_ _10"> </span>in<span class="_ _10"> </span>part<span class="_ _10"> </span>by<span class="_ _10"> </span>Qualcomm<span class="_ _10"> </span>Inc.<span class="_ _6"></span>,<span class="_ _10"> </span>in<span class="_ _10"> </span>part<span class="_ _10"> </span>by<span class="_ _10"> </span>the<span class="_ _d"> </span>NASA<span class="_ _2"></span>&#8217;<span class="_ _1"></span>s<span class="_ _d"> </span>Jet</div><div class="t m0 x1 h8 y28 ff1 fs5 fc0 sc0 ls2e ws0">Propulsion<span class="_ _a"> </span>L<span class="_ _6"></span>aboratory<span class="_ _a"> </span>through<span class="_ _c"> </span>the<span class="_ _a"> </span>Pre<span class="ls28">sident<span class="_ _a"> </span>and<span class="_ _c"> </span>Director&#8217;<span class="_ _1"></span>s<span class="_ _a"> </span>Fund,<span class="_ _a"> </span>in<span class="_ _a"> </span>part</span></div><div class="t m0 x1 h8 y29 ff1 fs5 fc0 sc0 ls2f ws0">by<span class="_ _d"> </span>King<span class="_ _d"> </span>Abdulaziz<span class="_ _10"> </span>University<span class="_ _2"></span>,<span class="_ _10"> </span>and<span class="_ _10"> </span>in<span class="_ _d"> </span>part<span class="_ _d"> </span>by<span class="_ _d"> </span>the<span class="_ _10"> </span>King<span class="_ _d"> </span>Abdullah<span class="_ _10"> </span>Univ<span class="_ _1"></span>ersity</div><div class="t m0 x1 h8 y2a ff1 fs5 fc0 sc0 ls30 ws0">of<span class="_ _d"> </span>Science<span class="_ _9"> </span>and<span class="_ _d"> </span>T<span class="_ _1"></span>echnology<span class="_ _1"></span>.<span class="_ _10"> </span>The<span class="_ _10"> </span>associ<span class="ls31">ate<span class="_ _9"> </span>editor<span class="_ _10"> </span>coordinating<span class="_ _9"> </span>the<span class="_ _10"> </span>revie<span class="_ _1"></span>w<span class="_ _10"> </span>of</span></div><div class="t m0 x1 h8 y2b ff1 fs5 fc0 sc0 ls32 ws0">this<span class="_ _d"> </span>paper<span class="_ _d"> </span>and<span class="_ _d"> </span>approving<span class="_ _10"> </span>it<span class="_ _d"> </span>for<span class="_ _e"> </span>publication<span class="_ _9"> </span>was<span class="_ _d"> </span>F<span class="_ _1"></span>.<span class="_ _e"> </span>Boccardi.<span class="_ _d"> </span><span class="ff2 ls2d">(Cor<span class="_ _6"></span>responding</span></div><div class="t m0 x1 h9 y2c ff2 fs5 fc0 sc0 ls28 ws0">author:<span class="_ _e"> </span>Mojtaba<span class="_ _10"> </span>Soltanalian.)</div><div class="t m0 x9 h8 y2d ff1 fs5 fc0 sc0 ls33 ws0">M.<span class="_ _10"> </span>S<span class="_ _6"></span>oltanalian<span class="_ _7"> </span>is<span class="_ _9"> </span>with<span class="_ _9"> </span>the<span class="_ _9"> </span>Depar<span class="_ _6"></span>tment<span class="_ _9"> </span>o<span class="_ _6"></span>f<span class="_ _10"> </span>E<span class="_ _6"></span>lectrical<span class="_ _7"> </span>and<span class="_ _9"> </span>Computer<span class="_ _7"> </span>Engi-</div><div class="t m0 x1 h8 y2e ff1 fs5 fc0 sc0 ls2f ws0">neering,<span class="_ _10"> </span>University<span class="_ _d"> </span>of<span class="_ _10"> </span>Illinois<span class="_ _9"> </span>at<span class="_ _d"> </span>Chicago,<span class="_ _9"> </span>Chicago,<span class="_ _10"> </span>IL<span class="_ _10"> </span>60607<span class="_ _10"> </span>USA<span class="_ _d"> </span>(e-mail:</div><div class="t m0 x1 h8 y2f ff1 fs5 fc0 sc0 ls28 ws0">msol@uic.edu).</div><div class="t m0 x9 h8 y30 ff1 fs5 fc0 sc0 ls34 ws0">M.<span class="_ _10"> </span>M.<span class="_ _9"> </span>Naghsh<span class="_ _9"> </span>is<span class="_ _10"> </span>with<span class="_ _9"> </span>the<span class="_ _9"> </span>Department<span class="_ _7"> </span>of<span class="_ _10"> </span>Electr<span class="_ _6"></span>ical<span class="_ _9"> </span>and<span class="_ _9"> </span>Computer<span class="_ _9"> </span>E<span class="_ _6"></span>ngi-</div><div class="t m0 x1 h8 y31 ff1 fs5 fc0 sc0 ls35 ws0">neering,<span class="_ _d"> </span>Isfahan<span class="_ _e"> </span>U<span class="_ _6"></span>ni<span class="_ _1"></span>versity<span class="_ _d"> </span>of<span class="_ _e"> </span>T<span class="_ _1"></span>echnology<span class="_ _1"></span>,<span class="_ _e"> </span>I<span class="_ _6"></span>sfahan<span class="_ _e"> </span>84156-83111,<span class="_ _10"> </span>Iran.</div><div class="t m0 x9 h8 y32 ff1 fs5 fc0 sc0 ls36 ws0">N.<span class="_ _7"> </span>Sh<span class="_ _6"></span>ariati<span class="_ _a"> </span>was<span class="_ _7"> </span>w<span class="_ _6"></span>ith<span class="_ _a"> </span>the<span class="_ _a"> </span>Department<span class="_ _a"> </span>o<span class="_ _6"></span>f<span class="_ _7"> </span>Signal<span class="_ _a"> </span>Pr<span class="_ _6"></span>ocessing,<span class="_ _a"> </span>K<span class="_ _6"></span>TH<span class="_ _7"> </span>Royal</div><div class="t m0 x1 h8 y33 ff1 fs5 fc0 sc0 ls2a ws0">Institute<span class="_ _3"> </span>of<span class="_ _3"> </span>T<span class="_ _1"></span>echnology<span class="_ _1"></span>,<span class="_ _0"> </span>10044<span class="_ _3"> </span>Stockholm,<span class="_ _e"> </span>Sweden.<span class="_ _3"> </span>She<span class="_ _3"> </span>is<span class="_ _0"> </span>now<span class="_ _0"> </span>w<span class="_ _6"></span>ith<span class="_ _0"> </span>E<span class="_ _6"></span>ricsson</div><div class="t m0 x1 h8 y34 ff1 fs5 fc0 sc0 ls37 ws0">Research,<span class="_ _d"> </span>16483<span class="_ _d"> </span>Stockholm,<span class="_ _d"> </span>Sweden.</div><div class="t m0 x9 h8 y35 ff1 fs5 fc0 sc0 ls38 ws0">P<span class="_ _2"></span>.<span class="_ _c"> </span>Stoica<span class="_ _11"> </span>is<span class="_ _11"> </span>with<span class="_ _11"> </span>the<span class="_ _11"> </span>Department<span class="_ _11"> </span>o<span class="_ _6"></span><span class="ls2f">f<span class="_ _11"> </span>Information<span class="_ _11"> </span>T<span class="_ _2"></span>echnology<span class="_ _1"></span>,<span class="_ _11"> </span>Upps<span class="_ _6"></span>ala</span></div><div class="t m0 x1 h8 y36 ff1 fs5 fc0 sc0 ls35 ws0">Uni<span class="_ _1"></span>versity<span class="_ _1"></span>,<span class="_ _e"> </span>75237<span class="_ _d"> </span>Uppsala,<span class="_ _d"> </span>Sweden.</div><div class="t m0 x9 h8 y37 ff1 fs5 fc0 sc0 ls34 ws0">B.<span class="_ _7"> </span>H<span class="_ _6"></span>assibi<span class="_ _a"> </span>is<span class="_ _a"> </span>with<span class="_ _a"> </span>the<span class="_ _a"> </span>Departm<span class="_ _6"></span>ent<span class="_ _a"> </span>of<span class="_ _a"> </span>E<span class="_ _6"></span>lectrical<span class="_ _c"> </span>Engineering,<span class="_ _c"> </span>California</div><div class="t m0 x1 h8 y38 ff1 fs5 fc0 sc0 ls2a ws0">Institute<span class="_ _d"> </span>of<span class="_ _d"> </span>T<span class="_ _1"></span>echnology<span class="_ _2"></span>,<span class="_ _10"> </span>Pasadena,<span class="_ _d"> </span>CA<span class="_ _e"> </span>91125<span class="_ _e"> </span>U<span class="_ _6"></span>SA.</div><div class="t m0 x9 h8 y39 ff1 fs5 fc0 sc0 ls39 ws0">Color<span class="_ _9"> </span>versions<span class="_ _7"> </span>of<span class="_ _9"> </span>one<span class="_ _7"> </span>or<span class="_ _7"> </span>more<span class="_ _9"> </span>of<span class="_ _7"> </span>the<span class="_ _9"> </span>&#64257;gures<span class="_ _7"> </span>in<span class="_ _9"> </span>this<span class="_ _a"> </span>paper<span class="_ _9"> </span>are<span class="_ _7"> </span>av<span class="_ _1"></span>ailable</div><div class="t m0 x1 h8 y3a ff1 fs5 fc0 sc0 ls3a ws0">online<span class="_ _e"> </span>at<span class="_ _d"> </span>http://ieeexplore.iee<span class="_ _6"></span>e.org.</div><div class="t m0 x9 h8 y3b ff1 fs5 fc0 sc0 ls2f ws0">Digital<span class="_ _d"> </span>Object<span class="_ _d"> </span>Identi&#64257;er<span class="_ _d"> </span>10.<span class="_ _6"></span>1109/TWC.<span class="_ _6"></span>2016.2639485</div><div class="t m0 xa h8 y3c ff1 fs5 fc0 sc0 ls35 ws0">Fig.<span class="_"> </span>1.<span class="_ _1b"> </span>MIMO<span class="_"> </span>training<span class="_ _3"> </span>for<span class="_"> </span>channel<span class="_ _0"> </span>es<span class="_ _6"></span>tim<span class="ls3b">ation:<span class="_ _0"> </span>T<span class="_ _6"></span>he<span class="_"> </span>optimized<span class="_ _3"> </span>training<span class="_ _0"> </span>s<span class="_ _6"></span>ignals</span></div><div class="t m0 xa h8 y3d ff1 fs5 fc0 sc0 ls29 ws0">are<span class="_"> </span>transmitted<span class="_ _3"> </span>during<span class="_ _0"> </span>the<span class="_"> </span><span class="ff2 ls31">training<span class="_ _0"> </span>phase<span class="_ _0"> </span></span><span class="ls2b">in<span class="_"> </span>order<span class="_ _0"> </span>to<span class="_"> </span>es<span class="_ _6"></span>timate<span class="_ _0"> </span>the<span class="_"> </span>instantaneous</span></div><div class="t m0 xa h8 y3e ff1 fs5 fc0 sc0 ls3c ws0">channel<span class="_ _d"> </span>information<span class="_ _d"> </span>based<span class="_ _d"> </span>on<span class="_ _d"> </span>the<span class="_ _e"> </span>received<span class="_ _d"> </span>signal<span class="_ _e"> </span>and<span class="_ _d"> </span>the<span class="_ _d"> </span>known<span class="_ _e"> </span>input.</div><div class="t m0 xa h6 y3f ff1 fs4 fc0 sc0 ls3d ws0">employed<span class="_ _10"> </span>at<span class="_ _a"> </span>the<span class="_ _9"> </span>base<span class="_ _7"> </span>stations.<span class="_ _9"> </span>Massiv<span class="_ _1"></span>e<span class="_ _7"> </span>MIMO<span class="_ _9"> </span>systems<span class="_ _7"> </span>hav<span class="_ _1"></span>e</div><div class="t m0 xa h6 y40 ff1 fs4 fc0 sc0 ls3e ws0">exhibit<span class="_ _1"></span>ed<span class="_ _d"> </span>superior<span class="_ _e"> </span>performance<span class="_ _e"> </span>with<span class="_ _10"> </span>respect<span class="_ _d"> </span>to<span class="_ _d"> </span>different<span class="_ _e"> </span>qual-</div><div class="t m0 xa h6 y41 ff1 fs4 fc0 sc0 ls1d ws0">ity<span class="_ _18"> </span>metrics,<span class="_ _18"> </span>includin<span class="_ _6"></span>g<span class="_ _19"> </span>cap<span class="_ _6"></span>acity<span class="_ _1"></span>,<span class="_ _19"> </span>transmit<span class="_ _18"> </span>energy<span class="_ _18"> </span>ef<span class="_ _1"></span>&#64257;ciency<span class="_ _1"></span>,</div><div class="t m0 xa h6 y42 ff1 fs4 fc0 sc0 ls3f ws0">latenc<span class="_ _1"></span>y<span class="_ _2"></span>,<span class="_ _7"> </span>and<span class="_ _a"> </span>robustness<span class="_ _9"> </span>to<span class="_ _a"> </span>jamming<span class="_ _7"> </span>[14]&#8211;[19].<span class="_ _9"> </span>Signal<span class="_ _7"> </span>design</div><div class="t m0 xa h6 y43 ff1 fs4 fc0 sc0 ls40 ws0">for<span class="_ _c"> </span>massiv<span class="_ _1"></span>e<span class="_ _c"> </span>MIMO<span class="_ _11"> </span>deals<span class="_ _c"> </span>with<span class="_ _11"> </span>man<span class="_ _1"></span>y<span class="_ _c"> </span>streams<span class="_ _11"> </span>of<span class="_ _c"> </span>signals<span class="_ _c"> </span>or,</div><div class="t m0 xa h6 y44 ff1 fs4 fc0 sc0 ls41 ws0">equi<span class="_ _1"></span>vale<span class="_ _1"></span>ntly<span class="_ _2"></span>,<span class="_ _9"> </span>many<span class="_ _9"> </span>design<span class="_ _7"> </span>variables<span class="_ _1"></span>.<span class="_ _9"> </span>Such<span class="_ _7"> </span>a<span class="_ _7"> </span>large<span class="_ _9"> </span>number<span class="_ _7"> </span>of</div><div class="t m0 xa h6 y45 ff1 fs4 fc0 sc0 ls42 ws0">degrees<span class="_"> </span>of<span class="_"> </span>fr<span class="_ _6"></span>eedom<span class="_"> </span>paves<span class="_"> </span>the<span class="_"> </span>way<span class="_ _e"> </span>for<span class="_ _e"> </span>a<span class="_"> </span>b<span class="_ _6"></span>etter<span class="_"> </span>qu<span class="_ _6"></span>ality<span class="_"> </span>of<span class="_ _e"> </span>signa<span class="_ _6"></span>l</div><div class="t m0 xa h6 y46 ff1 fs4 fc0 sc0 ls3f ws0">design,<span class="_ _f"> </span>but<span class="_ _f"> </span>at<span class="_"> </span>the<span class="_ _0"> </span>same<span class="_ _0"> </span>time,<span class="_ _0"> </span>makes<span class="_ _f"> </span>the<span class="_"> </span>des<span class="_ _1"></span>ign<span class="_"> </span>comput<span class="_ _1"></span>ationally</div><div class="t m0 xa h6 y47 ff1 fs4 fc0 sc0 ls1d ws0">expensive.<span class="_ _f"> </span>Hence,<span class="_"> </span>it<span class="_"> </span>is<span class="_"> </span>n<span class="_ _6"></span>o<span class="_"> </span>surprise<span class="_"> </span>that<span class="_"> </span>a<span class="_ _e"> </span>considerab<span class="_ _6"></span>le<span class="_"> </span>attention</div><div class="t m0 xa h6 y48 ff1 fs4 fc0 sc0 ls41 ws0">has<span class="_ _10"> </span>b<span class="_ _6"></span>een<span class="_ _10"> </span>paid<span class="_ _9"> </span>to<span class="_ _9"> </span>ef&#64257;cient<span class="_ _d"> </span>methods<span class="_ _9"> </span>that<span class="_ _9"> </span>can<span class="_ _9"> </span>handle<span class="_ _10"> </span>the<span class="_ _9"> </span>signal</div><div class="t m0 xa h6 y49 ff1 fs4 fc0 sc0 ls1e ws0">design<span class="_ _1a"> </span>complexity<span class="_ _1a"> </span>arising<span class="_ _19"> </span>from<span class="_ _19"> </span>such<span class="_ _18"> </span>lar<span class="_ _1"></span>ge-scale<span class="_ _1a"> </span>arrays<span class="_ _19"> </span>of</div><div class="t m0 xa h6 y4a ff1 fs4 fc0 sc0 ls1b ws0">antennas<span class="_"> </span>(see,<span class="_"> </span>e.g.<span class="_ _e"> </span>[11],<span class="_"> </span>[20]&#8211;[27],<span class="_"> </span>and<span class="_"> </span>the<span class="_ _e"> </span>references<span class="_"> </span>therein).</div><div class="t m0 xb h6 y4b ff1 fs4 fc0 sc0 ls1e ws0">This<span class="_ _d"> </span>work<span class="_ _10"> </span>is<span class="_ _10"> </span>concerned<span class="_ _d"> </span>with<span class="_ _10"> </span>an<span class="_ _10"> </span>ef&#64257;cient<span class="_ _e"> </span>design<span class="_ _10"> </span>of<span class="_ _10"> </span>training</div><div class="t m0 xa h6 y4c ff1 fs4 fc0 sc0 ls43 ws0">signals<span class="_ _19"> </span>for<span class="_ _19"> </span>chann<span class="_ _6"></span>el<span class="_ _1a"> </span>estimatio<span class="_ _6"></span>n<span class="_ _1a"> </span>in<span class="_ _19"> </span>massive<span class="_ _1a"> </span>MIMO<span class="_ _19"> </span>systems.</div><div class="t m0 xa h6 y4d ff1 fs4 fc0 sc0 ls44 ws0">W<span class="_ _8"></span>e<span class="_ _7"> </span>discuss<span class="_ _10"> </span>the<span class="_ _9"> </span>problem<span class="_ _10"> </span>formulation<span class="_ _d"> </span>and<span class="_ _7"> </span>the<span class="_ _10"> </span>contributi<span class="_ _1"></span>ons<span class="_ _10"> </span>of</div><div class="t m0 xa h6 y4e ff1 fs4 fc0 sc0 ls1d ws0">the<span class="_ _10"> </span>paper<span class="_ _10"> </span>in<span class="_ _10"> </span>the<span class="_ _9"> </span>following.<span class="_ _d"> </span>Notation<span class="_ _6"></span>s<span class="_ _d"> </span>an<span class="_ _6"></span>d<span class="_ _10"> </span>their<span class="_ _10"> </span>de&#64257;nitio<span class="_ _6"></span>ns<span class="_ _10"> </span>are</div><div class="t m0 xa h6 y4f ff1 fs4 fc0 sc0 ls1d ws0">provided<span class="_ _10"> </span>in<span class="_ _10"> </span>T<span class="_ _2"></span>ab<span class="_ _6"></span>le<span class="_ _10"> </span>I.</div><div class="t m0 xa ha y50 ff2 fs4 fc0 sc0 ls45 ws0">A.<span class="_ _10"> </span>Pr<span class="_ _1"></span>oblem<span class="_ _d"> </span>F<span class="_ _8"></span>o<span class="_ _6"></span>rmulati<span class="_ _1"></span>on</div><div class="t m0 xb h6 y51 ff1 fs4 fc0 sc0 ls46 ws0">W<span class="_ _8"></span>e<span class="_ _16"> </span>consider<span class="_ _1b"> </span>a<span class="_ _16"> </span>narro<span class="_ _1"></span>wband<span class="_ _1b"> </span>block<span class="_ _1b"> </span>fading<span class="_ _1b"> </span>point-to-point</div><div class="t m0 xa h6 y52 ff1 fs4 fc0 sc0 ls45 ws0">MIMO<span class="_ _c"> </span>communication<span class="_ _a"> </span>link<span class="_ _c"> </span>equipped<span class="_ _a"> </span>with<span class="_ _11"> </span><span class="ff2 ls1a">n</span></div><div class="t m0 xc hb y53 ff2 fs7 fc0 sc0 ls1a ws0">T</div><div class="t m0 xd h6 y54 ff1 fs4 fc0 sc0 ls47 ws0">transmit<span class="_ _11"> </span>and</div><div class="t m0 xa ha y55 ff2 fs4 fc0 sc0 ls1a ws0">n</div><div class="t m0 xe hb y56 ff2 fs7 fc0 sc0 ls1a ws0">R</div><div class="t m0 xf hc y57 ff1 fs4 fc0 sc0 ls48 ws0">recei<span class="_ _1"></span>ve<span class="_ _11"> </span>antennas.<span class="_ _11"> </span>Let<span class="_ _18"> </span><span class="ff3 ls1a">P<span class="_ _16"> </span><span class="ff5">&#8712;<span class="_ _18"> </span><span class="ff6">C</span></span></span></div><div class="t m0 x10 hb y58 ff2 fs7 fc0 sc0 ls1a ws0">B<span class="_ _1c"></span><span class="ff5">&#215;</span>n</div><div class="t m0 x11 hd y59 ff2 fs8 fc0 sc0 ls1a ws0">T</div><div class="t m0 x12 h6 y57 ff1 fs4 fc0 sc0 ls27 ws0">be<span class="_ _11"> </span>a<span class="_ _11"> </span>matrix<span class="_ _1a"> </span>whose</div><div class="t m0 xa h6 y5a ff1 fs4 fc0 sc0 ls49 ws0">rows<span class="_ _18"> </span>comprise<span class="_ _1b"> </span>the<span class="_ _1b"> </span>training<span class="_ _1b"> </span>symbols<span class="_ _1b"> </span>at<span class="_ _1b"> </span>each<span class="_ _1b"> </span>transmitter<span class="_ _1"></span>.</div><div class="t m0 x13 he y5b ff1 fs7 fc0 sc0 ls1a ws0">1</div><div class="t m0 xe hf y5c ff1 fs9 fc0 sc0 ls1a ws0">1</div><div class="t m0 xb h8 y5d ff1 fs5 fc0 sc0 ls4a ws0">Note<span class="_ _a"> </span>that<span class="_ _11"> </span><span class="ff2 ls1a">B<span class="_ _1a"> </span><span class="ff5">&#8805;<span class="_ _11"> </span></span>n</span></div><div class="t m0 x14 h10 y5e ff2 fs9 fc0 sc0 ls1a ws0">T</div><div class="t m0 x15 h8 y5d ff1 fs5 fc0 sc0 ls4b ws0">is<span class="_ _a"> </span>a<span class="_ _a"> </span>necessary<span class="_ _c"> </span>condition<span class="_ _c"> </span>for<span class="_ _a"> </span>obtaining<span class="_ _c"> </span>meaningf<span class="_ _6"></span>ul</div><div class="t m0 xa h8 y5f ff1 fs5 fc0 sc0 ls4c ws0">channel<span class="_ _e"> </span>estim<span class="_ _6"></span>ates<span class="_ _d"> </span>when<span class="_ _e"> </span>a<span class="_ _e"> </span>least-squares<span class="_ _d"> </span>es<span class="_ _6"></span>timation<span class="_ _d"> </span>of<span class="_ _e"> </span>the<span class="_ _e"> </span>channel<span class="_ _d"> </span>is<span class="_ _3"> </span>us<span class="_ _6"></span>ed<span class="_ _e"> </span>[2].</div><div class="t m0 xa h8 y60 ff1 fs5 fc0 sc0 ls39 ws0">Although<span class="_"> </span>a<span class="_"> </span>larger<span class="_ _3"> </span><span class="ff2 ls1a">B<span class="_ _0"> </span></span><span class="ls4c">would<span class="_"> </span>b<span class="_ _6"></span>e<span class="_"> </span>bene&#64257;cial<span class="_ _0"> </span>for<span class="_"> </span>obtaining<span class="_ _0"> </span>a<span class="_"> </span>more<span class="_"> </span>accurate<span class="_ _0"> </span>estim<span class="_ _6"></span>ate</span></div><div class="t m0 xa h8 y61 ff1 fs5 fc0 sc0 ls2b ws0">of<span class="_ _e"> </span>the<span class="_ _e"> </span>channel,<span class="_ _10"> </span>it<span class="_ _e"> </span>was<span class="_ _e"> </span>shown<span class="_ _e"> </span>in<span class="_ _d"> </span>[29]<span class="_ _e"> </span>that<span class="_ _d"> </span>using<span class="_ _d"> </span>a<span class="_ _e"> </span>smaller<span class="_ _9"> </span><span class="ff2 ls1a">B<span class="_ _10"> </span></span><span class="ls4d">leads<span class="_ _d"> </span>to<span class="_ _d"> </span>a<span class="_ _e"> </span>larger</span></div><div class="t m0 xa h8 y62 ff1 fs5 fc0 sc0 ls3c ws0">capacity<span class="_ _10"> </span>of<span class="_ _10"> </span>the<span class="_ _10"> </span>MIMO<span class="_ _d"> </span>channel<span class="_ _10"> </span>by<span class="_ _10"> </span>leaving<span class="_ _10"> </span>more<span class="_ _10"> </span>time<span class="_ _10"> </span>for<span class="_ _d"> </span>data<span class="_ _9"> </span>transmission.</div><div class="t m0 xa h8 y63 ff1 fs5 fc0 sc0 ls3c ws0">In<span class="_ _d"> </span>particular<span class="_ _1"></span>,<span class="_ _9"> </span>when<span class="_ _d"> </span>an<span class="_ _d"> </span>MMSE<span class="_ _d"> </span>es<span class="_ _6"></span>timat<span class="ls2f">e<span class="_ _10"> </span>of<span class="_ _d"> </span>the<span class="_ _d"> </span>channel<span class="_ _9"> </span>is<span class="_ _d"> </span>used<span class="_ _d"> </span>(which<span class="_ _10"> </span>is<span class="_ _d"> </span>the</span></div><div class="t m0 xa h8 y64 ff1 fs5 fc0 sc0 ls4c ws0">case<span class="_ _d"> </span>in<span class="_ _e"> </span>this<span class="_ _d"> </span>paper<span class="_ _6"></span>)<span class="_ _d"> </span>the<span class="_ _d"> </span>error<span class="_ _d"> </span>of<span class="_ _d"> </span>channel<span class="_ _d"> </span>es<span class="_ _6"></span>timation<span class="_ _10"> </span>can<span class="_ _d"> </span>be<span class="_ _e"> </span>reduced<span class="_ _10"> </span>ev<span class="_ _1"></span>en<span class="_ _d"> </span>if<span class="_ _9"> </span><span class="ff2 ls1a">B</span></div><div class="t m0 xa h8 y65 ff1 fs5 fc0 sc0 ls29 ws0">is<span class="_ _e"> </span>smaller<span class="_ _d"> </span>than<span class="_ _d"> </span>the<span class="_ _d"> </span>number<span class="_ _d"> </span>of<span class="_ _e"> </span>transm<span class="_ _6"></span>it<span class="_ _e"> </span>antennas<span class="_ _6"></span>.</div><div class="t m0 x16 h8 y66 ff1 fs5 fc0 sc0 ls4e ws0">1536-1276<span class="_ _e"> </span>&#169;<span class="_ _d"> </span>2016<span class="_ _e"> </span>I<span class="ls4f">EEE.<span class="_ _3"> </span>Personal<span class="_ _d"> </span>u<span class="ls50">se<span class="_ _e"> </span>is<span class="_ _e"> </span>perm<span class="ls3b">itted,<span class="_ _d"> </span>but<span class="_ _d"> </span>republication/redistri<span class="ls35">bution<span class="_ _9"> </span>requires<span class="_ _d"> </span>I<span class="_ _6"></span>EEE<span class="_ _e"> </span>permis<span class="_ _6"></span>sion.</span></span></span></span></div><div class="t m0 x17 h8 y67 ff1 fs5 fc0 sc0 ls31 ws0">See<span class="_ _e"> </span>http://www.ieee.org/publications_standa<span class="_ _6"></span>rds/publi<span class="_ _6"></span>cations/<span class="_ _6"></span>rights<span class="_ _6"></span>/index.html<span class="_ _7"> </span>for<span class="_ _e"> </span>more<span class="_ _e"> </span>information.</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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