PAPR降低方法

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一种有效降低通信系统PAPR的贝叶斯方法
An Efficient Bayesian PAPR Reduction Method.zip
  • EM-TGM-GAMP
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  • EM_TGM_GAMP.m
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  • An Efficient Bayesian PAPR Reduction Method for OFDM-Based Massive MIMO Systems.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/627384f07ec58a2c0130b3e1/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/627384f07ec58a2c0130b3e1/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">arXiv:1511.09013v1 [cs.IT] 29 Nov 2015</div><div class="t m1 x2 h3 y2 ff1 fs1 fc1 sc0 ls0 ws0">1</div><div class="t m1 x3 h4 y3 ff1 fs2 fc1 sc0 ls0 ws0">An<span class="_ _0"> </span>Ef<span class="_ _1"></span>&#64257;cient<span class="_ _0"> </span>Bayesian<span class="_ _0"> </span>P<span class="_ _2"></span>APR<span class="_ _0"> </span>Reduction<span class="_ _0"> </span>Method<span class="_ _0"> </span>for</div><div class="t m1 x4 h4 y4 ff1 fs2 fc1 sc0 ls0 ws0">OFDM-Based<span class="_ _0"> </span>Massi<span class="_ _1"></span>ve<span class="_ _0"> </span>M<span class="_ _3"></span>IMO<span class="_ _0"> </span>Systems</div><div class="t m1 x5 h5 y5 ff1 fs3 fc1 sc0 ls0 ws0">Hengyao<span class="_ _4"> </span>Bao,<span class="_ _4"> </span>Jun<span class="_ _4"> </span>Fang,<span class="_ _4"> </span>Zhi<span class="_ _4"> </span>Che<span class="_ _5"></span>n,<span class="_ _4"> </span>Hongbin<span class="_ _4"> </span>Li,<span class="_ _4"> </span><span class="ff2">Senior<span class="_ _4"> </span>Membe<span class="_ _5"></span>r<span class="_ _6"></span>,<span class="_ _4"> </span>IEEE<span class="ff1">,<span class="_ _4"> </span>a<span class="_ _5"></span>nd<span class="_ _4"> </span>Shaoqian<span class="_ _4"> </span>Li,<span class="_ _4"> </span></span>F<span class="_ _1"></span>ellow<span class="_ _1"></span>,<span class="_ _4"> </span>IEEE</span></div><div class="t m1 x6 h6 y6 ff3 fs4 fc1 sc0 ls0 ws0">Abstract<span class="ff4">&#8212;W<span class="_ _1"></span>e<span class="_ _7"> </span>consider<span class="_ _7"> </span>the<span class="_ _8"> </span>problem<span class="_ _8"> </span>of<span class="_ _7"> </span>peak-to-av<span class="_ _3"></span>erage<span class="_ _8"> </span>power</span></div><div class="t m1 x7 h6 y7 ff4 fs4 fc1 sc0 ls0 ws0">ratio<span class="_ _4"> </span>(P<span class="_ _1"></span>APR)<span class="_ _4"> </span>reduction<span class="_ _4"> </span>in<span class="_ _4"> </span>orthogonal<span class="_ _4"> </span>frequency-division<span class="_ _4"> </span>multi-</div><div class="t m1 x7 h6 y8 ff4 fs4 fc1 sc0 ls0 ws0">plexing<span class="_ _9"> </span>(OFDM)<span class="_ _9"> </span>based<span class="_ _9"> </span>massiv<span class="_ _3"></span>e<span class="_ _9"> </span>multip<span class="_ _5"></span>le-input<span class="_ _9"> </span>multiple-output</div><div class="t m1 x7 h6 y9 ff4 fs4 fc1 sc0 ls0 ws0">(MIMO)<span class="_ _9"> </span>downlink<span class="_ _9"> </span>sy<span class="_ _3"></span>stems.<span class="_ _9"> </span>Speci&#64257;cally<span class="_ _1"></span>,<span class="_ _9"> </span>gi<span class="_ _3"></span>ven<span class="_ _9"> </span>a<span class="_ _a"> </span>set<span class="_ _a"> </span>of<span class="_ _9"> </span>symbol</div><div class="t m1 x7 h6 ya ff4 fs4 fc1 sc0 ls0 ws0">vector<span class="_ _3"></span>s<span class="_ _4"> </span>to<span class="_ _7"> </span>be<span class="_ _4"> </span>transmitted<span class="_ _7"> </span>to<span class="_ _7"> </span><span class="ff5">K<span class="_ _a"> </span></span>users,<span class="_ _4"> </span>the<span class="_ _7"> </span>problem<span class="_ _7"> </span>is<span class="_ _4"> </span>to<span class="_ _7"> </span>&#64257;nd<span class="_ _7"> </span>an</div><div class="t m1 x7 h6 yb ff4 fs4 fc1 sc0 ls0 ws0">OFDM-modulated<span class="_"> </span>signal<span class="_"> </span>that<span class="_"> </span>has<span class="_"> </span>a<span class="_"> </span>low<span class="_"> </span>P<span class="_ _1"></span>APR<span class="_"> </span>and<span class="_"> </span>mea<span class="_ _3"></span>nwhile<span class="_"> </span>en-</div><div class="t m1 x7 h6 yc ff4 fs4 fc1 sc0 ls0 ws0">ables<span class="_ _7"> </span>multiu<span class="_ _5"></span>ser<span class="_ _8"> </span>i<span class="_ _5"></span>nterference<span class="_ _8"> </span>(MUI)<span class="_ _7"> </span>cancelation.<span class="_ _4"> </span>Unlike<span class="_ _7"> </span>pre<span class="_ _3"></span>vious</div><div class="t m1 x7 h6 yd ff4 fs4 fc1 sc0 ls0 ws0">works<span class="_ _a"> </span>that<span class="_ _4"> </span>tackled<span class="_ _a"> </span>the<span class="_ _a"> </span>problem<span class="_ _4"> </span>u<span class="_ _5"></span>sing<span class="_ _4"> </span>conv<span class="_ _3"></span>ex<span class="_ _a"> </span>optimization,<span class="_ _a"> </span>we</div><div class="t m1 x7 h6 ye ff4 fs4 fc1 sc0 ls0 ws0">take<span class="_ _8"> </span>a<span class="_ _8"> </span>Bayesian<span class="_ _8"> </span>approach<span class="_ _8"> </span>and<span class="_ _8"> </span>deve<span class="_ _3"></span>lop<span class="_ _8"> </span>an<span class="_ _7"> </span>ef&#64257;cient<span class="_ _8"> </span>P<span class="_ _1"></span>APR<span class="_ _8"> </span>reduc-</div><div class="t m1 x7 h6 yf ff4 fs4 fc1 sc0 ls0 ws0">tion<span class="_ _8"> </span>method<span class="_ _7"> </span>by<span class="_ _7"> </span>exploiting<span class="_ _7"> </span>the<span class="_ _7"> </span>redundant<span class="_ _8"> </span>degrees-of-<span class="_ _8"> </span>freedom<span class="_ _8"> </span>of</div><div class="t m1 x7 h6 y10 ff4 fs4 fc1 sc0 ls0 ws0">the<span class="_"> </span>transmit<span class="_"> </span>array<span class="_ _1"></span>.<span class="_"> </span>The<span class="_ _b"> </span>sought-after<span class="_"> </span>signal<span class="_"> </span>is<span class="_"> </span>treated<span class="_"> </span>as<span class="_"> </span>a<span class="_"> </span>random</div><div class="t m1 x7 h6 y11 ff4 fs4 fc1 sc0 ls0 ws0">vector<span class="_ _c"> </span>with<span class="_ _c"> </span>a<span class="_ _c"> </span>hierarchical<span class="_ _c"> </span>truncated<span class="_ _c"> </span>Gaussian<span class="_ _c"> </span>mixture<span class="_ _c"> </span>prior<span class="_ _6"></span>,</div><div class="t m1 x7 h6 y12 ff4 fs4 fc1 sc0 ls0 ws0">which<span class="_ _a"> </span>has<span class="_ _a"> </span>the<span class="_ _a"> </span>potential<span class="_ _a"> </span>to<span class="_ _a"> </span>encourage<span class="_ _a"> </span>a<span class="_ _a"> </span>low<span class="_ _a"> </span>P<span class="_ _1"></span>APR<span class="_ _a"> </span>signal<span class="_ _a"> </span>with</div><div class="t m1 x7 h6 y13 ff4 fs4 fc1 sc0 ls0 ws0">most<span class="_"> </span>of<span class="_"> </span>it<span class="_ _5"></span>s<span class="_"> </span>samples<span class="_"> </span>concen<span class="_ _5"></span>trated<span class="_"> </span>on<span class="_"> </span>the<span class="_"> </span>b<span class="_ _5"></span>oundaries.<span class="_"> </span>A<span class="_"> </span>variational</div><div class="t m1 x7 h6 y14 ff4 fs4 fc1 sc0 ls0 ws0">expectation-maximization<span class="_ _a"> </span>(EM)<span class="_ _a"> </span>strategy<span class="_ _4"> </span>is<span class="_ _a"> </span>developed<span class="_ _4"> </span>to<span class="_ _a"> </span>obtain</div><div class="t m1 x7 h6 y15 ff4 fs4 fc1 sc0 ls0 ws0">estimates<span class="_"> </span>of<span class="_ _d"> </span>the<span class="_"> </span>hy<span class="_ _3"></span>perparameters<span class="_"> </span>a<span class="_ _3"></span>ssociated<span class="_"> </span>with<span class="_"> </span>the<span class="_ _d"> </span>prior<span class="_"> </span>mo<span class="_ _3"></span>del,</div><div class="t m1 x7 h6 y16 ff4 fs4 fc1 sc0 ls0 ws0">along<span class="_ _4"> </span>with<span class="_ _7"> </span>t<span class="_ _5"></span>he<span class="_ _7"> </span>si<span class="_ _5"></span>gnal.<span class="_ _4"> </span>In<span class="_ _7"> </span>add<span class="_ _5"></span>ition,<span class="_ _7"> </span>th<span class="_ _5"></span>e<span class="_ _4"> </span>generalized<span class="_ _4"> </span>approx<span class="_ _3"></span>imate</div><div class="t m1 x7 h6 y17 ff4 fs4 fc1 sc0 ls0 ws0">message<span class="_ _4"> </span>passing<span class="_ _4"> </span>(GAMP)<span class="_ _7"> </span>is<span class="_ _4"> </span>embedded<span class="_ _4"> </span>into<span class="_ _4"> </span>the<span class="_ _4"> </span>v<span class="_ _3"></span>ariational<span class="_ _4"> </span>EM</div><div class="t m1 x7 h6 y18 ff4 fs4 fc1 sc0 ls0 ws0">framewo<span class="_ _3"></span>rk,<span class="_ _7"> </span>which<span class="_ _8"> </span>results<span class="_ _7"> </span>in<span class="_ _8"> </span>a<span class="_ _7"> </span>signi&#64257;cant<span class="_ _7"> </span>reduction<span class="_ _8"> </span>in<span class="_ _8"> </span>computa-</div><div class="t m1 x7 h6 y19 ff4 fs4 fc1 sc0 ls0 ws0">tional<span class="_ _4"> </span>complexity<span class="_ _7"> </span>of<span class="_ _4"> </span>the<span class="_ _4"> </span>proposed<span class="_ _7"> </span>algorithm.<span class="_ _4"> </span>Simulation<span class="_ _7"> </span>results</div><div class="t m1 x7 h6 y1a ff4 fs4 fc1 sc0 ls0 ws0">show<span class="_ _b"> </span>our<span class="_ _b"> </span>proposed<span class="_"> </span>algorithm<span class="_ _8"> </span>achie<span class="_ _3"></span>ves<span class="_"> </span>a<span class="_ _e"> </span>substantial<span class="_ _b"> </span>perform<span class="_ _3"></span>ance</div><div class="t m1 x7 h6 y1b ff4 fs4 fc1 sc0 ls0 ws0">impro<span class="_ _3"></span>vement<span class="_ _7"> </span>ov<span class="_ _3"></span>er<span class="_ _4"> </span>existing<span class="_ _7"> </span>methods<span class="_ _4"> </span>in<span class="_ _7"> </span>terms<span class="_ _4"> </span>of<span class="_ _7"> </span>b<span class="_ _5"></span>oth<span class="_ _7"> </span>the<span class="_ _4"> </span>P<span class="_ _1"></span>APR</div><div class="t m1 x7 h6 y1c ff4 fs4 fc1 sc0 ls0 ws0">reduction<span class="_ _8"> </span>and<span class="_ _7"> </span>computational<span class="_ _7"> </span>complexity<span class="_ _1"></span>.</div><div class="t m1 x6 h6 y1d ff3 fs4 fc1 sc0 ls0 ws0">Index<span class="_ _7"> </span>T<span class="_ _1"></span>erms<span class="ff4">&#8212;Massi<span class="_ _3"></span>ve<span class="_ _8"> </span>M<span class="_ _5"></span>IMO-OFDM,<span class="_ _8"> </span>P<span class="_ _1"></span>APR<span class="_ _7"> </span>reduction,<span class="_ _7"> </span>vari-</span></div><div class="t m1 x7 h6 y1e ff4 fs4 fc1 sc0 ls0 ws0">ational<span class="_ _7"> </span>EM,<span class="_ _7"> </span>GAMP<span class="_ _f"></span>.</div><div class="t m1 x8 h7 y1f ff1 fs5 fc1 sc0 ls0 ws0">I<span class="_ _5"></span>.<span class="_ _10"> </span>I<span class="_ _5"></span><span class="fs6">N<span class="_ _11"></span>T<span class="_ _5"></span>R<span class="_ _5"></span>O<span class="_ _5"></span>D<span class="_ _11"></span>U<span class="_ _5"></span>C<span class="_ _11"></span>T<span class="_ _5"></span>I<span class="_ _11"></span>O<span class="_ _5"></span>N</span></div><div class="t m1 x6 h7 y20 ff1 fs5 fc1 sc0 ls0 ws0">Massi<span class="_ _3"></span>ve<span class="_ _12"> </span>multiple-inp<span class="_ _5"></span>ut<span class="_ _12"> </span>multiple-outpu<span class="_ _5"></span>t<span class="_ _0"> </span>(MI<span class="_ _5"></span>MO),<span class="_ _12"> </span>also</div><div class="t m1 x7 h7 y21 ff1 fs5 fc1 sc0 ls0 ws0">known<span class="_ _c"> </span>as<span class="_ _c"> </span>large-scale<span class="_ _c"> </span>o<span class="_ _5"></span>r<span class="_ _c"> </span>very-large<span class="_ _c"> </span>MIMO,<span class="_ _c"> </span>is<span class="_ _13"> </span>a<span class="_ _c"> </span>pr<span class="_ _5"></span>omising</div><div class="t m1 x7 h7 y22 ff1 fs5 fc1 sc0 ls0 ws0">technolog<span class="_ _5"></span>y<span class="_ _13"> </span>to<span class="_ _13"> </span>m<span class="_ _5"></span>eet<span class="_ _10"> </span>the<span class="_ _13"> </span>ever<span class="_ _13"> </span>growing<span class="_ _13"> </span>dem<span class="_ _5"></span>ands<span class="_ _13"> </span>for<span class="_ _10"> </span>highe<span class="_ _5"></span>r</div><div class="t m1 x7 h7 y23 ff1 fs5 fc1 sc0 ls0 ws0">throug<span class="_ _5"></span>hput<span class="_ _13"> </span>and<span class="_ _10"> </span>better<span class="_ _10"> </span>q<span class="_ _5"></span>uality-of<span class="_ _5"></span>-service<span class="_ _13"> </span>of<span class="_ _10"> </span>next-gen<span class="_ _5"></span>eration</div><div class="t m1 x7 h7 y24 ff1 fs5 fc1 sc0 ls0 ws0">wireless<span class="_ _13"> </span>c<span class="_ _5"></span>ommunica<span class="_ _5"></span>tion<span class="_ _c"> </span>systems<span class="_ _10"> </span>[1].<span class="_ _10"> </span>Massive<span class="_ _13"> </span>MIMO<span class="_ _13"> </span>sys-</div><div class="t m1 x7 h7 y25 ff1 fs5 fc1 sc0 ls0 ws0">tems<span class="_ _13"> </span>are<span class="_ _13"> </span>th<span class="_ _5"></span>ose<span class="_ _13"> </span>that<span class="_ _13"> </span>are<span class="_ _13"> </span>equ<span class="_ _5"></span>ipped<span class="_ _13"> </span>with<span class="_ _13"> </span>a<span class="_ _13"> </span>large<span class="_ _13"> </span>numbe<span class="_ _5"></span>r<span class="_ _c"> </span>of</div><div class="t m1 x7 h7 y26 ff1 fs5 fc1 sc0 ls0 ws0">antennas<span class="_ _c"> </span>at<span class="_ _c"> </span>the<span class="_ _c"> </span>base<span class="_ _c"> </span>s<span class="_ _3"></span>tation<span class="_ _c"> </span>(BS)<span class="_ _c"> </span>simultaneously<span class="_ _c"> </span>serving<span class="_ _9"> </span>a</div><div class="t m1 x7 h7 y27 ff1 fs5 fc1 sc0 ls0 ws0">much<span class="_"> </span>smaller<span class="_"> </span>numb<span class="_ _5"></span>er<span class="_"> </span>of<span class="_"> </span>single-antenna<span class="_"> </span>users<span class="_"> </span>sharing<span class="_"> </span>the<span class="_"> </span>same</div><div class="t m1 x7 h7 y28 ff1 fs5 fc1 sc0 ls0 ws0">time-frequ<span class="_ _5"></span>ency<span class="_ _4"> </span>bandwid<span class="_ _5"></span>th.<span class="_ _4"> </span>I<span class="_ _5"></span>n<span class="_ _a"> </span>addition<span class="_ _a"> </span>to<span class="_ _a"> </span>highe<span class="_ _5"></span>r<span class="_ _4"> </span>th<span class="_ _5"></span>roughp<span class="_ _5"></span>ut,</div><div class="t m1 x7 h7 y29 ff1 fs5 fc1 sc0 ls0 ws0">massi<span class="_ _3"></span>ve<span class="_ _9"> </span>MIMO<span class="_ _9"> </span>systems<span class="_ _c"> </span>also<span class="_ _9"> </span>have<span class="_ _a"> </span>th<span class="_ _5"></span>e<span class="_ _9"> </span>potential<span class="_ _9"> </span>to<span class="_ _c"> </span>improve</div><div class="t m1 x7 h7 y2a ff1 fs5 fc1 sc0 ls0 ws0">the<span class="_ _7"> </span>en<span class="_ _5"></span>ergy<span class="_ _8"> </span>ef&#64257;ciency<span class="_ _8"> </span>and<span class="_ _7"> </span>en<span class="_ _5"></span>able<span class="_ _7"> </span>the<span class="_ _7"> </span>use<span class="_ _4"> </span>of<span class="_ _7"> </span>inexpensive,<span class="_ _e"> </span>low-</div><div class="t m1 x7 h7 y2b ff1 fs5 fc1 sc0 ls0 ws0">power<span class="_ _e"> </span>com<span class="_ _5"></span>ponents.<span class="_ _8"> </span>Hence,<span class="_ _8"> </span>it<span class="_ _7"> </span>is<span class="_ _8"> </span>expected<span class="_ _8"> </span>that<span class="_ _8"> </span>massive<span class="_ _e"> </span>MIMO</div><div class="t m1 x7 h7 y2c ff1 fs5 fc1 sc0 ls0 ws0">will<span class="_ _a"> </span>bring<span class="_ _a"> </span>radical<span class="_ _a"> </span>changes<span class="_ _a"> </span>to<span class="_ _a"> </span>future<span class="_ _a"> </span>wireless<span class="_ _a"> </span>communication</div><div class="t m1 x7 h7 y2d ff1 fs5 fc1 sc0 ls0 ws0">systems.</div><div class="t m1 x6 h7 y2e ff1 fs5 fc1 sc0 ls0 ws0">In<span class="_ _a"> </span>practice<span class="_ _5"></span>,<span class="_ _a"> </span>broadband<span class="_ _a"> </span>wireless<span class="_ _a"> </span>communicatio<span class="_ _5"></span>ns<span class="_ _4"> </span>m<span class="_ _5"></span>ay<span class="_ _a"> </span>suf-</div><div class="t m1 x7 h7 y2f ff1 fs5 fc1 sc0 ls0 ws0">fer<span class="_ _13"> </span>from<span class="_ _13"> </span>frequency-selective<span class="_ _c"> </span>fading.<span class="_ _c"> </span>Ortho<span class="_ _5"></span>gonal<span class="_ _c"> </span>fre<span class="_ _5"></span>quency-</div><div class="t m1 x7 h7 y30 ff1 fs5 fc1 sc0 ls0 ws0">division<span class="_ _7"> </span>multiplexing<span class="_ _7"> </span>(<span class="_ _5"></span>OFDM),<span class="_ _4"> </span>a<span class="_ _4"> </span>scheme<span class="_ _7"> </span>o<span class="_ _5"></span>f<span class="_ _4"> </span>encoding<span class="_ _7"> </span>d<span class="_ _5"></span>igital</div><div class="t m1 x9 h8 y31 ff1 fs6 fc1 sc0 ls0 ws0">Hengyao<span class="_ _b"> </span>Bao,<span class="_ _b"> </span>Jun<span class="_ _e"> </span>Fang,<span class="_ _b"> </span>Zhi<span class="_ _b"> </span>Chen,<span class="_ _e"> </span>and<span class="_ _b"> </span>Shaoqian<span class="_ _b"> </span>L<span class="_ _5"></span>i<span class="_ _b"> </span>are<span class="_ _b"> </span>with<span class="_ _e"> </span>the<span class="_ _b"> </span>Nationa<span class="_ _3"></span>l</div><div class="t m1 x7 h8 y32 ff1 fs6 fc1 sc0 ls0 ws0">Ke<span class="_ _1"></span>y<span class="_ _7"> </span>Laboratory<span class="_ _e"> </span>of<span class="_ _7"> </span>Scienc<span class="_ _3"></span>e<span class="_ _8"> </span>and<span class="_ _8"> </span>T<span class="_ _1"></span>echnology<span class="_ _7"> </span>on<span class="_ _e"> </span>Communications,<span class="_ _8"> </span>Univ<span class="_ _3"></span>ersity</div><div class="t m1 x7 h8 y33 ff1 fs6 fc1 sc0 ls0 ws0">of<span class="_ _4"> </span>Electroni<span class="_ _3"></span>c<span class="_ _a"> </span>Scienc<span class="_ _3"></span>e<span class="_ _a"> </span>and<span class="_ _4"> </span>T<span class="_ _f"></span>echnology<span class="_ _a"> </span>of<span class="_ _4"> </span>China<span class="_ _3"></span>,<span class="_ _4"> </span>Chengdu<span class="_ _a"> </span>611731,<span class="_ _4"> </span>China,</div><div class="t m1 x7 h8 y34 ff1 fs6 fc1 sc0 ls0 ws0">Email:<span class="_ _b"> </span>J<span class="_ _5"></span>unFa<span class="_ _3"></span>ng@uestc.e<span class="_ _3"></span>du.cn,<span class="_ _8"> </span>chenzhi@ue<span class="_ _3"></span>stc.edu.cn,<span class="_ _8"> </span>lsq@uestc.edu.cn</div><div class="t m1 x9 h8 y35 ff1 fs6 fc1 sc0 ls0 ws0">Hongbin<span class="_"> </span>Li<span class="_"> </span>is<span class="_"> </span>with<span class="_"> </span>the<span class="_"> </span>Departmen<span class="_ _3"></span>t<span class="_"> </span>of<span class="_"> </span>E<span class="_ _5"></span>lectr<span class="_ _3"></span>ical<span class="_"> </span>and<span class="_"> </span>Computer<span class="_"> </span>Engineering,</div><div class="t m1 x7 h8 y36 ff1 fs6 fc1 sc0 ls0 ws0">Ste<span class="_ _3"></span>ve<span class="_ _3"></span>ns<span class="_ _7"> </span>Institute<span class="_ _4"> </span>of<span class="_ _8"> </span>T<span class="_ _3"></span>echn<span class="_ _3"></span>ology<span class="_ _1"></span>,<span class="_ _4"> </span>Hoboke<span class="_ _3"></span>n,<span class="_ _7"> </span>NJ<span class="_ _7"> </span>07030,<span class="_ _4"> </span>USA,<span class="_ _7"> </span>E-mail:<span class="_ _8"> </span>Hong-</div><div class="t m1 x7 h8 y37 ff1 fs6 fc1 sc0 ls0 ws0">bin.Li@ste<span class="_ _1"></span>vens.edu</div><div class="t m1 x9 h8 y38 ff1 fs6 fc1 sc0 ls0 ws0">This<span class="_ _7"> </span>work<span class="_ _7"> </span>was<span class="_ _7"> </span>supported<span class="_ _7"> </span>in<span class="_ _7"> </span>part<span class="_ _7"> </span>by<span class="_ _7"> </span>the<span class="_ _4"> </span>Nati<span class="_ _3"></span>onal<span class="_ _7"> </span>Science<span class="_ _7"> </span>Foundation<span class="_ _7"> </span>of</div><div class="t m1 x7 h8 y39 ff1 fs6 fc1 sc0 ls0 ws0">China<span class="_ _e"> </span>under<span class="_ _b"> </span>Grant<span class="_ _8"> </span>61172114.</div><div class="t m1 xa h7 y3a ff1 fs5 fc1 sc0 ls0 ws0">data<span class="_ _c"> </span>on<span class="_ _c"> </span>multiple<span class="_ _9"> </span>car<span class="_ _5"></span>rier<span class="_ _c"> </span>frequencies,<span class="_ _9"> </span>h<span class="_ _5"></span>as<span class="_ _c"> </span>been<span class="_ _c"> </span>widely<span class="_ _9"> </span>u<span class="_ _5"></span>sed</div><div class="t m1 xa h7 y3b ff1 fs5 fc1 sc0 ls0 ws0">to<span class="_ _13"> </span>deal<span class="_ _13"> </span>with<span class="_ _13"> </span>frequ<span class="_ _5"></span>ency-selectiv<span class="_ _3"></span>e<span class="_ _c"> </span>fading.<span class="_ _c"> </span>Howev<span class="_ _3"></span>er<span class="_ _3"></span>,<span class="_ _c"> </span>a<span class="_ _13"> </span>majo<span class="_ _5"></span>r</div><div class="t m1 xa h7 y3c ff1 fs5 fc1 sc0 ls0 ws0">problem<span class="_ _c"> </span>associated<span class="_ _9"> </span>with<span class="_ _c"> </span>the<span class="_ _14"> </span>OFDM<span class="_ _14"> </span>is<span class="_ _14"> </span>that<span class="_ _14"> </span>it<span class="_ _c"> </span>is<span class="_ _14"> </span>sub<span class="_ _5"></span>ject<span class="_ _9"> </span>to</div><div class="t m1 xa h7 y3d ff1 fs5 fc1 sc0 ls0 ws0">a<span class="_ _10"> </span>h<span class="_ _5"></span>igh<span class="_ _10"> </span>peak-<span class="_ _5"></span>to-average<span class="_ _13"> </span>power<span class="_ _13"> </span>ratio<span class="_ _15"> </span>(P<span class="_ _6"></span>APR)<span class="_ _15"> </span>owing<span class="_ _10"> </span>to<span class="_ _15"> </span>the</div><div class="t m1 xa h7 y3e ff1 fs5 fc1 sc0 ls0 ws0">indepen<span class="_ _5"></span>dent<span class="_ _13"> </span>phases<span class="_ _10"> </span>of<span class="_ _10"> </span>th<span class="_ _5"></span>e<span class="_ _10"> </span>sub-c<span class="_ _5"></span>arriers<span class="_ _13"> </span>[2].<span class="_ _10"> </span>T<span class="_ _1"></span>o<span class="_ _10"> </span>avoid<span class="_ _13"> </span>ou<span class="_ _5"></span>t-</div><div class="t m1 xa h7 y3f ff1 fs5 fc1 sc0 ls0 ws0">of-ban<span class="_ _5"></span>d<span class="_ _c"> </span>rad<span class="_ _5"></span>iation<span class="_ _13"> </span>and<span class="_ _13"> </span>sig<span class="_ _5"></span>nal<span class="_ _13"> </span>distortion,<span class="_ _13"> </span>han<span class="_ _5"></span>dling<span class="_ _13"> </span>this<span class="_ _13"> </span>hig<span class="_ _5"></span>h</div><div class="t m1 xa h7 y40 ff1 fs5 fc1 sc0 ls0 ws0">P<span class="_ _6"></span>APR<span class="_ _13"> </span>requires<span class="_ _c"> </span>a<span class="_ _13"> </span>high<span class="_ _5"></span>-resolution<span class="_ _c"> </span>digital-to-<span class="_ _5"></span>analog<span class="_ _14"> </span>co<span class="_ _5"></span>n<span class="_ _3"></span>verter</div><div class="t m1 xa h7 y41 ff1 fs5 fc1 sc0 ls0 ws0">(D<span class="_ _3"></span>A<span class="_ _1"></span>C)<span class="_ _a"> </span>an<span class="_ _5"></span>d<span class="_ _a"> </span>a<span class="_ _a"> </span>linea<span class="_ _5"></span>r<span class="_ _a"> </span>power<span class="_ _a"> </span>ampli&#64257;er<span class="_ _a"> </span>(P<span class="_ _6"></span>A)<span class="_ _9"> </span>at<span class="_ _a"> </span>the<span class="_ _9"> </span>transmitter,</div><div class="t m1 xa h7 y42 ff1 fs5 fc1 sc0 ls0 ws0">which<span class="_"> </span>is<span class="_ _e"> </span>not<span class="_"> </span>o<span class="_ _5"></span>nly<span class="_"> </span>expe<span class="_ _5"></span>nsi<span class="_ _3"></span>ve<span class="_ _16"> </span>but<span class="_"> </span>also<span class="_"> </span>p<span class="_ _5"></span>ower<span class="_ _1"></span>-<span class="_ _5"></span>inef&#64257;cient<span class="_"> </span>[3].<span class="_"> </span>The</div><div class="t m1 xa h7 y43 ff1 fs5 fc1 sc0 ls0 ws0">situation<span class="_ _a"> </span>deteriorates<span class="_ _a"> </span>when<span class="_ _a"> </span>the<span class="_ _a"> </span>nu<span class="_ _5"></span>mber<span class="_ _a"> </span>of<span class="_ _a"> </span>antennas<span class="_ _a"> </span>is<span class="_ _a"> </span>large,</div><div class="t m1 xa h7 y44 ff1 fs5 fc1 sc0 ls0 ws0">leaving<span class="_ _a"> </span>such<span class="_ _9"> </span>systems<span class="_ _a"> </span>impr<span class="_ _5"></span>actical.<span class="_ _a"> </span>The<span class="_ _5"></span>refore,<span class="_ _a"> </span>it<span class="_ _9"> </span>is<span class="_ _a"> </span>o<span class="_ _5"></span>f<span class="_ _a"> </span>cru<span class="_ _5"></span>cial</div><div class="t m1 xa h7 y45 ff1 fs5 fc1 sc0 ls0 ws0">importan<span class="_ _5"></span>ce<span class="_ _14"> </span>to<span class="_ _14"> </span>r<span class="_ _5"></span>educe<span class="_ _c"> </span>the<span class="_ _14"> </span>P<span class="_ _f"></span>APR<span class="_ _13"> </span>of<span class="_ _14"> </span>m<span class="_ _5"></span>assi<span class="_ _3"></span>ve<span class="_ _14"> </span>MIMO-OFDM</div><div class="t m1 xa h7 y46 ff1 fs5 fc1 sc0 ls0 ws0">systems<span class="_ _c"> </span>to<span class="_ _13"> </span>facilitate<span class="_ _c"> </span>low-cost<span class="_ _c"> </span>and<span class="_ _13"> </span>power<span class="_ _3"></span>-ef&#64257;cient<span class="_ _14"> </span>hardware</div><div class="t m1 xa h7 y47 ff1 fs5 fc1 sc0 ls0 ws0">implementatio<span class="_ _5"></span>ns.</div><div class="t m1 xb h7 y48 ff1 fs5 fc1 sc0 ls0 ws0">Many<span class="_ _8"> </span>tech<span class="_ _5"></span>niques<span class="_ _7"> </span>have<span class="_ _8"> </span>been<span class="_ _4"> </span>de<span class="_ _3"></span>veloped<span class="_ _8"> </span>fo<span class="_ _5"></span>r<span class="_ _8"> </span>P<span class="_ _f"></span>APR<span class="_ _4"> </span>reduction</div><div class="t m1 xa h7 y49 ff1 fs5 fc1 sc0 ls0 ws0">in<span class="_ _8"> </span>single-in<span class="_ _5"></span>put<span class="_ _8"> </span>single-ou<span class="_ _5"></span>tput<span class="_ _e"> </span>(SISO)<span class="_ _7"> </span>OFDM<span class="_ _8"> </span>wirele<span class="_ _5"></span>ss<span class="_ _8"> </span>systems.</div><div class="t m1 xa h7 y4a ff1 fs5 fc1 sc0 ls0 ws0">The<span class="_ _a"> </span>m<span class="_ _5"></span>ost<span class="_ _a"> </span>p<span class="_ _5"></span>rominen<span class="_ _5"></span>t<span class="_ _a"> </span>are<span class="_ _a"> </span>clipp<span class="_ _5"></span>ing<span class="_ _a"> </span>[4],<span class="_ _9"> </span>tone<span class="_ _9"> </span>reservation<span class="_ _a"> </span>(T<span class="_ _5"></span>R)</div><div class="t m1 xa h7 y4b ff1 fs5 fc1 sc0 ls0 ws0">[5],<span class="_"> </span>acti<span class="_ _3"></span>ve<span class="_"> </span>constellation<span class="_"> </span>e<span class="_ _3"></span>xtension<span class="_"> </span>(A<span class="_ _1"></span>CE)<span class="_"> </span>[6],<span class="_"> </span>selected<span class="_"> </span>mappin<span class="_ _5"></span>g</div><div class="t m1 xa h7 y4c ff1 fs5 fc1 sc0 ls0 ws0">(SLM)<span class="_"> </span>[7],<span class="_"> </span>p<span class="_ _5"></span>artial<span class="_"> </span>transmission<span class="_"> </span>sequen<span class="_ _5"></span>ce<span class="_"> </span>(PTS)<span class="_"> </span>[8]<span class="_"> </span>an<span class="_ _5"></span>d<span class="_"> </span>others.</div><div class="t m1 xa h7 y4d ff1 fs5 fc1 sc0 ls0 ws0">For<span class="_ _e"> </span>a<span class="_ _8"> </span>detailed<span class="_ _e"> </span>overview<span class="_ _1"></span>,<span class="_"> </span>we<span class="_ _8"> </span>refe<span class="_ _5"></span>r<span class="_ _e"> </span>reader<span class="_ _5"></span>s<span class="_ _e"> </span>to<span class="_ _8"> </span>[3],<span class="_ _8"> </span>[9].<span class="_ _e"> </span>Althou<span class="_ _5"></span>gh</div><div class="t m1 xa h7 y4e ff1 fs5 fc1 sc0 ls0 ws0">these<span class="_ _a"> </span>P<span class="_ _6"></span>APR-r<span class="_ _5"></span>eduction<span class="_ _a"> </span>sche<span class="_ _5"></span>mes<span class="_ _a"> </span>can<span class="_ _a"> </span>be<span class="_ _a"> </span>extend<span class="_ _5"></span>ed<span class="_ _a"> </span>to<span class="_ _a"> </span>point-to-</div><div class="t m1 xa h7 y4f ff1 fs5 fc1 sc0 ls0 ws0">point<span class="_ _4"> </span>MIMO<span class="_ _7"> </span>system<span class="_ _5"></span>s<span class="_ _4"> </span>easily<span class="_ _7"> </span>[9<span class="_ _5"></span>]&#8211;[11],<span class="_ _4"> </span>extension<span class="_ _7"> </span>to<span class="_ _4"> </span>the<span class="_ _4"> </span>multi-</div><div class="t m1 xa h7 y50 ff1 fs5 fc1 sc0 ls0 ws0">user<span class="_ _e"> </span>(MU)<span class="_ _e"> </span>MIMO<span class="_ _e"> </span>downlink<span class="_"> </span>is<span class="_ _e"> </span>no<span class="_ _5"></span>t<span class="_"> </span>stra<span class="_ _5"></span>ightforward,<span class="_"> </span>main<span class="_ _5"></span>ly<span class="_"> </span>be-</div><div class="t m1 xa h7 y51 ff1 fs5 fc1 sc0 ls0 ws0">cause<span class="_"> </span>joint<span class="_"> </span>recei<span class="_ _3"></span>ver<span class="_ _3"></span>-side<span class="_ _d"> </span>sign<span class="_ _5"></span>al<span class="_"> </span>processing<span class="_"> </span>is<span class="_ _d"> </span>alm<span class="_ _5"></span>ost<span class="_"> </span>impossible</div><div class="t m1 xa h7 y52 ff1 fs5 fc1 sc0 ls0 ws0">in<span class="_ _8"> </span>practice<span class="_ _8"> </span>as<span class="_ _7"> </span>the<span class="_ _8"> </span>user<span class="_ _5"></span>s<span class="_ _e"> </span>a<span class="_ _5"></span>re<span class="_ _e"> </span>d<span class="_ _5"></span>istributed.<span class="_ _e"> </span>Recently<span class="_ _3"></span>,<span class="_ _e"> </span>a<span class="_ _8"> </span>n<span class="_ _5"></span>e<span class="_ _3"></span>w<span class="_ _8"> </span>P<span class="_ _6"></span>APR</div><div class="t m1 xa h7 y53 ff1 fs5 fc1 sc0 ls0 ws0">reduction<span class="_ _c"> </span>method<span class="_ _13"> </span>[12]<span class="_ _c"> </span>was<span class="_ _c"> </span>developed<span class="_ _14"> </span>for<span class="_ _c"> </span>m<span class="_ _5"></span>assi<span class="_ _3"></span>ve<span class="_ _14"> </span>MIMO-</div><div class="t m1 xa h7 y54 ff1 fs5 fc1 sc0 ls0 ws0">OFDM<span class="_ _7"> </span>sy<span class="_ _5"></span>stems.<span class="_ _7"> </span>T<span class="_ _5"></span>he<span class="_ _4"> </span>proposed<span class="_ _7"> </span>scheme<span class="_ _4"> </span>utilizes<span class="_ _4"> </span>the<span class="_ _7"> </span>red<span class="_ _5"></span>undan<span class="_ _5"></span>t</div><div class="t m1 xa h7 y55 ff1 fs5 fc1 sc0 ls0 ws0">degrees-of-f<span class="_ _5"></span>reedom<span class="_ _a"> </span>(DoFs)<span class="_ _9"> </span>resultin<span class="_ _5"></span>g<span class="_ _9"> </span>from<span class="_ _9"> </span>the<span class="_ _9"> </span>large<span class="_ _9"> </span>nu<span class="_ _5"></span>mber</div><div class="t m1 xa h7 y56 ff1 fs5 fc1 sc0 ls0 ws0">of<span class="_ _4"> </span>antenn<span class="_ _5"></span>as<span class="_ _4"> </span>at<span class="_ _4"> </span>the<span class="_ _a"> </span>BS<span class="_ _4"> </span>to<span class="_ _4"> </span>achieve<span class="_ _4"> </span>joint<span class="_ _4"> </span>multiuser<span class="_ _4"> </span>inter<span class="_ _5"></span>ference</div><div class="t m1 xa h7 y57 ff1 fs5 fc1 sc0 ls0 ws0">(MUI)<span class="_"> </span>can<span class="_ _5"></span>celation<span class="_"> </span>and<span class="_"> </span>P<span class="_ _f"></span>APR<span class="_ _e"> </span>reductio<span class="_ _5"></span>n.<span class="_"> </span>Speci&#64257;cally<span class="_ _f"></span>,<span class="_ _e"> </span>the<span class="_"> </span>pro<span class="_ _5"></span>b-</div><div class="t m1 xa h7 y58 ff1 fs5 fc1 sc0 ls0 ws0">lem<span class="_ _a"> </span>w<span class="_ _3"></span>as<span class="_ _a"> </span>formulated<span class="_ _4"> </span>as<span class="_ _a"> </span>a<span class="_ _a"> </span>linear<span class="_ _a"> </span>constrained<span class="_ _4"> </span><span class="ff6">&#8467;</span></div><div class="t m1 xc h9 y59 ff7 fs1 fc1 sc0 ls0 ws0">&#8734;</div><div class="t m1 xd h7 y58 ff1 fs5 fc1 sc0 ls0 ws0">optimization</div><div class="t m1 xa h7 y5a ff1 fs5 fc1 sc0 ls0 ws0">problem<span class="_ _13"> </span>and<span class="_ _13"> </span>a<span class="_ _13"> </span>fast<span class="_ _13"> </span>iterativ<span class="_ _3"></span>e<span class="_ _c"> </span>tr<span class="_ _5"></span>uncation<span class="_ _13"> </span>algorithm<span class="_ _13"> </span>(FITRA)</div><div class="t m1 xa h7 y5b ff1 fs5 fc1 sc0 ls0 ws0">was<span class="_ _8"> </span>developed<span class="_ _e"> </span>in<span class="_ _7"> </span>[12].<span class="_ _8"> </span>Howev<span class="_ _3"></span>er<span class="_ _3"></span>,<span class="_ _e"> </span>the<span class="_ _7"> </span>FITRA<span class="_ _8"> </span>alg<span class="_ _5"></span>orithm<span class="_ _e"> </span>sh<span class="_ _5"></span>ows</div><div class="t m1 xa h7 y5c ff1 fs5 fc1 sc0 ls0 ws0">to<span class="_ _14"> </span>h<span class="_ _5"></span>a<span class="_ _3"></span>ve<span class="_ _14"> </span>a<span class="_ _c"> </span>fairly<span class="_ _14"> </span>low<span class="_ _14"> </span>convergence<span class="_ _a"> </span>ra<span class="_ _5"></span>te.<span class="_ _14"> </span>Also,<span class="_ _c"> </span>the<span class="_ _c"> </span>algorith<span class="_ _5"></span>m</div><div class="t m1 xa h7 y5d ff1 fs5 fc1 sc0 ls0 ws0">employs<span class="_ _16"> </span>a<span class="_"> </span>regularization<span class="_ _d"> </span>param<span class="_ _5"></span>eter<span class="_ _d"> </span>to<span class="_"> </span>achieve<span class="_ _d"> </span>balance<span class="_"> </span>between</div><div class="t m1 xa h7 y5e ff1 fs5 fc1 sc0 ls0 ws0">the<span class="_ _9"> </span>P<span class="_ _f"></span>APR<span class="_ _14"> </span>reductio<span class="_ _5"></span>n<span class="_ _9"> </span>and<span class="_ _9"> </span>the<span class="_ _14"> </span>MUI<span class="_ _14"> </span>cancelation<span class="_ _9"> </span>(i.e.<span class="_ _14"> </span>data<span class="_ _14"> </span>&#64257;t-</div><div class="t m1 xa h7 y5f ff1 fs5 fc1 sc0 ls0 ws0">ting<span class="_ _9"> </span>error)<span class="_ _5"></span>.<span class="_ _a"> </span>The<span class="_ _9"> </span>choice<span class="_ _9"> </span>of<span class="_ _9"> </span>the<span class="_ _9"> </span>r<span class="_ _5"></span>egularization<span class="_ _a"> </span>parameter<span class="_ _9"> </span>may</div><div class="t m1 xa h7 y60 ff1 fs5 fc1 sc0 ls0 ws0">be<span class="_ _14"> </span>tricky<span class="_ _9"> </span>in<span class="_ _14"> </span>practice.<span class="_ _14"> </span>On<span class="_ _9"> </span>th<span class="_ _5"></span>e<span class="_ _9"> </span>o<span class="_ _5"></span>ther<span class="_ _9"> </span>han<span class="_ _5"></span>d,<span class="_ _9"> </span>the<span class="_ _14"> </span>regularizatio<span class="_ _5"></span>n</div><div class="t m1 xa h7 y61 ff1 fs5 fc1 sc0 ls0 ws0">parameter<span class="_ _c"> </span>may<span class="_ _13"> </span>be<span class="_ _c"> </span>seen<span class="_ _c"> </span>instead<span class="_ _13"> </span>as<span class="_ _c"> </span>an<span class="_ _13"> </span>additional<span class="_ _c"> </span>degree<span class="_ _c"> </span>of</div><div class="t m1 xa h7 y62 ff1 fs5 fc1 sc0 ls0 ws0">freedom<span class="_ _e"> </span>that<span class="_ _e"> </span>allows<span class="_ _e"> </span>to<span class="_ _e"> </span>regulate<span class="_ _e"> </span>the<span class="_ _e"> </span>oper<span class="_ _5"></span>ation<span class="_"> </span>o<span class="_ _5"></span>f<span class="_ _e"> </span>the<span class="_ _e"> </span>algorithm<span class="_ _5"></span>.</div><div class="t m1 xa h7 y63 ff1 fs5 fc1 sc0 ls0 ws0">In<span class="_"> </span>[13],<span class="_"> </span>a<span class="_"> </span>peak<span class="_"> </span>signal<span class="_"> </span>clippin<span class="_ _5"></span>g<span class="_"> </span>scheme<span class="_"> </span>was<span class="_"> </span>employed<span class="_ _16"> </span>to<span class="_"> </span>redu<span class="_ _5"></span>ce</div><div class="t m1 xa h7 y64 ff1 fs5 fc1 sc0 ls0 ws0">the<span class="_ _8"> </span>P<span class="_ _f"></span>APR<span class="_ _7"> </span>and<span class="_ _7"> </span>some<span class="_ _8"> </span>of<span class="_ _7"> </span>the<span class="_ _8"> </span>an<span class="_ _5"></span>tennas<span class="_ _8"> </span>at<span class="_ _7"> </span>the<span class="_ _8"> </span>BS<span class="_ _7"> </span>are<span class="_ _8"> </span>r<span class="_ _5"></span>eserved<span class="_ _e"> </span>to</div><div class="t m1 xa h7 y65 ff1 fs5 fc1 sc0 ls0 ws0">compen<span class="_ _5"></span>sate<span class="_ _d"> </span>for<span class="_"> </span>pe<span class="_ _5"></span>ak-clipping<span class="_"> </span>signals.<span class="_"> </span>This<span class="_"> </span>method<span class="_ _d"> </span>h<span class="_ _5"></span>as<span class="_"> </span>a<span class="_"> </span>lo<span class="_ _3"></span>wer</div><div class="t m1 xa h7 y66 ff1 fs5 fc1 sc0 ls0 ws0">computatio<span class="_ _5"></span>nal<span class="_ _8"> </span>c<span class="_ _5"></span>omplexity<span class="_ _1"></span>.<span class="_ _7"> </span>But<span class="_ _4"> </span>it<span class="_ _4"> </span>achiev<span class="_ _3"></span>es<span class="_ _7"> </span>only<span class="_ _4"> </span>a<span class="_ _7"> </span>m<span class="_ _5"></span>ild<span class="_ _7"> </span>P<span class="_ _f"></span>APR</div><div class="t m1 xa h7 y67 ff1 fs5 fc1 sc0 ls0 ws0">reduction<span class="_ _4"> </span>and<span class="_ _7"> </span>those<span class="_ _4"> </span>antennas<span class="_ _7"> </span>r<span class="_ _5"></span>eserved<span class="_ _7"> </span>for<span class="_ _4"> </span>compen<span class="_ _5"></span>sation<span class="_ _8"> </span>m<span class="_ _5"></span>ay</div><div class="t m1 xa h7 y68 ff1 fs5 fc1 sc0 ls0 ws0">incur<span class="_ _7"> </span>large<span class="_ _7"> </span>P<span class="_ _6"></span>APRs.</div><div class="t m1 xb h7 y69 ff1 fs5 fc1 sc0 ls0 ws0">In<span class="_ _14"> </span>this<span class="_ _c"> </span>paper,<span class="_ _9"> </span>we<span class="_ _14"> </span>d<span class="_ _5"></span>ev<span class="_ _3"></span>elop<span class="_ _14"> </span>a<span class="_ _14"> </span>novel<span class="_ _14"> </span>Bayesian<span class="_ _14"> </span>app<span class="_ _5"></span>roach<span class="_ _9"> </span>to</div><div class="t m1 xa h7 y6a ff1 fs5 fc1 sc0 ls0 ws0">address<span class="_ _7"> </span>the<span class="_ _4"> </span>joint<span class="_ _7"> </span>P<span class="_ _f"></span>APR<span class="_ _4"> </span>reduction<span class="_ _7"> </span>and<span class="_ _7"> </span>MUI<span class="_ _4"> </span>cancelation<span class="_ _7"> </span>p<span class="_ _5"></span>rob-</div><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" 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