数字预失真论文和辨识方法.rar

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几篇数字预失真的英文论文,可以参考,还有辨识算法
数字预失真论文和辨识方法.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/624fb7406caf596192eded87/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/624fb7406caf596192eded87/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">1468<span class="_ _0"> </span>IEEE<span class="_"> </span>TRANSACTIONS<span class="_"> </span>ON<span class="_"> </span>VEHICULAR<span class="_ _1"> </span>TECHNOLOGY<span class="_ _2"></span>,<span class="_"> </span>VOL.<span class="_"> </span>53,<span class="_"> </span>NO.<span class="_ _1"> </span>5,<span class="_"> </span>SEPTEMBER<span class="_ _1"> </span>2004</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls1 ws0">Orthogonal<span class="_ _3"> </span>Polynomials<span class="_ _3"> </span>for<span class="_ _3"> </span>Po<span class="_ _2"></span>wer<span class="_ _3"> </span>Ampli&#64257;er</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls1 ws0">Modeling<span class="_ _4"> </span>and<span class="_ _4"> </span>Predistorter<span class="_ _4"> </span>Design</div><div class="t m0 x4 h4 y4 ff1 fs2 fc0 sc0 ls1 ws0">Ravi<span class="_ _5"></span>v<span class="_ _6"> </span>Raich,<span class="_ _6"> </span>Hua<span class="_ _6"> </span>Qian,<span class="_"> </span>and<span class="_ _6"> </span>G.<span class="_ _6"> </span>T<span class="_ _2"></span>ong<span class="_ _6"> </span>Zhou</div><div class="t m0 x5 h5 y5 ff2 fs3 fc0 sc0 ls1 ws0">Abstract&#8212;<span class="ff3">The<span class="_ _7"> </span>polynomial<span class="_ _7"> </span>model<span class="_ _7"> </span>is<span class="_ _7"> </span>commonly<span class="_ _7"> </span>used<span class="_ _7"> </span>in<span class="_ _7"> </span>power</span></div><div class="t m0 x1 h6 y6 ff3 fs3 fc0 sc0 ls1 ws0">ampli&#64257;er<span class="_ _8"> </span>(P<span class="_ _5"></span>A)<span class="_ _8"> </span>modeling<span class="_ _8"> </span>and<span class="_ _8"> </span>pr<span class="_ _9"></span>edistorter<span class="_ _8"> </span>design.<span class="_ _8"> </span>Howev<span class="_ _9"></span>er<span class="_ _2"></span>,<span class="_ _8"> </span>the</div><div class="t m0 x1 h6 y7 ff3 fs3 fc0 sc0 ls1 ws0">con<span class="_ _5"></span>ventional<span class="_ _a"> </span>polynomial<span class="_ _a"> </span>model<span class="_ _a"> </span>exhibits<span class="_ _b"> </span>numerical<span class="_ _b"> </span>instabilities</div><div class="t m0 x1 h6 y8 ff3 fs3 fc0 sc0 ls1 ws0">when<span class="_"> </span>higher<span class="_"> </span>order<span class="_"> </span>terms<span class="_ _1"> </span>ar<span class="_ _9"></span>e<span class="_"> </span>included.<span class="_"> </span>In<span class="_"> </span>this<span class="_ _1"> </span>paper<span class="_ _2"></span>,<span class="_"> </span>we<span class="_"> </span>intr<span class="_ _5"></span>oduce</div><div class="t m0 x1 h6 y9 ff3 fs3 fc0 sc0 ls1 ws0">a<span class="_"> </span>nov<span class="_ _5"></span>el<span class="_"> </span>set<span class="_"> </span>of<span class="_ _1"> </span>orthogonal<span class="_ _1"> </span>polynomials,<span class="_ _1"> </span>which<span class="_ _1"> </span>can<span class="_"> </span>be<span class="_ _1"> </span>used<span class="_ _1"> </span>f<span class="_ _5"></span>or<span class="_"> </span>P<span class="_ _2"></span>A<span class="_"> </span>as</div><div class="t m0 x1 h6 ya ff3 fs3 fc0 sc0 ls1 ws0">well<span class="_"> </span>as<span class="_ _c"> </span>predistorter<span class="_"> </span>modeling.<span class="_"> </span>Theoretically<span class="_ _5"></span>,<span class="_"> </span>the<span class="_"> </span>conventional<span class="_"> </span>and</div><div class="t m0 x1 h6 yb ff3 fs3 fc0 sc0 ls1 ws0">orthogonal<span class="_ _c"> </span>polynomial<span class="_"> </span>models<span class="_ _c"> </span>are<span class="_ _c"> </span>&#8220;equivalent&#8221;<span class="_"> </span>and,<span class="_ _c"> </span>thus,<span class="_ _c"> </span>should</div><div class="t m0 x1 h6 yc ff3 fs3 fc0 sc0 ls1 ws0">behav<span class="_ _5"></span>e<span class="_ _8"> </span>similarly<span class="_ _5"></span>.<span class="_ _7"> </span>In<span class="_ _7"> </span>practice,<span class="_ _7"> </span>however<span class="_ _2"></span>,<span class="_ _7"> </span>the<span class="_ _7"> </span>two<span class="_ _8"> </span>appr<span class="_ _9"></span>oaches<span class="_ _7"> </span>can</div><div class="t m0 x1 h6 yd ff3 fs3 fc0 sc0 ls1 ws0">perform<span class="_ _6"> </span>quite<span class="_ _6"> </span>differ<span class="_ _5"></span>ently<span class="_ _d"> </span>in<span class="_ _6"> </span>the<span class="_ _6"> </span>presence<span class="_ _6"> </span>of<span class="_ _6"> </span>&#64257;nite<span class="_ _6"> </span>precision<span class="_ _6"> </span>pr<span class="_ _5"></span>o-</div><div class="t m0 x1 h6 ye ff3 fs3 fc0 sc0 ls1 ws0">cessing.<span class="_ _c"> </span>Simulation<span class="_ _6"> </span>r<span class="_ _5"></span>esults<span class="_ _6"> </span>sho<span class="_ _9"></span>w<span class="_ _c"> </span>that<span class="_ _6"> </span>the<span class="_ _c"> </span>orthogonal<span class="_ _6"> </span>polynomials</div><div class="t m0 x1 h6 yf ff3 fs3 fc0 sc0 ls1 ws0">can<span class="_"> </span>alle<span class="_ _9"></span>viate<span class="_"> </span>the<span class="_ _1"> </span>numerical<span class="_"> </span>instability<span class="_ _1"> </span>pr<span class="_ _5"></span>oblem<span class="_"> </span>associated<span class="_"> </span>with<span class="_ _1"> </span>the</div><div class="t m0 x1 h6 y10 ff3 fs3 fc0 sc0 ls1 ws0">con<span class="_ _5"></span>ventional<span class="_ _c"> </span>polynomials<span class="_ _c"> </span>and<span class="_ _c"> </span>generally<span class="_ _e"> </span>yield<span class="_ _c"> </span>better<span class="_ _c"> </span>P<span class="_ _5"></span>A<span class="_ _c"> </span>modeling</div><div class="t m0 x1 h6 y11 ff3 fs3 fc0 sc0 ls1 ws0">accuracy<span class="_"> </span>as<span class="_"> </span>well<span class="_"> </span>as<span class="_"> </span>predistortion<span class="_"> </span>linearization<span class="_"> </span>performance.</div><div class="t m0 x5 h5 y12 ff2 fs3 fc0 sc0 ls1 ws0">Index<span class="_ _b"> </span>T<span class="_ _2"></span>erms&#8212;<span class="ff3">Nonlinear<span class="_ _a"> </span>systems,<span class="_ _b"> </span>numerical<span class="_ _b"> </span>stability,<span class="_ _a"> </span>power</span></div><div class="t m0 x1 h6 y13 ff3 fs3 fc0 sc0 ls1 ws0">ampli&#64257;ers,<span class="_"> </span>predistortion,<span class="_"> </span>orthogonal<span class="_"> </span>polynomials.</div><div class="t m0 x6 h7 y14 ff1 fs4 fc0 sc0 ls1 ws0">I.<span class="_ _a"> </span>I<span class="fs5">NTRODUCTION</span></div><div class="t m0 x1 h8 y15 ff3 fs6 fc0 sc0 ls1 ws0">T</div><div class="t m0 x7 h7 y16 ff1 fs4 fc0 sc0 ls1 ws0">HE<span class="_"> </span>po<span class="_ _5"></span>wer<span class="_"> </span>ampli&#64257;er<span class="_ _1"> </span>(P<span class="_ _2"></span>A)<span class="_ _1"> </span>is<span class="_"> </span>a<span class="_ _1"> </span>major<span class="_"> </span>source<span class="_ _1"> </span>of<span class="_"> </span>nonlinearity</div><div class="t m0 x7 h7 y17 ff1 fs4 fc0 sc0 ls1 ws0">in<span class="_ _6"> </span>a<span class="_ _6"> </span>communication<span class="_ _6"> </span>system.<span class="_ _d"> </span>T<span class="_ _2"></span>o<span class="_ _6"> </span>increase<span class="_ _6"> </span>their<span class="_ _d"> </span>ef<span class="_ _9"></span>&#64257;ciency<span class="_ _2"></span>,</div><div class="t m0 x1 h7 y18 ff1 fs4 fc0 sc0 ls1 ws0">P<span class="_ _2"></span>As<span class="_ _a"> </span>are<span class="_ _a"> </span>sometimes<span class="_ _f"> </span>driv<span class="_ _5"></span>en<span class="_ _a"> </span>into<span class="_ _f"> </span>their<span class="_ _a"> </span>nonlinear<span class="_ _f"> </span>region,<span class="_ _a"> </span>thus</div><div class="t m0 x1 h7 y19 ff1 fs4 fc0 sc0 ls1 ws0">causing<span class="_ _6"> </span>spectral<span class="_ _d"> </span>regro<span class="_ _5"></span>wth<span class="_ _d"> </span>(broadening)<span class="_ _6"> </span>as<span class="_ _d"> </span>well<span class="_ _6"> </span>as<span class="_ _6"> </span>inband<span class="_ _d"> </span>dis-</div><div class="t m0 x1 h7 y1a ff1 fs4 fc0 sc0 ls1 ws0">tortion.<span class="_"> </span>P<span class="_ _2"></span>A<span class="_ _e"> </span>linearization<span class="_"> </span>is<span class="_ _c"> </span>often<span class="_ _e"> </span>necessary<span class="_ _c"> </span>to<span class="_ _c"> </span>suppress<span class="_ _e"> </span>spectral</div><div class="t m0 x1 h7 y1b ff1 fs4 fc0 sc0 ls1 ws0">regro<span class="_ _5"></span>wth,<span class="_ _a"> </span>contain<span class="_ _b"> </span>adjacent<span class="_ _a"> </span>channel<span class="_ _a"> </span>interference,<span class="_ _b"> </span>and<span class="_ _a"> </span>reduce</div><div class="t m0 x1 h7 y1c ff1 fs4 fc0 sc0 ls1 ws0">bit-error<span class="_ _e"> </span>rate<span class="_ _e"> </span>(BER).</div><div class="t m0 x8 h7 y1d ff1 fs4 fc0 sc0 ls1 ws0">The<span class="_"> </span>power<span class="_"> </span>series<span class="_ _c"> </span>model,<span class="_ _c"> </span>or<span class="_ _c"> </span>the<span class="_ _c"> </span>polynomial<span class="_ _e"> </span>model,<span class="_"> </span>is<span class="_ _c"> </span>widely</div><div class="t m0 x1 h7 y1e ff1 fs4 fc0 sc0 ls1 ws0">used<span class="_ _1"> </span>in<span class="_ _1"> </span>the<span class="_ _1"> </span>literature<span class="_ _1"> </span>to<span class="_ _10"> </span>describe<span class="_ _10"> </span>nonlinear<span class="_ _1"> </span>effects<span class="_ _10"> </span>in<span class="_ _1"> </span>the<span class="_ _1"> </span>P<span class="_ _2"></span>A<span class="_ _10"> </span>(see,</div><div class="t m0 x1 h7 y1f ff1 fs4 fc0 sc0 ls1 ws0">e.g.,<span class="_ _10"> </span>[1]<span class="_ _10"> </span>and<span class="_ _1"> </span>[2]).<span class="_ _10"> </span>In<span class="_ _10"> </span>[3],<span class="_ _1"> </span>it<span class="_ _10"> </span>is<span class="_ _1"> </span>shown<span class="_ _10"> </span>that<span class="_ _10"> </span>after<span class="_ _10"> </span>extracting<span class="_ _10"> </span>the<span class="_ _10"> </span>poly-</div><div class="t m0 x1 h7 y20 ff1 fs4 fc0 sc0 ls1 ws0">nomial<span class="_"> </span>coef<span class="_ _5"></span>&#64257;cients<span class="_"> </span>of<span class="_ _10"> </span>the<span class="_"> </span>P<span class="_ _2"></span>A,<span class="_ _1"> </span>it<span class="_"> </span>is<span class="_ _1"> </span>then<span class="_"> </span>possible<span class="_ _1"> </span>to<span class="_"> </span>predict<span class="_ _10"> </span>spec-</div><div class="t m0 x1 h7 y21 ff1 fs4 fc0 sc0 ls1 ws0">tral<span class="_ _6"> </span>regro<span class="_ _5"></span>wth<span class="_ _d"> </span>of<span class="_ _6"> </span>digitally<span class="_ _6"> </span>modulated<span class="_ _6"> </span>signals<span class="_ _6"> </span>using<span class="_ _d"> </span>the<span class="_ _6"> </span>concept</div><div class="t m0 x1 h7 y22 ff1 fs4 fc0 sc0 ls1 ws0">of<span class="_ _6"> </span>cumulant.<span class="_ _6"> </span>Recently<span class="_ _5"></span>,<span class="_ _6"> </span>in<span class="_ _6"> </span>[4],<span class="_ _6"> </span>a<span class="_ _d"> </span>memory<span class="_ _6"> </span>polynomial<span class="_ _6"> </span>model<span class="_ _6"> </span>is</div><div class="t m0 x1 h7 y23 ff1 fs4 fc0 sc0 ls1 ws0">proposed<span class="_ _e"> </span>to<span class="_ _e"> </span>&#64257;t<span class="_ _6"> </span>nonlinear<span class="_ _e"> </span>P<span class="_ _2"></span>As<span class="_ _e"> </span>with<span class="_ _6"> </span>memory<span class="_ _5"></span>.<span class="_ _e"> </span>The<span class="_ _e"> </span>more<span class="_ _6"> </span>general</div><div class="t m0 x1 h7 y24 ff1 fs4 fc0 sc0 ls1 ws0">V<span class="_ _11"></span>olterra<span class="_ _d"> </span>series<span class="_ _d"> </span>(which<span class="_ _7"> </span>is<span class="_ _d"> </span>polynomial<span class="_ _7"> </span>in<span class="_ _7"> </span>nature)<span class="_ _d"> </span>has<span class="_ _d"> </span>also<span class="_ _7"> </span>been</div><div class="t m0 x1 h7 y25 ff1 fs4 fc0 sc0 ls1 ws0">used<span class="_"> </span>to<span class="_ _c"> </span>model<span class="_ _c"> </span>nonlinear<span class="_ _c"> </span>devices<span class="_"> </span>with<span class="_"> </span>memory<span class="_ _c"> </span>[5].</div><div class="t m0 x8 h7 y26 ff1 fs4 fc0 sc0 ls1 ws0">If<span class="_ _8"> </span>the<span class="_ _b"> </span>nonlinear<span class="_ _8"> </span>P<span class="_ _2"></span>A<span class="_ _8"> </span>is<span class="_ _b"> </span>used<span class="_ _8"> </span>to<span class="_ _8"> </span>transmit<span class="_ _8"> </span>nonconstant<span class="_ _b"> </span>mod-</div><div class="t m0 x1 h7 y27 ff1 fs4 fc0 sc0 ls1 ws0">ulus<span class="_"> </span>signals,<span class="_"> </span>P<span class="_ _11"></span>A<span class="_"> </span>linearization<span class="_"> </span>is<span class="_ _1"> </span>often<span class="_"> </span>necessary<span class="_ _5"></span>.<span class="_"> </span>Among<span class="_ _1"> </span>all<span class="_"> </span>lin-</div><div class="t m0 x1 h7 y28 ff1 fs4 fc0 sc0 ls1 ws0">earization<span class="_ _6"> </span>techniques,<span class="_ _d"> </span>digital<span class="_ _d"> </span>baseband<span class="_ _6"> </span>predistortion<span class="_ _d"> </span>is<span class="_ _d"> </span>one<span class="_ _6"> </span>of</div><div class="t m0 x1 h7 y29 ff1 fs4 fc0 sc0 ls1 ws0">the<span class="_ _e"> </span>most<span class="_ _6"> </span>cost<span class="_ _6"> </span>effecti<span class="_ _5"></span>ve.<span class="_ _e"> </span>A<span class="_ _6"> </span>predistorter<span class="_ _5"></span>,<span class="_ _6"> </span>which<span class="_ _e"> </span>(ideally)<span class="_ _6"> </span>has<span class="_ _6"> </span>the</div><div class="t m0 x1 h7 y2a ff1 fs4 fc0 sc0 ls1 ws0">in<span class="_ _5"></span>verse<span class="_ _e"> </span>characteristic<span class="_ _6"> </span>of<span class="_ _6"> </span>the<span class="_ _6"> </span>P<span class="_ _2"></span>A,<span class="_ _6"> </span>is<span class="_ _e"> </span>used<span class="_ _6"> </span>to<span class="_ _6"> </span>compensate<span class="_ _6"> </span>for<span class="_ _e"> </span>the</div><div class="t m0 x1 h7 y2b ff1 fs4 fc0 sc0 ls1 ws0">nonlinearity<span class="_ _1"> </span>in<span class="_"> </span>the<span class="_ _1"> </span>P<span class="_ _2"></span>A.<span class="_ _1"> </span>T<span class="_ _5"></span>o<span class="_ _1"> </span>linearize<span class="_ _1"> </span>a<span class="_"> </span>memoryless<span class="_ _1"> </span>nonlinear<span class="_ _1"> </span>P<span class="_ _2"></span>A,</div><div class="t m0 x1 h7 y2c ff1 fs4 fc0 sc0 ls1 ws0">one<span class="_ _6"> </span>can<span class="_ _6"> </span>pursue<span class="_ _6"> </span>approaches<span class="_ _6"> </span>based<span class="_ _6"> </span>on<span class="_ _6"> </span>the<span class="_ _6"> </span>LUT<span class="_ _6"> </span>or<span class="_ _6"> </span>models.<span class="_ _6"> </span>The</div><div class="t m0 x1 h7 y2d ff1 fs4 fc0 sc0 ls1 ws0">LUT<span class="_ _e"> </span>approach<span class="_ _e"> </span>is<span class="_ _6"> </span>easy<span class="_ _e"> </span>to<span class="_ _6"> </span>implement,<span class="_ _e"> </span>but<span class="_ _e"> </span>may<span class="_ _e"> </span>take<span class="_ _e"> </span>a<span class="_ _e"> </span>relatively</div><div class="t m0 x1 h7 y2e ff1 fs4 fc0 sc0 ls1 ws0">long<span class="_ _d"> </span>time<span class="_ _7"> </span>to<span class="_ _d"> </span>conv<span class="_ _5"></span>erge.<span class="_ _d"> </span>Moreover<span class="_ _5"></span>,<span class="_ _d"> </span>the<span class="_ _d"> </span>piece-wise<span class="_ _7"> </span>linear<span class="_ _d"> </span>curve</div><div class="t m0 x9 h9 y2f ff1 fs5 fc0 sc0 ls1 ws0">Manuscript<span class="_ _12"> </span>receiv<span class="_ _5"></span>ed<span class="_ _12"> </span>January<span class="_ _12"> </span>6,<span class="_ _12"> </span>2003;<span class="_ _12"> </span>revised<span class="_ _12"> </span>March<span class="_ _1"> </span>10,<span class="_ _12"> </span>2004<span class="_ _c"> </span>and<span class="_ _1"> </span>May<span class="_ _12"> </span>25,</div><div class="t m0 x1 h9 y30 ff1 fs5 fc0 sc0 ls1 ws0">2004.<span class="_ _13"> </span>This<span class="_ _13"> </span>work<span class="_ _13"> </span>was<span class="_ _13"> </span>supported<span class="_ _13"> </span>in<span class="_ _13"> </span>part<span class="_ _13"> </span>by<span class="_ _13"> </span>the<span class="_ _13"> </span>National<span class="_ _13"> </span>Science<span class="_ _13"> </span>Foundation<span class="_ _13"> </span>under</div><div class="t m0 x1 h9 y31 ff1 fs5 fc0 sc0 ls1 ws0">Grant<span class="_"> </span>ECS-0219262,<span class="_"> </span>the<span class="_ _1"> </span>Georgia<span class="_"> </span>Electronics<span class="_"> </span>Design<span class="_ _12"> </span>Center<span class="_ _5"></span>,<span class="_"> </span>Atlanta,<span class="_ _12"> </span>GA,<span class="_"> </span>and</div><div class="t m0 x1 h9 y32 ff1 fs5 fc0 sc0 ls1 ws0">Danam<span class="_ _12"> </span>USA,<span class="_ _1"> </span>Inc.,<span class="_ _12"> </span>San<span class="_ _12"> </span>Jose,<span class="_ _12"> </span>CA.</div><div class="t m0 x9 h9 y33 ff1 fs5 fc0 sc0 ls1 ws0">The<span class="_ _e"> </span>authors<span class="_ _e"> </span>are<span class="_ _6"> </span>with<span class="_ _e"> </span>the<span class="_ _e"> </span>School<span class="_ _6"> </span>of<span class="_ _e"> </span>Electrical<span class="_ _e"> </span>and<span class="_ _e"> </span>Computer<span class="_ _6"> </span>Engineering,</div><div class="t m0 x1 h9 y34 ff1 fs5 fc0 sc0 ls1 ws0">Georgia<span class="_ _b"> </span>Institute<span class="_ _b"> </span>of<span class="_ _b"> </span>T<span class="_ _5"></span>echnology<span class="_ _5"></span>,<span class="_ _b"> </span>Atlanta,<span class="_ _a"> </span>GA<span class="_ _b"> </span>30332-0250<span class="_ _b"> </span>USA<span class="_ _a"> </span>(e-mail:</div><div class="t m0 x1 h9 y35 ff1 fs5 fc0 sc0 ls1 ws0">ravi<span class="_ _5"></span>v@ece.gatech.edu;<span class="_"> </span>qianhua@ece.gatech.edu;<span class="_"> </span>gtz@ece.gatech.edu).</div><div class="t m0 x9 h9 y36 ff1 fs5 fc0 sc0 ls1 ws0">Digital<span class="_"> </span>Object<span class="_ _12"> </span>Identi&#64257;er<span class="_"> </span>10.1109/TVT<span class="_ _5"></span>.2004.832415</div><div class="t m0 xa h7 y37 ff1 fs4 fc0 sc0 ls1 ws0">has<span class="_"> </span>a<span class="_"> </span>zig-zag<span class="_ _c"> </span>appearance<span class="_ _c"> </span>that<span class="_ _c"> </span>may<span class="_ _c"> </span>introduce<span class="_ _c"> </span>additional<span class="_ _c"> </span>nonlin-</div><div class="t m0 xa h7 y38 ff1 fs4 fc0 sc0 ls1 ws0">earities<span class="_ _6"> </span>that<span class="_ _6"> </span>degrade<span class="_ _6"> </span>the<span class="_ _d"> </span>linearization<span class="_ _6"> </span>performance<span class="_ _d"> </span>[6].<span class="_ _6"> </span>As<span class="_ _d"> </span>for</div><div class="t m0 xa h7 y39 ff1 fs4 fc0 sc0 ls1 ws0">model-based<span class="_ _6"> </span>approaches,<span class="_ _d"> </span>the<span class="_ _d"> </span>polynomial<span class="_ _d"> </span>model<span class="_ _d"> </span>is<span class="_ _d"> </span>a<span class="_ _d"> </span>common</div><div class="t m0 xa h7 y3a ff1 fs4 fc0 sc0 ls1 ws0">choice<span class="_"> </span>due<span class="_"> </span>to<span class="_"> </span>its<span class="_"> </span>simplicity<span class="_"> </span>and<span class="_"> </span>ease<span class="_ _c"> </span>of<span class="_"> </span>implementation<span class="_"> </span>[1,<span class="_ _c"> </span>sec.</div><div class="t m0 xa h7 y3b ff1 fs4 fc0 sc0 ls1 ws0">3.3],<span class="_"> </span>[7].<span class="_"> </span>The<span class="_ _1"> </span>V<span class="_ _11"></span>olterra<span class="_"> </span>series<span class="_"> </span>[8]<span class="_"> </span>and<span class="_ _1"> </span>certain<span class="_"> </span>special<span class="_"> </span>cases<span class="_"> </span>of<span class="_"> </span>the</div><div class="t m0 xa h7 y3c ff1 fs4 fc0 sc0 ls1 ws0">V<span class="_ _11"></span>olterra<span class="_ _10"> </span>series<span class="_ _10"> </span>(for<span class="_ _10"> </span>example,<span class="_ _10"> </span>the<span class="_ _10"> </span>Hammerstein<span class="_ _10"> </span>model<span class="_ _1"> </span>[9]<span class="_ _10"> </span>and<span class="_ _10"> </span>the</div><div class="t m0 xa h7 y3d ff1 fs4 fc0 sc0 ls1 ws0">memory<span class="_ _e"> </span>polynomial<span class="_ _e"> </span>model<span class="_ _e"> </span>[10]),<span class="_ _6"> </span>hav<span class="_ _5"></span>e<span class="_ _e"> </span>been<span class="_ _6"> </span>proposed<span class="_ _e"> </span>for<span class="_ _e"> </span>pre-</div><div class="t m0 xa h7 y3e ff1 fs4 fc0 sc0 ls1 ws0">distorter<span class="_"> </span>design<span class="_ _c"> </span>that<span class="_ _e"> </span>includes<span class="_"> </span>memory<span class="_ _c"> </span>effects.</div><div class="t m0 xb h7 y3f ff1 fs4 fc0 sc0 ls1 ws0">Higher<span class="_ _7"> </span>order<span class="_ _7"> </span>polynomials<span class="_ _7"> </span>present<span class="_ _8"> </span>a<span class="_ _d"> </span>challenge<span class="_ _8"> </span>for<span class="_ _d"> </span>both<span class="_ _8"> </span>P<span class="_ _2"></span>A</div><div class="t m0 xa h7 y40 ff1 fs4 fc0 sc0 ls1 ws0">modeling<span class="_"> </span>and<span class="_ _c"> </span>predistorter<span class="_ _c"> </span>design.<span class="_ _e"> </span>As<span class="_"> </span>we<span class="_ _e"> </span>sho<span class="_ _9"></span>w<span class="_"> </span>in<span class="_ _c"> </span>Section<span class="_ _c"> </span>II,<span class="_ _e"> </span>in</div><div class="t m0 xa h7 y41 ff1 fs4 fc0 sc0 ls1 ws0">the<span class="_ _6"> </span>process<span class="_ _6"> </span>of<span class="_ _6"> </span>solving<span class="_ _d"> </span>for<span class="_ _6"> </span>the<span class="_ _6"> </span>model<span class="_ _d"> </span>coef&#64257;cients,<span class="_ _e"> </span>a<span class="_ _6"> </span>matrix<span class="_ _d"> </span>in-</div><div class="t m0 xa h7 y42 ff1 fs4 fc0 sc0 ls1 ws0">version<span class="_ _10"> </span>is<span class="_ _1"> </span>needed<span class="_"> </span>that<span class="_ _10"> </span>can<span class="_"> </span>cause<span class="_ _10"> </span>a<span class="_ _1"> </span>numerical<span class="_ _1"> </span>instability<span class="_"> </span>problem</div><div class="t m0 xa h7 y43 ff1 fs4 fc0 sc0 ls1 ws0">if<span class="_"> </span>higher<span class="_"> </span>order<span class="_"> </span>polynomial<span class="_"> </span>terms<span class="_"> </span>are<span class="_ _1"> </span>included.<span class="_"> </span>The<span class="_"> </span>objective<span class="_ _1"> </span>of</div><div class="t m0 xa h7 y44 ff1 fs4 fc0 sc0 ls1 ws0">this<span class="_ _d"> </span>paper<span class="_ _d"> </span>is<span class="_ _d"> </span>to<span class="_ _d"> </span>derive<span class="_ _6"> </span>an<span class="_ _7"> </span>orthogonal<span class="_ _d"> </span>polynomial<span class="_ _d"> </span>basis<span class="_ _d"> </span>and<span class="_ _d"> </span>to</div><div class="t m0 xa h7 y45 ff1 fs4 fc0 sc0 ls1 ws0">model<span class="_"> </span>the<span class="_"> </span>P<span class="_ _11"></span>A<span class="_"> </span>or<span class="_"> </span>predistorter<span class="_"> </span>using<span class="_ _1"> </span>such<span class="_"> </span>basis.<span class="_"> </span>The<span class="_"> </span>resulting<span class="_"> </span>or<span class="_ _5"></span>-</div><div class="t m0 xa h7 y46 ff1 fs4 fc0 sc0 ls1 ws0">thogonal<span class="_ _6"> </span>polynomial<span class="_ _6"> </span>model<span class="_ _6"> </span>coef&#64257;cients<span class="_ _6"> </span>can<span class="_ _6"> </span>be<span class="_ _6"> </span>extracted<span class="_ _6"> </span>with</div><div class="t m0 xa h7 y47 ff1 fs4 fc0 sc0 ls1 ws0">much<span class="_ _c"> </span>improved<span class="_"> </span>numerical<span class="_ _e"> </span>stability<span class="_ _2"></span>.</div><div class="t m0 xb h7 y48 ff1 fs4 fc0 sc0 ls1 ws0">Orthogonal<span class="_ _7"> </span>polynomials<span class="_ _7"> </span>have<span class="_ _d"> </span>been<span class="_ _7"> </span>proposed<span class="_ _7"> </span>by<span class="_ _8"> </span>others<span class="_ _d"> </span>for</div><div class="t m0 xa h7 y49 ff1 fs4 fc0 sc0 ls1 ws0">predistorter<span class="_"> </span>design<span class="_ _1"> </span>[11],<span class="_"> </span>[12].<span class="_ _1"> </span>Our<span class="_"> </span>approach<span class="_ _1"> </span>is<span class="_"> </span>dif<span class="_ _5"></span>ferent<span class="_"> </span>and<span class="_"> </span>has</div><div class="t m0 xa h7 y4a ff1 fs4 fc0 sc0 ls1 ws0">the<span class="_ _e"> </span>following<span class="_ _e"> </span>advantages.<span class="_ _e"> </span>1)<span class="_ _e"> </span>Our<span class="_ _6"> </span>orthogonal<span class="_ _6"> </span>polynomial<span class="_ _e"> </span>basis</div><div class="t m0 xa h7 y4b ff1 fs4 fc0 sc0 ls1 ws0">functions<span class="_ _e"> </span>are<span class="_ _6"> </span>expressed<span class="_ _c"> </span>in<span class="_ _6"> </span>closed<span class="_ _e"> </span>form<span class="_ _6"> </span>(noniterativ<span class="_ _5"></span>e);<span class="_ _6"> </span>they<span class="_ _e"> </span>are</div><div class="t m0 xa h7 y4c ff1 fs4 fc0 sc0 ls1 ws0">predetermined<span class="_ _6"> </span>and<span class="_ _6"> </span>can<span class="_ _6"> </span>be<span class="_ _d"> </span>implemented<span class="_ _6"> </span>with<span class="_ _6"> </span>little<span class="_ _6"> </span>demand<span class="_ _d"> </span>on</div><div class="t m0 xa h7 y4d ff1 fs4 fc0 sc0 ls1 ws0">the<span class="_"> </span>computation<span class="_ _1"> </span>resources.<span class="_"> </span>In<span class="_"> </span>[11]<span class="_"> </span>and<span class="_"> </span>[12],<span class="_ _1"> </span>the<span class="_"> </span>basis<span class="_"> </span>functions</div><div class="t m0 xa h7 y4e ff1 fs4 fc0 sc0 ls1 ws0">are<span class="_"> </span>calculated<span class="_ _e"> </span>online<span class="_"> </span>and<span class="_ _e"> </span>iterativ<span class="_ _5"></span>ely<span class="_ _5"></span>,<span class="_ _c"> </span>thus<span class="_ _c"> </span>requiring<span class="_ _e"> </span>much<span class="_ _c"> </span>more</div><div class="t m0 xa h7 y4f ff1 fs4 fc0 sc0 ls1 ws0">computational<span class="_ _6"> </span>power<span class="_ _5"></span>.<span class="_ _6"> </span>2)<span class="_ _6"> </span>Our<span class="_ _6"> </span>basis<span class="_ _d"> </span>consists<span class="_ _6"> </span>of<span class="_ _d"> </span>both<span class="_ _6"> </span>ev<span class="_ _9"></span>en-<span class="_ _6"> </span>and</div><div class="t m0 xa h7 y50 ff1 fs4 fc0 sc0 ls1 ws0">odd-order<span class="_ _1"> </span>terms,<span class="_"> </span>whereas<span class="_ _10"> </span>that<span class="_"> </span>of<span class="_ _10"> </span>[11]<span class="_"> </span>and<span class="_ _1"> </span>[12]<span class="_ _1"> </span>allows<span class="_ _1"> </span>odd-pow-</div><div class="t m0 xa h7 y51 ff1 fs4 fc0 sc0 ls1 ws0">ered<span class="_"> </span>series<span class="_ _e"> </span>only<span class="_ _2"></span>.<span class="_ _e"> </span>3)<span class="_"> </span>Our<span class="_ _e"> </span>basis<span class="_"> </span>function<span class="_ _e"> </span>expressions<span class="_"> </span>are<span class="_ _c"> </span>for<span class="_ _e"> </span>gen-</div><div class="t m0 xa h7 y52 ff1 fs4 fc0 sc0 ls1 ws0">erally<span class="_ _e"> </span>complex-valued<span class="_ _e"> </span>baseband<span class="_ _e"> </span>data;<span class="_ _6"> </span>application<span class="_ _e"> </span>to<span class="_ _6"> </span>nonlinear</div><div class="t m0 xa h7 y53 ff1 fs4 fc0 sc0 ls1 ws0">systems<span class="_"> </span>with<span class="_ _e"> </span>memory<span class="_"> </span>is<span class="_ _e"> </span>also<span class="_"> </span>prescribed.</div><div class="t m0 xb h7 y54 ff1 fs4 fc0 sc0 ls1 ws0">The<span class="_ _7"> </span>organization<span class="_ _7"> </span>of<span class="_ _7"> </span>the<span class="_ _8"> </span>paper<span class="_ _7"> </span>is<span class="_ _7"> </span>as<span class="_ _8"> </span>follows.<span class="_ _d"> </span>In<span class="_ _8"> </span>Section<span class="_ _7"> </span>II,</div><div class="t m0 xa h7 y55 ff1 fs4 fc0 sc0 ls1 ws0">we<span class="_"> </span>&#64257;rst<span class="_ _c"> </span>introduce<span class="_ _e"> </span>the<span class="_"> </span>conv<span class="_ _5"></span>entional<span class="_ _c"> </span>polynomial<span class="_ _e"> </span>model<span class="_"> </span>and<span class="_ _e"> </span>note</div><div class="t m0 xa h7 y56 ff1 fs4 fc0 sc0 ls1 ws0">its<span class="_ _6"> </span>de&#64257;ciencies.<span class="_ _d"> </span>Next,<span class="_ _6"> </span>we<span class="_ _d"> </span>deriv<span class="_ _5"></span>e<span class="_ _d"> </span>novel<span class="_ _6"> </span>orthogonal<span class="_ _6"> </span>polynomial</div><div class="t m0 xa h7 y57 ff1 fs4 fc0 sc0 ls1 ws0">basis<span class="_ _d"> </span>functions<span class="_ _6"> </span>and<span class="_ _d"> </span>illustrate<span class="_ _7"> </span>their<span class="_ _6"> </span>bene&#64257;t<span class="_ _d"> </span>in<span class="_ _d"> </span>P<span class="_ _2"></span>A<span class="_ _d"> </span>modeling.<span class="_ _d"> </span>In</div><div class="t m0 xa h7 y58 ff1 fs4 fc0 sc0 ls1 ws0">Section<span class="_ _b"> </span>III,<span class="_ _b"> </span>we<span class="_ _a"> </span>formulate<span class="_ _b"> </span>a<span class="_ _a"> </span>predistortion<span class="_ _b"> </span>linearization<span class="_ _a"> </span>algo-</div><div class="t m0 xa h7 y59 ff1 fs4 fc0 sc0 ls1 ws0">rithm<span class="_ _8"> </span>with<span class="_ _8"> </span>orthogonal<span class="_ _8"> </span>polynomials.<span class="_ _8"> </span>Numerical<span class="_ _b"> </span>examples<span class="_ _7"> </span>are</div><div class="t m0 xa h7 y5a ff1 fs4 fc0 sc0 ls1 ws0">presented<span class="_ _1"> </span>alongside<span class="_ _1"> </span>theoretical<span class="_"> </span>analysis.<span class="_ _10"> </span>Finally<span class="_ _5"></span>,<span class="_ _1"> </span>the<span class="_ _1"> </span>conclusion</div><div class="t m0 xa h7 y5b ff1 fs4 fc0 sc0 ls1 ws0">is<span class="_ _e"> </span>drawn<span class="_"> </span>in<span class="_ _e"> </span>Section<span class="_ _e"> </span>IV<span class="_ _11"></span>.</div><div class="t m0 xc h7 y5c ff1 fs4 fc0 sc0 ls1 ws0">II.<span class="_ _a"> </span>P</div><div class="t m0 xd h9 y5d ff1 fs5 fc0 sc0 ls1 ws0">OL<span class="_ _2"></span>YNOMIAL</div><div class="t m0 xe h7 y5e ff1 fs4 fc0 sc0 ls1 ws0">M<span class="fs5">ODEL</span></div><div class="t m0 xa ha y5f ff4 fs4 fc0 sc0 ls1 ws0">A.<span class="_ _a"> </span>Con<span class="_ _5"></span>ventional<span class="_ _e"> </span>P<span class="_ _2"></span>olynomial<span class="_ _e"> </span>Model</div><div class="t m0 xb h7 y60 ff1 fs4 fc0 sc0 ls1 ws0">Let<span class="_ _10"> </span>us<span class="_ _10"> </span>denote<span class="_ _13"> </span>by</div><div class="t m0 xf h7 y61 ff1 fs4 fc0 sc0 ls1 ws0">the<span class="_ _10"> </span>passband<span class="_ _10"> </span>input<span class="_ _13"> </span>to<span class="_ _10"> </span>a<span class="_ _10"> </span>nonlinear<span class="_ _10"> </span>system</div><div class="t m0 xa h7 y62 ff1 fs4 fc0 sc0 ls1 ws0">(e.g.,<span class="_ _8"> </span>a<span class="_ _8"> </span>P<span class="_ _2"></span>A<span class="_ _b"> </span>or<span class="_ _8"> </span>a<span class="_ _8"> </span>predistorter)<span class="_ _8"> </span>and<span class="_ _b"> </span>by</div><div class="t m0 x10 h7 y63 ff1 fs4 fc0 sc0 ls1 ws0">the<span class="_ _8"> </span>corresponding</div><div class="t m0 xa h7 y64 ff1 fs4 fc0 sc0 ls1 ws0">passband<span class="_"> </span>output.<span class="_ _e"> </span>If<span class="_ _c"> </span>the<span class="_ _e"> </span>nonlinear<span class="_"> </span>system<span class="_ _e"> </span>obeys<span class="_"> </span>the<span class="_ _e"> </span>polynomial</div><div class="t m0 xa h7 y65 ff1 fs4 fc0 sc0 ls1 ws0">model</div><div class="t m0 x11 h7 y66 ff1 fs4 fc0 sc0 ls1 ws0">(1)</div><div class="t m0 x12 h9 y67 ff1 fs5 fc0 sc0 ls1 ws0">0018-9545/04$20.00<span class="_ _12"> </span>&#169;<span class="_ _12"> </span>2004<span class="_ _12"> </span>IEEE</div><div class="t m0 x13 hb y68 ff5 fs7 fc0 sc0 ls1 ws0">Authorized licensed use limited to: National Huaqiao University. Downloaded on August 05,2020 at 08:01:19 UTC from IEEE Xplore. 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