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MIMO通信系统的检测算法,PDA算法,是算法研究的热点!
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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/625cc8fbbe9ad24cfa66049a/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/625cc8fbbe9ad24cfa66049a/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">IEEE<span class="_ _0"> </span>COMMUNICA<span class="_ _1"></span>TION<span class="_"> </span>LETTERS,<span class="_ _0"> </span>VOL.<span class="_"> </span>5,<span class="_ _0"> </span>NO.<span class="_"> </span>9,<span class="_ _0"> </span>SEPTEMBER<span class="_ _0"> </span>2001<span class="_ _2"> </span>361</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls0 ws0">Near-Optimal<span class="_ _3"> </span>Multiuser<span class="_ _3"> </span>Detection<span class="_ _3"> </span>in<span class="_ _3"> </span>Synchronous</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls0 ws0">CDMA<span class="_"> </span>Using<span class="_ _3"> </span>Probabilistic<span class="_"> </span>Data<span class="_"> </span>Association</div><div class="t m0 x4 h4 y4 ff1 fs2 fc0 sc0 ls0 ws0">J.<span class="_ _4"> </span>Luo<span class="ff2">,<span class="_ _4"> </span>Student<span class="_ _4"> </span>Member<span class="_ _5"></span>,<span class="_ _4"> </span>IEEE<span class="ff1">,<span class="_ _4"> </span>K.<span class="_ _4"> </span>R.<span class="_ _4"> </span>Pattipati</span>,<span class="_ _4"> </span>F<span class="_ _5"></span>ellow<span class="_ _1"></span>,<span class="_ _6"> </span>IEEE<span class="ff1">,<span class="_ _4"> </span>P<span class="_ _5"></span>.<span class="_ _4"> </span>K.<span class="_ _4"> </span>W<span class="_ _7"></span>illett<span class="ff2">,<span class="_ _4"> </span>Senior<span class="_ _4"> </span>Member<span class="_ _5"></span>,<span class="_ _4"> </span>IEEE<span class="ff1">,<span class="_ _4"> </span>and</span></span></span></span></div><div class="t m0 x5 h4 y5 ff1 fs2 fc0 sc0 ls1 ws0">F<span class="_ _5"></span>.<span class="_ _4"> </span>Hasegaw<span class="_ _7"></span>a<span class="_ _8"></span><span class="ff2 ls0">,<span class="_ _4"> </span>Member<span class="_ _5"></span>,<span class="_ _9"> </span>IEEE</span></div><div class="t m0 x2 h5 y6 ff3 fs3 fc0 sc0 ls0 ws0">Abstract&#8212;<span class="ff4">A<span class="_ _6"> </span>Probabilistic<span class="_ _6"> </span>Data<span class="_ _6"> </span>Association<span class="_ _a"> </span>(PD<span class="_ _7"></span>A)<span class="_ _a"> </span>method<span class="_ _6"> </span>is</span></div><div class="t m0 x1 h5 y7 ff4 fs3 fc0 sc0 ls0 ws0">proposed<span class="_ _9"> </span>in<span class="_ _4"> </span>this<span class="_ _4"> </span>letter<span class="_ _9"> </span>for<span class="_ _9"> </span>multiuser<span class="_ _4"> </span>detection<span class="_ _4"> </span>over<span class="_ _9"> </span>synchronous</div><div class="t m0 x1 h5 y8 ff4 fs3 fc0 sc0 ls0 ws0">code-division<span class="_ _b"> </span>multiple-access<span class="_ _b"> </span>(CDMA)<span class="_ _b"> </span>communication<span class="_ _c"> </span>chan-</div><div class="t m0 x1 h5 y9 ff4 fs3 fc0 sc0 ls0 ws0">nels.<span class="_ _4"> </span>PDA<span class="_ _4"> </span>models<span class="_ _6"> </span>the<span class="_ _4"> </span>undecided<span class="_ _6"> </span>user<span class="_ _4"> </span>signals<span class="_ _6"> </span>as<span class="_ _6"> </span>binary<span class="_ _4"> </span>random</div><div class="t m0 x1 h5 ya ff4 fs3 fc0 sc0 ls0 ws0">variables.<span class="_ _4"> </span>By<span class="_ _4"> </span>approximating<span class="_ _9"> </span>the<span class="_ _6"> </span>inter-user<span class="_ _4"> </span>interference<span class="_ _9"> </span>(IUI)<span class="_ _6"> </span>as</div><div class="t m0 x1 h5 yb ff4 fs3 fc0 sc0 ls0 ws0">Gaussian<span class="_"> </span>noise<span class="_ _d"> </span>with<span class="_"> </span>an<span class="_ _d"> </span>appropriately<span class="_"> </span>elevated<span class="_"> </span>cov<span class="_ _7"></span>ariance<span class="_ _d"> </span>matrix,</div><div class="t m0 x1 h5 yc ff4 fs3 fc0 sc0 ls0 ws0">the<span class="_ _e"> </span>probability<span class="_ _e"> </span>associated<span class="_ _e"> </span>with<span class="_ _e"> </span>each<span class="_ _e"> </span>user<span class="_ _e"> </span>signal<span class="_ _e"> </span>is<span class="_ _e"> </span>iterati<span class="_ _7"></span>vely</div><div class="t m0 x1 h5 yd ff4 fs3 fc0 sc0 ls0 ws0">updated.<span class="_"> </span>Computer<span class="_"> </span>simulations<span class="_"> </span>show<span class="_"> </span>that<span class="_"> </span>the<span class="_"> </span>system<span class="_"> </span>usually<span class="_"> </span>con-</div><div class="t m0 x1 h5 ye ff4 fs3 fc0 sc0 ls0 ws0">verges<span class="_ _0"> </span>within<span class="_ _f"> </span>three<span class="_ _f"> </span>to<span class="_"> </span>f<span class="_ _7"></span>our<span class="_ _f"> </span>iterations,<span class="_"> </span>and<span class="_ _f"> </span>the<span class="_"> </span>r<span class="_ _7"></span>esulting<span class="_"> </span>pr<span class="_ _7"></span>obability</div><div class="t m0 x1 h5 yf ff4 fs3 fc0 sc0 ls0 ws0">of<span class="_ _9"> </span>error<span class="_ _9"> </span>is<span class="_ _9"> </span>very<span class="_ _9"> </span>close<span class="_ _9"> </span>to<span class="_ _9"> </span>that<span class="_ _9"> </span>of<span class="_ _9"> </span>the<span class="_ _9"> </span>optimal<span class="_ _4"> </span>maximum-likelihood</div><div class="t m0 x1 h5 y10 ff4 fs3 fc0 sc0 ls0 ws0">(ML)<span class="_ _10"> </span>detector<span class="_ _5"></span>.<span class="_ _3"> </span>Further<span class="_ _10"> </span>modif<span class="_ _7"></span>ications<span class="_ _10"> </span>are<span class="_ _10"> </span>also<span class="_ _10"> </span>presented<span class="_ _10"> </span>to</div><div class="t m0 x1 h5 y11 ff4 fs3 fc0 sc0 ls0 ws0">significantly<span class="_"> </span>reduce<span class="_"> </span>the<span class="_"> </span>computational<span class="_ _d"> </span>cost.</div><div class="t m0 x6 h5 y12 ff3 fs3 fc0 sc0 ls0 ws0">Index<span class="_ _6"> </span>T<span class="_ _1"></span>erms&#8212;<span class="ff4">Code<span class="_ _6"> </span>division<span class="_ _6"> </span>multiple<span class="_ _6"> </span>access,<span class="_ _a"> </span>multiuser<span class="_ _6"> </span>detec-</span></div><div class="t m0 x1 h5 y13 ff4 fs3 fc0 sc0 ls0 ws0">tion,<span class="_ _d"> </span>pr<span class="_ _7"></span>obabilistic<span class="_ _d"> </span>data<span class="_ _d"> </span>association.</div><div class="t m0 x7 h6 y14 ff1 fs4 fc0 sc0 ls0 ws0">I.<span class="_ _e"> </span>I<span class="fs5">NTR<span class="_ _7"></span>ODUCTION</span></div><div class="t m0 x1 h7 y15 ff4 fs6 fc0 sc0 ls0 ws0">T</div><div class="t m0 x8 h6 y16 ff1 fs4 fc0 sc0 ls0 ws0">HE<span class="_ _11"> </span>MUL<span class="_ _5"></span>TIUSER<span class="_ _11"> </span>detection<span class="_ _11"> </span>(MUD)<span class="_ _11"> </span>problem<span class="_ _10"> </span>in<span class="_ _11"> </span>syn-</div><div class="t m0 x8 h6 y17 ff1 fs4 fc0 sc0 ls0 ws0">chronous<span class="_ _12"> </span>code-division<span class="_ _12"> </span>multiple-access<span class="_ _12"> </span>(CDMA)</div><div class="t m0 x1 h6 y18 ff1 fs4 fc0 sc0 ls0 ws0">communication<span class="_ _13"> </span>systems<span class="_ _13"> </span>has<span class="_ _13"> </span>been<span class="_ _13"> </span>widely<span class="_ _13"> </span>studied<span class="_ _13"> </span>in<span class="_ _13"> </span>the<span class="_ _13"> </span>past</div><div class="t m0 x1 h6 y19 ff1 fs4 fc0 sc0 ls0 ws0">decade.<span class="_ _6"> </span>Since<span class="_ _a"> </span>the<span class="_ _a"> </span>computation<span class="_ _a"> </span>of<span class="_ _a"> </span>an<span class="_ _6"> </span>optimal<span class="_ _a"> </span>maximum-like-</div><div class="t m0 x1 h6 y1a ff1 fs4 fc0 sc0 ls0 ws0">lihood<span class="_ _13"> </span>(ML)<span class="_ _a"> </span>detector<span class="_ _13"> </span>is<span class="_ _13"> </span>exponential<span class="_ _a"> </span>in<span class="_ _13"> </span>the<span class="_ _13"> </span>number<span class="_ _13"> </span>of<span class="_ _13"> </span>users,</div><div class="t m0 x1 h6 y1b ff1 fs4 fc0 sc0 ls0 ws0">suboptimal<span class="_"> </span>solutions<span class="_"> </span>are<span class="_"> </span>proposed<span class="_"> </span>to<span class="_"> </span>pro<span class="_ _7"></span>vide<span class="_"> </span>reliable<span class="_"> </span>decisions</div><div class="t m0 x1 h6 y1c ff1 fs4 fc0 sc0 ls0 ws0">with<span class="_ _a"> </span>relativ<span class="_ _7"></span>ely<span class="_ _a"> </span>low<span class="_ _a"> </span>computational<span class="_ _a"> </span>cost.<span class="_ _a"> </span>Among<span class="_ _13"> </span>them<span class="_ _a"> </span>are<span class="_ _a"> </span>the</div><div class="t m0 x1 h6 y1d ff1 fs4 fc0 sc0 ls0 ws0">con<span class="_ _7"></span>ventional<span class="_ _a"> </span>decorrelator<span class="_ _13"> </span>[1],<span class="_ _a"> </span>the<span class="_ _13"> </span>decision<span class="_ _13"> </span>feedback<span class="_ _a"> </span>detector</div><div class="t m0 x1 h6 y1e ff1 fs4 fc0 sc0 ls0 ws0">(DFD)<span class="_ _14"> </span>[3],<span class="_ _14"> </span>[6],<span class="_ _14"> </span>the<span class="_ _14"> </span>multistage<span class="_ _14"> </span>detector<span class="_ _14"> </span>[2]<span class="_ _14"> </span>and<span class="_ _14"> </span>the<span class="_ _14"> </span>group</div><div class="t m0 x1 h6 y1f ff1 fs4 fc0 sc0 ls0 ws0">detector<span class="_ _a"> </span>[5],<span class="_ _a"> </span>[8].<span class="_ _a"> </span>Although<span class="_ _a"> </span>DFD<span class="_ _13"> </span>is<span class="_ _a"> </span>one<span class="_ _a"> </span>of<span class="_ _a"> </span>the<span class="_ _13"> </span>most<span class="_ _a"> </span>eff<span class="_ _7"></span>icient</div><div class="t m0 x1 h6 y20 ff1 fs4 fc0 sc0 ls0 ws0">methods,<span class="_"> </span>in<span class="_ _0"> </span>most<span class="_"> </span>cases<span class="_"> </span>the<span class="_"> </span>g<span class="_ _7"></span>ap<span class="_"> </span>between<span class="_"> </span>the<span class="_ _0"> </span>probability<span class="_"> </span>of<span class="_"> </span>error</div><div class="t m0 x1 h6 y21 ff1 fs4 fc0 sc0 ls0 ws0">of<span class="_ _4"> </span>the<span class="_ _9"> </span>DFD<span class="_ _4"> </span>and<span class="_ _4"> </span>that<span class="_ _4"> </span>of<span class="_ _9"> </span>a<span class="_ _4"> </span>ML<span class="_ _4"> </span>detector<span class="_ _4"> </span>is<span class="_ _4"> </span>still<span class="_ _9"> </span>large.<span class="_ _4"> </span>The<span class="_ _9"> </span>DFD</div><div class="t m0 x1 h6 y22 ff1 fs4 fc0 sc0 ls0 ws0">can<span class="_"> </span>be<span class="_ _d"> </span>considered<span class="_ _9"> </span>a<span class="_"> </span>special<span class="_"> </span>case<span class="_ _9"> </span>of<span class="_"> </span>a<span class="_"> </span>group<span class="_ _d"> </span>detector<span class="_ _9"> </span>with<span class="_"> </span>unity</div><div class="t m0 x1 h6 y23 ff1 fs4 fc0 sc0 ls0 ws0">maximum<span class="_ _4"> </span>group<span class="_ _4"> </span>size,<span class="_ _6"> </span>and<span class="_ _4"> </span>the<span class="_ _4"> </span>performance<span class="_ _6"> </span>gap<span class="_ _4"> </span>becomes<span class="_ _4"> </span>nar-</div><div class="t m0 x1 h6 y24 ff1 fs4 fc0 sc0 ls0 ws0">rower<span class="_"> </span>as<span class="_ _9"> </span>this<span class="_ _9"> </span>is<span class="_ _9"> </span>increased.<span class="_ _9"> </span>Ho<span class="_ _7"></span>wever<span class="_ _1"></span>,<span class="_ _9"> </span>despite<span class="_ _9"> </span>the<span class="_ _9"> </span>impro<span class="_ _7"></span>vements</div><div class="t m0 x1 h6 y25 ff1 fs4 fc0 sc0 ls0 ws0">described<span class="_"> </span>in<span class="_ _0"> </span>[8],<span class="_"> </span>finding<span class="_ _0"> </span>the<span class="_"> </span>optimal<span class="_ _0"> </span>group<span class="_"> </span>assignment<span class="_"> </span>and<span class="_ _0"> </span>user</div><div class="t m0 x1 h6 y26 ff1 fs4 fc0 sc0 ls0 ws0">ordering<span class="_ _9"> </span>remains<span class="_"> </span>expensiv<span class="_ _7"></span>e.</div><div class="t m0 x9 h6 y27 ff1 fs4 fc0 sc0 ls0 ws0">The<span class="_"> </span>probabilistic<span class="_"> </span>data<span class="_ _0"> </span>association<span class="_"> </span>(PD<span class="_ _7"></span>A)<span class="_"> </span>filter<span class="_ _0"> </span>[4]<span class="_"> </span>is<span class="_"> </span>a<span class="_"> </span>highly</div><div class="t m0 x1 h6 y28 ff1 fs4 fc0 sc0 ls0 ws0">successful<span class="_"> </span>approach<span class="_"> </span>to<span class="_"> </span>target<span class="_ _0"> </span>tracking<span class="_"> </span>in<span class="_"> </span>the<span class="_"> </span>case<span class="_"> </span>that<span class="_"> </span>measure-</div><div class="t m0 x1 h6 y29 ff1 fs4 fc0 sc0 ls0 ws0">ments<span class="_ _4"> </span>are<span class="_ _4"> </span>unlabeled<span class="_ _9"> </span>and<span class="_ _4"> </span>may<span class="_ _4"> </span>be<span class="_ _4"> </span>spurious.<span class="_ _4"> </span>Its<span class="_ _4"> </span>key<span class="_ _9"> </span>feature<span class="_ _4"> </span>is<span class="_ _4"> </span>a</div><div class="t m0 x1 h6 y2a ff1 fs4 fc0 sc0 ls0 ws0">repeated<span class="_ _9"> </span>con<span class="_ _7"></span>version<span class="_ _9"> </span>of<span class="_ _4"> </span>a<span class="_ _9"> </span>multimodal<span class="_ _9"> </span>Gaussian<span class="_ _4"> </span>mixture<span class="_ _9"> </span>proba-</div><div class="t m0 x1 h6 y2b ff1 fs4 fc0 sc0 ls0 ws0">bility<span class="_"> </span>structure<span class="_ _0"> </span>to<span class="_"> </span>a<span class="_ _0"> </span>single<span class="_"> </span>Gaussian<span class="_ _0"> </span>with<span class="_"> </span>matched<span class="_ _0"> </span>mean<span class="_"> </span>and<span class="_ _0"> </span>co-</div><div class="t m0 x1 h6 y2c ff1 fs4 fc0 sc0 ls0 ws0">variance.<span class="_ _9"> </span>This<span class="_ _4"> </span>is<span class="_ _4"> </span>a<span class="_ _4"> </span>bold<span class="_ _4"> </span>and<span class="_ _4"> </span>to<span class="_ _4"> </span>some<span class="_ _9"> </span>extent<span class="_ _4"> </span>unjustifiable<span class="_ _9"> </span>step,</div><div class="t m0 xa h8 y2d ff1 fs5 fc0 sc0 ls0 ws0">Manuscript<span class="_ _d"> </span>recei<span class="_ _7"></span>ved<span class="_ _d"> </span>March<span class="_"> </span>30,<span class="_ _d"> </span>2001.<span class="_ _d"> </span>The<span class="_"> </span>associate<span class="_ _d"> </span>editor<span class="_ _d"> </span>coordinating<span class="_"> </span>the</div><div class="t m0 x1 h8 y2e ff1 fs5 fc0 sc0 ls0 ws0">revie<span class="_ _7"></span>w<span class="_ _4"> </span>of<span class="_ _4"> </span>this<span class="_ _9"> </span>letter<span class="_ _4"> </span>and<span class="_ _4"> </span>approving<span class="_ _9"> </span>it<span class="_ _4"> </span>for<span class="_ _4"> </span>publication<span class="_ _4"> </span>was<span class="_ _4"> </span>Prof.<span class="_ _4"> </span>S.<span class="_ _9"> </span>W<span class="_ _1"></span>.<span class="_ _4"> </span>Kim.</div><div class="t m0 x1 h8 y2f ff1 fs5 fc0 sc0 ls0 ws0">This<span class="_ _6"> </span>work<span class="_ _4"> </span>was<span class="_ _6"> </span>supported<span class="_ _4"> </span>by<span class="_ _6"> </span>the<span class="_ _6"> </span>Office<span class="_ _4"> </span>of<span class="_ _4"> </span>Naval<span class="_ _4"> </span>Research<span class="_ _6"> </span>under<span class="_ _6"> </span>Contract</div><div class="t m0 x1 h8 y30 ff1 fs5 fc0 sc0 ls0 ws0">N00014-98-1-0465,<span class="_ _11"> </span>N00014-00-1-0101,<span class="_ _14"> </span>and<span class="_ _11"> </span>by<span class="_ _11"> </span>NUWC<span class="_ _11"> </span>under<span class="_ _14"> </span>Contract</div><div class="t m0 x1 h8 y31 ff1 fs5 fc0 sc0 ls0 ws0">N66604-01-1-1125.</div><div class="t m0 xa h8 y32 ff1 fs5 fc0 sc0 ls0 ws0">The<span class="_ _14"> </span>authors<span class="_ _14"> </span>are<span class="_ _14"> </span>with<span class="_ _15"> </span>the<span class="_ _15"> </span>Electrical<span class="_ _14"> </span>and<span class="_ _14"> </span>Computer<span class="_ _14"> </span>Engineering<span class="_ _15"> </span>De-</div><div class="t m0 x1 h8 y33 ff1 fs5 fc0 sc0 ls0 ws0">partment,<span class="_ _11"> </span>University<span class="_ _11"> </span>of<span class="_ _11"> </span>Connecticut,<span class="_ _11"> </span>Storrs,<span class="_ _10"> </span>CT<span class="_ _11"> </span>06269<span class="_ _11"> </span>USA<span class="_ _10"> </span>(e-mail:</div><div class="t m0 x1 h8 y34 ff1 fs5 fc0 sc0 ls0 ws0">krishna@engr<span class="_ _7"></span>.uconn.edu).</div><div class="t m0 xa h8 y35 ff1 fs5 fc0 sc0 ls0 ws0">Publisher<span class="_"> </span>Item<span class="_ _16"> </span>Identifier<span class="_"> </span>S<span class="_"> </span>1089-7798(01)06463-8.</div><div class="t m0 xb h6 y6 ff1 fs4 fc0 sc0 ls0 ws0">but<span class="_"> </span>it<span class="_"> </span>is<span class="_"> </span>dif<span class="_ _7"></span>ficult<span class="_"> </span>to<span class="_"> </span>ar<span class="_ _7"></span>gue<span class="_"> </span>with<span class="_"> </span>good<span class="_"> </span>performance<span class="_"> </span>and<span class="_"> </span>low<span class="_"> </span>com-</div><div class="t m0 xb h6 y36 ff1 fs4 fc0 sc0 ls0 ws0">plexity<span class="_ _1"></span>.<span class="_"> </span>No<span class="_ _7"></span>w<span class="_ _1"></span>,<span class="_"> </span>in<span class="_ _0"> </span>the<span class="_"> </span>CDMA<span class="_ _0"> </span>case<span class="_"> </span>the<span class="_ _0"> </span>true<span class="_"> </span>probability<span class="_ _0"> </span>function<span class="_"> </span>is</div><div class="t m0 xb h6 y37 ff1 fs4 fc0 sc0 ls0 ws0">also<span class="_ _9"> </span>a<span class="_ _9"> </span>Gaussian<span class="_ _4"> </span>mixture,<span class="_ _9"> </span>and<span class="_ _9"> </span>complexity<span class="_ _9"> </span>is<span class="_ _9"> </span>also<span class="_ _4"> </span>the<span class="_ _9"> </span>issue.<span class="_ _9"> </span>W<span class="_ _1"></span>e</div><div class="t m0 xb h6 y38 ff1 fs4 fc0 sc0 ls0 ws0">thus<span class="_ _9"> </span>propose<span class="_ _9"> </span>to<span class="_ _9"> </span>apply<span class="_ _9"> </span>the<span class="_ _9"> </span>Gaussian<span class="_ _9"> </span>&#8220;forcing&#8221;<span class="_ _d"> </span>idea;<span class="_ _9"> </span>whereas<span class="_ _9"> </span>in</div><div class="t m0 xb h6 y39 ff1 fs4 fc0 sc0 ls0 ws0">the<span class="_ _9"> </span>tracking<span class="_ _4"> </span>application<span class="_ _4"> </span>this<span class="_ _4"> </span>forcing<span class="_ _9"> </span>occurs<span class="_ _4"> </span>once<span class="_ _4"> </span>per<span class="_ _9"> </span>scan<span class="_ _4"> </span>and</div><div class="t m0 xb h6 y3a ff1 fs4 fc0 sc0 ls0 ws0">there<span class="_ _0"> </span>is<span class="_"> </span>no<span class="_ _0"> </span>revisit,<span class="_ _0"> </span>in<span class="_"> </span>CDMA<span class="_ _0"> </span>it<span class="_ _0"> </span>occurs<span class="_"> </span>for<span class="_ _0"> </span>each<span class="_"> </span>user<span class="_ _7"></span>,<span class="_ _0"> </span>and<span class="_"> </span>there<span class="_ _0"> </span>is</div><div class="t m0 xb h6 y3b ff1 fs4 fc0 sc0 ls0 ws0">iteration.<span class="_"> </span>Instead<span class="_ _0"> </span>of<span class="_"> </span>f<span class="_ _7"></span>ixing<span class="_"> </span>the<span class="_ _0"> </span>binary<span class="_"> </span>signal<span class="_"> </span>v<span class="_ _7"></span>ariables<span class="_"> </span>at</div><div class="t m0 xc h6 y3c ff1 fs4 fc0 sc0 ls0 ws0">1,<span class="_"> </span>the</div><div class="t m0 xb h6 y3d ff1 fs4 fc0 sc0 ls0 ws0">PD<span class="_ _7"></span>A<span class="_ _9"> </span>employs<span class="_"> </span>a<span class="_ _9"> </span>soft<span class="_ _d"> </span>IUI<span class="_ _9"> </span>cancellation<span class="_ _9"> </span>by<span class="_"> </span>increasing<span class="_ _9"> </span>the<span class="_ _9"> </span>cov<span class="_ _7"></span>ari-</div><div class="t m0 xb h6 y3e ff1 fs4 fc0 sc0 ls0 ws0">ance<span class="_"> </span>of<span class="_"> </span>the<span class="_"> </span>ef<span class="_ _7"></span>fective<span class="_ _0"> </span>noise<span class="_"> </span>based<span class="_"> </span>on<span class="_"> </span>the<span class="_"> </span>uncertainty<span class="_"> </span>in<span class="_"> </span>the<span class="_"> </span>other</div><div class="t m0 xb h6 y3f ff1 fs4 fc0 sc0 ls0 ws0">user<span class="_ _a"> </span>signals.<span class="_ _a"> </span>When<span class="_ _13"> </span>the<span class="_ _a"> </span>binary<span class="_ _a"> </span>variables<span class="_ _a"> </span>con<span class="_ _7"></span>verge<span class="_ _6"> </span>to<span class="_ _13"> </span>the<span class="_ _a"> </span>true</div><div class="t m0 xb h6 y40 ff1 fs4 fc0 sc0 ls0 ws0">value,<span class="_ _9"> </span>the<span class="_ _4"> </span>cov<span class="_ _7"></span>ariance<span class="_ _4"> </span>approaches<span class="_ _4"> </span>to<span class="_ _4"> </span>that<span class="_ _4"> </span>of<span class="_ _4"> </span>the<span class="_ _4"> </span>original<span class="_ _4"> </span>noise.</div><div class="t m0 xb h6 y41 ff1 fs4 fc0 sc0 ls0 ws0">This,<span class="_ _0"> </span>we<span class="_ _0"> </span>believe,<span class="_ _f"> </span>helps<span class="_"> </span>PD<span class="_ _1"></span>A<span class="_"> </span>a<span class="_ _7"></span>void<span class="_ _0"> </span>local<span class="_ _0"> </span>minima.<span class="_ _0"> </span>Simulation<span class="_"> </span>re-</div><div class="t m0 xb h6 y42 ff1 fs4 fc0 sc0 ls0 ws0">sults<span class="_ _6"> </span>show<span class="_ _4"> </span>that<span class="_ _a"> </span>the<span class="_ _6"> </span>PD<span class="_ _7"></span>A<span class="_ _6"> </span>detector<span class="_ _a"> </span>giv<span class="_ _7"></span>es<span class="_ _6"> </span>a<span class="_ _a"> </span>probability<span class="_ _6"> </span>of<span class="_ _6"> </span>error</div><div class="t m0 xb h6 y43 ff1 fs4 fc0 sc0 ls0 ws0">very<span class="_ _4"> </span>close<span class="_ _4"> </span>to<span class="_ _4"> </span>and<span class="_ _6"> </span>often<span class="_ _4"> </span>indistinguishable<span class="_ _4"> </span>from<span class="_ _6"> </span>that<span class="_ _4"> </span>of<span class="_ _6"> </span>the<span class="_ _4"> </span>op-</div><div class="t m0 xb h6 y44 ff1 fs4 fc0 sc0 ls0 ws0">timal<span class="_ _4"> </span>ML<span class="_ _4"> </span>detector<span class="_ _7"></span>.<span class="_ _4"> </span>Simulations<span class="_ _6"> </span>also<span class="_ _4"> </span>show<span class="_ _4"> </span>that<span class="_ _4"> </span>the<span class="_ _6"> </span>worst<span class="_ _4"> </span>case</div><div class="t m0 xb h6 y45 ff1 fs4 fc0 sc0 ls0 ws0">computational<span class="_ _9"> </span>cost<span class="_ _d"> </span>of<span class="_ _9"> </span>the<span class="_ _9"> </span>PD<span class="_ _7"></span>A<span class="_ _9"> </span>method<span class="_ _9"> </span>is</div><div class="t m0 xd h6 y46 ff1 fs4 fc0 sc0 ls0 ws0">,<span class="_ _9"> </span>where<span class="_ _17"> </span>is</div><div class="t m0 xb h6 y47 ff1 fs4 fc0 sc0 ls0 ws0">the<span class="_ _9"> </span>number<span class="_ _d"> </span>of<span class="_ _9"> </span>users.</div><div class="t m0 xe h6 y48 ff1 fs4 fc0 sc0 ls0 ws0">II.<span class="_ _e"> </span>T</div><div class="t m0 xf h6 y49 ff1 fs5 fc0 sc0 ls0 ws0">HE<span class="_ _d"> </span><span class="fs4">M</span>UL<span class="_ _1"></span>TIST<span class="_ _7"></span>A<span class="_ _7"></span>GE<span class="_ _d"> </span><span class="fs4">PDA<span class="_"> </span>D</span>ETECTOR</div><div class="t m0 xb h9 y4a ff2 fs4 fc0 sc0 ls0 ws0">A.<span class="_ _e"> </span>Pr<span class="_ _7"></span>oblem<span class="_ _9"> </span>F<span class="_ _5"></span>ormulation</div><div class="t m0 x10 h6 y4b ff1 fs4 fc0 sc0 ls0 ws0">A<span class="_ _4"> </span>discrete-time<span class="_ _6"> </span>model<span class="_ _6"> </span>for<span class="_ _6"> </span>the<span class="_ _6"> </span>matched-filter<span class="_ _4"> </span>outputs<span class="_ _4"> </span>at<span class="_ _6"> </span>the</div><div class="t m0 xb h6 y4c ff1 fs4 fc0 sc0 ls0 ws0">receiv<span class="_ _7"></span>er<span class="_ _0"> </span>of<span class="_ _f"> </span>a<span class="_ _0"> </span>CDMA<span class="_ _0"> </span>channel<span class="_ _f"> </span>is<span class="_ _0"> </span>given<span class="_ _f"> </span>by<span class="_ _f"> </span>the</div><div class="t m0 x11 h6 y4d ff1 fs4 fc0 sc0 ls0 ws0">-length<span class="_ _f"> </span>vector<span class="_ _0"> </span>[1]</div><div class="t m0 x12 h6 y4e ff1 fs4 fc0 sc0 ls0 ws0">(1)</div><div class="t m0 xb h6 y4f ff1 fs4 fc0 sc0 ls0 ws0">where</div><div class="t m0 x13 h6 y50 ff1 fs4 fc0 sc0 ls0 ws0">denotes<span class="_ _a"> </span>the<span class="_ _12"> </span>-length<span class="_ _6"> </span>vector<span class="_ _a"> </span>of<span class="_ _a"> </span>bits</div><div class="t m0 xb h6 y51 ff1 fs4 fc0 sc0 ls0 ws0">transmitted<span class="_ _d"> </span>by<span class="_ _9"> </span>the</div><div class="t m0 x14 h6 y52 ff1 fs4 fc0 sc0 ls0 ws0">activ<span class="_ _7"></span>e<span class="_ _9"> </span>users;<span class="_ _12"> </span>is<span class="_"> </span>the<span class="_ _9"> </span>symmetric<span class="_ _d"> </span>normal-</div><div class="t m0 xb h6 y53 ff1 fs4 fc0 sc0 ls0 ws0">ized<span class="_ _9"> </span>signature<span class="_ _4"> </span>correlation<span class="_ _4"> </span>matrix<span class="_ _4"> </span>with<span class="_ _4"> </span>unit<span class="_ _4"> </span>diagonal<span class="_ _4"> </span>elements;</div><div class="t m0 xb h6 y54 ff1 fs4 fc0 sc0 ls0 ws0">and</div><div class="t m0 x15 h6 y55 ff1 fs4 fc0 sc0 ls0 ws0">is<span class="_ _4"> </span>a<span class="_ _6"> </span>diagonal<span class="_ _6"> </span>matrix<span class="_ _4"> </span>whose<span class="_ _6"> </span>diagonal<span class="_ _4"> </span>elements<span class="_ _6"> </span>are<span class="_ _6"> </span>the</div><div class="t m0 xb h6 y56 ff1 fs4 fc0 sc0 ls0 ws0">signal<span class="_ _9"> </span>amplitudes<span class="_ _9"> </span>of<span class="_ _9"> </span>the<span class="_ _4"> </span>corresponding<span class="_ _9"> </span>users.<span class="_ _9"> </span>Here</div><div class="t m0 x16 h6 y57 ff1 fs4 fc0 sc0 ls0 ws0">is<span class="_ _9"> </span>a<span class="_ _9"> </span>col-</div><div class="t m0 xb h6 y58 ff1 fs4 fc0 sc0 ls0 ws0">ored<span class="_"> </span>Gaussian<span class="_"> </span>noise<span class="_"> </span>v<span class="_ _7"></span>ector<span class="_"> </span>with<span class="_"> </span>zero<span class="_"> </span>mean<span class="_"> </span>and<span class="_"> </span>cov<span class="_ _7"></span>ariance<span class="_"> </span>ma-</div><div class="t m0 xb h6 y59 ff1 fs4 fc0 sc0 ls0 ws0">trix</div><div class="t m0 x17 h6 y5a ff1 fs4 fc0 sc0 ls0 ws0">,<span class="_ _9"> </span>where<span class="_ _18"> </span>is<span class="_ _d"> </span>the<span class="_ _9"> </span>power<span class="_"> </span>of<span class="_ _d"> </span>the<span class="_ _9"> </span>white<span class="_ _9"> </span>noise</div><div class="t m0 xb h6 y5b ff1 fs4 fc0 sc0 ls0 ws0">before<span class="_ _9"> </span>the<span class="_"> </span>matched<span class="_ _9"> </span>filter<span class="_ _1"></span>.</div><div class="t m0 x10 h6 y5c ff1 fs4 fc0 sc0 ls0 ws0">When<span class="_ _9"> </span>all<span class="_ _4"> </span>the<span class="_ _4"> </span>user<span class="_ _4"> </span>signals<span class="_ _4"> </span>are<span class="_ _4"> </span>equally<span class="_ _9"> </span>probable,<span class="_ _4"> </span>the<span class="_ _4"> </span>optimal</div><div class="t m0 xb h6 y5d ff1 fs4 fc0 sc0 ls0 ws0">solution<span class="_"> </span>of<span class="_ _d"> </span>(1)<span class="_ _d"> </span>is<span class="_ _d"> </span>the<span class="_ _9"> </span>output<span class="_"> </span>of<span class="_"> </span>a<span class="_ _d"> </span>ML<span class="_ _d"> </span>detector<span class="_ _9"> </span>[1]</div><div class="t m0 x12 h6 y5e ff1 fs4 fc0 sc0 ls0 ws0">(2)</div><div class="t m0 xb h6 y5f ff1 fs4 fc0 sc0 ls0 ws0">It<span class="_ _0"> </span>is<span class="_ _f"> </span>known<span class="_ _f"> </span>that<span class="_ _0"> </span>obtaining<span class="_ _0"> </span>the<span class="_ _0"> </span>ML<span class="_ _0"> </span>solution<span class="_ _0"> </span>is<span class="_ _0"> </span>generally<span class="_ _0"> </span>NP-hard<span class="_ _0"> </span>[1],</div><div class="t m0 xb h6 y60 ff1 fs4 fc0 sc0 ls0 ws0">unless<span class="_ _f"> </span>the<span class="_ _0"> </span>signature<span class="_ _0"> </span>correlation<span class="_ _0"> </span>matrix<span class="_ _0"> </span>has<span class="_ _0"> </span>a<span class="_ _0"> </span>special<span class="_ _0"> </span>structure.</div><div class="t m0 x10 h6 y61 ff1 fs4 fc0 sc0 ls0 ws0">Multiplying<span class="_ _9"> </span>by</div><div class="t m0 x18 h6 y62 ff1 fs4 fc0 sc0 ls0 ws0">on<span class="_ _9"> </span>both<span class="_"> </span>sides<span class="_ _9"> </span>of<span class="_ _9"> </span>(1)<span class="_ _d"> </span>from<span class="_ _9"> </span>the<span class="_ _9"> </span>left,</div><div class="t m0 xb h6 y63 ff1 fs4 fc0 sc0 ls0 ws0">the<span class="_"> </span>system<span class="_ _9"> </span>model<span class="_"> </span>can<span class="_ _d"> </span>be<span class="_ _9"> </span>reformulated<span class="_"> </span>as</div><div class="t m0 x12 h6 y64 ff1 fs4 fc0 sc0 ls0 ws0">(3)</div><div class="t m0 xb h6 y65 ff1 fs4 fc0 sc0 ls0 ws0">where</div><div class="t m0 x19 h6 y66 ff1 fs4 fc0 sc0 ls0 ws0">and<span class="_ _19"> </span>.<span class="_ _9"> </span>The<span class="_ _4"> </span>variable</div><div class="t m0 xb h6 y67 ff1 fs4 fc0 sc0 ls0 ws0">represents<span class="_ _6"> </span>the<span class="_ _1a"> </span>th<span class="_ _6"> </span>element<span class="_ _a"> </span>of<span class="_ _a"> </span>vector<span class="_ _1b"> </span>;<span class="_ _1c"> </span>is<span class="_ _6"> </span>a<span class="_ _a"> </span>column<span class="_ _a"> </span>vector</div><div class="t m0 x1a h8 y68 ff1 fs5 fc0 sc0 ls0 ws0">1089&#8211;7798/01$10.00<span class="_ _16"> </span>&#169;<span class="_ _16"> </span>2001<span class="_ _16"> </span>IEEE</div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></div><div class="d m1"></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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