Direction Finding With MUSIC and CLEAN.rar

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  • 2021-03-02 22:00
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关于MUSIC算法中的参考文献,与CLEAN算法结合,可对不同强度信号区分有一定的指导意义。
Direction Finding With MUSIC and CLEAN.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/624f0a626caf596192b85f6c/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/624f0a626caf596192b85f6c/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">IEEE<span class="_ _0"> </span>TRANSACTIONS<span class="_ _0"> </span>ON<span class="_ _0"> </span>ANTENNAS<span class="_ _0"> </span>AND<span class="_ _0"> </span>PROP<span class="_ _1"></span>AGA<span class="_ _2"></span>TION,<span class="_ _0"> </span>VOL.<span class="_ _0"> </span>61,<span class="_ _0"> </span>NO.<span class="_ _0"> </span>7,<span class="_ _0"> </span>JUL<span class="_ _2"></span>Y<span class="_ _0"> </span>2013<span class="_ _3"> </span><span class="ls1">3839</span></div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls2 ws0">Direction<span class="_ _4"> </span>Finding<span class="_ _4"> </span>W<span class="_ _2"></span>i<span class="_ _1"></span>th<span class="_ _4"> </span>MUSIC<span class="_ _4"> </span>and<span class="_ _4"> </span>CLEAN</div><div class="t m0 x3 h4 y3 ff1 fs2 fc0 sc0 ls3 ws0">Greg<span class="_ _5"> </span>Hislop<span class="ff2 ls4">,M<span class="_ _6"></span>e<span class="_ _6"></span>m<span class="_ _6"></span>b<span class="_ _6"></span>e<span class="_ _6"></span>r<span class="_ _7"></span>,I<span class="_ _6"></span>E<span class="_ _6"></span>E<span class="_ _6"></span>E<span class="_ _6"></span><span class="ff1 ls5">,<span class="_ _8"> </span>Nida<span class="_ _5"> </span>Sak<span class="_ _1"></span>ar,<span class="_ _5"> </span>and<span class="_ _8"> </span>Christ<span class="_ _1"></span>ophe<span class="_ _5"> </span>Craeye<span class="ff2 ls3">,<span class="_ _5"> </span>Senior<span class="_ _9"> </span>Member<span class="_ _a"></span>,<span class="_ _9"> </span>IEEE</span></span></span></div><div class="t m0 x4 h5 y4 ff3 fs3 fc0 sc0 ls6 ws0">Abstract&#8212;<span class="ff4 ls7">The<span class="_ _b"> </span>well<span class="_ _b"> </span>known<span class="_ _c"> </span>MUSIC<span class="_ _b"> </span>algorithm<span class="_ _c"> </span>for<span class="_ _b"> </span>direc-</span></div><div class="t m0 x1 h5 y5 ff4 fs3 fc0 sc0 ls8 ws0">tion-<span class="ff5 ls1">&#64257;</span><span class="ls9">nding<span class="_ _9"> </span>is<span class="_ _9"> </span>improved<span class="_ _9"> </span>by<span class="_ _9"> </span>applying<span class="_ _9"> </span>the<span class="_ _9"> </span>CLEAN<span class="_ _9"> </span>post-processing</span></div><div class="t m0 x1 h5 y6 ff4 fs3 fc0 sc0 lsa ws0">method.<span class="_ _b"> </span>A<span class="_ _b"> </span>mathematical<span class="_ _b"> </span>explanation<span class="_ _b"> </span>for<span class="_ _b"> </span>the<span class="_ _d"> </span>performance</div><div class="t m0 x1 h5 y7 ff4 fs3 fc0 sc0 lsb ws0">improvement,<span class="_ _9"> </span>is<span class="_ _5"> </span>presented<span class="_ _9"> </span>along<span class="_ _5"> </span>w<span class="lsc">ith<span class="_ _5"> </span>both<span class="_ _9"> </span>synthetic<span class="_ _5"> </span>and<span class="_ _5"> </span>experi-</span></div><div class="t m0 x1 h5 y8 ff4 fs3 fc0 sc0 lsd ws0">mental<span class="_ _9"> </span>validations.</div><div class="t m0 x4 h5 y9 ff3 fs3 fc0 sc0 lse ws0">Index<span class="_ _0"> </span>T<span class="_ _2"></span>erms&#8212;<span class="ff4 lsf">Astronomy<span class="_ _2"></span>,<span class="_ _e"> </span>directi<span class="_ _1"></span>on<span class="_ _e"> </span>of<span class="_ _e"> </span>arrival<span class="_ _e"> </span>estimation,<span class="_ _0"> </span>signal</span></div><div class="t m0 x1 h5 ya ff4 fs3 fc0 sc0 ls10 ws0">proces<span class="_ _1"></span>sing,<span class="_ _9"> </span>signal<span class="_ _f"> </span>repr<span class="_ _1"></span>esentations.</div><div class="t m0 x5 h6 yb ff1 fs4 fc0 sc0 ls11 ws0">I.<span class="_ _10"> </span>I<span class="fs5 ls12">NTRODUCTION</span></div><div class="t m0 x1 h7 yc ff4 fs6 fc0 sc0 ls1 ws0">T</div><div class="t m0 x6 h6 yd ff1 fs4 fc0 sc0 ls13 ws0">HE<span class="_ _11"> </span>problem<span class="_ _11"> </span>of<span class="_ _11"> </span>localizing<span class="_ _11"> </span>radio<span class="_ _11"> </span>sources<span class="_ _11"> </span>with<span class="_ _11"> </span>a</div><div class="t m0 x6 h6 ye ff1 fs4 fc0 sc0 ls14 ws0">narrow-band<span class="_ _12"> </span>receiving<span class="_ _12"> </span>array<span class="_ _12"> </span>is<span class="_ _12"> </span>of<span class="_ _12"> </span>great<span class="_ _12"> </span>interest<span class="_ _12"> </span>to<span class="_ _12"> </span>a</div><div class="t m0 x1 h6 yf ff1 fs4 fc0 sc0 ls15 ws0">range<span class="_ _9"> </span>of<span class="_ _5"> </span>applications<span class="_ _5"> </span>including<span class="_ _9"> </span>pe<span class="ls16">ople<span class="_ _5"> </span>or<span class="_ _9"> </span>asset<span class="_ _5"> </span>tracking,<span class="_ _9"> </span>local-</span></div><div class="t m0 x1 h6 y10 ff1 fs4 fc0 sc0 ls17 ws0">ization<span class="_ _9"> </span>of<span class="_ _5"> </span>military<span class="_ _9"> </span>targets,<span class="_ _9"> </span>locating<span class="_ _5"> </span>buried<span class="_ _9"> </span>objects,<span class="_ _5"> </span>neutralizing</div><div class="t m0 x1 h6 y11 ff1 fs4 fc0 sc0 ls18 ws0">illegal<span class="_ _13"> </span>transmitters,<span class="_ _13"> </span>telecommunications<span class="_ _13"> </span>etc.<span class="_ _14"> </span>For<span class="_ _13"> </span>instance<span class="_ _14"> </span>the</div><div class="t m0 x1 h6 y12 ff1 fs4 fc0 sc0 ls19 ws0">authors&#8217;<span class="_ _15"> </span>initial<span class="_ _15"> </span>interests<span class="_ _15"> </span>invol<span class="ls14">ved<span class="_ _15"> </span>the<span class="_ _15"> </span>localization<span class="_ _15"> </span>of<span class="_ _15"> </span>passive</span></div><div class="t m0 x1 h6 y13 ff1 fs4 fc0 sc0 ls13 ws0">RFID<span class="_ _13"> </span>tags<span class="_ _15"> </span>in<span class="_ _13"> </span>a<span class="_ _13"> </span>warehouse<span class="_ _15"> </span>enviro<span class="ls1a">nment<span class="_ _13"> </span>with<span class="_ _15"> </span>a<span class="_ _14"> </span>phased<span class="_ _15"> </span>array</span></div><div class="t m0 x1 h6 y14 ff1 fs4 fc0 sc0 ls1b ws0">[1]&#8211;[3].<span class="_ _9"> </span>Thus<span class="_ _9"> </span>the<span class="_ _9"> </span>problem<span class="_ _9"> </span>at<span class="_ _9"> </span>hand<span class="_ _9"> </span>involves<span class="_ _9"> </span>sources<span class="_ _9"> </span>which<span class="_ _9"> </span>may</div><div class="t m0 x1 h6 y15 ff1 fs4 fc0 sc0 ls18 ws0">be<span class="_ _0"> </span>located<span class="_ _e"> </span>anywhere<span class="_ _0"> </span>in<span class="_ _e"> </span>an<span class="_ _0"> </span>unconstrained<span class="_ _e"> </span>two<span class="_ _0"> </span>dimensional<span class="_ _e"> </span>space</div><div class="t m0 x1 h6 y16 ff1 fs4 fc0 sc0 ls1c ws0">(azimuth<span class="_ _5"> </span>and<span class="_ _5"> </span>elevation).<span class="_ _5"> </span>A<span class="_ _9"> </span>wi<span class="_ _16"></span>de<span class="_ _5"> </span>range<span class="_ _9"> </span>o<span class="_"> </span>f<span class="_ _5"> </span>algorithm<span class="_ _16"></span>s<span class="_ _5"> </span>currently</div><div class="t m0 x1 h6 y17 ff1 fs4 fc0 sc0 ls1d ws0">exists,<span class="_ _9"> </span>including<span class="_ _5"> </span>minimum<span class="_ _9"> </span>variance,<span class="_ _9"> </span>ESPRIT<span class="_ _1"></span>,<span class="_ _9"> </span>neural<span class="_ _5"> </span>networks</div><div class="t m0 x1 h6 y18 ff1 fs4 fc0 sc0 ls1e ws0">and<span class="_ _13"> </span>many<span class="_ _14"> </span>more<span class="_ _13"> </span>[4]&#8211;[15].<span class="_ _14"> </span>Unde<span class="ls17">r<span class="_ _13"> </span>certain<span class="_ _13"> </span>conditions,<span class="_ _13"> </span>m<span class="_"> </span>any<span class="_ _15"> </span>of</span></div><div class="t m0 x1 h6 y19 ff1 fs4 fc0 sc0 ls16 ws0">these<span class="_ _f"> </span>techniques<span class="_ _f"> </span>outperform<span class="_ _9"> </span>th<span class="ls1f">e<span class="_ _9"> </span>classic<span class="_ _9"> </span>MUSIC<span class="_ _f"> </span>algorithm<span class="_ _9"> </span>[16]</span></div><div class="t m0 x1 h6 y1a ff1 fs4 fc0 sc0 ls20 ws0">which<span class="_ _8"> </span>suffers<span class="_ _15"> </span>from:<span class="_ _8"> </span>requiring<span class="_ _8"> </span>knowledge<span class="_ _8"> </span>of<span class="_ _15"> </span>the<span class="_ _8"> </span>number<span class="_ _8"> </span>of</div><div class="t m0 x1 h6 y1b ff1 fs4 fc0 sc0 ls1a ws0">sources,<span class="_ _13"> </span>needing<span class="_ _15"> </span>calibration,<span class="_ _14"> </span>being<span class="_ _15"> </span>limited<span class="_ _13"> </span>in<span class="_ _13"> </span>t<span class="_"> </span>he<span class="_ _15"> </span>number<span class="_ _14"> </span>of</div><div class="t m0 x1 h6 y1c ff1 fs4 fc0 sc0 ls14 ws0">sources<span class="_ _f"> </span>it<span class="_ _9"> </span>can<span class="_ _9"> </span>locate<span class="_ _9"> </span>etc.<span class="_ _f"> </span>Despite<span class="_ _9"> </span>this<span class="_ _9"> </span>the<span class="_ _f"> </span>M<span class="_"> </span>USIC<span class="_ _9"> </span>algorithm<span class="_ _9"> </span>re-</div><div class="t m0 x1 h6 y1d ff1 fs4 fc0 sc0 ls1f ws0">mains<span class="_ _5"> </span>popular<span class="_ _9"> </span>due<span class="_ _5"> </span>to<span class="_ _9"> </span>its<span class="_ _5"> </span>often<span class="_ _9"> </span>advantageous<span class="_ _9"> </span>trade-off<span class="_ _5"> </span>between</div><div class="t m0 x1 h6 y1e ff1 fs4 fc0 sc0 ls17 ws0">precision,<span class="_ _f"> </span>com<span class="_ _16"></span>putational<span class="_ _f"> </span>requ<span class="_ _16"></span>ire<span class="ls21">ments,<span class="_ _e"> </span>ease<span class="_ _f"> </span>of<span class="_ _f"> </span>implemen<span class="_ _1"></span>tation</span></div><div class="t m0 x1 h6 y1f ff1 fs4 fc0 sc0 ls19 ws0">etc</div><div class="t m0 x7 h6 y20 ff1 fs4 fc0 sc0 ls13 ws0">[17]&#8211;[24].</div><div class="t m0 x8 h6 y21 ff1 fs4 fc0 sc0 ls1d ws0">Recently<span class="_ _2"></span>,<span class="_ _17"> </span>a<span class="_ _5"> </span>com<span class="_"> </span>parison<span class="_ _17"> </span>between<span class="_ _17"> </span>the<span class="_ _5"> </span>MUSIC<span class="_ _17"> </span>algorithm<span class="_ _17"> </span>and</div><div class="t m0 x1 h6 y22 ff1 fs4 fc0 sc0 ls22 ws0">radio<span class="_ _5"> </span>astronomy<span class="_"> </span>&#8217;<span class="_ _1"></span>s<span class="_ _17"> </span>interferometric<span class="_ _5"> </span>imagin<span class="_ _16"></span>g<span class="_ _5"> </span>has<span class="_ _17"> </span>been<span class="_ _5"> </span>presented</div><div class="t m0 x1 h6 y23 ff1 fs4 fc0 sc0 ls16 ws0">[25].<span class="_ _f"> </span>As<span class="_ _f"> </span>a<span class="_ _9"> </span>result<span class="_ _f"> </span>of<span class="_ _9"> </span>this<span class="_ _f"> </span>comparison,<span class="_ _9"> </span>the<span class="_ _f"> </span>authors<span class="_ _f"> </span>h<span class="_"> </span>ave<span class="_ _9"> </span>identi<span class="ff6 ls1">&#64257;</span><span class="ls1d">ed</span></div><div class="t m0 x1 h6 y24 ff1 fs4 fc0 sc0 ls23 ws0">that<span class="_ _5"> </span>MUSIC<span class="_ _5"> </span>does<span class="_ _5"> </span>not<span class="_ _5"> </span>fully<span class="_ _9"> </span>account<span class="_ _5"> </span>for<span class="_ _5"> </span>the<span class="_ _5"> </span>array&#8217;<span class="_ _2"></span>s<span class="_ _5"> </span>impulse<span class="_ _5"> </span>re-</div><div class="t m0 x1 h6 y25 ff1 fs4 fc0 sc0 ls23 ws0">sponse<span class="_ _9"> </span>(also<span class="_ _9"> </span>known<span class="_ _5"> </span>as<span class="_ _9"> </span>the<span class="_ _9"> </span>&#8220;dirty<span class="_ _9"> </span>beam<span class="_"> </span>&#8221;<span class="_ _5"> </span>or<span class="_ _9"> </span>&#8220;array<span class="_ _9"> </span>point-spread</div><div class="t m0 x1 h6 y26 ff1 fs4 fc0 sc0 ls15 ws0">function&#8221;).<span class="_ _e"> </span>On<span class="_ _f"> </span>the<span class="_ _e"> </span>other<span class="_ _e"> </span>hand,<span class="_ _f"> </span>interferometry<span class="_ _e"> </span>(which<span class="_ _f"> </span>in<span class="_ _e"> </span>its<span class="_ _e"> </span>most</div><div class="t m0 x9 h8 y27 ff1 fs5 fc0 sc0 ls24 ws0">Manuscript<span class="_ _5"> </span>received<span class="_ _17"> </span>June<span class="_ _5"> </span>11,<span class="_ _5"> </span>2012;<span class="_ _5"> </span><span class="ls25">revised<span class="_ _17"> </span>February<span class="_ _17"> </span>03,<span class="_ _5"> </span>2013;<span class="_ _17"> </span>accepted</span></div><div class="t m0 x1 h8 y28 ff1 fs5 fc0 sc0 ls26 ws0">March<span class="_ _9"> </span>19,<span class="_ _9"> </span>2013.<span class="_ _5"> </span>Date<span class="_ _9"> </span>of<span class="_ _9"> </span>publication<span class="_ _9"> </span>April<span class="_ _9"> </span>01,<span class="_ _9"> </span>2013;<span class="_ _5"> </span>date<span class="_ _9"> </span>of<span class="_ _9"> </span>current<span class="_ _9"> </span>version</div><div class="t m0 x1 h8 y29 ff1 fs5 fc0 sc0 ls27 ws0">July<span class="_ _14"> </span>01,<span class="_ _13"> </span>2013.<span class="_ _14"> </span>This<span class="_ _13"> </span>work<span class="_ _14"> </span>was<span class="_ _13"> </span>supported<span class="_ _14"> </span>by<span class="_ _13"> </span>the<span class="_ _14"> </span>R&#233;gion<span class="_ _13"> </span>W<span class="_ _1"></span>allone<span class="_ _14"> </span>RFT<span class="_ _1"></span>AG</div><div class="t m0 x1 h8 y2a ff1 fs5 fc0 sc0 ls28 ws0">Project,<span class="_ _e"> </span>and<span class="_ _e"> </span>the<span class="_ _e"> </span>Univer<span class="_"> </span>sit&#233;<span class="_ _e"> </span>cat<span class="_ _16"></span>holique<span class="_ _e"> </span>de<span class="_ _e"> </span>Louvain<span class="_ _e"> </span>Postd<span class="_ _16"></span>octoral<span class="_ _e"> </span>Program<span class="_"> </span>.</div><div class="t m0 x9 h8 y2b ff1 fs5 fc0 sc0 ls29 ws0">G.<span class="_ _8"> </span>Hislop<span class="_ _8"> </span>was<span class="_ _8"> </span>with<span class="_ _8"> </span>the<span class="_ _8"> </span>Institute<span class="_ _8"> </span>of<span class="_ _12"> </span>Information<span class="_ _8"> </span>and<span class="_ _8"> </span>Commu<span class="_ _16"></span>nication</div><div class="t m0 x1 h8 y2c ff1 fs5 fc0 sc0 ls2a ws0">T<span class="_ _2"></span>e<span class="_"> </span>chnologies,<span class="_ _17"> </span>Electronics<span class="_ _17"> </span>and<span class="_ _14"> </span>Applied<span class="_ _17"> </span>Mathematics<span class="_ _14"> </span>(ICTEAM),<span class="_ _17"> </span>Universit&#233;</div><div class="t m0 x1 h8 y2d ff1 fs5 fc0 sc0 ls2b ws0">catholique<span class="_ _5"> </span>de<span class="_ _5"> </span>Louv<span class="_ _16"></span>ain<span class="_ _5"> </span>(UCL),<span class="_ _5"> </span>Louvain<span class="_ _5"> </span>la<span class="_ _5"> </span>Neuve,<span class="_ _5"> </span>Belgium<span class="_"> </span>.<span class="_ _5"> </span>H<span class="_ _16"></span>e<span class="_ _5"> </span>is<span class="_ _5"> </span>now<span class="_ _5"> </span>with</div><div class="t m0 x1 h8 y2e ff1 fs5 fc0 sc0 ls2c ws0">CSIRO<span class="_ _0"> </span>Ea<span class="_ _16"></span>rth<span class="_ _0"> </span>Science<span class="_ _e"> </span>and<span class="_ _e"> </span>Resource<span class="_ _0"> </span>E<span class="_ _16"></span>ngineering,<span class="_ _0"> </span>Pu<span class="_"> </span>llen<span class="_ _16"></span>vale<span class="_ _0"> </span>Austra<span class="_"> </span>lia<span class="_ _e"> </span>(e-mail:</div><div class="t m0 x1 h8 y2f ff1 fs5 fc0 sc0 ls2d ws0">greg.hislop@csir<span class="_ _16"></span>o.au)</div><div class="t m0 x9 h8 y30 ff1 fs5 fc0 sc0 ls2e ws0">N.<span class="_ _0"> </span>Sakar<span class="_ _18"> </span>was<span class="_ _18"> </span>with<span class="_ _0"> </span>the<span class="_ _18"> </span>Institute<span class="_ _0"> </span>of<span class="_ _18"> </span>Inform<span class="_"> </span>atio<span class="_"> </span>n<span class="_ _0"> </span>and<span class="_ _18"> </span>Comm<span class="_ _16"></span>unication<span class="_ _18"> </span>Technolo-</div><div class="t m0 x1 h8 y31 ff1 fs5 fc0 sc0 ls2e ws0">gies,<span class="_ _f"> </span>Elec<span class="_ _16"></span>tronics<span class="_ _9"> </span>and<span class="_ _f"> </span>Ap<span class="_ _16"></span>plied<span class="_ _f"> </span>M<span class="_ _16"></span>athematics<span class="_ _9"> </span>(ICTEAM),<span class="_ _9"> </span>Universit&#233;<span class="_ _9"> </span>catholiqu<span class="_"> </span>e</div><div class="t m0 x1 h8 y32 ff1 fs5 fc0 sc0 ls2f ws0">de<span class="_ _5"> </span>Louvain<span class="_ _5"> </span>(UCL),<span class="_ _9"> </span>Louvain<span class="_ _5"> </span>la<span class="_ _5"> </span>Neuve,<span class="_ _5"> </span>Belgium.<span class="_ _5"> </span>She<span class="_ _5"> </span>is<span class="_ _9"> </span>now<span class="_ _5"> </span>with<span class="_ _5"> </span>the<span class="_ _5"> </span>Earth</div><div class="t m0 x1 h8 y33 ff1 fs5 fc0 sc0 ls30 ws0">Oriented<span class="_ _5"> </span>Spac<span class="_"> </span>e<span class="_ _17"> </span>Science<span class="_ _17"> </span>an<span class="ls31">d<span class="_ _5"> </span>Technology<span class="_ _5"> </span>(ESP<span class="_ _1"></span>ACE),<span class="_ _17"> </span>T<span class="_ _2"></span>ec<span class="_ _16"></span>hnische<span class="_ _17"> </span>Universit&#228;t</span></div><div class="t m0 x1 h8 y34 ff1 fs5 fc0 sc0 ls32 ws0">M&#252;nchen,<span class="_ _17"> </span>Institut<span class="_ _14"> </span>fr<span class="_ _17"> </span>Astronomische<span class="_ _17"> </span>und<span class="_ _14"> </span>Physikalische<span class="_ _17"> </span>Geod&#228;sie,<span class="_ _14"> </span>Germany</div><div class="t m0 x1 h8 y35 ff1 fs5 fc0 sc0 ls2f ws0">(e-mail:<span class="_ _e"> </span>nida.sakar@tum.de).</div><div class="t m0 x9 h8 y36 ff1 fs5 fc0 sc0 ls2c ws0">C.<span class="_ _10"> </span>Craeye<span class="_ _12"> </span>is<span class="_ _10"> </span>with<span class="_ _12"> </span>the<span class="_ _10"> </span>Institute<span class="_ _10"> </span>of<span class="_ _12"> </span>Inform<span class="_"> </span>atio<span class="_ _16"></span>n<span class="_ _10"> </span>and<span class="_ _12"> </span>Communica<span class="_ _16"></span>tion</div><div class="t m0 x1 h8 y37 ff1 fs5 fc0 sc0 ls2c ws0">T<span class="_ _2"></span>e<span class="_ _16"></span>chnologies,<span class="_ _8"> </span>Electr<span class="_"> </span>on<span class="_"> </span>ics<span class="_ _12"> </span>and<span class="_ _8"> </span>Applied<span class="_ _8"> </span>Ma<span class="_ _16"></span>thematics<span class="_ _8"> </span>(ICTE<span class="_"> </span>AM<span class="_ _16"></span>),<span class="_ _8"> </span>Univer-</div><div class="t m0 x1 h8 y38 ff1 fs5 fc0 sc0 ls33 ws0">sit&#233;<span class="_ _15"> </span>catholique<span class="_ _15"> </span>de<span class="_ _15"> </span>Louvain<span class="_ _15"> </span>(UCL),<span class="_ _8"> </span>Louv<span class="_ _1"></span>ain<span class="_ _8"> </span>la<span class="_ _15"> </span>Neuve,<span class="_ _15"> </span>Belgium<span class="_ _15"> </span>(e-mail:</div><div class="t m0 x1 h8 y39 ff1 fs5 fc0 sc0 ls30 ws0">christophe.craeye@uclouvain.be).</div><div class="t m0 x9 h8 y3a ff1 fs5 fc0 sc0 ls34 ws0">Dig</div><div class="t m0 xa h8 y3b ff1 fs5 fc0 sc0 ls30 ws0">ital<span class="_ _e"> </span>Object<span class="_ _e"> </span>Identi<span class="ff6 ls1">&#64257;</span><span class="ls2f">er<span class="_ _f"> </span>10.1<span class="_ _1"></span>109/T<span class="_ _2"></span>AP.2013.2255854</span></div><div class="t m0 xb h6 y4 ff1 fs4 fc0 sc0 ls13 ws0">elementary<span class="_ _f"> </span>form<span class="_ _9"> </span>is<span class="_ _f"> </span>a<span class="_ _f"> </span>beam-forme<span class="ls35">r<span class="_ _9"> </span>with<span class="_ _f"> </span>unif<span class="_"> </span>orm<span class="_ _9"> </span>weigh<span class="_"> </span>tin<span class="_ _16"></span>g)<span class="_ _f"> </span>ac-</span></div><div class="t m0 xb h6 y3c ff1 fs4 fc0 sc0 ls22 ws0">counts<span class="_ _f"> </span>for<span class="_ _f"> </span>the<span class="_ _f"> </span>array&#8217;<span class="_ _1"></span>s<span class="_ _f"> </span>point-spread<span class="_ _f"> </span>function<span class="_ _f"> </span>by<span class="_ _9"> </span>using<span class="_ _f"> </span>both<span class="_ _f"> </span>array</div><div class="t m0 xb h6 y3d ff1 fs4 fc0 sc0 ls1f ws0">design<span class="_ _f"> </span>optimization<span class="_ _f"> </span>[26]&#8211;[28]<span class="_ _f"> </span>and<span class="_ _9"> </span>the<span class="_ _f"> </span>CLEAN<span class="_ _f"> </span>post-processing</div><div class="t m0 xb h6 y3e ff1 fs4 fc0 sc0 ls36 ws0">method<span class="_ _5"> </span>[26],<span class="_ _5"> </span>[27].</div><div class="t m0 xc h6 y3f ff1 fs4 fc0 sc0 ls36 ws0">The<span class="_ _14"> </span>existing<span class="_ _14"> </span>direction-<span class="ff6 ls1">&#64257;</span><span class="ls1a">nding<span class="_ _14"> </span>literature<span class="_ _14"> </span>applies<span class="_ _14"> </span>CLEAN<span class="_ _14"> </span>in</span></div><div class="t m0 xb h6 y40 ff1 fs4 fc0 sc0 ls37 ws0">the<span class="_ _0"> </span>case<span class="_ _0"> </span>of<span class="_ _0"> </span>correlated<span class="_ _0"> </span>sources<span class="_ _0"> </span>[6]<span class="_ _0"> </span>and<span class="_ _0"> </span>the<span class="_ _0"> </span>speci<span class="ff6 ls1">&#64257;</span><span class="ls22">c<span class="_ _0"> </span>case<span class="_ _0"> </span>of<span class="_ _0"> </span>a<span class="_ _0"> </span>single</span></div><div class="t m0 xb h6 y41 ff1 fs4 fc0 sc0 ls25 ws0">rotating<span class="_ _9"> </span>antenna<span class="_ _9"> </span>[29],<span class="_ _9"> </span>but<span class="_ _9"> </span>not<span class="_ _f"> </span>in<span class="_ _9"> </span>the<span class="_ _9"> </span>more<span class="_ _9"> </span>commonly<span class="_ _9"> </span>occurrin<span class="_"> </span>g</div><div class="t m0 xb h6 y42 ff1 fs4 fc0 sc0 ls13 ws0">problem<span class="_ _17"> </span>of<span class="_ _17"> </span>locating<span class="_ _17"> </span>uncorrelated<span class="_ _17"> </span>s<span class="_"> </span>ig<span class="_"> </span>nals<span class="_ _14"> </span>with<span class="_ _17"> </span>a<span class="_ _17"> </span>phased<span class="_ _17"> </span>array.</div><div class="t m0 xb h6 y43 ff1 fs4 fc0 sc0 ls19 ws0">The<span class="_ _9"> </span>autho<span class="_"> </span>rs<span class="_ _5"> </span>brie<span class="ff6 ls1">&#64258;</span><span class="ls22">y<span class="_ _9"> </span>introduced<span class="_ _5"> </span>the<span class="_ _9"> </span>idea<span class="_ _9"> </span>of<span class="_ _5"> </span>applying<span class="_ _9"> </span>CLEAN<span class="_ _9"> </span>to</span></div><div class="t m0 xb h6 y44 ff1 fs4 fc0 sc0 ls36 ws0">MUSIC<span class="_ _9"> </span>in<span class="_ _9"> </span>[30],<span class="_ _9"> </span>however<span class="_ _9"> </span>only<span class="_ _9"> </span>lim<span class="_"> </span>it<span class="_"> </span>ed<span class="_ _9"> </span>simu<span class="_"> </span>lated<span class="_ _9"> </span>resu<span class="_"> </span>lts<span class="_ _9"> </span>and<span class="_ _9"> </span>no</div><div class="t m0 xb h6 y45 ff1 fs4 fc0 sc0 ls38 ws0">theoretical<span class="_ _9"> </span>justi<span class="ff6 ls1">&#64257;</span><span class="ls1a">cation<span class="_ _9"> </span>or<span class="_ _f"> </span>experim<span class="_"> </span>ental<span class="_ _9"> </span>results<span class="_ _f"> </span>were<span class="_ _9"> </span>given.</span></div><div class="t m0 xc h6 y46 ff1 fs4 fc0 sc0 ls39 ws0">T<span class="_ _19"></span>h<span class="_ _19"></span>ew<span class="_ _19"></span>o<span class="_ _19"></span>r<span class="_ _19"></span>ka<span class="_ _19"></span>th<span class="_ _19"></span>a<span class="_ _19"></span>n<span class="_ _19"></span>di<span class="_ _19"></span>d<span class="_ _19"></span>e<span class="_ _1a"></span>n<span class="_ _1a"></span>t<span class="_ _19"></span>i<span class="_ _19"></span><span class="ff6 ls1">&#64257;<span class="ff1 ls16">es<span class="_ _e"> </span>the<span class="_ _e"> </span>C<span class="_"> </span>LEAN<span class="_ _f"> </span>algorithm<span class="_ _e"> </span>as<span class="_ _e"> </span>a<span class="_ _e"> </span>useful</span></span></div><div class="t m0 xb h6 y47 ff1 fs4 fc0 sc0 ls19 ws0">post-processing<span class="_ _f"> </span>m<span class="_ _16"></span>ethod<span class="_ _f"> </span>for<span class="_ _f"> </span>direction<span class="_ _9"> </span><span class="ff6 ls1">&#64257;</span><span class="ls37">nding<span class="_ _f"> </span>based<span class="_ _f"> </span>on<span class="_ _f"> </span>MUSIC.</span></div><div class="t m0 xb h6 y48 ff1 fs4 fc0 sc0 ls3a ws0">It<span class="_ _9"> </span>is<span class="_ _5"> </span>shown<span class="_ _5"> </span>that<span class="_ _9"> </span>MUSIC<span class="_ _5"> </span>possesses<span class="_ _9"> </span>a<span class="_ _5"> </span>failure<span class="_ _9"> </span>mode<span class="_ _5"> </span>whereby<span class="_ _5"> </span>the</div><div class="t m0 xb h6 y49 ff1 fs4 fc0 sc0 ls3a ws0">returns<span class="_ _5"> </span>fro<span class="_"> </span>m<span class="_ _17"> </span>two<span class="_ _17"> </span>sources<span class="_ _17"> </span>add<span class="_ _17"> </span>to<span class="_ _5"> </span>giv<span class="_"> </span>e<span class="_ _17"> </span>only<span class="_ _17"> </span>one<span class="_ _17"> </span>maximum<span class="_ _17"> </span>and</div><div class="t m0 xb h6 y4a ff1 fs4 fc0 sc0 ls1d ws0">that<span class="_ _e"> </span>CLEAN<span class="_ _f"> </span>may<span class="_ _f"> </span>be<span class="_ _f"> </span>applied<span class="_ _f"> </span>to<span class="_ _e"> </span>sep<span class="ls1b">arate<span class="_ _f"> </span>the<span class="_ _f"> </span>two<span class="_ _f"> </span>returns.<span class="_ _f"> </span>This<span class="_ _e"> </span>is</span></div><div class="t m0 xb h6 y4b ff1 fs4 fc0 sc0 ls37 ws0">done<span class="_ _9"> </span>using<span class="_ _5"> </span>mathematical<span class="_ _9"> </span>explan<span class="ls3b">a<span class="_ _6"></span>t<span class="_ _6"></span>i<span class="_ _6"></span>o<span class="_ _1a"></span>na<span class="_ _6"></span>sw<span class="_ _6"></span>e<span class="_ _6"></span>l<span class="_ _6"></span>la<span class="_ _6"></span>st<span class="_ _1b"></span>h<span class="_ _6"></span>o<span class="_ _6"></span>r<span class="_ _1b"></span>o<span class="_ _6"></span>u<span class="_ _6"></span>g<span class="_ _6"></span>h<span class="_ _16"></span>s<span class="_ _6"></span>i<span class="_ _6"></span>m<span class="_ _1b"></span>-</span></div><div class="t m0 xb h6 y4c ff1 fs4 fc0 sc0 ls3c ws0">ulated<span class="_ _9"> </span>and<span class="_ _5"> </span>experimental<span class="_ _9"> </span>results.</div><div class="t m0 xc h6 y4d ff1 fs4 fc0 sc0 ls3d ws0">Beam-space-MUSIC<span class="_ _14"> </span>is<span class="_ _17"> </span>another<span class="_ _17"> </span><span class="ls1d">technique<span class="_ _14"> </span>which<span class="_ _14"> </span>uses<span class="_ _17"> </span>prior</span></div><div class="t m0 xb h6 y4e ff1 fs4 fc0 sc0 ls3c ws0">knowledge<span class="_ _15"> </span>of<span class="_ _15"> </span>the<span class="_ _8"> </span>array&#8217;<span class="_ _2"></span>s<span class="_ _15"> </span>beam<span class="_ _15"> </span>shape<span class="_ _8"> </span>to<span class="_ _15"> </span>improve<span class="_ _15"> </span>MUSIC&#8217;<span class="_ _1"></span>s</div><div class="t m0 xb h6 y4f ff1 fs4 fc0 sc0 ls1b ws0">ability<span class="_ _13"> </span>t<span class="_"> </span>o<span class="_ _15"> </span>resolve<span class="_ _15"> </span>sources<span class="_ _13"> </span>[4],<span class="_ _15"> </span>[31],<span class="_ _13"> </span>[32].<span class="_ _15"> </span>This<span class="_ _13"> </span>technique<span class="_ _15"> </span>de-</div><div class="t m0 xb h6 y50 ff6 fs4 fc0 sc0 ls1 ws0">&#64257;<span class="ff1 ls25">nes<span class="_ _12"> </span>a<span class="_ _8"> </span>region<span class="_ _12"> </span>of<span class="_ _8"> </span>interest<span class="_ _12"> </span>in<span class="_ _8"> </span>wh<span class="_ _16"></span>ich<span class="_ _8"> </span>the<span class="_ _12"> </span>sources<span class="_ _12"> </span>are<span class="_ _8"> </span>known</span></div><div class="t m0 xb h6 y51 ff1 fs4 fc0 sc0 ls23 ws0">to<span class="_ _13"> </span>lie<span class="_ _15"> </span>and<span class="_ _13"> </span>constructs<span class="_ _13"> </span>a<span class="_ _15"> </span>series<span class="_ _13"> </span>of<span class="_ _15"> </span>beams<span class="_ _13"> </span>which<span class="_ _13"> </span>cover<span class="_ _15"> </span>this<span class="_ _13"> </span>re-</div><div class="t m0 xb h6 y52 ff1 fs4 fc0 sc0 ls1f ws0">gion.<span class="_ _10"> </span>These<span class="_ _10"> </span>beams<span class="_ _4"> </span>are<span class="_ _10"> </span>used<span class="_ _10"> </span>to<span class="_ _10"> </span>precondition<span class="_ _10"> </span>the<span class="_ _4"> </span>received</div><div class="t m0 xb h6 y53 ff1 fs4 fc0 sc0 ls1f ws0">data<span class="_ _12"> </span>and<span class="_ _8"> </span>the<span class="_ _12"> </span>steering<span class="_ _12"> </span>vectors<span class="_ _12"> </span>prior<span class="_ _8"> </span>to<span class="_ _12"> </span>performing<span class="_ _12"> </span>MUSIC.</div><div class="t m0 xb h6 y54 ff1 fs4 fc0 sc0 ls3e ws0">As<span class="_ _15"> </span>beam-space-MUSIC<span class="_ _8"> </span>restricts<span class="_ _15"> </span>the<span class="_ _15"> </span>solution<span class="_ _8"> </span>space,<span class="_ _15"> </span>it<span class="_ _15"> </span>is<span class="_ _8"> </span>of</div><div class="t m0 xb h6 y55 ff1 fs4 fc0 sc0 ls3f ws0">limited<span class="_ _10"> </span>use<span class="_ _4"> </span>for<span class="_ _10"> </span>the<span class="_ _4"> </span>authors&#8217;<span class="_ _10"> </span>preferr<span class="_"> </span>ed<span class="_ _4"> </span>application<span class="_ _10"> </span>[<span class="_"> </span>1]<span class="_"> </span>&#8211;[<span class="_"> </span>3].</div><div class="t m0 xb h6 y56 ff1 fs4 fc0 sc0 ls3d ws0">However<span class="_ _1"></span>,<span class="_ _15"> </span>as<span class="_ _15"> </span>both<span class="_ _15"> </span>beam-space-MUSIC<span class="_ _15"> </span>and<span class="_ _15"> </span>MUSIC-CLEAN</div><div class="t m0 xb h6 y57 ff1 fs4 fc0 sc0 ls17 ws0">improve<span class="_ _17"> </span>M<span class="_"> </span>USIC<span class="_ _16"></span>&#8217;<span class="_ _2"></span>s<span class="_ _14"> </span>resolving<span class="_ _17"> </span>power<span class="_ _14"> </span>through<span class="_ _17"> </span>the<span class="_ _14"> </span>incorporation</div><div class="t m0 xb h6 y58 ff1 fs4 fc0 sc0 ls14 ws0">of<span class="_ _5"> </span>beam<span class="_ _5"> </span>patterns,<span class="_ _5"> </span>a<span class="_ _5"> </span>comparison<span class="_ _5"> </span>is<span class="_ _5"> </span>performed<span class="_ _5"> </span>between<span class="_ _17"> </span>the<span class="_ _5"> </span>two</div><div class="t m0 xb h6 y59 ff1 fs4 fc0 sc0 ls23 ws0">techniques.<span class="_ _14"> </span>In<span class="_ _17"> </span>said<span class="_ _14"> </span>compariso<span class="ls11">n<span class="_ _14"> </span>MUSIC-CLEAN<span class="_ _14"> </span>outperforms</span></div><div class="t m0 xb h6 y5a ff1 fs4 fc0 sc0 ls40 ws0">beam-space-MUSIC.</div><div class="t m0 xc h6 y5b ff1 fs4 fc0 sc0 ls20 ws0">Throughout<span class="_ _e"> </span>this<span class="_ _e"> </span>paper<span class="_ _1"></span>,<span class="_ _e"> </span>a<span class="_ _e"> </span>Cartesian<span class="_ _e"> </span>coordin<span class="_ _16"></span>ate<span class="_ _e"> </span>system<span class="_ _e"> </span>is<span class="_ _e"> </span>used.</div><div class="t m0 xb h6 y5c ff1 fs4 fc0 sc0 ls14 ws0">The<span class="_ _f"> </span>direction-<span class="ff6 ls1">&#64257;</span><span class="ls35">n<span class="_"> </span>din<span class="_ _16"></span>g<span class="_ _f"> </span>array<span class="_ _9"> </span>is<span class="_ _f"> </span>assum<span class="_ _16"></span>ed<span class="_ _f"> </span>to<span class="_ _9"> </span>lie<span class="_ _f"> </span>in<span class="_ _9"> </span>the</span></div><div class="t m0 xd h6 y5d ff1 fs4 fc0 sc0 ls13 ws0">plane</div><div class="t m0 xb h6 y5e ff1 fs4 fc0 sc0 ls18 ws0">and<span class="_ _5"> </span>directions<span class="_ _5"> </span>are<span class="_ _9"> </span>de<span class="ff6 ls1">&#64257;</span><span class="ls41">ned<span class="_ _5"> </span>using<span class="_ _5"> </span>either<span class="_ _5"> </span>azimuth</span></div><div class="t m0 xe h6 y5f ff1 fs4 fc0 sc0 ls18 ws0">and<span class="_ _5"> </span>eleva-</div><div class="t m0 xb h6 y60 ff1 fs4 fc0 sc0 ls2e ws0">tion</div><div class="t m0 xf h6 y61 ff1 fs4 fc0 sc0 ls42 ws0">or<span class="_ _9"> </span>the<span class="_ _5"> </span>direction<span class="_ _9"> </span>cosines:</div><div class="t m0 x10 h6 y62 ff1 fs4 fc0 sc0 ls43 ws0">(1)</div><div class="t m0 xb h6 y63 ff1 fs4 fc0 sc0 ls3e ws0">Fig.<span class="_ _f"> </span>1<span class="_ _f"> </span>dep</div><div class="t m0 x11 h6 y64 ff1 fs4 fc0 sc0 ls1c ws0">icts<span class="_ _f"> </span>the<span class="_ _9"> </span>coordinate<span class="_ _9"> </span>system<span class="_ _f"> </span>and<span class="_ _f"> </span>a<span class="_"> </span>n<span class="_ _9"> </span>example<span class="_ _9"> </span>of<span class="_ _f"> </span>a<span class="_ _f"> </span>dir<span class="_"> </span>ec-</div><div class="t m0 xb h6 y65 ff1 fs4 fc0 sc0 ls20 ws0">tion-<span class="ff6 ls1">&#64257;<span class="ff1">n</span></span></div><div class="t m0 x12 h6 y66 ff1 fs4 fc0 sc0 ls14 ws0">ding<span class="_ _5"> </span>array.</div><div class="t m0 xc h6 y67 ff1 fs4 fc0 sc0 ls18 ws0">The<span class="_ _1c"> </span>paper</div><div class="t m0 x13 h6 y68 ff1 fs4 fc0 sc0 ls22 ws0">starts<span class="_ _1c"> </span>with<span class="_ _1c"> </span>a<span class="_ _1c"> </span>mathematical<span class="_ _1c"> </span>form<span class="_ _16"></span>ulation:</div><div class="t m0 xb h6 y69 ff1 fs4 fc0 sc0 ls44 ws0">Section</div><div class="t m0 x14 h6 y6a ff1 fs4 fc0 sc0 ls45 ws0">II.A<span class="_ _d"> </span>devel<span class="_ _1"></span>ops<span class="_ _d"> </span>the<span class="_ _d"> </span>mathematics<span class="_ _1d"> </span>behind<span class="_ _1d"> </span>MUSIC&#8217;<span class="_ _1"></span>s</div><div class="t m0 xb h6 y6b ff1 fs4 fc0 sc0 ls25 ws0">perform</div><div class="t m0 x15 h6 y6c ff1 fs4 fc0 sc0 ls19 ws0">ance<span class="_ _f"> </span>limitations,<span class="_ _f"> </span>Section<span class="_ _9"> </span>II.B<span class="_ _f"> </span>then<span class="_ _f"> </span>reviews<span class="_ _f"> </span>the<span class="_ _f"> </span>CL<span class="_"> </span>EA<span class="_ _16"></span>N</div><div class="t m0 xb h6 y6d ff1 fs4 fc0 sc0 ls42 ws0">algori</div><div class="t m0 x16 h6 y6e ff1 fs4 fc0 sc0 ls25 ws0">thm<span class="_ _e"> </span>and<span class="_ _0"> </span>ex<span class="_"> </span>plains<span class="_ _e"> </span>how<span class="_ _e"> </span>it<span class="_ _e"> </span>improves<span class="_ _e"> </span>MUSIC&#8217;<span class="_ _1"></span>s<span class="_ _e"> </span>performance.</div><div class="t m0 xb h6 y6f ff1 fs4 fc0 sc0 ls23 ws0">Secti</div><div class="t m0 x17 h6 y70 ff1 fs4 fc0 sc0 ls23 ws0">on<span class="_ _e"> </span>III<span class="_ _f"> </span>provides<span class="_ _f"> </span>simulated<span class="_ _e"> </span>(Sect<span class="ls1f">ion<span class="_ _f"> </span>III.A)<span class="_ _e"> </span>and<span class="_ _f"> </span>experimental</span></div><div class="t m0 xb h6 y71 ff1 fs4 fc0 sc0 ls20 ws0">syste</div><div class="t m0 x17 h6 y72 ff1 fs4 fc0 sc0 ls1f ws0">m<span class="_ _15"> </span>results<span class="_ _13"> </span>(Section<span class="_ _15"> </span>III.B)<span class="_ _15"> </span>that<span class="_ _13"> </span>compare<span class="_ _15"> </span>the<span class="_ _15"> </span>performance</div><div class="t m0 xb h6 y73 ff1 fs4 fc0 sc0 ls46 ws0">of<span class="_ _d"> </span>MU</div><div class="t m0 x18 h6 y74 ff1 fs4 fc0 sc0 ls2f ws0">SIC,<span class="_ _d"> </span>MUSIC-CLEAN<span class="_ _1d"> </span>and<span class="_ _d"> </span>beam-space-MUSIC.<span class="_ _d"> </span>A</div><div class="t m0 xb h6 y75 ff1 fs4 fc0 sc0 ls37 ws0">disc</div><div class="t m0 x19 h6 y76 ff1 fs4 fc0 sc0 ls3f ws0">ussion<span class="_ _f"> </span>of<span class="_ _9"> </span>the<span class="_ _9"> </span>results<span class="_ _f"> </span>is<span class="_ _9"> </span>given<span class="_ _9"> </span>in<span class="_ _f"> </span>Section<span class="_ _9"> </span>IV,<span class="_ _9"> </span>and<span class="_ _f"> </span>conclu<span class="_ _16"></span>ding</div><div class="t m0 xb h6 y77 ff1 fs4 fc0 sc0 ls1f ws0">com</div><div class="t m0 x1a h6 y78 ff1 fs4 fc0 sc0 ls1f ws0">ments<span class="_ _9"> </span>are<span class="_ _5"> </span>provided<span class="_ _9"> </span>in<span class="_ _9"> </span>Section<span class="_ _9"> </span>V<span class="_ _16"></span>.</div><div class="t m0 x1b h8 y79 ff1 fs5 fc0 sc0 ls47 ws0">0018-926X/$31.<span class="_ _1"></span>00<span class="_ _f"> </span>&#169;<span class="_ _f"> </span>2013<span class="_ _f"> </span>IEEE</div></div><div class="pi" data-data='{"ctm":[1.621622,0.000000,0.000000,1.621622,0.000000,0.000000]}'></div></div> </body> </html>
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