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基于分数低阶循环相关的快速波达方向估计算法,对于通信领域的学者很有用
cyclic correlation.rar
  • A fast direction-of-arrival estimation based on the fractional lower order cyclic correlation.pdf
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内容介绍
<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/625509e2b744eb386fd71296/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/625509e2b744eb386fd71296/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Proceedings of AIAI2010</div><div class="t m0 x2 h3 y2 ff2 fs1 fc0 sc0 ls1 ws1">A FAST DIRECTION-OF-ARRIVAL ESTIMATION </div><div class="t m0 x3 h3 y3 ff2 fs1 fc0 sc0 ls2 ws2">BASED ON THE FRACTIONAL LOWER ORDER </div><div class="t m0 x4 h3 y4 ff2 fs1 fc0 sc0 ls2 ws2">CYCLIC CORRELATION </div><div class="t m0 x5 h4 y5 ff2 fs2 fc0 sc0 ls3 ws3">Xiaoou Zhao, Li Li, Xiaojun Jing </div><div class="t m0 x6 h5 y6 ff3 fs3 fc0 sc0 ls4 ws4">School of Telecommunicati<span class="ls5 ws5">on a<span class="_ _0"></span>nd Information System<span class="_ _0"></span>s, </span></div><div class="t m0 x7 h5 y7 ff3 fs3 fc0 sc0 ls6 ws6">Beijing University o<span class="_ _1"></span>f Posts and Telecommunication<span class="_ _1"></span>s, Beijing, China </div><div class="t m0 x8 h5 y8 ff3 fs3 fc0 sc0 ls7 ws7">zhaoxiaoou19@gmail.com, buptlily@g<span class="ls8 ws8">mail.com<span class="_ _0"></span>, Jxiaojun@bupt.edu.cn </span></div><div class="t m0 x1 h4 y9 ff2 fs2 fc0 sc0 ls9 ws1">Abstract</div><div class="t m0 x1 h5 ya ff3 fs3 fc0 sc0 ls5 ws9">A new algorithm<span class="_ _0"></span> for Direction-of-Arrival (DOA) </div><div class="t m0 x1 h5 yb ff3 fs3 fc0 sc0 lsa wsa">estimation is presen<span class="_ _1"></span>ted in </div><div class="t m1 x9 h6 yc ff4 fs4 fc0 sc0 ls1 ws1">D</div><div class="t m0 xa h5 yc ff3 fs3 fc0 sc0 lsb wsb">-stable distribution </div><div class="t m0 x1 h5 yd ff3 fs3 fc0 sc0 ls7 wsc">noise environment. Since t<span class="_ _0"></span>he DOA estimation </div><div class="t m0 x1 h5 ye ff3 fs3 fc0 sc0 lsc wsd">algorithms based on the <span class="_ _0"></span>second order cyclic </div><div class="t m0 x1 h5 yf ff3 fs3 fc0 sc0 lsd wse">stationary correlation<span class="_ _1"></span> degrade seriously in non-</div><div class="t m0 x1 h5 y10 ff3 fs3 fc0 sc0 lse wsf">Gaussian noise environm<span class="lsf ws10">ent and nee<span class="_ _0"></span>d a large </span></div><div class="t m0 x1 h5 y11 ff3 fs3 fc0 sc0 ls10 ws11">amount of calc<span class="_ _0"></span>ulation, this new algorithm<span class="_ _0"></span> based on </div><div class="t m0 x1 h5 y12 ff3 fs3 fc0 sc0 ls11 ws12">fractional lower order statistics can get the accurate </div><div class="t m0 x1 h5 y13 ff3 fs3 fc0 sc0 ls12 ws13">DOA estimation i<span class="_ _0"></span>n impulsive n<span class="_ _0"></span>oise environment<span class="_ _0"></span> </div><div class="t m0 x1 h5 y14 ff3 fs3 fc0 sc0 lsb ws14">and also it is fast because it avoids searc<span class="_ _0"></span>hing the </div><div class="t m0 x1 h5 y15 ff3 fs3 fc0 sc0 ls13 ws15">spatial spectrum. Simulation results show the </div><div class="t m0 x1 h5 y16 ff3 fs3 fc0 sc0 ls13 ws16">effectiveness of the algorithm. </div><div class="t m0 x1 h5 y17 ff2 fs3 fc0 sc0 ls14 ws1">Keywords: <span class="_ _2"></span><span class="ff3 ls7 ws17">wireless location; non-Gaussian signal;<span class="_ _0"></span> </span></div><div class="t m0 x1 h5 y18 ff3 fs3 fc0 sc0 ls15 ws18">array signal processing;<span class="_ _0"></span> Direction-of-Arrival<span class="_ _0"></span> </div><div class="t m0 x1 h5 y19 ff3 fs3 fc0 sc0 ls5 ws5">estimation; fast algorithm<span class="_ _0"></span>; </div><div class="t m0 x1 h4 y1a ff2 fs2 fc0 sc0 ls1 ws1">1 Introduction </div><div class="t m0 x1 h5 y1b ff3 fs3 fc0 sc0 ls16 ws19">Spatial spectrum estimation is one of t<span class="_ _0"></span>he most </div><div class="t m0 x1 h5 y1c ff3 fs3 fc0 sc0 ls7 ws1a">significant fields in <span class="ls8 ws1b">array signal processing, an<span class="_ _0"></span>d </span></div><div class="t m0 x1 h5 y1d ff3 fs3 fc0 sc0 ls17 ws1c">the Direction-of-Arrival (DOA) estimation is one </div><div class="t m0 x1 h5 y1e ff3 fs3 fc0 sc0 lsa ws1d">of the main content in the field<span class="_ _1"></span> of spatial spectrum </div><div class="t m0 x1 h5 y1f ff3 fs3 fc0 sc0 ls16 ws1e">estimation. DOA estimation is widely used in </div><div class="t m0 x1 h5 y20 ff3 fs3 fc0 sc0 ls15 ws1f">radar, sona<span class="_ _0"></span>r, seismi<span class="_ _0"></span>c wave and electrocardiogram </div><div class="t m0 x1 h5 y21 ff3 fs3 fc0 sc0 ls1 ws20">etc. High resolution algorithms based on signal<span class="_ _0"></span> </div><div class="t m0 x1 h5 y22 ff3 fs3 fc0 sc0 ls18 ws21">subspaces grow rapidly am<span class="_ _0"></span>ong the different types </div><div class="t m0 x1 h5 y23 ff3 fs3 fc0 sc0 ls17 ws22">of DOA estimation, such as MUSIC<span class="_ _0"></span> algorithms</div><div class="t m0 xb h7 y24 ff3 fs5 fc0 sc0 ls19 ws1">[2]</div><div class="t m0 x1 h5 y25 ff3 fs3 fc0 sc0 ls1a ws23">and ESPRIT algorithms</div><div class="t m0 xc h7 y26 ff3 fs5 fc0 sc0 ls19 ws1">[3]</div><div class="t m0 xd h5 y27 ff3 fs3 fc0 sc0 ls1 ws1">.</div><div class="t m0 x1 h5 y28 ff3 fs3 fc0 sc0 ls1b ws24">One particular type of no<span class="ls1 ws25">n-stationa<span class="_ _0"></span>ry signals </span></div><div class="t m0 x1 h5 y29 ff3 fs3 fc0 sc0 ls1c ws26">widely exists in telecommu<span class="_ _1"></span>nication, astronomy </div><div class="t m0 x1 h5 y2a ff3 fs3 fc0 sc0 ls1c ws27">and acoustics. Although these signals are non-</div><div class="t m0 x1 h5 y2b ff3 fs3 fc0 sc0 ls1c ws28">stationary, the statistical pr<span class="_ _1"></span>operties of the signals </div><div class="t m0 x1 h5 y2c ff3 fs3 fc0 sc0 ls1d ws29">vary cyclically</div><div class="t m0 xe h7 y2d ff3 fs5 fc0 sc0 ls19 ws1">[5]</div><div class="t m0 xf h5 y2e ff3 fs3 fc0 sc0 ls15 ws2a">. In the Gaussian noise<span class="_ _0"></span> </div><div class="t m0 x1 h5 y2f ff3 fs3 fc0 sc0 lse ws2b">environment, the algorithm<span class="_ _0"></span>s based on the second </div><div class="t m0 x1 h5 y30 ff3 fs3 fc0 sc0 ls1a ws2c">order cyclic correlation can inhibit the<span class="_ _0"></span> noise and </div><div class="t m0 x1 h5 y31 ff3 fs3 fc0 sc0 ls1a ws2d">extract the useful DOA estimation effectivel<span class="_ _0"></span>y. But </div><div class="t m0 x1 h5 y32 ff3 fs3 fc0 sc0 lsd ws2e">when impulsive noise exists in<span class="_ _1"></span> the environment, </div><div class="t m0 x1 h5 y33 ff3 fs3 fc0 sc0 ls1 ws2f">the algorithms based on the second order cyclic </div><div class="t m0 x1 h5 y34 ff3 fs3 fc0 sc0 lsb ws30">correlation degenerate seriously in pe<span class="_ _0"></span>rformance. </div><div class="t m0 x1 h5 y35 ff3 fs3 fc0 sc0 lsb ws31">With the development of t<span class="_ _0"></span>he signal processing </div><div class="t m0 x1 h5 y36 ff3 fs3 fc0 sc0 ls8 ws32">theory, we find that the impulsi<span class="_ _0"></span>ve noise can be<span class="_ _0"></span> </div><div class="t m0 x1 h5 y37 ff3 fs3 fc0 sc0 ls10 ws33">described by the </div><div class="t m2 x10 h8 y38 ff4 fs6 fc0 sc0 ls1 ws1">D</div><div class="t m0 x11 h5 y39 ff3 fs3 fc0 sc0 lse ws2b">-stable distribution which has<span class="_ _0"></span> </div><div class="t m0 x12 h5 y3a ff3 fs3 fc0 sc0 ls7 ws34">thicker tails</div><div class="t m0 x13 h7 y3b ff3 fs5 fc0 sc0 ls19 ws1">[4]</div><div class="t m0 x14 h5 y3c ff3 fs3 fc0 sc0 ls1e ws35">. So the </div><div class="c x15 y3d w2 h9"><div class="t m1 x0 h6 y3e ff4 fs4 fc0 sc0 ls1 ws1">D</div></div><div class="t m0 x16 h5 y3c ff3 fs3 fc0 sc0 ls16 ws36">-stable distribution is </div><div class="t m0 x12 h5 y3f ff3 fs3 fc0 sc0 ls5 ws37">suitable for modeling the si<span class="_ _0"></span>gnals and noise<span class="_ _0"></span>s that </div><div class="t m0 x12 h5 y40 ff3 fs3 fc0 sc0 ls5 ws5">have impulsive nature. </div><div class="t m0 x12 h5 y41 ff3 fs3 fc0 sc0 ls4 ws38">In this paper, a fast DOA estim<span class="_ _0"></span>ation is presented </div><div class="t m0 x12 h5 y42 ff3 fs3 fc0 sc0 ls1 ws39">based on the concept of fractional l<span class="_ _0"></span>ower order </div><div class="t m0 x12 h5 y43 ff3 fs3 fc0 sc0 ls16 ws3a">cyclic correlation</div><div class="t m0 x17 h7 y44 ff3 fs5 fc0 sc0 ls19 ws1">[1]</div><div class="t m0 x18 h5 y45 ff3 fs3 fc0 sc0 ls1f ws3b">, and the algorithm is used to </div><div class="t m0 x12 h5 y46 ff3 fs3 fc0 sc0 ls20 ws3c">find the DOA esti<span class="_ _1"></span>mation and the location o<span class="_ _1"></span>f the </div><div class="t m0 x12 h5 y47 ff3 fs3 fc0 sc0 ls21 ws3d">signal source. Simulation<span class="_ _1"></span> results show that the </div><div class="t m0 x12 h5 y48 ff3 fs3 fc0 sc0 ls22 ws3e">performance of the new algo<span class="ls17 ws3f">rithm<span class="_ _0"></span> is superior to </span></div><div class="t m0 x12 h5 y49 ff3 fs3 fc0 sc0 ls8 ws40">the original DOA estimation algorithm<span class="_ _0"></span>s based on </div><div class="t m0 x12 h5 y4a ff3 fs3 fc0 sc0 lsb ws41">the second order cyclic correlation. </div><div class="t m0 x12 h4 y4b ff2 fs2 fc0 sc0 ls23 ws42">2 Signal model and noise model </div><div class="t m0 x12 h5 y4c ff3 fs3 fc0 sc0 ls24 ws43">Assume the antenna array is a uniform linear array, </div><div class="t m0 x12 ha y4d ff3 fs3 fc0 sc0 ls1 ws44">the number of array ele<span class="_ _0"></span>ments is <span class="ff1 ws1">M</span><span class="ls25 ws45">, and the </span></div><div class="t m0 x12 ha y4e ff3 fs3 fc0 sc0 ls1a ws46">distance between neighbori<span class="_ _0"></span>ng elements is <span class="ff1 ls1 ws1">d<span class="ff3">,</span></span></div><div class="t m0 x19 hb y4f ff3 fs7 fc0 sc0 ls1 ws1">0</div><div class="t m0 x1a hc y50 ff3 fs8 fc0 sc0 ls26 ws1">/2<span class="_ _3"></span><span class="ff1 ls1">d</span></div><div class="t m2 x1b hd y50 ff4 fs9 fc0 sc0 ls1 ws1">O</div><div class="t m0 x1c he y50 ff4 fs8 fc0 sc0 ls1 ws1">d<span class="_ _4"> </span><span class="ff3 fs2">,</span></div><div class="t m0 x1d hb y4f ff3 fs7 fc0 sc0 ls27 ws1">00</div><div class="t m0 x1e hc y50 ff3 fs8 fc0 sc0 ls28 ws1">2/<span class="_ _5"></span><span class="ff1 ls1">c</span></div><div class="t m2 x1f hd y50 ff4 fs9 fc0 sc0 ls29 ws1">OS<span class="_ _6"></span>Z</div><div class="t m0 x20 he y50 ff4 fs8 fc0 sc0 ls1 ws1"> <span class="_ _7"> </span><span class="ff3 fs2">,<span class="_ _8"> </span><span class="fs3 ls2a">where</span></span></div><div class="t m0 x21 hb y4f ff3 fs7 fc0 sc0 ls1 ws1">0</div><div class="t m2 x22 hd y50 ff4 fs9 fc0 sc0 ls1 ws1">Z</div><div class="t m0 x23 h5 y50 ff3 fs3 fc0 sc0 lse ws47"> <span class="_ _9"></span>is the central </div><div class="t m0 x12 ha y51 ff3 fs3 fc0 sc0 ls4 ws48">frequency of t<span class="_ _0"></span>he signal. There are <span class="_ _0"></span><span class="ff1 ls1 ws1">l<span class="ff3 lsf ws49"> incident signal<span class="_ _0"></span>s </span></span></div><div class="t m0 x12 h5 y52 ff3 fs3 fc0 sc0 ls5 ws4a">with the angles of inci<span class="_ _0"></span>dence</div><div class="t m0 x24 hf y53 ff3 fsa fc0 sc0 ls2b ws1">12</div><div class="t m0 x25 h10 y54 ff3 fsb fc0 sc0 ls2c ws1">,,<span class="_ _2"></span>,</div><div class="c x26 y55 w3 h11"><div class="t m0 x0 h12 y56 ff1 fsa fc0 sc0 ls1 ws1">p</div></div><div class="t m3 x27 h13 y54 ff4 fsc fc0 sc0 ls2d ws1">TT<span class="_ _a"> </span>T</div><div class="t m0 x28 h14 y54 ff5 fsb fc0 sc0 ls1 ws1">"<span class="_ _b"> </span><span class="ff3 fs2">,</span></div><div class="t m0 x12 h5 y57 ff3 fs3 fc0 sc0 ls7 ws7">respectively. The matrix of the array signals <span class="_ _0"></span>is </div><div class="t m0 x29 h10 y58 ff3 fsb fc0 sc0 ls2e ws1">()<span class="_ _c"> </span>(<span class="_ _d"> </span>)<span class="_ _e"> </span>()<span class="_ _c"> </span>()</div><div class="c x2a y59 w4 h15"><div class="t m0 x2b hc y5a ff1 fs8 fc0 sc0 ls1 ws1">X</div></div><div class="t m0 x2c hc y58 ff1 fs8 fc0 sc0 ls2f ws1">tA<span class="_ _f"></span>S<span class="_ _10"></span>t<span class="_ _9"></span>N<span class="_ _10"></span>t</div><div class="t m3 x2d h13 y58 ff4 fsc fc0 sc0 ls1 ws1">T</div><div class="t m0 x2e he y58 ff4 fs8 fc0 sc0 ls30 ws1"> &#58894;<span class="_ _11"></span><span class="ff3 fs3 ls31"> <span class="_ _a"> </span> <span class="_ _12"> </span> (1)<span class="_ _0"></span> </span></div><div class="t m0 x12 h5 y5b ff3 fs3 fc0 sc0 ls32 ws1">Where </div><div class="t m4 x20 h16 y5c ff4 fsd fc0 sc0 ls33 ws1">&gt;@</div><div class="t m0 x1e h17 y5d ff3 fse fc0 sc0 ls34 ws1">12</div><div class="t m0 x2f h18 y5e ff3 fsf fc0 sc0 ls35 ws1">()<span class="_ _13"> </span>()<span class="_ _14"></span>,<span class="_ _15"> </span>()<span class="_ _14"></span>,<span class="_ _16"> </span>,<span class="_ _17"> </span>()</div><div class="t m0 x30 h19 y5f ff1 fse fc0 sc0 ls1 ws1">T</div><div class="t m0 x31 h19 y60 ff1 fse fc0 sc0 ls1 ws1">M</div><div class="c x32 y61 w5 h15"><div class="t m0 x2b h1a y5a ff1 fsf fc0 sc0 ls1 ws1">X</div></div><div class="t m0 x33 h1b y5e ff1 fsf fc0 sc0 ls36 ws1">tx<span class="_ _18"></span>t<span class="_ _19"></span>x<span class="_ _1a"></span>t<span class="_ _e"> </span>x<span class="_ _1b"></span>t<span class="_ _1c"></span><span class="ff4 ls1"> <span class="_ _1d"> </span><span class="ff5">"<span class="_ _1e"> </span><span class="ff3 ls37 ws4b"> is <span class="_ _1f"> </span>the <span class="_ _1f"> </span>signal </span></span></span></div><div class="t m0 x12 h18 y62 ff3 fsf fc0 sc0 ls38 ws4c">vector which the antenna<span class="_ _0"></span> array receives, and <span class="_ _20"></span> </div><div class="t m5 x34 h1c y63 ff4 fs10 fc0 sc0 ls39 ws1">&gt;@</div><div class="t m0 x35 h1d y64 ff3 fs11 fc0 sc0 ls3a ws1">12</div><div class="t m0 x36 h1e y65 ff3 fs12 fc0 sc0 ls3b ws1">()<span class="_ _21"> </span>()<span class="_ _14"></span>,<span class="_ _22"> </span>()<span class="_ _14"></span>,<span class="_ _16"> </span>,<span class="_ _8"> </span>()</div><div class="t m0 x37 h1f y66 ff1 fs11 fc0 sc0 ls1 ws1">T</div><div class="t m0 x38 h1f y67 ff1 fs11 fc0 sc0 ls1 ws1">l</div><div class="t m0 x39 h20 y65 ff1 fs12 fc0 sc0 ls3c ws1">St<span class="_ _c"> </span>s<span class="_ _23"> </span>t<span class="_ _24"> </span>s<span class="_ _25"> </span>t<span class="_ _26"> </span>s<span class="_ _23"> </span>t<span class="_ _27"></span><span class="ff4 ls1"> <span class="_ _28"> </span><span class="ff5">"<span class="_ _29"> </span><span class="ff3 fsf ls38 ws4d"> <span class="_ _2a"></span>is the incident signal </span></span></span></div><div class="t m0 x12 h18 y68 ff3 fsf fc0 sc0 ls3d ws4e">vector. We assume </div><div class="t m0 x3a h1d y69 ff3 fs11 fc0 sc0 ls3e ws1">12</div><div class="t m0 x15 h1e y6a ff3 fs12 fc0 sc0 ls3b ws1">()<span class="_ _14"></span>,<span class="_ _22"> </span>()<span class="_ _14"></span>,<span class="_ _16"> </span>,<span class="_ _8"> </span>()</div><div class="t m0 x3b h21 y69 ff1 fs7 fc0 sc0 ls1 ws1">l</div><div class="c x3c y6b w6 h15"><div class="t m0 x0 h22 y5a ff1 fs12 fc0 sc0 ls1 ws1">s</div></div><div class="t m0 x3d h23 y6a ff1 fs12 fc0 sc0 ls3f ws1">ts<span class="_ _0"></span>t<span class="_ _2b"> </span>s<span class="_ _9"></span>t<span class="_ _2c"></span><span class="ff5 fs8 ls1">"<span class="_ _2d"> </span><span class="ff3 fsf ls40 ws4f"> are <span class="_ _2e"> </span>all </span></span></div><div class="t m0 x12 h18 y6c ff3 fsf fc0 sc0 ls41 ws50">second order cyclostationary signals, and </div><div class="t m0 x1f h1d y6d ff3 fs11 fc0 sc0 ls42 ws1">12</div><div class="t m0 x3e h1e y6e ff3 fs12 fc0 sc0 ls43 ws1">()<span class="_ _24"> </span>[(<span class="_ _23"> </span>)<span class="_ _2f"></span>,<span class="_ _2"></span>(<span class="_ _25"> </span>)<span class="_ _2f"></span>,<span class="_ _8"> </span>,<span class="_ _2"></span>(<span class="_ _30"> </span>)<span class="_ _2f"></span>]</div><div class="t m0 x3f h21 y6d ff1 fs7 fc0 sc0 ls1 ws1">l</div><div class="t m0 x40 h22 y6e ff1 fs12 fc0 sc0 ls44 ws1">Aa<span class="_ _31"></span>a<span class="_ _16"> </span>a</div><div class="t m3 x41 h13 y6e ff4 fsc fc0 sc0 ls45 ws1">TT<span class="_ _6"></span>T<span class="_ _16"> </span>T</div><div class="t m0 x19 h20 y6e ff4 fs12 fc0 sc0 ls1 ws1"> <span class="_ _32"> </span><span class="ff5 fs8">"<span class="_ _1e"> </span><span class="ff3 fsf ls38 ws51"> <span class="_ _6"></span>is the direction </span></span></div><div class="t m0 x12 h18 y6f ff3 fsf fc0 sc0 ls46 ws52">matrix of antenna array, where</div><div class="t m0 x42 h24 y70 ff3 fs13 fc0 sc0 ls47 ws1">()<span class="_ _1"></span>[<span class="_ _33"></span>1<span class="_ _33"></span>,<span class="_ _34"> </span>,</div><div class="t m0 x43 h25 y71 ff1 fs14 fc0 sc0 ls1 ws1">k</div><div class="t m0 x44 h26 y72 ff1 fs15 fc0 sc0 ls48 ws1">jw</div><div class="t m0 x45 h26 y73 ff1 fs15 fc0 sc0 ls1 ws1">k</div><div class="t m0 x46 h27 y70 ff1 fs13 fc0 sc0 ls49 ws1">ae</div><div class="t m1 x23 h28 y70 ff4 fs16 fc0 sc0 ls1 ws1">T</div><div class="t m0 x47 h29 y72 ff4 fs15 fc0 sc0 ls1 ws1">&#58896;</div><div class="t m0 x48 h2a y70 ff4 fs13 fc0 sc0 ls1 ws1"> </div><div class="t m0 x49 h2b y74 ff3 fs17 fc0 sc0 ls4a ws1">(1<span class="_ _19"></span>)</div><div class="t m0 x41 h2c y75 ff3 fs18 fc0 sc0 ls4b ws1">,]</div><div class="t m0 x4a h2d y76 ff1 fs19 fc0 sc0 ls1 ws1">k</div><div class="t m0 x4b h2e y74 ff1 fs17 fc0 sc0 ls4c ws1">jM<span class="_ _35"> </span>w</div><div class="t m0 x4c h2e y77 ff1 fs17 fc0 sc0 ls1 ws1">T</div><div class="t m0 x4d h2f y75 ff1 fs18 fc0 sc0 ls1 ws1">e</div><div class="t m0 x4e h30 y74 ff4 fs17 fc0 sc0 ls4d ws1">&#58896;&#58896;</div><div class="t m0 x4f h31 y75 ff5 fs18 fc0 sc0 ls1 ws1">"<span class="_ _1d"> </span><span class="ff3 fsf">,</span></div><div class="t m0 x50 h2b y78 ff3 fs17 fc0 sc0 ls1 ws1">0</div><div class="t m0 x51 h2c y75 ff3 fs18 fc0 sc0 ls4e ws1">(2<span class="_ _c"> </span>/<span class="_ _36"> </span>)<span class="_ _2"></span>si<span class="_ _0"></span>n<span class="_ _0"></span>(<span class="_ _37"> </span>)</div><div class="t m0 x52 h2e y78 ff1 fs17 fc0 sc0 ls4f ws1">kk</div><div class="t m0 x53 h2f y75 ff1 fs18 fc0 sc0 ls1 ws1">d</div><div class="t m3 x54 h13 y75 ff4 fsc fc0 sc0 ls50 ws1">ZS<span class="_ _33"></span>OT</div><div class="t m0 x55 h20 y75 ff4 fs12 fc0 sc0 ls1 ws1"> <span class="_ _38"> </span><span class="ff3 fs2">.</span></div><div class="t m0 x12 h18 y79 ff3 fsf fc0 sc0 ls51 ws53">The Vanderm<span class="_ _0"></span>onde m<span class="_ _0"></span>atrix of </div><div class="t m0 x56 h2f y7a ff3 fs18 fc0 sc0 ls52 ws1">()<span class="_ _39"></span><span class="ff1 ls1">A</span></div><div class="t m3 x57 h13 y7a ff4 fsc fc0 sc0 ls1 ws1">T</div><div class="t m0 x46 h18 y7a ff3 fsf fc0 sc0 ls53 ws54"> is </div><div class="t m0 x58 h32 y7b ff3 fs1a fc0 sc0 ls54 ws1">12</div><div class="t m0 x3d h32 y7c ff3 fs1a fc0 sc0 ls1 ws1">2</div><div class="t m0 x59 h33 y7d ff3 fs1b fc0 sc0 ls55 ws1">(1<span class="_ _3a"></span>)<span class="_ _3b"> </span>(1<span class="_ _3a"></span>)</div><div class="t m0 x5a h33 y7e ff3 fs1b fc0 sc0 ls55 ws1">(1<span class="_ _3a"></span>)</div><div class="t m0 x1f h34 y7f ff3 fs1c fc0 sc0 ls56 ws1">11<span class="_ _3c"> </span>1</div><div class="t m0 x36 h34 y80 ff3 fs1c fc0 sc0 ls57 ws1">()</div><div class="t m0 x25 h35 y81 ff1 fs1a fc0 sc0 ls1 ws1">l</div><div class="t m0 x5b h35 y82 ff1 fs1a fc0 sc0 ls58 ws1">kl</div><div class="t m0 x5c h36 y83 ff1 fs1b fc0 sc0 ls1 ws1">j</div><div class="t m0 x13 h36 y84 ff1 fs1b fc0 sc0 ls59 ws1">jj</div><div class="t m0 x2c h36 y85 ff1 fs1b fc0 sc0 ls5a ws1">jM<span class="_ _3d"> </span>jM</div><div class="t m0 x5d h36 y86 ff1 fs1b fc0 sc0 ls5a ws1">jM</div><div class="t m0 x2c h37 y87 ff1 fs1c fc0 sc0 ls5b ws1">ee<span class="_ _26"> </span>e</div><div class="t m0 x39 h37 y88 ff1 fs1c fc0 sc0 ls1 ws1">A</div><div class="t m0 x5e h37 y89 ff1 fs1c fc0 sc0 ls5c ws1">ee<span class="_ _3c"> </span>e</div><div class="t m6 x24 h38 y83 ff4 fs1d fc0 sc0 ls1 ws1">Z</div><div class="t m6 x2e h38 y84 ff4 fs1d fc0 sc0 ls5d ws1">ZZ</div><div class="t m6 x20 h38 y85 ff4 fs1d fc0 sc0 ls5e ws1">ZZ</div><div class="t m6 x15 h38 y86 ff4 fs1d fc0 sc0 ls1 ws1">Z</div><div class="t m1 x1c h39 y8a ff4 fs1e fc0 sc0 ls1 ws1">T</div><div class="t m0 x30 h3a y83 ff4 fs1b fc0 sc0 ls1 ws1">&#58896;</div><div class="t m0 x5f h3a y84 ff4 fs1b fc0 sc0 ls5f ws1">&#58896;&#58896;</div><div class="t m0 x60 h3a y85 ff4 fs1b fc0 sc0 ls60 ws1">&#58896;&#58896;<span class="_ _3e"> </span>&#58896;&#58896;</div><div class="t m0 x55 h3a y86 ff4 fs1b fc0 sc0 ls60 ws1">&#58896;&#58896;</div><div class="t m0 x1a h3b y8b ff4 fs1c fc0 sc0 ls61 ws1">&#170;&#186;</div><div class="t m0 x1a h3b y8c ff4 fs1c fc0 sc0 ls61 ws1">&#171;&#187;</div><div class="t m0 x1a h3b y8d ff4 fs1c fc0 sc0 ls61 ws1">&#171;&#187;</div><div class="t m0 x61 h3b y8e ff4 fs1c fc0 sc0 ls1 ws1"> </div><div class="t m0 x1a h3b y8f ff4 fs1c fc0 sc0 ls61 ws1">&#171;&#187;</div><div class="t m0 x1a h3b y90 ff4 fs1c fc0 sc0 ls61 ws1">&#171;&#187;</div><div class="t m0 x1a h3b y91 ff4 fs1c fc0 sc0 ls61 ws1">&#172;&#188;</div><div class="t m0 x62 h3c y92 ff5 fs1c fc0 sc0 ls1 ws1">"</div><div class="t m0 x62 h3c y93 ff5 fs1c fc0 sc0 ls1 ws1">"</div><div class="t m0 x63 h3c y94 ff5 fs1c fc0 sc0 ls62 ws1">""<span class="_ _3f"></span>"<span class="_ _40"></span>"</div><div class="t m0 x62 h3c y95 ff5 fs1c fc0 sc0 ls1 ws1">"</div><div class="t m0 x64 h18 y96 ff3 fsf fc0 sc0 ls63 ws1"> (2<span class="_ _0"></span>)<span class="_ _0"></span> </div><div class="t m0 x12 h18 y97 ff3 fsf fc0 sc0 ls64 ws1">Where</div><div class="t m0 x1e h2b y98 ff3 fs17 fc0 sc0 ls65 ws1">12</div><div class="t m0 x2f h2c y99 ff3 fs18 fc0 sc0 ls66 ws1">()<span class="_ _22"> </span>[<span class="_ _8"> </span>()<span class="_ _14"></span>,<span class="_ _15"> </span>()<span class="_ _14"></span>,<span class="_ _41"> </span>()<span class="_ _14"></span>]</div><div class="t m0 x65 h2e y98 ff1 fs17 fc0 sc0 ls1 ws1">M</div><div class="t m0 x66 h20 y99 ff1 fs18 fc0 sc0 ls67 ws1">Nt<span class="_ _2b"> </span>n<span class="_ _1f"> </span>t<span class="_ _25"> </span>n<span class="_ _e"> </span>t<span class="_ _2b"> </span>n<span class="_ _22"> </span>t<span class="_ _42"></span><span class="ff4 fs12 ls1"> <span class="_ _43"> </span><span class="ff5 fs18">"<span class="_ _44"> </span><span class="ff3 fsf ls68 ws55"> <span class="_ _20"></span>is the noise </span></span></span></div><div class="t m0 x12 h18 y9a ff3 fsf fc0 sc0 ls38 ws56">vector which the antenna array received, and all<span class="_ _0"></span> </div><div class="t m0 x12 h18 y9b ff3 fsf fc0 sc0 ls38 ws57">the noises that each array element receives obey<span class="_ _0"></span> </div><div class="t m0 x12 h18 y9c ff3 fsf fc0 sc0 ls69 ws1">the</div><div class="t m1 x67 h6 y9d ff4 fs4 fc0 sc0 ls1 ws1">D</div><div class="t m0 x68 h18 y9d ff3 fsf fc0 sc0 ls69 ws58">-stable distribution</div><div class="t m0 x69 h7 y9e ff3 fs5 fc0 sc0 ls19 ws1">[7]</div><div class="t m0 x37 h18 y9d ff3 fsf fc0 sc0 ls1 ws1">.</div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div> </body> </html>
评论
  • 维生素 2020-01-21 01:36:34
    论文,不是程序
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