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<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/62562e866817e268f0e0a266/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Description o<span class="_ _0"></span>f the MA<span class="_ _1"></span>TLAB</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls1 ws1">®</div><div class="t m0 x3 h2 y1 ff1 fs0 fc0 sc0 ls2 ws2"> implementation</div><div class="t m0 x4 h2 y3 ff1 fs0 fc0 sc0 ls3 ws3">of a MIMO c<span class="_ _0"></span>hannel model</div><div class="t m0 x5 h2 y4 ff1 fs0 fc0 sc0 ls4 ws4">suited for link-le<span class="_ _2"></span>v<span class="_ _0"></span>el simulations</div><div class="t m0 x6 h4 y5 ff2 fs2 fc0 sc0 ls5 ws5">Laurent Schumacher, AAU-TKN/I<span class="_ _2"></span>ES/KOM/CPK/CSys</div><div class="t m0 x7 h4 y6 ff2 fs2 fc0 sc0 ls6 ws6">Implementation note version 0.1 – March 2002</div><div class="t m0 x8 h5 y7 ff1 fs3 fc0 sc0 ls7 ws7">Table of contents</div><div class="t m0 x8 h6 y8 ff2 fs3 fc1 sc0 ls8 ws1">1.<span class="_ _3"> </span>Introduction</div><div class="t m0 x9 h6 y9 ff2 fs3 fc0 sc0 ls9 ws1">.................................................................................<span class="_ _4"> </span>2</div><div class="t m0 x8 h6 ya ff2 fs3 fc1 sc0 lsa ws8">2.<span class="_ _3"> </span>Spatial correlation<span class="_ _1"></span> – Directory <span class="ff3 lsb ws1">Correlation_M<span class="_ _1"></span>ultiple_Cluster<span class="_ _4"> </span><span class="ff2 fc0 ls9">........<span class="_ _4"> </span>3</span></span></div><div class="t m0 x8 h6 yb ff2 fs3 fc1 sc0 ls1 ws9">3.<span class="_ _3"> </span>MIMO radio channel<span class="_ _1"></span> – Directory <span class="ff3 lsc ws1">UM<span class="_ _1"></span>TS_Testbed<span class="_ _5"> </span><span class="ff2 fc0 ls9">........................<span class="_ _4"> </span>5</span></span></div><div class="t m0 xa h7 yc ff2 fs4 fc1 sc0 lsd wsa">1.<span class="_ _6"> </span>Initialisatio<span class="_ _2"></span>n phase<span class="_ _7"> </span><span class="fc0 lse ws1">.....................................................................................<span class="_"> </span>5</span></div><div class="t m0 xa h7 yd ff2 fs4 fc1 sc0 lsf wsb">2.<span class="_ _6"> </span>Processing<span class="_ _1"></span> phase<span class="_ _7"></span><span class="fc0 lse ws1">......................................................................................<span class="_ _8"> </span>6</span></div><div class="t m0 xa h7 ye ff2 fs4 fc1 sc0 lsf wsb">3.<span class="_ _6"> </span>Post-processi<span class="_ _1"></span>ng phase<span class="_ _7"></span><span class="fc0 lse ws1">..............................................................................<span class="_ _8"> </span>8</span></div><div class="t m0 x8 h6 yf ff2 fs3 fc1 sc0 ls10 wsc">4.<span class="_ _3"> </span>Distribution<span class="_ _0"></span> terms<span class="_"> </span><span class="fc0 ls11 ws1">......................................................................<span class="_ _4"> </span>11</span></div><div class="t m0 x8 h6 y10 ff2 fs3 fc1 sc0 ls12 ws1">5.<span class="_ _3"> </span>Conclusion<span class="_"> </span><span class="fc0 ls11">................................................................................<span class="_ _4"> </span>11</span></div><div class="t m0 x8 h6 y11 ff2 fs3 fc1 sc0 ls13 ws1">6.<span class="_ _3"> </span>References<span class="_ _7"></span><span class="fc0 ls11">................................................................................<span class="_ _4"> </span>11</span></div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>
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<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62562e866817e268f0e0a266/bg2.jpg"><div class="t m0 x8 h8 y12 ff1 fs5 fc0 sc0 ls14 wsd">1. Introduction</div><div class="t m0 x8 h4 y13 ff2 fs2 fc0 sc0 ls15 wse">This document describes the content o<span class="_ _0"></span>f the two MATLAB</div><div class="t m0 xb h9 y14 ff2 fs6 fc0 sc0 ls1 ws1">®</div><div class="t m0 xc h4 y13 ff2 fs2 fc0 sc0 ls16 wsf"> directories</div><div class="t m0 x8 h4 y15 ff3 fs2 fc0 sc0 ls17 ws1">Correlation_Multiple_Clust<span class="_ _2"></span>er<span class="ff2 ls15 ws10"> and </span><span class="ls18">UMTS_Testbed<span class="ff2 ls19 ws11">. They contain MATLAB</span></span></div><div class="t m0 xd h9 y16 ff2 fs6 fc0 sc0 ls1 ws1">®</div><div class="t m0 xe h4 y17 ff2 fs2 fc0 sc0 ls1a ws12"> scripts<span class="_ _0"></span> that</div><div class="t m0 x8 h4 y18 ff2 fs2 fc0 sc0 ls1b ws13">enable their user to</div><div class="t m0 xf ha y19 ff4 fs2 fc0 sc0 ls1 ws1">•<span class="ff2 ls1b ws14"> <span class="_ _9"> </span>Derive the spatial correlation properties of a Uniform Linear Array (ULA)</span></div><div class="t m0 x10 h4 y1a ff2 fs2 fc0 sc0 ls1c ws15">impinged by a variety of Power Azimuth <span class="_ _2"></span>Spectra (PAS), namely <span class="_ _2"></span>uniform,</div><div class="t m0 x10 h4 y1b ff2 fs2 fc0 sc0 ls6 ws16">truncated Gaussian and truncated Laplacian, w<span class="_ _1"></span>her<span class="_ _2"></span>e the waves are <span class="_ _0"></span>gathered in a</div><div class="t m0 x10 h4 y1c ff2 fs2 fc0 sc0 ls17 ws17">single or in <span class="_ _1"></span>mult<span class="_ _2"></span>iple clusters. <span class="_ _0"></span>The relations applied to derive these properties are</div><div class="t m0 x10 h4 y1d ff2 fs2 fc0 sc0 ls1c ws18">detailed in [1].</div><div class="t m0 xf ha y1e ff4 fs2 fc0 sc0 ls1 ws1">•<span class="ff2 ls1d ws19"> <span class="_ _a"> </span>Simulate a Multiple-Input<span class="_ _2"></span> Multiple-Output (MIMO) radio channel at link-level in</span></div><div class="t m0 x10 h4 y1f ff2 fs2 fc0 sc0 ls1e ws1a">compliance with 3GPP specifications [2]. The <span class="_ _2"></span>simulated model <span class="_ _2"></span>is of stochastic</div><div class="t m0 x10 h4 y20 ff2 fs2 fc0 sc0 ls1f ws1b">type. It is fully described in [3, 4].</div><div class="t m0 x8 h4 y21 ff2 fs2 fc0 sc0 ls16 ws1c">Figure 1 summarises the interactions between the scripts o<span class="_ _0"></span>f the two directories.</div><div class="t m1 x11 hb y22 ff5 fs7 fc0 sc0 ls1 ws1"><span class="fc2 sc0"> </span></div><div class="t m1 x12 hc y23 ff2 fs7 fc0 sc0 ls20 ws1">exampl<span class="_ _0"></span>e_mimo.<span class="_ _1"></span>m </div><div class="t m1 x13 hc y24 ff2 fs7 fc0 sc0 ls21 ws1">Three_GPP_cases.m </div><div class="t m1 x14 hc y25 ff2 fs7 fc0 sc0 ls22 ws1">correlat<span class="_ _2"></span>ion.m </div><div class="t m1 x15 hc y26 ff2 fs7 fc0 sc0 ls23 ws1">init_<span class="_ _2"></span>Rice.m<span class="_ _2"></span> </div><div class="t m1 x13 hc y27 ff2 fs7 fc0 sc0 ls24 ws1">init_f<span class="_ _2"></span>ading.m </div><div class="t m1 x13 hc y28 ff2 fs7 fc0 sc0 ls25 ws1">init_MIM<span class="_ _0"></span>O_channel.m<span class="_ _1"></span> </div><div class="t m1 x13 hc y29 ff2 fs7 fc0 sc0 ls26 ws1">MIMO_c<span class="_ _0"></span>hannel.m </div><div class="t m1 x12 hc y2a ff2 fs7 fc0 sc0 ls27 ws1">plot_mim<span class="_ _1"></span>o.m </div><div class="t m1 x16 hc y23 ff2 fs7 fc0 sc0 ls25 ws1">geometry2<span class="_ _1"></span>c<span class="_ _2"></span>orrelatio<span class="_ _1"></span>n.m</div><div class="t m1 x14 hc y24 ff2 fs7 fc0 sc0 ls28 ws1">dialog<span class="_ _0"></span>.m </div><div class="t m1 x17 hc y28 ff2 fs7 fc0 sc0 ls29 ws1">AS2<span class="_ _2"></span>si<span class="_ _2"></span>gma_<span class="_ _2"></span>gau<span class="_ _2"></span>ssi<span class="_ _2"></span>an<span class="_ _2"></span>.ma<span class="_ _2"></span>t </div><div class="t m1 x17 hc y2a ff2 fs7 fc0 sc0 ls2a ws1">AS2sigma_lapl<span class="_ _1"></span>acian.mat </div><div class="t m1 x14 hc y2b ff2 fs7 fc0 sc0 ls2b ws1">plot_uni<span class="_ _1"></span>f<span class="_ _2"></span>orm.m </div><div class="t m1 x14 hc y2c ff2 fs7 fc0 sc0 ls2c ws1">plot_la<span class="_ _0"></span>placian.m </div><div class="t m1 x14 hc y2d ff2 fs7 fc0 sc0 ls2d ws1">plot_gauss<span class="_ _0"></span>ian.m </div><div class="t m1 x18 hc y2e ff2 fs7 fc0 sc0 ls28 ws1">Rxy<span class="_ _0"></span>_uniform.m </div><div class="t m1 x18 hc y2f ff2 fs7 fc0 sc0 ls2e ws1">Rxy<span class="_ _1"></span>_laplacian.m </div><div class="t m1 x18 hc y30 ff2 fs7 fc0 sc0 ls2f ws1">Rxy<span class="_ _1"></span>_gaussian.m </div><div class="t m1 x19 hc y31 ff2 fs7 fc0 sc0 ls2f ws1">erfcom<span class="_ _0"></span>p.m </div><div class="t m1 x18 hc y32 ff2 fs7 fc0 sc0 ls28 ws1">Rxx<span class="_ _0"></span>_uniform.m </div><div class="t m1 x18 hc y29 ff2 fs7 fc0 sc0 ls30 ws1">normal<span class="_ _0"></span>isation<span class="_ _1"></span>_laplacian.m </div><div class="t m1 x18 hc y33 ff2 fs7 fc0 sc0 ls2f ws1">Rxx<span class="_ _1"></span>_gaussian.m </div><div class="t m1 x18 hc y34 ff2 fs7 fc0 sc0 ls2e ws1">Rxx<span class="_ _1"></span>_laplacian.m </div><div class="t m1 x18 hc y26 ff2 fs7 fc0 sc0 ls31 ws1">normal<span class="_ _0"></span>isation<span class="_ _1"></span>_uniform.m </div><div class="t m1 x18 hc y27 ff2 fs7 fc0 sc0 ls2f ws1">normal<span class="_ _0"></span>isation<span class="_ _1"></span>_gaussian.m </div><div class="t m1 x1a hd y35 ff6 fs7 fc0 sc0 ls32 ws1">UMT<span class="_ _0"></span>S_Testbed <span class="_ _b"> </span><span class="ls33">Correlation<span class="_ _0"></span>_Multiple_C<span class="_ _0"></span>luster</span></div><div class="t m0 x1b he y36 ff1 fs2 fc0 sc0 ls19 ws1d">Figure 1: Interactions bet<span class="_ _0"></span>ween the MATLAB</div><div class="t m0 x1c hf y37 ff1 fs6 fc0 sc0 ls1 ws1">®</div><div class="t m0 x1d he y36 ff1 fs2 fc0 sc0 ls34 ws1e"> scripts</div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>
<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62562e866817e268f0e0a266/bg3.jpg"><div class="t m0 x8 h4 y38 ff2 fs2 fc0 sc0 ls16 ws1f">Following the description <span class="_ _1"></span>of t<span class="_ _2"></span>hese packages, v<span class="_ _0"></span>alidation results are presented. The</div><div class="t m0 x8 h4 y39 ff2 fs2 fc0 sc0 ls16 ws6">distribution terms of these packages are stated at the end<span class="_ _1"></span> of the document.</div><div class="t m0 x8 h8 y3a ff1 fs5 fc0 sc0 ls35 ws20">2. <span class="_ _c"> </span>Spatial correlation – Director<span class="_ _2"></span>y <span class="_ _0"></span><span class="ff6 ws1">Correlation<span class="_ _2"></span>_Multiple_Cl<span class="_ _2"></span>uster</span></div><div class="t m0 x8 h4 y3b ff2 fs2 fc0 sc0 ls18 ws21">The main script is <span class="ff3 ls36 ws1">geometry2<span class="_ _0"></span>correl<span class="_ _0"></span>ation<span class="_ _1"></span>.m<span class="ff2 ls1b ws22">. Through a dialogue with the user, this script</span></span></div><div class="t m0 x8 h4 y3c ff2 fs2 fc0 sc0 ls18 ws23">first collects all the infor<span class="_ _2"></span>mation requested to fully characterise the scenario, namely t<span class="_ _2"></span>he</div><div class="t m0 x8 h4 y3d ff2 fs2 fc0 sc0 ls19 ws24">number of antenna elements of the ULAs at the User Equipment (UE) <span class="_ _2"></span>and at the <span class="_ _2"></span>Node</div><div class="t m0 x8 h4 y3e ff2 fs2 fc0 sc0 ls1c ws25">B, their spacings, the PAS types of the impinging waves, their Azimuth Spreads (AS),</div><div class="t m0 x8 h4 y3f ff2 fs2 fc0 sc0 ls37 ws26">and their Angle of Departure (AoD)/Angle of Arrival (AoA).</div><div class="t m0 x8 h4 y40 ff2 fs2 fc0 sc0 ls19 ws27">In a second<span class="_ _0"></span> phase, the spatial correlation properties are derived by the script</div><div class="t m0 x8 h4 y41 ff3 fs2 fc0 sc0 ls38 ws1">correla<span class="_ _0"></span>tion<span class="_ _0"></span>.m<span class="ff2 ls1">.</span></div><div class="t m0 x8 h4 y42 ff2 fs2 fc0 sc0 ls1b ws28">The first step of this phase is to nor<span class="_ _0"></span>malise the PAS such that it can be regarded <span class="_ _2"></span>as a</div><div class="t m0 x8 h4 y43 ff2 fs2 fc0 sc0 ls1b ws13">probability distribution,<span class="_ _2"></span> which means that</div><div class="t m2 x1e h10 y44 ff4 fs8 fc0 sc0 ls39 ws1">()</div><div class="t m0 x1f h11 y45 ff7 fs9 fc0 sc0 ls1 ws1">ò</div><div class="t m0 x20 h12 y46 ff4 fs9 fc0 sc0 ls1 ws1">=</div><div class="t m0 x21 h13 y47 ff4 fsa fc0 sc0 ls1 ws1">−</div><div class="t m3 x22 h14 y48 ff4 fsb fc0 sc0 ls1 ws1">π</div><div class="t m3 x23 h14 y49 ff4 fsb fc0 sc0 ls1 ws1">π</div><div class="t m4 x24 h15 y4a ff4 fsc fc0 sc0 ls1 ws1">ϕ<span class="_ _d"></span>ϕ</div><div class="t m0 x25 h16 y4a ff2 fs9 fc0 sc0 ls1 ws1">1<span class="_ _e"></span><span class="ff3">d<span class="_ _f"></span>PAS</span></div><div class="t m0 x26 h4 y4b ff2 fs2 fc0 sc0 ls3a ws1">(1)</div><div class="t m0 x8 h4 y4c ff2 fs2 fc0 sc0 ls1e ws29">On the other hand, this normalisation step, <span class="_ _2"></span>performed in <span class="ff3 ws1">normalisat<span class="_ _2"></span>ion_*.m</span><span class="ls3b ws2a"> scripts,</span></div><div class="t m0 x8 h4 y4d ff2 fs2 fc0 sc0 ls6 ws2b">serves to <span class="_ _1"></span>der<span class="_ _2"></span>ive the <span class="_ _1"></span>st<span class="_ _2"></span>andard deviation <span class="_ _0"></span>of this pdf, based on<span class="_ _0"></span> the AS defined by the user<span class="_ _0"></span>,</div><div class="t m0 x8 h4 y4e ff2 fs2 fc0 sc0 ls1b ws13">as there is not necessarily an identity between them.</div><div class="t m0 x8 h4 y4f ff2 fs2 fc0 sc0 ls17 ws2c">Being normalised, th<span class="_ _2"></span>e PAS is then in<span class="_ _0"></span>tegrated over <span class="_ _2"></span>its definition dom<span class="_ _2"></span>ain according to t<span class="_ _2"></span>he</div><div class="t m0 x8 h4 y50 ff2 fs2 fc0 sc0 ls19 ws2d">relations established in [1] to derive the spatial correlation coefficients. The coefficients</div><div class="t m0 x8 h4 y51 ff2 fs2 fc0 sc0 ls3c ws2e">of the homogeneous products betw<span class="_ _0"></span>een real (imaginary) parts ar<span class="_ _2"></span>e derived in <span class="ff3 ls3d ws1">Rxx_*.m</span></div><div class="t m0 x8 h4 y52 ff2 fs2 fc0 sc0 ls16 ws2f">scripts, while <span class="_ _0"></span>the mixed products between real and imaginary parts are handled by</div><div class="t m0 x8 h4 y53 ff3 fs2 fc0 sc0 ls3e ws1">Rxy_*.m<span class="ff2 ls6 ws30"> scripts. Their outcome is co<span class="_ _0"></span>mbined to produce either complex f<span class="_ _2"></span>ield spatial</span></div><div class="t m0 x8 h4 y54 ff2 fs2 fc0 sc0 ls19 ws31">correlation coefficients or real pow<span class="_ _1"></span>er<span class="_ _2"></span> ones, depending on the value o<span class="_ _1"></span>f<span class="_ _2"></span> a calling variable</div><div class="t m0 x8 h4 y55 ff2 fs2 fc0 sc0 ls37 ws32">of the <span class="_ _2"></span><span class="ff3 ls38 ws1">correl<span class="_ _0"></span>ation<span class="_ _1"></span>.m<span class="ff2 ls3f ws33"> script.</span></span></div><div class="t m0 x8 h4 y56 ff2 fs2 fc0 sc0 ls17 ws34">Finally, the correlation coefficients fill two matrices defined at the UE and a<span class="_ _0"></span>t the Node B,</div><div class="t m0 x8 h4 y57 ff2 fs2 fc0 sc0 ls19 ws1">respectively </div><div class="t m0 x27 h17 y58 ff3 fsd fc0 sc0 ls1 ws1">UE</div><div class="t m0 x28 h18 y59 ff1 fs4 fc0 sc0 ls1 ws1">R<span class="_ _10"> </span><span class="ff2 fs2 ls15 ws35"> and </span></div><div class="t m0 x29 h19 y58 ff3 fsd fc0 sc0 ls1 ws1">B<span class="_ _11"></span>Node<span class="ff2"> </span></div><div class="t m0 x2a h18 y59 ff1 fs4 fc0 sc0 ls1 ws1">R<span class="_ _12"> </span><span class="ff2 fs2 ls16 ws36">. These s<span class="_ _0"></span>patial correlation matrices are combined through</span></div><div class="t m0 x8 h4 y5a ff2 fs2 fc0 sc0 ls17 ws37">a Kronecker p<span class="_ _0"></span>roduct as proposed in [3, 4]. The structure of the Kronec<span class="_ _0"></span>ker product</div><div class="t m0 x8 h4 y5b ff2 fs2 fc0 sc0 ls6 ws6">depends whether one w<span class="_ _0"></span>ants to simulate a downlink transmission</div><div class="t m0 x2b h17 y5c ff3 fsd fc0 sc0 ls1 ws1">UE<span class="_ _13"></span>B<span class="_ _11"></span>Node</div><div class="t m0 x2c h1a y5d ff1 fs4 fc0 sc0 ls1 ws1">R<span class="_ _14"></span>R<span class="_ _15"></span>R<span class="_ _16"> </span><span class="ff4">⊗<span class="_ _17"></span>=</span></div><div class="t m0 x2d h19 y5c ff2 fsd fc0 sc0 ls1 ws1"> </div><div class="t m0 x2e h4 y5e ff2 fs2 fc0 sc0 ls3a ws1">(2)</div><div class="t m0 x8 h4 y5f ff2 fs2 fc0 sc0 ls6 ws6">or an uplink one</div><div class="t m0 x14 h19 y60 ff3 fsd fc0 sc0 ls1 ws1">B<span class="_ _11"></span>Node<span class="_ _18"></span>UE<span class="_ _19"> </span><span class="ff2"> </span></div><div class="t m0 x2f h1a y61 ff1 fs4 fc0 sc0 ls1 ws1">R<span class="_ _1a"></span>R<span class="_ _15"></span>R<span class="_ _1b"> </span><span class="ff4">⊗<span class="_ _1c"></span>=</span></div><div class="t m0 x30 h4 y62 ff2 fs2 fc0 sc0 ls3a ws1">(3)</div><div class="t m0 x8 h4 y63 ff2 fs2 fc0 sc0 ls15 ws1">where </div><div class="t m0 x31 h1b y64 ff4 fse fc0 sc0 ls1 ws1">⊗<span class="_ _4"></span><span class="ff2 fs2 ls19 ws1d">r<span class="_ _2"></span>epresents the operator of the Kronecker produc<span class="_ _0"></span>t.</span></div><div class="t m0 x8 h4 y65 ff2 fs2 fc0 sc0 ls17 ws38">As a <span class="_ _1"></span>m<span class="_ _2"></span>atter of illustration, Figure 2 shows 2-cluster PASs, where both clusters are</div><div class="t m0 x8 h4 y66 ff2 fs2 fc0 sc0 ls6 ws39">constrained within [-60°, 60°] around their AOAs {-90°, 90°}<span class="_ _0"></span> and exhibit an AS of 30°.</div><div class="t m0 x8 h4 y67 ff2 fs2 fc0 sc0 ls19 ws3a">Note that the second cluster has hal<span class="_ _1"></span>f<span class="_ _2"></span> the power of the first one. <span class="_ _0"></span>The <span class="_ _2"></span>envelope correlation</div><div class="t m0 x8 h4 y68 ff2 fs2 fc0 sc0 ls16 ws3b">coefficient of two distant antennas impinged by these PASs is<span class="_ _0"></span> shown in Figur<span class="_ _2"></span>e 3 <span class="_ _2"></span>as a</div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>
