PDA_Detection.zip_mimo_mimo detection_通讯编程下载-pudn.com

<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 COMMUNICATION LETTERS, VOL. 5, NO. 9, SEPTEMBER 2001 361</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls0 ws0">Near-Optimal Multiuser Detection in Synchronous</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls0 ws0">CDMA Using Probabilistic Data Association</div><div class="t m0 x4 h4 y4 ff1 fs2 fc0 sc0 ls0 ws0">J. Luo, Student Member, IEEE, K. R. Pattipati, Fellow, IEEE, P. K. Willett, Senior Member, IEEE, and</div><div class="t m0 x5 h4 y5 ff1 fs2 fc0 sc0 ls1 ws0">F. Hasegawa, Member, IEEE</div><div class="t m0 x2 h5 y6 ff3 fs3 fc0 sc0 ls0 ws0">Abstract—A Probabilistic Data Association (PDA) method is</div><div class="t m0 x1 h5 y7 ff4 fs3 fc0 sc0 ls0 ws0">proposed in this letter for multiuser detection over synchronous</div><div class="t m0 x1 h5 y8 ff4 fs3 fc0 sc0 ls0 ws0">code-division multiple-access (CDMA) communication chan-</div><div class="t m0 x1 h5 y9 ff4 fs3 fc0 sc0 ls0 ws0">nels. PDA models the undecided user signals as binary random</div><div class="t m0 x1 h5 ya ff4 fs3 fc0 sc0 ls0 ws0">variables. By approximating the inter-user interference (IUI) as</div><div class="t m0 x1 h5 yb ff4 fs3 fc0 sc0 ls0 ws0">Gaussian noise with an appropriately elevated covariance matrix,</div><div class="t m0 x1 h5 yc ff4 fs3 fc0 sc0 ls0 ws0">the probability associated with each user signal is iteratively</div><div class="t m0 x1 h5 yd ff4 fs3 fc0 sc0 ls0 ws0">updated. Computer simulations show that the system usually con-</div><div class="t m0 x1 h5 ye ff4 fs3 fc0 sc0 ls0 ws0">verges within three to four iterations, and the resulting probability</div><div class="t m0 x1 h5 yf ff4 fs3 fc0 sc0 ls0 ws0">of error is very close to that of the optimal maximum-likelihood</div><div class="t m0 x1 h5 y10 ff4 fs3 fc0 sc0 ls0 ws0">(ML) detector. Further modifications are also presented to</div><div class="t m0 x1 h5 y11 ff4 fs3 fc0 sc0 ls0 ws0">significantly reduce the computational cost.</div><div class="t m0 x6 h5 y12 ff3 fs3 fc0 sc0 ls0 ws0">Index Terms—Code division multiple access, multiuser detec-</div><div class="t m0 x1 h5 y13 ff4 fs3 fc0 sc0 ls0 ws0">tion, probabilistic data association.</div><div class="t m0 x7 h6 y14 ff1 fs4 fc0 sc0 ls0 ws0">I. INTRODUCTION</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 MULTIUSER detection (MUD) problem in syn-</div><div class="t m0 x8 h6 y17 ff1 fs4 fc0 sc0 ls0 ws0">chronous code-division multiple-access (CDMA)</div><div class="t m0 x1 h6 y18 ff1 fs4 fc0 sc0 ls0 ws0">communication systems has been widely studied in the past</div><div class="t m0 x1 h6 y19 ff1 fs4 fc0 sc0 ls0 ws0">decade. Since the computation of an optimal maximum-like-</div><div class="t m0 x1 h6 y1a ff1 fs4 fc0 sc0 ls0 ws0">lihood (ML) detector is exponential in the number of users,</div><div class="t m0 x1 h6 y1b ff1 fs4 fc0 sc0 ls0 ws0">suboptimal solutions are proposed to provide reliable decisions</div><div class="t m0 x1 h6 y1c ff1 fs4 fc0 sc0 ls0 ws0">with relatively low computational cost. Among them are the</div><div class="t m0 x1 h6 y1d ff1 fs4 fc0 sc0 ls0 ws0">conventional decorrelator [1], the decision feedback detector</div><div class="t m0 x1 h6 y1e ff1 fs4 fc0 sc0 ls0 ws0">(DFD) [3], [6], the multistage detector [2] and the group</div><div class="t m0 x1 h6 y1f ff1 fs4 fc0 sc0 ls0 ws0">detector [5], [8]. Although DFD is one of the most efficient</div><div class="t m0 x1 h6 y20 ff1 fs4 fc0 sc0 ls0 ws0">methods, in most cases the gap between the probability of error</div><div class="t m0 x1 h6 y21 ff1 fs4 fc0 sc0 ls0 ws0">of the DFD and that of a ML detector is still large. The DFD</div><div class="t m0 x1 h6 y22 ff1 fs4 fc0 sc0 ls0 ws0">can be considered a special case of a group detector with unity</div><div class="t m0 x1 h6 y23 ff1 fs4 fc0 sc0 ls0 ws0">maximum group size, and the performance gap becomes nar-</div><div class="t m0 x1 h6 y24 ff1 fs4 fc0 sc0 ls0 ws0">rower as this is increased. However, despite the improvements</div><div class="t m0 x1 h6 y25 ff1 fs4 fc0 sc0 ls0 ws0">described in [8], finding the optimal group assignment and user</div><div class="t m0 x1 h6 y26 ff1 fs4 fc0 sc0 ls0 ws0">ordering remains expensive.</div><div class="t m0 x9 h6 y27 ff1 fs4 fc0 sc0 ls0 ws0">The probabilistic data association (PDA) filter [4] is a highly</div><div class="t m0 x1 h6 y28 ff1 fs4 fc0 sc0 ls0 ws0">successful approach to target tracking in the case that measure-</div><div class="t m0 x1 h6 y29 ff1 fs4 fc0 sc0 ls0 ws0">ments are unlabeled and may be spurious. Its key feature is a</div><div class="t m0 x1 h6 y2a ff1 fs4 fc0 sc0 ls0 ws0">repeated conversion of a multimodal Gaussian mixture proba-</div><div class="t m0 x1 h6 y2b ff1 fs4 fc0 sc0 ls0 ws0">bility structure to a single Gaussian with matched mean and co-</div><div class="t m0 x1 h6 y2c ff1 fs4 fc0 sc0 ls0 ws0">variance. This is a bold and to some extent unjustifiable step,</div><div class="t m0 xa h8 y2d ff1 fs5 fc0 sc0 ls0 ws0">Manuscript received March 30, 2001. The associate editor coordinating the</div><div class="t m0 x1 h8 y2e ff1 fs5 fc0 sc0 ls0 ws0">review of this letter and approving it for publication was Prof. S. W. Kim.</div><div class="t m0 x1 h8 y2f ff1 fs5 fc0 sc0 ls0 ws0">This work was supported by the Office of Naval Research under Contract</div><div class="t m0 x1 h8 y30 ff1 fs5 fc0 sc0 ls0 ws0">N00014-98-1-0465, N00014-00-1-0101, and by NUWC under 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 authors are with the Electrical and Computer Engineering De-</div><div class="t m0 x1 h8 y33 ff1 fs5 fc0 sc0 ls0 ws0">partment, University of Connecticut, Storrs, CT 06269 USA (e-mail:</div><div class="t m0 x1 h8 y34 ff1 fs5 fc0 sc0 ls0 ws0">krishna@engr.uconn.edu).</div><div class="t m0 xa h8 y35 ff1 fs5 fc0 sc0 ls0 ws0">Publisher Item Identifier S 1089-7798(01)06463-8.</div><div class="t m0 xb h6 y6 ff1 fs4 fc0 sc0 ls0 ws0">but it is difficult to argue with good performance and low com-</div><div class="t m0 xb h6 y36 ff1 fs4 fc0 sc0 ls0 ws0">plexity. Now, in the CDMA case the true probability function is</div><div class="t m0 xb h6 y37 ff1 fs4 fc0 sc0 ls0 ws0">also a Gaussian mixture, and complexity is also the issue. We</div><div class="t m0 xb h6 y38 ff1 fs4 fc0 sc0 ls0 ws0">thus propose to apply the Gaussian “forcing” idea; whereas in</div><div class="t m0 xb h6 y39 ff1 fs4 fc0 sc0 ls0 ws0">the tracking application this forcing occurs once per scan and</div><div class="t m0 xb h6 y3a ff1 fs4 fc0 sc0 ls0 ws0">there is no revisit, in CDMA it occurs for each user, and there is</div><div class="t m0 xb h6 y3b ff1 fs4 fc0 sc0 ls0 ws0">iteration. Instead of fixing the binary signal variables at</div><div class="t m0 xc h6 y3c ff1 fs4 fc0 sc0 ls0 ws0">1, the</div><div class="t m0 xb h6 y3d ff1 fs4 fc0 sc0 ls0 ws0">PDA employs a soft IUI cancellation by increasing the covari-</div><div class="t m0 xb h6 y3e ff1 fs4 fc0 sc0 ls0 ws0">ance of the effective noise based on the uncertainty in the other</div><div class="t m0 xb h6 y3f ff1 fs4 fc0 sc0 ls0 ws0">user signals. When the binary variables converge to the true</div><div class="t m0 xb h6 y40 ff1 fs4 fc0 sc0 ls0 ws0">value, the covariance approaches to that of the original noise.</div><div class="t m0 xb h6 y41 ff1 fs4 fc0 sc0 ls0 ws0">This, we believe, helps PDA avoid local minima. Simulation re-</div><div class="t m0 xb h6 y42 ff1 fs4 fc0 sc0 ls0 ws0">sults show that the PDA detector gives a probability of error</div><div class="t m0 xb h6 y43 ff1 fs4 fc0 sc0 ls0 ws0">very close to and often indistinguishable from that of the op-</div><div class="t m0 xb h6 y44 ff1 fs4 fc0 sc0 ls0 ws0">timal ML detector. Simulations also show that the worst case</div><div class="t m0 xb h6 y45 ff1 fs4 fc0 sc0 ls0 ws0">computational cost of the PDA method is</div><div class="t m0 xd h6 y46 ff1 fs4 fc0 sc0 ls0 ws0">, where is</div><div class="t m0 xb h6 y47 ff1 fs4 fc0 sc0 ls0 ws0">the number of users.</div><div class="t m0 xe h6 y48 ff1 fs4 fc0 sc0 ls0 ws0">II. T</div><div class="t m0 xf h6 y49 ff1 fs5 fc0 sc0 ls0 ws0">HE MULTISTAGE PDA DETECTOR</div><div class="t m0 xb h9 y4a ff2 fs4 fc0 sc0 ls0 ws0">A. Problem Formulation</div><div class="t m0 x10 h6 y4b ff1 fs4 fc0 sc0 ls0 ws0">A discrete-time model for the matched-filter outputs at the</div><div class="t m0 xb h6 y4c ff1 fs4 fc0 sc0 ls0 ws0">receiver of a CDMA channel is given by the</div><div class="t m0 x11 h6 y4d ff1 fs4 fc0 sc0 ls0 ws0">-length vector [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 the -length vector of bits</div><div class="t m0 xb h6 y51 ff1 fs4 fc0 sc0 ls0 ws0">transmitted by the</div><div class="t m0 x14 h6 y52 ff1 fs4 fc0 sc0 ls0 ws0">active users; is the symmetric normal-</div><div class="t m0 xb h6 y53 ff1 fs4 fc0 sc0 ls0 ws0">ized signature correlation matrix with unit diagonal 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 a diagonal matrix whose diagonal elements are the</div><div class="t m0 xb h6 y56 ff1 fs4 fc0 sc0 ls0 ws0">signal amplitudes of the corresponding users. Here</div><div class="t m0 x16 h6 y57 ff1 fs4 fc0 sc0 ls0 ws0">is a col-</div><div class="t m0 xb h6 y58 ff1 fs4 fc0 sc0 ls0 ws0">ored Gaussian noise vector with zero mean and covariance 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">, where is the power of the white noise</div><div class="t m0 xb h6 y5b ff1 fs4 fc0 sc0 ls0 ws0">before the matched filter.</div><div class="t m0 x10 h6 y5c ff1 fs4 fc0 sc0 ls0 ws0">When all the user signals are equally probable, the optimal</div><div class="t m0 xb h6 y5d ff1 fs4 fc0 sc0 ls0 ws0">solution of (1) is the output of a ML detector [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 is known that obtaining the ML solution is generally NP-hard [1],</div><div class="t m0 xb h6 y60 ff1 fs4 fc0 sc0 ls0 ws0">unless the signature correlation matrix has a special structure.</div><div class="t m0 x10 h6 y61 ff1 fs4 fc0 sc0 ls0 ws0">Multiplying by</div><div class="t m0 x18 h6 y62 ff1 fs4 fc0 sc0 ls0 ws0">on both sides of (1) from the left,</div><div class="t m0 xb h6 y63 ff1 fs4 fc0 sc0 ls0 ws0">the system model can be reformulated 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 . The variable</div><div class="t m0 xb h6 y67 ff1 fs4 fc0 sc0 ls0 ws0">represents the th element of vector ; is a column vector</div><div class="t m0 x1a h8 y68 ff1 fs5 fc0 sc0 ls0 ws0">1089–7798/01$10.00 © 2001 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>