ma112006id337

Multiuser Detection Algorithms for CDMA based on the Message Passing Algorithms Waseda University, Japan Shunsuke Horii Tota Suko Toshiyasu Matsushima

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Contents

[object Object],[object Object],[object Object],[object Object],１． Introduction detection problem can be regarded as 　 a probabilistic inference problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[Kabashima, 2003] [Tonosaki et al., 2004]

[object Object],１． Introduction

2 ． Synchronous DS CDMA Channel Model with K users ,[object Object],[object Object],【information bit】【signature sequence】： number of chips ： chip cycle 【modulated signal】

2 ． Synchronous DS CDMA Channel Model with K users Channel receiver Gaussian noise The signals of all users are multiplexed. Gaussian noise is added.

[object Object],[object Object],【 MPM (Maximum Posterior Marginal) detector 】 Uniform Prior: Gaussian Channel: 3 ． MPM detector

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],3 ． MPM detector Computational Complexity Problem

[object Object],[object Object],[object Object],4 ． The Belief Propagation and the Concave Convex Procedure Ex. [Kschischang et al. 01]

[object Object],[object Object],[object Object],[object Object],[object Object],4 ． The Belief Propagation and the Concave Convex Procedure [Yedidia et al. 2005] [Yuille, 2002 ]

[object Object],neighboring nodes of 【 factor node->variable node 】 arguments of neighboring nodes of 【 variable node->factor node 】【 belief 】 approximation to marginal probability function normalization constant 4 ． The Belief Propagation and the Concave Convex Procedure computational complexity increases exponentially with the number of variable nodes which are connecting to a factor node

[object Object],[object Object],the number of neighboring factor nodes of the variable node convergent value of in the inner loop ,[object Object],4 ． The Belief Propagation and the Concave Convex Procedure After the enough number of the updates in the inner loop, the convergent value of the λ ai is used for the updates in the outer loop. computational complexity increases exponentially with the number of variable nodes which are connecting to a factor node

[object Object],5 ． Approximate BP Detector and Approximate CCCP Detector Factor graph Ⅰ [Kabashima, 2003] [Tonosaki et al., 2004]

[object Object],5 ． Approximate BP Detector and Approximate CCCP Detector ,[object Object],Update rule for the message of the BP Update rule for the inner loop of the CCCP

[object Object],[object Object],5 ． Approximate BP Detector and Approximate CCCP Detector

[object Object],[object Object],5 ． Proposed BP Detector and Proposed CCCP Detector Point There are many ways to factorize. Point in our proposition

5 ． Proposed BP Detector and Proposed CCCP Detector ,[object Object],Sufficient statistics Cross correlations

5 ． Proposed BP Detector and Proposed CCCP Detector ,[object Object],Factor graph Ⅱ(proposed)

5 ． Proposed BP Detector and Proposed CCCP Detector ,[object Object],[object Object],Factor graph Ⅱ(proposed)

6 ． Simulations Simulation Conditions Ⅰ ． Comparison of the detectors with the bit error rate ※ assumption to approximate

6 ． Simulations The performance of the BP for the Factor Graph Ⅱis not good. The performance of the CCCP for the Factor Graph Ⅱis near to the MPM detector’s performance

The performance of the BP for the Factor graph Ⅱ is improved. The performance of the approx. CCCP for the FG Ⅰ is not good. 6 ． Simulations ※Absolute values of the cross correlations tends to take small values when the length of the signature sequence is large.

6 ． Simulations Simulation Conditions Ⅱ ． Comparison of the approx. CCCP for the FGⅠ and the CCCP for the FGⅡ

6 ． Simulations The bit error rate of the approx. CCCP for the Factor Graph Ⅰ doesn’t decrease for the increase in the number of updates in the outer loop.

6 ． Simulations The bit error rate of the approx. CCCP for the Factor Graph Ⅰdecreases for the increase in the number of updates in the outer loop. imply The approx. CCCP for the Factor Graph Ⅰ needs more number of updates in the Inner loop.

7 ． Discussions ,[object Object],[object Object],Reason It seems to me that the fact that “the strengths of functions are strong, the BP tends to not converge” is one of reasons. Ref.[Welling and Teh, 2001] ※

7 ． Discussions ,[object Object],[object Object],Reason It seems to me, the number of edges effects on the necessary number of updates for the CCCP to converge. The number of edges is reduced in the Factor graph Ⅱ.

[object Object],8 ． Conclusion ,[object Object]

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