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Multiuser Detection Algorithm for CDMA based on  the Belief Propagation Algorithm Shunsuke Horii Tota Suko Toshiyasu Matsushima Shigeichi Hirasawa Waseda Univ.
Research background ,[object Object],[object Object],Demand :Sub-optimal Low-complexity detector ,[object Object],[object Object],[object Object],[object Object],[object Object],Computational complexity increases with the number of users
Research background They said in the paper it is impossible to apply the BP for MUD directly. Parallel Interference Canceller (PIC) is derived as an approximation of the BP. Analysis of the PIC for large size system.   (large number of users) Develop the BP based MUD algorithm which provides good performance for moderate size system. Purpose of our research Assertion of them: Main result The BP can be applied for the MUD problem by converting the graph structure. Proposed graph has some superior points comparing with existing one. Purpose:
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Discrete model for synchronous DS-CDMA channel ,[object Object],Channel receiver Gaussian noise (output of the chip matched filter)
MUD problem Uniform Prior: Gaussian Channel: MPM detector estimate Posterior distribution of information bits
[object Object],MUD problem Computational difficulty We need sub-optimal low-complexity detector. Research target Approximate the MPM detector by the BP.
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],The Factor graph and the Belief Propagation Ex. [Kschischang et al. 01]
[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  The Factor graph and the Belief Propagation The BP is an iterative algorithm. which updates “messages” iteratively at the nodes. computational complexity increases exponentially with the  degree  of factor nodes. (degree : number of neighboring variable nodes)
[object Object],The Factor graph and the Belief Propagation no cycles the BP outputs exact marginal probability function. any cycles the BP outputs only approximation of marginal probability function. However,…….. When the factor graph has
[object Object],The Factor graph and the Belief Propagation The BP provides good performance for the decoding problem of  LDPC codes  or  Turbo codes . Knowledge obtained from coding theory ,[object Object],[object Object],[object Object]
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Previous work FG representation [T. Tanaka and M. Okada]
Previous work [T. Tanaka and M. Okada] Aspects of the FG ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Previous work The approximated BP is equivalent to the PIC [T. Tanaka and M. Okada] Idea: Use the hard-bits instead of the soft bits. ,[object Object]
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
BP based MUD  - Proposed work - ,[object Object],Key Insight Many ways to factorize a function ,[object Object],Outputs of Sample Matched Filter Cross correlations
BP based MUD  - Proposed work - ,[object Object],Two kind of factor nodes
BP based MUD  - Proposed work - Aspects of the proposed FG ,[object Object],[object Object],Moreover………. The BP can be applied directly
BP based MUD  - Proposed work - The number of cycles decreases furthermore for some cases! The number of cycles of proposed FG is possibly small depending on the signature sequence.
BP based MUD  - Proposed work - Collection of  superior points of the proposed factor graph ,[object Object],[object Object],[object Object],( Especially, when there are many 0 elements in cross correlations )
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Numerical Simulation Simulation Conditions Performances of the detectors depend on the signature sequence. Especially, that of the BP depends on the number of cycles. Simulate under the three kind of the signature sequences ※ Sequence C is Shift-M sequence 0.143 (all) 0/21 Sequence C 0.262 5/21 Sequence B 0.167 11/21 Sequence A Absolute value of  cross correlations (average) Portion of 0 elements  in cross correlations
Numerical Simulation The BP outperforms the PIC The BP’s performance is near to optimum Sequence A ( Number of cycles : small )
The BP doesn’t provide good performance Numerical Simulation Sequence B ( Number of cycles : large  Correlation : strong ) The BP outperforms the PIC
Numerical Simulation Sequence C ( Number of cycles : large  Correlation : weak ) BP’s performance is near to optimum The BP outperforms the PIC
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Conclusion Conclusion Future work
Appendix Algorithm of the PIC
Appendix
Appendix ,[object Object],Sequence A ( Number of loops : small )
Appendix Sequence B ( Number of loops : large  Correlation : strong )
Appendix Sequence C ( Number of loops : large  Correlation : weak )
Consideration The BP outperforms the PIC Factor ,[object Object],Number of cycles Proposed FG < Previous FG Previous FG  =>  4 Proposed FG  =>  6 ( Especially, when there are many 0 elements in cross correlations ) ,[object Object],[object Object],Length 4 cycle causes a performance degradation
Consideration ,[object Object],If we use “hard decision” for the proposed FG….. ⇒ Algorithm coincide with the PIC BP outperforms PIC Factor 2

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ma112008id371

  • 1. Multiuser Detection Algorithm for CDMA based on the Belief Propagation Algorithm Shunsuke Horii Tota Suko Toshiyasu Matsushima Shigeichi Hirasawa Waseda Univ.
  • 2.
  • 3. Research background They said in the paper it is impossible to apply the BP for MUD directly. Parallel Interference Canceller (PIC) is derived as an approximation of the BP. Analysis of the PIC for large size system. (large number of users) Develop the BP based MUD algorithm which provides good performance for moderate size system. Purpose of our research Assertion of them: Main result The BP can be applied for the MUD problem by converting the graph structure. Proposed graph has some superior points comparing with existing one. Purpose:
  • 4.
  • 5.
  • 6.
  • 7. MUD problem Uniform Prior: Gaussian Channel: MPM detector estimate Posterior distribution of information bits
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15. Previous work FG representation [T. Tanaka and M. Okada]
  • 16.
  • 17.
  • 18.
  • 19.
  • 20.
  • 21.
  • 22. BP based MUD  - Proposed work - The number of cycles decreases furthermore for some cases! The number of cycles of proposed FG is possibly small depending on the signature sequence.
  • 23.
  • 24.
  • 25. Numerical Simulation Simulation Conditions Performances of the detectors depend on the signature sequence. Especially, that of the BP depends on the number of cycles. Simulate under the three kind of the signature sequences ※ Sequence C is Shift-M sequence 0.143 (all) 0/21 Sequence C 0.262 5/21 Sequence B 0.167 11/21 Sequence A Absolute value of cross correlations (average) Portion of 0 elements in cross correlations
  • 26. Numerical Simulation The BP outperforms the PIC The BP’s performance is near to optimum Sequence A ( Number of cycles : small )
  • 27. The BP doesn’t provide good performance Numerical Simulation Sequence B ( Number of cycles : large Correlation : strong ) The BP outperforms the PIC
  • 28. Numerical Simulation Sequence C ( Number of cycles : large Correlation : weak ) BP’s performance is near to optimum The BP outperforms the PIC
  • 29.
  • 30.
  • 33.
  • 34. Appendix Sequence B ( Number of loops : large Correlation : strong )
  • 35. Appendix Sequence C ( Number of loops : large Correlation : weak )
  • 36.
  • 37.