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Blind Multiuser Detection by Kurtosis Maximization for Asynchronous Multirate DS/CDMA Systems


Chi et al. proposed a fast kurtosis maximization algorithm (FKMA) for blind equalization/deconvolution of multiple-input multiple-output (MIMO) linear time-invariant systems. This algorithm has been applied to blind multiuser detection of single-rate direct-sequence/code-division multiple-access (DS/CDMA) systems and blind source separation (or independent component analysis). In this paper, the FKMA is further applied to blind multiuser detection for multirate DS/CDMA systems. The ideas are to properly formulate discrete-time MIMO signal models by converting real multirate users into single-rate virtual users, followed by the use of FKMA for extraction of virtual users' data sequences associated with the desired user, and recovery of the data sequence of the desired user from estimated virtual users' data sequences. Assuming that all the users' spreading sequences are given a priori, two multirate blind multiuser detection algorithms (with either a single receive antenna or multiple antennas), which also enjoy the merits of superexponential convergence rate and guaranteed convergence of the FKMA, are proposed in the paper, one based on a convolutional MIMO signal model and the other based on an instantaneous MIMO signal model. Some simulation results are then presented to demonstrate their effectiveness and to provide a performance comparison with some existing algorithms.


  1. 1.

    Wong D, Lim TJ: Soft handoffs in CDMA mobile systems. IEEE Personal Communications 1997, 4(6):6–17. 10.1109/98.637378

    Article  Google Scholar 

  2. 2.

    Verdu S: Multiuser Detection. Cambridge University Press, Cambridge, UK; 1998.

    Google Scholar 

  3. 3.

    Moshavi S: Multi-user detection for DS-CDMA communications. IEEE Communications Magazine 1996, 34(10):124–136. 10.1109/35.544334

    Article  Google Scholar 

  4. 4.

    Ojanperä T, Prasad R: An overview of air interface multiple access for IMT-2000/UMTS. IEEE Communications Magazine 1998, 36(9):82–86. 10.1109/35.714623

    Article  Google Scholar 

  5. 5.

    Zeng M, Annamalai A, Bhargava VK: Harmonization of global third-generation mobile systems. IEEE Communications Magazine 2000, 38(12):94–104. 10.1109/35.888263

    Article  Google Scholar 

  6. 6.

    Chi C-Y, Feng C-C, Chen C-H, Chen C-Y: Blind Equalization and System Identification. Springer, London, UK; 2006.

    Google Scholar 

  7. 7.

    Chi C-Y, Chen C-Y, Chen C-H, Feng C-C: Batch processing algorithms for blind equalization using higher-order statistics. IEEE Signal Processing Magazine 2003, 20(1):25–49. 10.1109/MSP.2003.1166627

    Article  Google Scholar 

  8. 8.

    Chi C-Y, Chen C-H, Chen C-Y: Blind MAI and ISI suppression for DS/CDMA systems using HOS-based inverse filter criteria. IEEE Transactions on Signal Processing 2002, 50(6):1368–1381. 10.1109/TSP.2002.1003061

    Article  Google Scholar 

  9. 9.

    I C-L, Gitlin RD: Multi-code CDMA wireless personal communications networks. Proceedings of the IEEE International Conference on Communications, June 1995, Seattle, Wash, USA 2: 1060–1064.

    Article  Google Scholar 

  10. 10.

    Ottosson T, Svensson A: Multi-rate schemes in DS/CDMA systems. Proceedings of the 45th IEEE Vehicular Technology Conference, July 1995, Chicago, Ill, USA 2: 1006–1010.

    Google Scholar 

  11. 11.

    Tsatsanis MK, Xu Z, Lu X: Blind multiuser detectors for dual rate DS-CDMA systems over frequency selective channels. Proceedings of European Signal Processing Conference, September 2000, Tampere, Finland 2: 631–634.

    Google Scholar 

  12. 12.

    Roy S, Yan H: Blind channel estimation in multi-rate CDMA systems. IEEE Transactions on Communications 2002, 50(6):995–1004. 10.1109/TCOMM.2002.1010619

    Article  Google Scholar 

  13. 13.

    Ma J, Tugnait JK: Blind detection of multirate asynchronous CDMA signals in multipath channels. IEEE Transactions on Signal Processing 2002, 50(9):2258–2272. 10.1109/TSP.2002.801939

    MathSciNet  Article  Google Scholar 

  14. 14.

    Xu Z, Liu P: Code constrained CMA-based multirate multiuser detection. Proceedings of the Conference Record of the 35th Asilomar Conference on Signals, Systems and Computers , November 2001, Pacific Grove, Calif, USA 2: 1455–1459.

    Google Scholar 

  15. 15.

    Saquib M, Yates RD, Ganti A: An asynchronous multirate decorrelator. IEEE Transactions on Communications 2000, 48(5):739–742. 10.1109/26.843182

    Article  Google Scholar 

  16. 16.

    Chung M-H, Chen K-C, You MY: MMSE multiuser detection for multi-rate wideband CDMA communications. Proceedings of 11th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC '00), September 2000, London, UK 1: 534–538.

    Google Scholar 

  17. 17.

    Mitra U: Comparison of maximum-likelihood-based detection for two multirate access schemes for CDMA signals. IEEE Transactions on Communications 1999, 47(1):64–77. 10.1109/26.747814

    Article  Google Scholar 

  18. 18.

    Proakis JG: Digital Communications. 4th edition. McGraw-Hill, New York,USA; 2001.

    Google Scholar 

  19. 19.

    Tsatsanis MK, Xu Z: Performance analysis of minimum variance CDMA receivers. IEEE Transactions on Signal Processing 1998, 46(11):3014–3022. 10.1109/78.726814

    Article  Google Scholar 

  20. 20.

    Torlak M, Xu G: Blind multiuser channel estimation in asynchronous CDMA systems. IEEE Transactions on Signal Processing 1997, 45(1):137–147. 10.1109/78.552212

    Article  Google Scholar 

  21. 21.

    Bensley SE, Aazhang B: Subspace-based channel estimation for code division multiple access communication systems. IEEE Transactions on Communications 1996, 44(8):1009–1020. 10.1109/26.535441

    Article  Google Scholar 

  22. 22.

    Tsatsanis MK, Giannakis GB: Optimal decorrelating receivers for DS-CDMA systems: a signal processing framework. IEEE Transactions on Signal Processing 1996, 44(12):3044-3055. 10.1109/78.553478

    Article  Google Scholar 

  23. 23.

    Chi C-Y, Chen C-H: Cumulant-based inverse filter criteria for MIMO blind deconvolution: properties, algorithms, and application to DS/CDMA systems in multipath. IEEE Transactions on Signal Processing 2001, 49(7):1282-1299. 10.1109/78.928684

    Article  Google Scholar 

  24. 24.

    Wang X, Poor HV: Blind equalization and multiuser detection in dispersive CDMA channels. IEEE Transactions on Communications 1998, 46(1):91-103. 10.1109/26.655407

    Article  Google Scholar 

  25. 25.

    Ristaniemi T, Joutsensalo J: Advanced ICA-based receivers for block fading DS-CDMA channels. Signal Processing 2002, 82(3):417-431. 10.1016/S0165-1684(01)00194-3

    Article  Google Scholar 

  26. 26.

    Chi C-Y, Chen C-Y: Blind beamforming and maximum ratio combining by kurtosis maximization for source separation in multipath. Proceedings of IEEE Workshop on Signal Processing Advances in Wireless Communications, March 2001, Taoyuan, Taiwan 243–246.

    Google Scholar 

  27. 27.

    Shalvi O, Weinstein E: Super-exponential methods for blind deconvolution. IEEE Transactions on Information Theory 1993, 39(2):504-519. 10.1109/18.212280

    Article  Google Scholar 

  28. 28.

    Tugnait JK: Identification and deconvolution of multichannel linear non-Gaussian processes using higher order statistics and inverse filter criteria. IEEE Transactions on Signal Processing 1997, 45(3):658-672. 10.1109/78.558482

    Article  Google Scholar 

  29. 29.

    Chi C-Y, Peng C-H: Turbo source extraction algorithm and noncancellation source separation algorithms by kurtosis maximization. IEEE Transactions on Signal Processing 2006, 54(8):2929-2942.

    Article  Google Scholar 

  30. 30.

    Peng C-H, Chi C-Y, Chang I-C, Kuo C-H: A blind space-time decoding algorithm by kurtosis maximization for the down-link of MC-CDMA systems. Proceedings of 5th IEEE International Conference on Information, Communications and Signal Processing (ICICS '05), December 2005, Bangkok, Thailand

    Google Scholar 

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Correspondence to Chun-Hsien Peng.

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Peng, C., Chi, C. & Chang, C. Blind Multiuser Detection by Kurtosis Maximization for Asynchronous Multirate DS/CDMA Systems. EURASIP J. Adv. Signal Process. 2006, 084930 (2006).

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