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A Simplified Constant Modulus Algorithm for Blind Recovery of MIMO QAM and PSK Signals: A Criterion with Convergence Analysis
EURASIP Journal on Wireless Communications and Networking volume 2007, Article number: 090401 (2007)
The problem of blind recovery of QAM and PSK signals for multiple-input multiple-output (MIMO) communication systems is investigated. We propose a simplified version of the well-known constant modulus algorithm (CMA), named simplified CMA (SCMA). The SCMA cost function consists in projection of the MIMO equalizer outputs on one dimension (either real or imaginary part). A study of stationary points of SCMA reveals the absence of any undesirable local stationary points, which ensures a perfect recovery of all signals and a global convergence of the algorithm. Taking advantage of the phase ambiguity in the solution of the new cost function for QAM constellations, we propose a modified cross-correlation term. It is shown that the proposed algorithm presents a lower computational complexity compared to the constant modulus algorithm (CMA) without loss in performances. Some numerical simulations are provided to illustrate the effectiveness of the proposed algorithm.
Foschini GJ: Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas. Bell Labs Technical Journal 1996,1(2):41-59.
Mansour A, Barros AK, Ohnishi N: Blind separation of sources: methods, assumptions and applications. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2000,E83-A(8):1498-1512.
Cichocki A, Amari S-I: Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. John Wiley & Sons, New York, NY, USA; 2003.
Abed-Meraim K, Cardoso J-F, Gorokhov AY, Loubaton P, Moulines E: On subspace methods for blind identification of single-input multiple-output FIR systems. IEEE Transactions on Signal Processing 1997,45(1):42-55. 10.1109/78.552204
Gorokhov A, Loubaton P: Blind identification of MIMO-FIR systems: a generalized linear prediction approach. Signal Processing 1999,73(1-2):105-124. 10.1016/S0165-1684(98)00187-X
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
Hassibi B, Vikalo H: On the sphere-decoding algorithm—II: generalizations, second-order statistics, and applications to communications. IEEE Transactions on Signal Processing 2005,53(8):2819-2834.
Hassibi B: An efficient square-root algorithm for BLAST. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '00), June 2000, Istanbul, Turkey 2: 737-740.
Sato Y: A method of self-recovering equalization for multilevel amplitude-modulation systems. IEEE Transactions on Communications 1975,23(6):679-682. 10.1109/TCOM.1975.1092854
Godard D: Self-recovering equalization and carrier tracking in two-dimensional data communication systems. IEEE Transactions on Communications 1980,28(11):1867-1875. 10.1109/TCOM.1980.1094608
Treichler J, Agee B: A new approach to multipath correction of constant modulus signals. IEEE Transactions on Acoustics, Speech, and Signal Processing 1983,31(2):459-472. 10.1109/TASSP.1983.1164062
Larimore MG, Treichler J: Convergence behavior of the constant modulus algorithm. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '83), April 1983, Boston, Mass, USA 1: 13-16.
Treichler J, Larimore MG: New processing techniques based on the constant modulus adaptive algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing 1985,33(2):420-431. 10.1109/TASSP.1985.1164567
Gooch , Lundell J: The CM array: an adaptive beamformer for constant modulus signals. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '86), April 1986, Tokyo, Japan 11: 2523-2526.
Castedo L, Escudero CJ, Dapena A: A blind signal separation method for multiuser communications. IEEE Transactions on Signal Processing 1997,45(5):1343-1348. 10.1109/78.575706
Papadias CB, Paulraj AJ: A constant modulus algorithm for multiuser signal separation in presence of delay spread using antenna arrays. IEEE Signal Processing Letters 1997,4(6):178-181. 10.1109/97.586042
Oh KN, Chin YO: Modified constant modulus algorithm: blind equalization and carrier phase recovery algorithm. Proceedings of the IEEE International Conference on Communications (ICC '95), June 1995, Seattle, Wash, USA 1: 498-502.
Yang J, Werner J-J, Dumont GA: The multimodulus blind equalization and its generalized algorithms. IEEE Journal on Selected Areas in Communications 2002,20(5):997-1015. 10.1109/JSAC.2002.1007381
Garth LM, Yang J, Werner J-J: Blind equalization algorithms for dual-mode CAP-QAM reception. IEEE Transactions on Communications 2001,49(3):455-466. 10.1109/26.911453
Sansrimahachai P, Ward DB, Constantinides AG: Blind source separation for BLAST. Proceedings of the 14th International Conference on Digital Signal Processing (DSP '02), July 2002, Santorini, Greece 1: 139-142.
Goupil A, Palicot J: Constant norm algorithms class. proceedings of the 11th European Signal Processing Conference (EUSIPCO '02), September 2002, Toulouse, France 1: 641-644.
Ikhlef A, Le Guennec D, Palicot J: Constant norm algorithms for MIMO communication systems. Proceedings of the 13th European Signal Processing Conference (EUSIPCO '05), September 2005, Antalya, Turkey
Ikhlef A, Le Guennec D: Blind recovery of MIMO QAM signals : a criterion with its convergence analysis. Proceedings of the 14th European Signal Processing Conference (EUSIPCO '06), September 2006, Florence, Italy
Papadias CB: Globally convergent blind source separation based on a multiuser kurtosis maximization criterion. IEEE Transactions on Signal Processing 2000,48(12):3508-3519. 10.1109/78.887044
Haykin S: Adaptive Filter Theory. 4th edition. Prentice-Hall, Upper Saddle River, NJ, USA; 2002.
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Ikhlef, A., Le Guennec, D. A Simplified Constant Modulus Algorithm for Blind Recovery of MIMO QAM and PSK Signals: A Criterion with Convergence Analysis. J Wireless Com Network 2007, 090401 (2007). https://doi.org/10.1155/2007/90401
- Cost Function
- Imaginary Part
- Computational Complexity
- Stationary Point
- Convergence Analysis