Blind equalization using the constant modulus algorithm

The constant modulus algorithm (CMA) proposed by Godard (1980) and Treichler (1983) is an effective technique for blind receiver design in practice. A geometrical approach, generalized from an approach of Zeng and Tong (see Proc. 28th Conf. Information Science and Systems, Princeton, NJ, 1996), is presented that related the CMA with the well-known minimum mean square error (MMSE) receivers. Given the MSE and the inter-symbol/user interference of an MMSE receiver, a CMA local minimum is located in a neighborhood nearby. The MSE bounds of the CMA receiver are also derived. This analysis reveals some close relationships between the CMA and MMSE receivers in both the parameter and the output spaces. The analysis shows that, while in some cases, the CMA receiver performs almost as well as the (nonblind) MMSE receiver, it is also possible that, due to its blind nature, the CMA may perform considerably worse than a nonblind MMSE design.

[1]  G. J. Foschini,et al.  Equalizing without altering or detecting data , 1985, AT&T Technical Journal.

[2]  H. Zeng,et al.  Blind equalization using CMA: performance analysis and a new algorithm , 1996, Proceedings of ICC/SUPERCOMM '96 - International Conference on Communications.

[3]  Zhi Ding,et al.  Local convergence of the Sato blind equalizer and generalizations under practical constraints , 1993, IEEE Trans. Inf. Theory.

[4]  Zhi Ding,et al.  Ill-convergence of Godard blind equalizers in data communication systems , 1991, IEEE Trans. Commun..

[5]  D. Godard,et al.  Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems , 1980, IEEE Trans. Commun..

[6]  Zhi Ding,et al.  On the nonvanishing stability of undesirable equilibria for FIR Godard blind equalizers , 1993, IEEE Trans. Signal Process..

[7]  J. Treichler,et al.  A new approach to multipath correction of constant modulus signals , 1983 .

[8]  Zhi Ding,et al.  Global convergence of fractionally spaced Godard equalizers , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.

[9]  Lang Tong,et al.  Connections between the least-squares and the subspace approaches to blind channel estimation , 1996, IEEE Trans. Signal Process..

[10]  Zhi Ding,et al.  Length- and cost-dependent local minima of unconstrained blind channel equalizers , 1996, IEEE Trans. Signal Process..

[11]  Chrysostomos L. Nikias,et al.  Blind equalization , 1991, Optics & Photonics.

[12]  Rodney A. Kennedy,et al.  On the (non)existence of undesirable equilibria of Godard blind equalizers , 1992, IEEE Trans. Signal Process..