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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.