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An exact block formulation of the constant modulus algorithm (CMA) is presented, in which a reduction of arithmetic complexity is achieved. Two types of fast algorithms are explained, either in time-domain or in frequencydomain. The first one is of greater interest for small block lengths and the second one, using the FFT as an intermediate step, has greater advantage for large blocks. Due to the equivalence between the original CMA formulation and this one, the convergence properties of the CMA are maintained, which is not the case in the Treichler et al. implementation in frequency domain of this algorithm. Furthermore, this approach allows the use of very small block lengths (e.g. N = 2), the reduction of the arithmetic complexity increasing with the block size.
Benesty et al. (Tue,) studied this question.
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