Avoiding divergence in the constant modulus algorithm

One of the most popular algorithms for blind equalization is the constant modulus algorithm (CMA), due to its simplicity and low computational cost. However, if the step-size is not properly chosen or if the initialization is distant from the optimal solution, CMA can diverge or converge to undesirable local minima. In order to avoid divergence, we propose a dual-mode algorithm, which works as CMA with a time-variant step-size, but rejects non-consistent estimates of the transmitted signal. We present a deterministic analysis of the stability of the new algorithm for scalar filters. In the vector case, the good performance of the new algorithm is confirmed through numerical simulations.