Avoiding Divergence in the Shalvi-Weinstein Algorithm

The most popular algorithms for blind equalization are the constant-modulus algorithm (CMA) and the ShalviWeinstein algorithm (SWA). It is well-known that SWA presents a higher convergence rate than CMA, at the expense of higher computational complexity. If the forgetting factor is not sufficiently close to one, if the initialization is distant from the optimal solution, or if the signal-to-noise ratio is low, SWA can converge to undesirable local minima or even diverge. In this paper, we show that divergence can be caused by the inconsistency in the nonlinear estimate of the transmitted signal, or (when the algorithm is implemented in finite precision) by the loss of positiveness of the estimate of the autocorrelation matrix, or by a combination of both. In order to avoid the first cause of divergence, we propose a dual-mode SWA (DM-SWA). In the first mode of operation, the new algorithm works as SWA, and in the second mode, it rejects non-consistent estimates of the transmitted sign...

• Type: Journal
• Year: 2008
• Where: TSP
• Authors: Maria D. Miranda, Magno T. M. Silva, Victor H. Nascimento
• Keywords: Algorithms, Computational Complexity, TSP 2008, Undesirable Local Minima