Parallel Jacobi-Davidson method for multichannel blind equalization criterium

Some recent works have represented novel techniques that exploit cyclostationarity for channel identification in data communication systems using only second order statistics. In particular, work has shown the feasibility of blind identification based on the forward shift structure of the correlation matrices of the source. We propose an alternative high performance algorithm based on the above property but with an improved choice of the autocorrelation of the equalization matrices to be considered. The new representation of the equalization problem provides a cost function formulated as a large generalized eigenvalue problem, which can be efficiently solved by the Jacobi-Davidson method. We mainly focus on the parallel aspects of the Jacobi-Davidson method on massively distributed memory computers. The performance of this method on this kind of architecture is always limited because of the global communication required for the inner products due to the Modified Gram-Schmidt (MGS) process. We use Given rotations which require only local communications avoiding the global communication of inner products since this represents the bottleneck of the parallel performance on distributed memory computers. The corresponding data distribution and communication scheme is presented as well. Several simulation experiments over different data transmission constellations carried out on Parsytec systems are presented as well.