Optimal Equalization of Discrete Signals Passed Through a Random Channel

The problem of equalizing a discrete signal that has been transmitted through a channel selected at random from an ensemble of channels is considered. Using mean-square error as the performance index, the minimum number of adjustable parameters required to achieve a given level of performance is sought. For certain special cases, it is shown that, using nonrecursive sampled data filters, the optimum tap weights are given by the eigenvectors of the matrix formed from the covariances of the channel's impulse response. A numerical algorithm is developed to find the optimum equalizer structure for a wide class of channels with the restriction that the number of channels in the given ensemble is finite. Results worked out for several examples show that the optimum equalizer structure requires significantly fewer adjustable parameters than the standard transversal equalizer in order to obtain the same level of performance.