Blind channel equalization with colored sources based on second-order statistics: a linear prediction approach

We consider the blind equalization and estimation of single-user, multichannel models from the second-order statistics of the channel output when the channel input statistics are colored but known. By exploiting certain results from linear prediction theory, we generalize the algorithm of Tong et al. (1994), which was derived under the assumption of a white transmitted sequence. In particular, we show that all one needs to estimate the channel to within an unitary scaling constant, and thus to find its equalizers, is (a) that a standard channel matrix have full column rank, and (b) a vector of the input signal and its delays have positive definite lag zero autocorrelation. An algorithm is provided to determine the equalizer under these conditions. We argue that because this algorithm makes explicit use of the input statistics, the equalizers thus obtained should outperform those obtained by other methods that neither require, nor exploit, the knowledge of the input statistics. Simulation results are provided to verify this fact.