Automatic delay selection in blind channel equalization: a prewhitening + eigenvector approach

We consider the problem of blindly equalizing a single input single output communication channel, assuming that the tap input vector to the equalizer has mutually uncorrelated components. This can be achieved if the received signal is preprocessed by an adaptive all-pole filter (which has been suggested as a means for both MSE improvement and DFE initialization), or by a standard lattice predictor. In the former case, it has been observed recently that an eigenvector of the (prewhitened) input quadricovariance matrix /spl Psi/ may provide a good initial estimate for the equalizer. Analytical justification for this fact is provided and show that if the MSE of a Wiener equalizer for a given delay is small, then this Wiener equalizer is close to an eigenvector of /spl Psi/. The corresponding eigenvalue decreases with the MSE, and thus picking the smallest eigenvalue automatically provides blind delay optimization.