Optimal Delay Estimation and Performance Evaluation in Blind Equalization

This paper deals with the problem of recovering the input signal applied to a linear time-invariant system from the measurements of its output and the a-priori knowledge of the input statistics (blind equalization). Under the assumption of an i.i.d. non-gaussian input sequence, a new iterative procedure based on phase sensitive high-order cumulants for adjusting the coefficients of a transversal equalizer is introduced. The main feature of the proposed technique is the automatic selection of the equalization delay so as to improve the equalization performance. A method for the a-posteriori evaluation of the obtained accuracy in PAM systems is also introduced. It consists in the computation of an upper bound on the probability of error depending on certain moments of the equalizer output and the statistics of the channel input, and therefore it can be used in a blind equalization context. Based on the result of such a computation, it can be decided whether it is necessary to consider a longer equalization filter in the iterative procedure.