A weighted energy concentration criterion for improving the performance of deterministic least squares blind channel identification

Xu, Liu, Tong, and Kailath [1995] previously presented a powerful blind channel identification scheme based on the so-called Cross-Relation (C:R) that holds when different channels are fed by the same input: y_i[n]*h_j[n]=y_j[n]*h_i [n], where h,[n] and yi[n] are the impulse response and output of the i-th channel, respectively. This relationship can be exploited to identify the multipath channels in digital communications using linear modulation to effect equalization. Oversampling of the channel outputs, i.e., sampling higher than the symbol rate, can lead to improved performance, but can also lead to trivial solutions for which y_i [n]*h_j[n]=0 and y_j[n]+h_i[n]=0; this occurs when h_i[n] and h_j[n] are chosen to be highpass filters. We here develop procedures for averting these trivial solutions based on a weighted energy concentration criterion. Incorporation of this criterion in the CR method employing basis functions derived from the known symbol waveform facilitates accurate identification of multiple channels under adverse multipath conditions, relatively low SNR, and with a relatively small number of symbols