Cross-spectrum based blind channel identification

A novel cross-correlation based framework is proposed for the problem of blind equalization in communications. We assume that we have access to two observations obtained either by sampling, at the symbol rate, the outputs of two sensors or by oversampling, by a factor of two, the output of a single sensor. In either case, the two observations correspond to the outputs of two channels excited by the same input. The channels are estimated using the theory of signal reconstruction from phase only. The phase used is the phase of the cross spectrum of the observations filtered through their minimum phase equivalent filters. We provide an analytical study of the propagation of noise effects in the phase estimate. Comparisons with existing methods indicate that the proposed approach is robust to noise and, at low signal-to-noise ratio (SNR), leads to significantly smaller channel estimation errors. Besides robustness to noise, the proposed method does not require knowledge of channel lengths, which are determined via an iterative procedure.