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A novel discrete-time method is proposed for estimating the impulse response of a frequency-selective digitally modulated communication channel. The received signal is first demodulated and sampled and then the fourth-order cumulants of the resulting discrete-time sequence are estimated. The method estimates the channel impulse response from the complex cepstrum of the aforementioned fourth-order cumulants (i.e. tricepstrum). The method depends only on the second- and fourth-order statistics of the transmitted sequence and is capable of reconstructing nonminimum-phase impulse responses. Monte Carlo simulation results demonstrate the effectiveness of the method, its low sensitivity to observation noise, and its improved performance in terms of probability of error or the reconstructed transmitted sequence.>
Hatzinakos et al. (1989) studied this question.