Blind deconvolution based on signal reconstruction from partial information using higher-order spectra

The authors present a blind deconvolution scheme for the reconstruction of a signal that propagates in a multipath environment in the presence of additive zero-mean Gaussian noise. Two receivers are placed to record the transmitted signal convolved with a different channel for each receiver, embedded in noise. The recorded signals are transformed in the bicepstrum domain where the additive zero-mean Gaussian noise is suppressed, and then the differences of their minimum phase cepstra coefficients and the differences of their maximum phase cepstra coefficients are computed. These differences correspond to the Fourier phases of two FIR (finite impulse response) sequences that can be reconstructed out of phase information only, as long as the transmission channels are FIR and they have no zeros on the unit circle. The reconstruction of these sequences leads to the computation of the minimum and maximum phase cepstra coefficients of the two channels, and subsequently the cepstra coefficients of the transmitted signal can be computed and combined to reconstruct the signal itself