Non-iterative blind deconvolution of colored or deterministic signals using higher order cepstra and group delay

The authors consider an unknown deterministic or nonGaussian nonwhite stochastic signal transmitted through two different unknown LTI mixed phase FIR systems with only noisy observations of the system outputs. The goal is to identify the systems and/or deconvolve the input, to within a magnitude factor and a time delay. The systems must have no zeros on the unit circle and satisfy other mild conditions on the mutual location of their zeros. Previous approaches have been iterative or assumed the input to be stochastic and white or well-separated from the channel impulse response in some sense. A new non-iterative solution is based on the observation that cepstra (calculated via higher order spectra) corresponding to two 'difference' systems which have zeros due to the minimum (or reflected maximum) phase part of the first system and poles due to the second system can be obtained. Via the group delay separated the 'difference' cepstra are into pole and zero parts and thereby the systems and/or signal are reconstructed.<>