Blind MISO deconvolution using the distribution of output differences

We present a novel blind identification and source separation method for linear multi input single output (MISO) convolutive systems driven by PAM sources. The method is based on the distribution estimation of the differences of pairs of outputs. We show that the most likely differences are the ones corresponding to the columns of the mixing matrix (upto a sign). The columns can be arranged in the correct order by using the Toeplitz property of the submatrices forming the overall transfer matrix. Thus the problem is transformed into the density estimation problem. The method is conceptually simple and can work with relatively small data sets although it is exponentially complex with the channel length or the number of input signals.