A least-squares interpretation of the single-stage maximization criterion for multichannel blind deconvolution

In order to attain multichannel blind deconvolution of linear time-invariant nonminimum-phase dynamic systems. Inouye and Habe (see Proc. IEEE Signal Processing Workshop on Higher-Order Statistics, p.96-100, 1995) proposed 1995 a single-stage maximization criterion. The criterion function is the sum of squared fourth-order cumulants of the equalizer outputs, and the coefficients of the equalizer are determined at once. On the other hand, one of possible approaches for multichannel blind deconvolution is to construct an equalizer based on the system identified by higher-order cumulant-matching. In this paper, it is shown that the single-stage maximization criterion is equivalent to a least-squares fourth-order cumulant-matching criterion after multichannel pre-whitening of channel outputs. This result provides us with an important interpretation of the single-stage maximization criterion