Comment on the "Unnecessary assumption of statistical independence between reference signal and filter weights in feedforward adaptive systems"

Minkoff (see IEEE Trans. Signal Processing, vol.45, p.2993-3004, 1997) presented a formulation in which the time-evolving weight-iteration equation for random signals is derived without the necessity of invoking the usual unsatisfactory assumption that is customarily made, namely, that the weights W and the reference signal X the weight-iteration equation are statistically independent. Minkoff neglected, however, to give a physical argument for it. That is, in this derivation, it is not necessary for W to be independent of X but only of XX which does not contain the phase information of X. The off-diagonal terms of XX contain only phase differences, which could be produced by an infinite number of different, arbitrary Xs.