On the robustness of FIR channel identification from fractionally spaced received signal second-order statistics

A number of papers have studied blind channel identification/equalization algorithms relying purely on second-order statistics of the fractionally sampled received signal. A class of cyclic allpass channels is shown to be the only class of IIR channels whose cascade with a core channel results in no change in the second-order-statistics indicators used by several of these algorithms. FIR approximations to the poles of these allpass channels result in robustness concerns for the second-order-statistics algorithms, even when FIR identifiability conditions are well satisfied. This sensitivity suggests that excluding only those channels with common subchannel roots is insufficient when applying these second-order-statistics algorithms.