Inverse filter criteria for blind deconvolution and equalization using two cumulants

Cumulant (higher-order statistics) based inverse filter criteria maximizing J,,, = / C,l’/IC,I”, where m # r and C, (C,) denotes the mth-order (rth-order) cumulant of the inverse filter output, have been proposed for blind deconvolution and equalization with only non-Gaussian output measurements of an unknown linear time-invariant (LTI) system. This paper shows that the maximum of J,,,, associated with the true inverse filter of the unknown LTI system, exists only for r to be even and m > r, otherwise J,,, is unbounded. The admissible values for (r, m) = (2s, 1 + s) where I > s 2 1 include (2,3), (2,4) and (4,6) proposed by Tugnait, Wiggins, Shalvi and Weinstein in addition to the new ones such as (2, S), (2,6) and (4,5). Some simulation results associated with the inverse filter criteria J,,, with the admissible values for (I, m) are then provided. Finally, we draw some conclusions.