Performance of cumulant based inverse filters for blind deconvolution

Chi and Wu proposed a class of inverse filter criteria Jr;m using rth-order and mth-order cumulants (where r is even and m > r 2) for blind deconvolution (equalization) of a (nonminimum phase) linear time-invariant (LTI) system with only non-Gaussian measurements. The inverse filter criteria Jr;m for r = 2 are frequently used such as Wiggins’ criterion, Donoho’s criteria, and Tugnait’s inverse filter criteria for which the identifiability of the LTI system is based on infinite signal-tonoise ratio (SNR). In this paper, we analyze the performance of the inverse filter criteria J2;m (r = 2) when the SNR is finite. The analysis shows that the inverse filter associated with J2;m is related to the minimum mean square error (MMSE) equalizer in a nonlinear manner, with some common properties such as perfect phase (but not perfect amplitude) equalization. Furthermore, the former approaches the latter either for higher SNR, cumulant-order m, or for wider system bandwidth. Moreover, as the MMSE equalizer does, the inverse filter associated with J2;m also performs noise reduction besides equalization. Some simulation results, as well as some calculation results, are provided to support the proposed analytic results.