Performance of cumulant based inverse filters for blind deconvolution

Chi and Wu proposed a class of inverse filter criteria J(r,m) using rth-ord er and mth-order cumulants (where r is even and m > r greater than or equal to 2) for blind deconvolution (equalization) of a (nonminimum phase) linea r time-invariant (LTI) system with only non-Gaussian measurements. The inve rse filter criteria J(r,m) for r = 2 are frequently used such as Wiggins' c riterion, Donoho's criteria, and Tugnait's inverse filter criteria for whic h the identifiability of the LTI system is based on infinite signal-to-nois e ratio (SNR), In this paper, we analyze the performance of the inverse fil ter criteria J(2,m) (r = 2) when the SNR is finite. The analysis shows that the inverse filter associated with J(2,m) is related to the minimum mean s quare error (MMSE) equalizer in a nonlinear manner, with some common proper ties such as perfect phase (but not perfect amplitude) equalization. Furthe rmore, the former approaches the latter either for higher SNR, cumulant-ord er in, or for wider system bandwidth. Moreover, as the MMSE equalizer does, the inverse filter associated with J(2,m) also performs noise reduction be sides equalization. Some simulation results, as well as some calculation re sults, are provided to support the proposed analytic results.