Performance of cumulant based inverse filters for blind deconvolution
Chih-Chun Feng, Chong‐Yung Chi · IEEE Transactions on Signal Processing · 1999
Chi and Wu (1963) proposed a class of inverse filter criteria J/sub r,m/ using rth-order and rth-order cumulants (where r is even and m>r/spl ges/2) for blind deconvolution (equalization) of a (nonminimum phase) linear time-invariant (LTI) system with only non-Gaussian measurements. The inverse filter criteria J/sub r,m/ for r=2 are frequently used such as Wiggins' (1978) criterion, Donoho's (1981) criteria, and Tugnait's (1993) inverse filter criteria for which the identifiability of the LTI system is based on infinite signal-to-noise ratio (SNR). We analyze the performance of the inverse filter criteria J/sub 2,m/ (r=2) when the SNR is finite. The analysis shows that the inverse filter associated with J/sub 2,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 J/sub 2,m/, also performs noise reduction besides equalization. Some simulation results, as well as some calculation results, are provided to support the proposed analytic results.