Performance of a class of blind deconvolution and equalization criteria using cumulant based inverse filters

Chi and Wu (1995) proposed a unified class of inverse filter criteria J/sub r,m/ using rth-order and mth-order cumulants (where r is even and m>r/spl ges/2) which includes Wiggins´ (1978) criterion, Shalvi and Weinstein´s (1990) criterion and Tugnait´s (1993) criteria as special cases, for blind deconvolution and equalization with only non-Gaussian output measurements of a nonminimum phase linear time-invariant (LTI) system (channel) h(n). In this paper, we theoretically prove that for finite SNR, as Mendel´s (nonblind) minimum-variance deconvolution (MVD) filter, the optimum inverse filter v(n) associated with the criteria J/sub 2,m/ is a perfect phase equalizer but not a perfect amplitude equalizer, and the latter approaches the former as either m or SNR is increased or as the system h(n) has wider bandwidth. For the other J/sub r,m/ (r/spl ges/4), perfect equalization can be attained at the expense of SNR degradation. Finally, some simulation results are provided to support the proposed analytic results.