Power, Bandwidth and Complexity in Maximum Likelihood Sequence Estimation

Abstract

This thesis develops a two dimensional Viterbi Algorithm for the maximum likelihood sequence estimation over band limited baseband channels with intersymbol interference. Degradation, decision depth, 99% energy bandwidth and the channel cost are used as the performance measures for the comparisons of different channels. The four measures are extensively evaluated for channels with length up to four signalling intervals. The results of each measure are presented in contour form. Error events analysis shows that the degradation contours are governed by elliptical equations. Maximum degradation results from state path merge at a depth equal to the channel length plus one. By analysing periodic state sequences, we found that catastrophic error propagation contours are mainly governed by linear equations. Generally, channels with longer length have narrower minimum bandwidth but higher degradation. A channel cost similar to Shannon capacity equation is proposed to jointly minimize both degradation suffered and bandwidth required for signalling over a channel. According to the equation, the channel cost is influenced more by the bandwidth than by the degradation and thus the regions of low channel cost lie on the regions of narrow bandwidth. Also low channel cost regions are found to be on the regions of long decision depth and thus require higher complexity for maximum likelihood sequence estimation. In addition, it is found that minimum channel cost decreases with increasing channel length.