An application of the HMM Theory to optimal nonlinear Equlisation of Quantised-Output Digital ISI Channels

Starting from some general results about Hidden Markov Models (HMMs) recently appeared in literature (Baccarelli and Cusani, 1996; Elliott et al., 1995), low-complexity decision-delay constrained symbol-by-symbol maximum-likelihood detectors for data-transmission over noisy time-dispersive time-variant waveform channels with quantised demodulation are presented. The resulting equalisers are recursive and nonlinear, minimise the symbol error probability and their complexity grows only linearly (and not exponentially) with the value assumed by the decision-delay. A new family of Bhattacharyya-like upper bounds is also presented for the analytical evaluation of their performance.