Equalization in digital satellite communication systems using robust Kalman filtering

The problem of digital data transmission over handlimited, nonlinear channels in the presence of intersymbol interference and white Gaussian and/or non-Gaussian noise in the uplink and downlink paths is considered. The satellite transponder is assumed to be of soft-limiting type. A recursive, adaptive, real time equalizer structure employing the standard Kalman filter is developed for bindary-phase-shift-keyed (BPSK) satellite systems. The simulation results obtained using a digital computer point to a superior performance of the Kalman filter type equalizer when compared to the Wiener filter equalizer used in the past. The scheme is then extended to the case of an M = 6 PAM system and a four-phase PSK system for which optimum sampling times are derived. It is observed that in contrast to the BPSK system, in which the probability of error decreases exponentially with increasing signal-to-noise ratio, in the the M = 6 PAM system and the four-phase PSK system the probability of error decreases linearly with increasing SNR.