In this paper, the first time in the literature, partial response-fading channel is introduced. The new channel model acts lire partial response signalling (PRS) hating Rician probability density function. Analytical upper bounds of the trellis coded M-PSK structures are derived using Chernoff bounding technique, combined with the modified generating functional approach for partial response-fading channel with ideal slate information (CSI) and infinite interleaving/deinterleaving. One interesting result is that trellis coded 4PSK systems have better error performance over partial response- fading channel than classical Rician channels for signal to noise ratios greater than a threshold value, which has the best error performance in the literature. Neural network models of trellis coded 4PSK scheme is introduced the first time ire literature over partial response-lading channels. The hit error event curves are derived using back propogation algorithm.