Multiamplitude minimum shift keying trellis codes for AWGN and fading channels

In this paper, we propose multiamplitude minimum shift keying (MAMSK) trellis codes with improved error performance based on multiple signal sets for AWGN and fading channels. Our aim is to obtain schemes, we call them multiple MAMSK trellis codes, that have the same number of Viterbi decoder trellis states as MAMSK. The design procedure has two steps: The determination of the optimal reduced multiple MAMSK signal set and then the external convolutional encoder which will realize this reduction. Since the design criteria for fading channels are different from those of AWGN channels, we develop two different search algorithms in order to obtain good trellis codes for each types of channel. Analytical bit error probability upper bounds are derived for each case and it is shown that the proposed codes have improved error performance with respect to the ordinary MAMSK and MSK. Computer simulations also verify these results.