Performance analysis of TCM with generalized selection combining on Rayleigh fading channels

In this paper, we analyze the performance of trellis coded modulation (TCM) schemes with generalized selection combining (GSC) on fading channels. We first derive the computational cutoff rate, R₀, for coherent TCM schemes on i.i.d. Rayleigh fading channels with (K, L) GSC diversity which combines the K paths with the largest instantaneous SNR among the L available diversity paths. The cutoff rate is shown to be a simple function of the moment generating function (MGF) of the SNR at the output of the (K, L) GSC receiver. The cutoff rate results show that, at a cutoff rate of 1 bit/sec/Hz, 8-PSK modulation with (1, 3) GSC requires about the same E_b/N₀ as QPSK modulation with (2,3) GSC. Also, at 1.5 bits/sec/Hz, 8-PSK with (1, 3) GSC and QPSK with (3,3) GSC require about the same E_b/N₀. This illustrates that in TCM schemes with GSC diversity, the modulation complexity (i.e., alphabet size, M) and the GSC receiver complexity (i.e., the number of combined diversity paths, K) can be traded off to achieve a desired performance. Next, we derive the union bound on the bit error probability of TCM schemes with (K, L) GSC reception in the form of a simple, finite integral. The effectiveness of this bound is verified through simulations.