Error performance of rotated phase shift keying modulation over fading channels

In this paper, the modulation diversity is used to improve the performance of M-PSK modulation over fading channels. Modulation diversity can be achieved by rotating the signal constellation and using component interleaving. We derive symbol error probability expressions for rotated uncoded M-PSK over Ricean fading channels and obtain optimal rotation angles for M-PSK (M = 2, 4, 8). We show that rotated signal constellations with component interleaving improve the performance of M-PSK significantly as compared to the unrotated one over Rayleigh and Ricean fading channels. For example, when the ratio of the direct path power to the multipath signal power, K is 0 and 10, 8 and 1.5 dB gains are obtained, respectively, at a symbol error probability of 10^-3 for 8PSK modulation. We also show that as K gets larger, the gain obtained by the rotation rapidly decreases. We develop a new asymmetric 8PSK signal constellation obtained from two QPSK signal constellations that are optimally rotated by different angles. This asymmetric 8PSK and also the rotated 8PSK signal constellation together with component interleaving are applied to four-state trellis-coded schemes. Simulation results show that these new schemes provide good performance improvements over the original TCM schemes and previous relevant works over Rayleigh and Ricean fading channels.