Performance Analysis of a System using Coordinate Interleaving and Constellation Rotation in Rayleigh Fading Channels

Diversity can play an important role in the performance improvement of a communication system in fading channels. The achievable performance with signal space diversity (SSD) is analyzed and a closed form expression for the upper bound of average probability of bit error (P_b) for M-ary phase shift keying (MPSK) in Rayleigh fading channel is presented. The problem of calculating P_b of coherent MPSK over a Rayleigh fading channel has been studied previously in the literature. A solution based on the nearest neighbors was given. In this paper we show that the results with the nearest neighbor approximation represent an expurgated bound and are only valid for a small range of rotational angles. Exact pair-wise error probability (PEP) is derived for Rayleigh fading channels. It is shown that Gray signal constellation mapping is not necessarily the best option for a system employing coordinate interleaving and constellation rotation. Rotation angles are optimized by finding the minimum of the upper bound of P_b. It is shown that the new derived bound is tight for the entire range of rotational angles at high signal-to-noise ratio. Furthermore, the performance of the system in case of phase estimation error is also investigated by simulations.