System analysis of relaying with modulation diversity

The performance analysis of a relaying system implementing modulation diversity is investigated in this work. Our relaying system is quite novel, since, we assume that the relay always transmits during the relaying phase, i.e., is never silent. Whereas in the other related works assume that the relay first decodes its received signal and upon a successful decoding, transmits to the destination, i.e., the relay is silent upon an unsuccessful decoding. Modulation diversity creates diversity by transforming the angle of a classical modulation to create signal points with distinct components, followed by subsequent interleaving over the components. Assuming transmission over independent Rayleigh fading channels and maximum likelihood detection on the reordered signals at the receiver, the analysis starts with finding the probability density function of the end-to-end signal-to-noise (SNR) ratio. Then, a tight upper-bound expression for the error probability is obtained. Following that, we achieve the exact outage probability of the relaying system under-study. Then, exact and upper-bound expressions for the system capacity are presented. Finally, numerical results and comparisons with Monte Carlo simulations are presented.