Asymptotic Error Rate Approximation of Amplify-and-Forward Cooperative Diversity Network with Relay Selection

Abstract

In this paper, we present simple approximate closed-form formulas for the average symbol error rate (SER) of M-ary phase shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM) using only basic mathematical technique in the amplify-and-forward (AF) cooperative system with a relay selection over independent and identically distributed (i.i.d.) Rayleigh fading channels. Through some numerical results obtained from the derived formulas, we can easily observe the achievability of the selection diversity gain with a different number of relays. In addition, by comparing the error rate curves from the derived simple high signal-to-noise ratio (SNR) approximate SER formulas with Monte Carlo simulation results as well as the existing relatively complicated lower-bound expressions, we can clearly verify that the analytical results from the proposed formulas are more similar to the Monte-Carlo results than those of the conventional complex ones in sufficiently wide SNR range and thus it is possible to more efficiently evaluate the advantages of relay selection in the cooperative systems.