Sum of Ratios of Complex Gaussian RVs and Its Application to a Simple OFDM Relay Network

The sum of ratios of two complex Gaussian random variables appears frequently in the mathematical analysis of telecommunication systems when zero-forcing equalization is applied. This paper is focused on the study of one of those systems: a simple Orthogonal Frequency Division Multiplexing (OFDM) relay network. The reason behind the election of this particular scenario is the recent interest on employing relay networks in wireless and mobile broadband systems to increase the coverage and throughput in a cost-effective way. Thus, the probability distribution of enhanced noise, made up by the sum of ratios of complex Gaussian random variables, is used to obtain a closed-form expression for the BER in the scenario under study.