Asymptotic Capacity Analysis of Large-Scale MIMO AF Relay Networks in a Composite Fading Environment

Large-scale multiple-input-multiple-output ( MIMO) networks, together with relay technology, have received considerable attention due to their remarkable capacity potential. Nevertheless, the majority of recent research studies on the asymptotic capacity of large-scale MIMO amplify-and-forward ( AF) relay networks are limited to a fundamental assumption of small-scale fading, where the effect of large-scale fading, including shadow fading and path loss, is ignored. Motivated by this observation, in this paper, we present an extended model for the asymptotic capacity analysis in a composite fading environment, where Rayleigh fading, shadow fading, and path loss effect are incorporated altogether. Moreover, a realistic relay distribution is considered for real-world application of our capacity analysis. The proposed model consists of one source and one destination that are both equipped with M antennas, which communicate through K relays, each having N antennas. We first employ random matrix theory to derive the empirical cumulative distribution of the channel covariance matrix and analyze the asymptotic capacity per source-destination antenna pair as both M and NK tend to infinity, but their ratio remains as a constant. We then consider the asymptotic capacity under two asymptotic cases for a finite and an infinite number of relays, respectively. It is shown through both theoretical analysis and Monte Carlo simulations that increasing the shadowing standard deviation can improve asymptotic capacity, whereas increasing the path loss exponent would lead to a capacity reduction. Our simulation results also reveal the effects of the relay distribution, as well as the source and relay transmission powers, on the asymptotic capacity.