Performance Analysis of Distributed MIMO With ZF Receivers Over Semi-Correlated $\mathcal {K}$ Fading Channels

Distributed multiple-input multiple-output (D-MIMO) systems have drawn considerable attention as they can combine the advantages of point-to-point MIMO with distributed antenna system (DAS). However, the performance analysis of D-MIMO system with zero-forcing (ZF) receivers over semi-correlated K fading channels involves special functions, such as Bessel and Meijer-G functions, which do not enable us to further analysis. In this paper, by using moment matching method, we present a new method that use a Gamma distribution to approximate the K distribution (Rayleigh/Gamma distribution). Using the approximate distribution as a starting point, we derive the approximate analytical expressions on the achievable sum rate (ASR), symbol error ratio (SER), and outage probability (OP) of D-MIMO systems operating in semi-correlated K fading channels employing ZF receivers. To get useful insight into implications of system and fading parameters on the performance, the analytical asymptotic approximations on the ASR in high signal-to-noise ratio (SNR) and low-SNR regime are provided, respectively. Finally, we perform the approximate large-system analysis in the high-SNR and provide asymptotic sum rate expressions when the number of antennas at the base station (BS) grows large, and when the number of antennas at both ends grows large with a fixed and finite ratio. It is demonstrated that the proposed approximate expressions accurately match with the analytical expressions, especially for large-system limit.