Effects of Spatial Correlation on the Sum Rate Distribution of ZF Receivers in MU-MIMO Systems

The performance of multi-user multiple-input multiple-output (MU-MIMO) systems is not only affected by multi-path fading, but also by shadowing and path-loss. In this paper, we concentrate on the sum rate distribution of MU-MIMO systems employing linear zero-forcing receivers, accounting for both multi-path fading and shadowing effects, as well as spatial correlation at the transmit and receiver sides. In particular, we consider the classical spatially correlated lognormal model, and propose closed-form bounds on the distribution of achievable sum rates in MU-MIMO systems. With the help of these bounds, we derive a relationship between the inter-user distance and channel 10% outage sum rate under different environmental features. A practical conclusion from our results is that the effect of spatially correlated shadowing can be considered as independent when the inter-user distance is approximately five times the shadowing correlation distance. A detailed analysis of the effects of composite channel attenuation consisting of multi-path fading and shadowing is also provided.