Sum Rate Analysis of ZF Receivers in Distributed MIMO Systems

The performance of single-cell distributed multiple-input multiple-output (D-MIMO) systems is not only affected by small-scale Rayleigh fading but also from large-scale fading and path-loss. In this paper, we elaborate on the sum rate of D-MIMO systems employing linear zero-forcing receivers, accounting for both large and small-scale fading effects, as well as spatial correlation at the transmit side. In particular, we consider the classical lognormal model and propose closed-form upper and lower bounds on the achievable sum rate. Using these bounds as a starting point, we pursue a "large-system" analysis and provide asymptotic expressions when the number of antennas at the base station (BS) grow large, and when the number of antennas at both ends grow large with a fixed and finite ratio. A detailed characterization in the asymptotically high and low signal to noise ratio regimes is also provided. An interesting observation from our results is that in order to maximize the sum rate, the RPs should be placed at unequal distances to the BS when they experience the same level of shadowing. The resulting closed-form expressions are compared with the corresponding results on MIMO optimal receivers.