Asymptotic Analysis of the Downlink in Cooperative Massive MIMO Systems

We consider the downlink of a cooperative cellular communications system, where several base-stations around each mobile cooperate and perform zero-forcing to reduce the received interference at the mobile. We derive, for the first time, closed-form expressions for the asymptotic performance of the network as the number of antennas per base station grows large. These expressions capture the trade-offs between various system parameters, and characterize the joint effect of noise and interference (where either noise or interference is asymptotically dominant and where both are asymptotically relevant). The presented analysis is significantly more challenging than the uplink analysis due to the dependence between beamforming vectors of nearby base stations. This statistical dependence is handled by introducing novel bounds on marked shot-noise point processes with dependent marks, which are also useful in other contexts. The asymptotic results are verified using Monte Carlo simulations, which indicate that they are useful even when the number of antennas per base station is only moderately large. Based on these expressions, we present a novel power allocation algorithm that is asymptotically optimal while significantly reducing the coordination overhead between base stations.