Performance of ZF Precoder in Downlink Massive MIMO with Non-Uniform User Distribution

In this paper, we investigate the achievable sum rate and energy efficiency of downlink massive multiple-input multiple- output antenna systems with zero-forcing precoding, by taking into account the randomness of user locations. Specifically, we propose two types of non-uniform user distributions, namely, center-intensive user distribution and edge-intensive user distribution. Based on these user distributions, we derive novel tight lower and upper bounds on the average sum rate. In addition, the impact of user distributions on the optimal number of users maximizing the sum rate is characterized. Moreover, by adopting a realistic power consumption model which accounts for the transmit power, circuit power and signal processing power, the energy efficiency of the sys- tem is studied. In particular, closed-form solutions for the key system parameters, such as the number of antennas and the optimal transmit signal-to-noise ratio maximizing the energy efficiency, are obtained. The findings of the paper suggest that user distribution has a significant impact on the system performance: for instance, the highest average sum rate is achieved with the center-intensive user distribution, while the lowest average sum rate is obtained with the edge-intensive user distribution. Also, more users can be served with the center-intensive user distribution.