Optimal number of users in zero-forcing based multiuser MIMO systems with large number of antennas

The optimal number of users achieving the maximum sum throughput is analyzed in zero-forcing (ZF) based multiuser multiple-input multiple-output (MIMO) systems with a large number of base station (BS) antennas. By utilizing deterministic ergodic sum rates for the ZF-beamforming (ZF-BF) and ZF-receiver (ZF-R) with a large number of BS antennas [1], [2], we can obtain the ergodic sum throughputs for the ZF-BF and ZF-R for the uplink and downlink frame structures, respectively. Then, we can also formulate and solve the optimization problems maximizing the ergodic sum throughputs with respect to the number of users. This paper shows that the approximate downlink sum throughput for the ZF-BF is a concave function and the approximate uplink sum throughput for the ZF-R is also a concave function in a feasible range with respect to the number of users. The simulation results verify the analyses and show that the derived numbersof users provide the maximum sum throughputs for the ZF-BF as well as ZF-R in multiuser MIMO systems with a large number of BS antennas.