Performance analysis for uplink massive MIMO systems with a large and random number of UEs

In this paper, we analyze the ergodic achievable rate of an uplink massive multi-user multipleinput multiple-output (MIMO) system with a large and Poisson distributed number of users. In the considered scenario, multiple user equipments (UEs) transmit their information to a base station equipped with a very large number of antennas. New asymptotic expressions for the ergodic achievable rate for large and deterministic number of users are derived for both maximum ratio combining (MRC) detector and zero-forcing (ZF) detector, as well as the ergodic achievable rate for large and random number of users. Simulation results assess the accuracy of these analytical expressions. It is shown that compared with the MRC detector, ZF detector can achieve much higher spectrum efficiency. Also, the results provide a meaningful fact that with different settings the randomness of the number of users will result in different extents of impact on the performance of massive MIMO.