these methods are not applicable for TDD systems either. This is because in TDD scenarios, the feedback signals from a large number of candidate-UEs will increase the uplink proportion of the uplink-downlink shared frequency band at each coherence slot, resulting in reduced resources left for downlink data transmission. In summary, neither the instantaneous-CSI estimation based nor the uplink-feedback based user selection methods are suitable for the downlink of TDD-based massive MIMO systems. At the time of writing, the design of user selection for massive MIMO systems with the TDD mode remains a largely open area. Hence, the novel user selection methods which cause no or just little decrease of downlink transmission resources represent a new promising research subject.

In this paper, we consider the downlink of a TDD based massive MIMO system where pilot-based channel estimation and zero-forcing (ZF) precoding are invoked for serving a number of UEs. First, with the aid of the random matrix theory (RMT)-based large system analysis, we derive approximations of the ergodic sum rates of the systems invoking the conventional RUS and the location-dependent user selection (LUS). The optimal number of simultaneously served UEs, denoted as $K^*$, is solved offline for maximizing the sum rate 