  In this paper we propose a pair of low-complexity user selection schemes with
zero-forcing precoding for multiuser massive MIMO downlink systems, in which
the base station is equipped with a large-scale antenna array. First, we derive
approximations of the ergodic sum rates of the systems invoking the
conventional random user selection (RUS) and the location-dependant user
selection (LUS). Then, the optimal number of simultaneously served user
equipments (UEs), $K^*$, is investigated to maximize the sum rate
approximations. Upon exploiting $K^*$, we develop two user selection schemes,
namely $K^*$-RUS and $K^*$-LUS, where $K^*$ UEs are selected either randomly or
based on their locations. Both of the proposed schemes are independent of the
instantaneous channel state information of small-scale fading, therefore
enjoying the same extremely-low computational complexity as that of the
conventional RUS scheme. Moreover, both of our proposed schemes achieve
significant sum rate improvement over the conventional RUS. In addition, it is
worth noting that like the conventional RUS, the $K^*$-RUS achieves good
fairness among UEs.
