  We address the problem of power allocation and secondary user (SU) selection
in the downlink from a secondary base station (SBS) equipped with a large
number of antennas in an underlay cognitive radio network. A new optimization
framework is proposed in order to select the maximum number of SUs and compute
power allocations in order to satisfy instantaneous rate or QoS requirements of
SUs. The optimization framework also aims to restrict the interference to
primary users (PUs) below a predefined threshold using available imperfect CSI
at the SBS. In order to obtain a feasible solution for power allocation and
user selection, we propose a low-complexity algorithm called
DeleteSU-with-Maximum-Power-allocation (DMP). Theoretical analysis is provided
to compute the interference to PUs and the number of SUs exceeding the required
rate. The analysis and simulations show that the proposed DMP algorithm
outperforms the stateof-the art selection algorithm in terms of serving more
users with minimum rate constraints, and it approaches the optimal solution if
the number of antennas is an order of magnitude greater than the number of
users.
