  In this paper, we analyze the feasibility of serving K secondary users (SUs)
on the downlink using a secondary base station (SBS), equipped with a large
antenna array, in an underlay cognitive radio (CR) network. First, we formulate
a feasibility problem in order to compute beamforming vectors and power
allocations for K SUs with constraints on the maximum allowable interference to
primary users (PUs), required minimum rate at SUs, and maximum transmit power
from SBS. The problem formulation takes into account the imperfect channel
state information between SUs and PUs. We propose a two step approach to solve
the non-convex problem. In the first step, beamforming vectors are computed
using one of the two alternative schemes: maximum eigenmode beamforming (MEB)
or zero forcing beamforming (ZFB). We show that the power allocations can be
computed by solving a linear programming feasibility problem. Further, we
provide theoretical feasibility analysis of serving K SUs with equal power
allocation by deriving the distributions of SINR at SUs and interference to
PUs, thereby computing the probability of serving K SUs as a function of the
constraints. The analytical and simulation results are presented to demonstrate
the impact of constraints on the feasibility of serving K SUs in the CR
network.
