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.
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