Robust coordinated downlink beamforming for multicell-cognitive radio networks with probabilistic constraints

In this paper, we design downlink (DL) beam-forming vectors for a multiuser multicell cognitive radio (CR) network with imperfect channel state information (CSI) at base stations (BS). Specifically, we model channel estimation error as a random vector with known statistical distribution. Our objective is to minimize the total DL transmit power subject to probabilistic quality of service (QoS) constraints of every secondary user (SU) and primary user (PU). Utilizing Bernstein-type inequalities [12], we replace the probabilistic constraints with conservative deterministic constraints. By applying rank relaxation, the original problem is reformulated as semidefinite programming (SDP). Interestingly, numerical results show that the obtained solutions fulfill the rank constraint.