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In this paper, the authors Design DownLink (DL) beamforming vectors for a multiuser multicell Cognitive Radio (CR) network with imperfect Channel State Information (CSI) at Base Stations (BS). Specifically, they model channel estimation error as a random vector with known statistical distribution. Their 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, they replace the probabilistic constraints with conservative deterministic constraints. By applying rank relaxation, the original problem is reformulated as Semi-Definite Programming (SDP). Interestingly, numerical results show that the obtained solutions fulfill the rank constraint.
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