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The optimal beamforming problems for cognitive multicast transmission are quadratic nonconvex optimization problems. The standard approach is to convert the problems into the form of semi-definite programming (SDP) with the aid of rank relaxation and later employ randomization techniques for solution search. However, in many cases, this approach brings solutions that are far from the optimal ones. We consider the problem of minimizing the total power transmitted by the antenna array subject to quality-of-service (QoS) at the secondary receivers and interference constraints at the primary receivers. It is shown that this problem, which is known to be nonconvex NP-hard, can be approximated by a convex second-order cone programming (SOCP) problem. Then, an iterative algorithm in which the SOCP approximation is successively improved is presented. Simulation results demonstrate the superior performance of the proposed approach in terms of total transmitted power and feasibility, together with a reduced computational complexity, as compared to the existing ones, for both the perfect and imperfect channel state information (CSI) cases. It is further shown that the proposed approach can be used to address the max-min fairness (MMF) based beamforming problem.
Date of Publication: November 2012