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The authors address the problem of multi-user downlink beamforming and power allocation in a Cognitive Radio (CR) Secondary Network (SN) with constraints on the total interference in the Primary Network (PN). They derive the Lagrange dual of the problem and show that both problems are equivalent. Two algorithms are proposed to solve the problem. The first is based on convex optimization and the second algorithm exploits the uplink-downlink duality that is enforced by the introduction of appropriate slack variables in the constrained optimization problem. This leads to a simple iterative technique that enjoys easy implementation and low computational costs. Simulation results illustrate that the proposed iterative technique converges to the global optimum in all cases.
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