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The authors investigate a weighted sum rate maximization and rate balancing problem for a spectrum sharing Multiple Input Multiple Output (MIMO) based wireless relay network. The aim is to maximize the sum rate of the wireless relay network whilst ensuring the interference leakage to the primary user terminals during two time slots are below a specific value. They solve this problem by asymmetrically allocating the power to different time slots and using the principle of MAC-BC duality. The algorithm in its dual form has been solved using sub-gradient methods. The simulation results demonstrate the convergence of the algorithm and the simultaneous satisfaction of maximum power and the interference constraints.
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