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Maximizing the minimum weighted SIR, minimizing the weighted sum MSE and maximizing the weighted sum rate in a multiuser downlink system are three important performance objectives in joint transceiver and power optimization, where all the users have a total power constraint. The authors show that, through connections with the nonlinear Perron-Frobenius theory, jointly optimizing power and beam-formers in the max-min weighted SIR problem can be solved optimally in a distributed fashion. Then, connecting these three performance objectives through the arithmetic-geometric mean inequality and non-negative matrix theory, they solve the weighted sum MSE minimization and weighted sum rate maximization in the low to moderate interference regimes using fast algorithms.
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