Asymptotic analysis of max-min weighted SINR in multiuser downlink

In this paper, we study the problem of jointly optimizing the beamformer and the power in a multiuser downlink system wherein the number of transmit antennas and the number of users grow asymptotically large with a bounded ratio. The max-min weighted SINR problem with a weighted sum power constraint is considered. Techniques developed from random matrix theory are employed to derive asymptotically optimal solutions that only rely on statistical channel information and can be further leveraged to design the asymptotically optimal beamformers in a non-iterative manner. Moreover, by using nonlinear Perron-Frobenius theory and random matrix theory, an effective uplink system and an effective downlink system are proposed to characterize and interpret the asymptotically optimal solutions.