Max-Min SINR Coordinated Multipoint Downlink Transmission—Duality and Algorithms
This paper considers the max-min weighted signal-to-interference-plus-noise ratio (SINR) problem subject to multiple weighted-sum power constraints, where the weights can represent relative power costs of serving different users. First, we study the power control problem. We apply nonlinear Perron-Frobenius theory to derive closed-form expressions for the optimal value and solution and an iterative algorithm which converges geometrically fast to the optimal solution. Then, we use the structure of the closed-form solution to show that the problem can be decoupled into subproblems each involving only one power constraint. Next, we study the multiple-input-single-output (MISO) transmit beamforming and power control problem. We use uplink-downlink duality to show that this problem can be decoupled into subproblems each involving only one power constraint. We apply this decoupling result to derive an iterative subgradient projection algorithm for the problem.
© 2012 IEEE. Manuscript received July 07, 2011; revised February 12, 2012 and June 17,2012; accepted June 21, 2012. Date of publication July 13, 2012; date of current version September 11, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Mathini Sellathurai. The work in this paper is partially supported by grants from the Research Grants Council of Hong Kong, Project No. RGC CityU 125212, Qualcomm Inc., ARO MURI Grant W911NF-08-1-0233, NSF NetSE Grant CNS 0911041, SRG ISTD 2012 037, CAS Fellowship for Young International Scientists Grant 2011Y2GA02, and Bell Labs Lucent-Alcatel. The material in this paper was presented in part at the IEEE International Conference on Communications (ICC), Kyoto, Japan, June 2011, and at the Ninth International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), Princeton, NJ, May 2011.