A Unified Analysis of Max-Min Weighted SINR for MIMO Downlink System

Abstract

Abstract-This paper studies the max-min weighted signal-to-interference-plus-noise ratio (SINR) problem in the multipleinput-multiple-output (MIMO) downlink, where multiple users are weighted according to priority and are subject to a weighted-sum-power constraint. First, we study the multiple-input-single-output (MISO) and single-input-multipleoutput (SIMO) problems using nonlinear Perron-Frobenius theory. As a by-product, we solve the open problem of convergence for a previously proposed MISO algorithm by Wiesel, Eldar, and Shamai in 2006. Furthermore, we unify our analysis with respect to the previous alternate optimization algorithm proposed by Tan, Chiang, and Srikant in 2009, by showing that our MISO result can, in fact, be derived from their algorithm. Next, we combine our MISO and SIMO results into an algorithm for the MIMO problem. We show that our proposed algorithm is optimal when the channels are rank-one, or when the network is operating in the low signal-to-noise ratio (SNR) region. Finally, we prove the parametric continuity of the MIMO problem in the power constraint, and we use this insight to propose a heuristic initialization strategy for improving the performance of our (generally) suboptimal MIMO algorithm. The proposed initialization strategy exhibits improved performance over random initialization.Index Terms-Beamforming, multiple-input-multiple-output (MIMO), uplink-downlink duality.

Grab-n-Pull: An optimization framework for fairness-achieving networks

“…Note that P1 may also be used to formulate the weighted SINR optimization problems; see [1,2] for details.…”

“…The above precoding design problem has been studied extensively in the literature when Ω denotes a total-power or per-antenna power constraint (see e.g., [1][2][3][4][5][6][7][8] and the references therein). As a result, different approaches have been proposed to solve the design problem, including those based on uplink-downlink duality [1], the Lagrangian duality [3] and quasi-convex formulations [8].…”

“…A widely used proactive interpretation of fairness in wireless networks, referred to as the max-min fairness [1][2][3][4][5][6][7][8], is to allocate the available resources in order to maximize the minimal user performance in the network. In such scenarios, a judicious design of the precoding signals for different users can be viewed as a vital part of the network configuration.…”

Optimal Resource Allocation in Coordinated Multi-Cell Systems

“…The duality can in this case be utilized to design iterative fixed-point algorithms that quickly find the optimal dual variables and thereby solve both the downlink and uplink problems [42,59,208,226,227,296]. We refer to [227,228] for further details on such algorithms and the related topic of general interference functions.…”

“…For weighted max-min optimization with a total power constraint, there are computation-ally efficient fixed-point algorithms [42,208,226,228,296] that are also amenable to distributed implementation [42,59,208]. These algorithms are less suitable under general multi-cell power constraints, although such constraints can be handled exactly for single-antenna transmitters [43], by iterative subgradient methods for multi-antenna transmitters [59,308], or by suboptimal approximation of the power constraints [43,108].…”