Maximizing sum rate and minimizing MSE on multiuser downlink: Optimality, fast algorithms and equivalence via max-min SIR

Abstract

Algorithm 2 Nonlinear PerronFrobenius theory: _ _~g~t~L~o~r~(lI~o~nà bstract-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. We show that, through connections with the nonlinear Perron-Frobenius theory, jointly optimizing power and beam formers in the max-m in weighted SIR problem can be solved optimally in a distributed fashion . Then, connecting these three performance objectives through the arithmetic-geometric mean inequality and nonnegative matrix theory, we solve the weighted sum MSE minimization and weighted sum rate maximization in the low to moderate interference regimes using fast algorithms. nonconvex problems suboptimally. We develop fast algorithms (independent of stepsize) to solve these two nonconvex problems optimally under low to medium interference conditions. We leverage the standard interference function approach in [II] to show that our algorithms converge under synchronous and asynchronous updates. Proofs can be found in [12]. Fig. 1. Overview of the connect ion (solid lines) between the three optimization problems in the paper: i) Weighted sum MSE minimization in (I8), ii) weighted sum rate maximizati on in (28), and iii) max-min weighted SIR in (5). The upper half of the dotted line considers power control only, while the lower half considers both power control and beamforming.

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

“…In this paper, we extend the recent results in [16] to the MIMO max-min weighted SINR problem with linear beamforming. First, we analyze the MISO and single-input-multiple-output (SIMO) problems using nonlinear Perron-Frobenius theory.…”

“…Then, in Section III-B, we show that nonlinear Perron-Frobenius theory can resolve the open problem of convergence of the MISO max-min SINR algorithm proposed in [1]. Next, in Section III-C, we show that our new MISO result can, in fact, be derived from the alternate optimization algorithm proposed in [16]. In Section III-D, we exploit the connection between Perron-Frobenius theory and the Friedland-Karlin inequalities in [18] to draw further insights on the optimal solutions.…”

“…Unfortunately, this approach, when extended to the MISO/MIMO problems via alternate optimization [8], [11]- [15], required a centralized power update involving an eigenvector computation. Recently, the authors in [16] and [17] derived a different algorithm for the max-min weighted SINR power control problem. The key insight was that the problem is equivalent to solving an affine eigenvalue equation, in which the optimal value is associated with the eigenvalue and the optimal power is given by the eigenvector.…”

“…As a by-product, we solve the open problem of convergence for the previously proposed MISO algorithm in [1]. We also show that our fixed-point iteration can, in fact, be decoupled and interpreted as an alternate optimization of power, via nonlinear Perron-Frobenius theory [16], and beamformers, via minimum-variance distortionless response (MVDR) beamforming (cf. Fig.…”

Radio Resource Allocation Over Fading Channels Under Statistical Delay Constraints

“…The problem (6.19) is similar to the weighted sum-rate maximization problem [124]. We can see that in this case, the optimal B-FD-APA solution ensures equal average (ergodic) rates of the S-R and R-D links.…”