Resource allocation in multiantenna systems-achieving max-min fairness by optimizing a sum of inverse SIR

Abstract

We address the problem of jointly optimizing transmit powers and linear preequalizers (e.g., beamformers) for a multiuser downlink channel. All results can be transferred to the dual uplink channel. The link quality of each user is determined by the signal-to-interference ratio (SIR). Two common strategies for distributing the system resources by joint optimization of transmit powers and beamformers are 1) maximize the minimum SIR, to which we refer as max-min fairness, and 2) minimize the sum of weighted inverse SIR. Both strategies are generally not equivalent. In this paper, it is shown how the weighting factors should be chosen so that the sum optimization approach achieves optimal max-min fairness. An efficient iterative algorithm is proposed for solving this nonlinear optimization problem. Monotonicity and convergence are proved.Index Terms-Beamforming, max-min fairness, power control, resource allocation, signal-to-interference ratio (SIR) balancing.

A characterization of max–min SIR-balanced power allocation with applications

“…The following observation summarizes two important properties of the power allocation " p 0 defined by (6). The observation is an immediate consequence of (3), Lemma 1 and the properties of F proven in Lemma 2.…”

“…This result was used in [16] to solve the max-min SIR-balancing problem over the joint space of admissible power vectors and receive beamformers. Thus, the results of this paper provide key tools to generalize the results of [6] to noisy channels under general power constraints and to a larger class of utility functions. The discussed results are presented in Sect.…”

“…A connection between the utility-based approach and the max-min SIR-balancing approach is known in the noiseless case [8] and constitutes the starting point for the analysis in [6]. The connection established in [8] (see also [45,Sect.…”

“…A max-min fair power allocation is therefore also max-min SIR-balanced (provided that the feasible SIR region is downward comprehensive); the converse is in general not true. However, if the max-min SIR-balancing problem has a unique solution given by (6), this solution is also max-min fair and there are no other max-min fair power allocations. These relations can be observed in Fig.…”

Peak power minimization in symbol-level precoding for cognitive MISO downlink channels

“…In this work, we propose a symbollevel precoding scheme that controls the instantaneous per-antenna transmit power, thus minimizing the power peaks, which are detrimental with respect to the aforementioned non-linearity problem. In contrary to symbol-level precoding, the conventional schemes designs the precoding for an entire codeword, therefore, the transmitted power can be controlled only in average and not symbol by symbol [26]- [28]. In this paper, we want to limit the effects of non-linearities in the downlink of multiple-antenna cognitive system, while satisfying the quality of service demands of the cognitive users without violating interference temperature constraints imposed by primary system.…”