Robust Monotonic Optimization Framework for Multicell MISO Systems

The performance of multiuser systems is both difficult to measure fairly and to optimize. Most resource allocation problems are non-convex and NP-hard, even under simplifying assumptions such as perfect channel knowledge, homogeneous channel properties among users, and simple power constraints. We establish a general optimization framework that systematically solves these problems to global optimality. The proposed branch-reduce-and-bound (BRB) algorithm handles general multicell downlink systems with single-antenna users, multiantenna transmitters, arbitrary quadratic power constraints, and robustness to channel uncertainty. A robust fairness-profile optimization (RFO) problem is solved at each iteration, which is a quasi-convex problem and a novel generalization of max-min fairness. The BRB algorithm is computationally costly, but it shows better convergence than the previously proposed outer polyblock approximation algorithm. Our framework is suitable for computing benchmarks in general multicell systems with or without channel uncertainty. We illustrate this by deriving and evaluating a zero-forcing solution to the general problem.Comment: Published in IEEE Transactions on Signal Processing, 16 pages, 9 figures, 2 table

Multicell Coordinated Beamforming with Rate Outage Constraint--Part I: Complexity Analysis

This paper studies the coordinated beamforming (CoBF) design in the multiple-input single-output interference channel, assuming only channel distribution information given a priori at the transmitters. The CoBF design is formulated as an optimization problem that maximizes a predefined system utility, e.g., the weighted sum rate or the weighted max-min-fairness (MMF) rate, subject to constraints on the individual probability of rate outage and power budget. While the problem is non-convex and appears difficult to handle due to the intricate outage probability constraints, so far it is still unknown if this outage constrained problem is computationally tractable. To answer this, we conduct computational complexity analysis of the outage constrained CoBF problem. Specifically, we show that the outage constrained CoBF problem with the weighted sum rate utility is intrinsically difficult, i.e., NP-hard. Moreover, the outage constrained CoBF problem with the weighted MMF rate utility is also NP-hard except the case when all the transmitters are equipped with single antenna. The presented analysis results confirm that efficient approximation methods are indispensable to the outage constrained CoBF problem.Comment: submitted to IEEE Transactions on Signal Processin

Distributed Multicell Beamforming Design Approaching Pareto Boundary with Max-Min Fairness

This paper addresses coordinated downlink beamforming optimization in multicell time-division duplex (TDD) systems where a small number of parameters are exchanged between cells but with no data sharing. With the goal to reach the point on the Pareto boundary with max-min rate fairness, we first develop a two-step centralized optimization algorithm to design the joint beamforming vectors. This algorithm can achieve a further sum-rate improvement over the max-min optimal performance, and is shown to guarantee max-min Pareto optimality for scenarios with two base stations (BSs) each serving a single user. To realize a distributed solution with limited intercell communication, we then propose an iterative algorithm by exploiting an approximate uplink-downlink duality, in which only a small number of positive scalars are shared between cells in each iteration. Simulation results show that the proposed distributed solution achieves a fairness rate performance close to the centralized algorithm while it has a better sum-rate performance, and demonstrates a better tradeoff between sum-rate and fairness than the Nash Bargaining solution especially at high signal-to-noise ratio.Comment: 8 figures. To Appear in IEEE Trans. Wireless Communications, 201