Dual-Based Bounds for Resource Allocation in Zero-forcing Beamforming OFDMA-SDMA Systems

TL;DR

This paper introduces a dual-based bounding technique for resource allocation in OFDMA-SDMA systems with zero-forcing beamforming, providing bounds that help evaluate heuristic solutions for complex, non-convex optimization problems.

Contribution

It formulates a dual problem to compute tight upper bounds and develops a method to find feasible solutions, enabling benchmarking of heuristics in resource allocation.

Findings

Dual bounds are close to primal solutions in realistic cases.

The dual method effectively benchmarks heuristic algorithms.

Significant room for improvement in existing heuristics is demonstrated.

Abstract

We consider multi-antenna base stations using orthogonal frequency division multiple access and space division multiple access techniques to serve single-antenna users. Some users, called real-time users, have minimum rate requirements and must be served in the current time slot while others, called non real-time users, do not have strict timing constraints and are served on a best-effort basis. The resource allocation problem is to find the assignment of users to subcarriers and the transmit beamforming vectors that maximize the total user rates subject to power and minimum rate constraints. In general, this is a nonlinear and non-convex program and the zero-forcing technique used here makes it integer as well, exact optimal solutions cannot be computed in reasonable time for realistic cases. For this reason, we present a technique to compute both upper and lower bounds and show that these are quite close for some realistic cases. First, we formulate the dual problem whose optimum provides an upper bound to all feasible solutions. We then use a simple method to get a primal-feasible point starting from the dual optimal solution, which is a lower bound on the primal optimal solution. Numerical results for several cases show that the two bounds are close so that the dual method can be used to benchmark any heuristic used to solve this problem. As an example, we provide numerical results showing the performance gap of the well-known weight adjustment method and show that there is considerable room for improvement.