Dual-based bounds for resource allocation in zero-forcing beamforming OFDMA-SDMA systems

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 (RA) 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

Efficient Heuristic for Resource Allocation in Zero-forcing OFDMA-SDMA Systems with Minimum Rate Constraints

4G wireless access systems require high spectral efficiency to support the ever increasing number of users and data rates for real time applications. Multi-antenna OFDM-SDMA systems can provide the required high spectral efficiency and dynamic usage of the channel, but the resource allocation process becomes extremely complex because of the augmented degrees of freedom. In this paper, we propose two heuristics to solve the resource allocation problem that have very low computational complexity and give performances not far from the optimal. The proposed heuristics select a set of users for each subchannel, but contrary to the reported methods that solve the throughput maximization problem, our heuristics consider the set of real-time (RT) users to ensure that their minimum rate requirements are met. We compare the heuristics' performance against an upper bound and other methods proposed in the literature and find that they give a somewhat lower performance, but support a wider range of minimum rates while reducing the computational complexity. The gap between the objective achieved by the heuristics and the upper bound is not large. In our experiments this gap is 10.7% averaging over all performed numerical evaluations for all system configurations. The increase in the range of the supported minimum rates when compared with a method reported in the literature is 14.6% on average.Comment: 8 figure