[Paper Review] Fast Heuristics for Power Allocation in Zero-Forcing OFDMA-SDMA Systems with Minimum Rate Constraints

Diego Perea-Vega, A. Girard+1 more|arXiv (Cornell University)|Aug 5, 2014

Advanced Wireless Network Optimization12 references3 citations

TL;DR

This paper proposes fast, suboptimal heuristics for power allocation in zero-forcing OFDMA-SDMA systems with minimum rate constraints for real-time users. It introduces a non-iterative, one-step dual-domain adjustment method that achieves near-optimal performance in ~10 ms—over 100× faster than exact solvers—while maintaining low infeasibility for practical deployment.

ABSTRACT

We investigate in this paper the optimal power allocation in an OFDM-SDMA system when some users have minimum downlink transmission rate requirements. We first solve the unconstrained power allocation problem for which we propose a fast zero-finding technique that is guaranteed to find an optimal solution, and an approximate solution that has lower complexity but is not guaranteed to converge. For the more complex minimum rate constrained problem, we propose two approximate algorithms. One is an iterative technique that finds an optimal solution on the rate boundaries so that the solution is feasible, but not necessarily optimal. The other is not iterative but cannot guarantee a feasible solution. We present numerical results showing that the computation time for the iterative heuristic is one order of magnitude faster than finding the exact solution with a numerical solver, and the non-iterative technique is an additional order of magnitude faster than the iterative heuristic. We also show that in most cases, the amount of infeasibility with the non-iterative technique is small enough that it could probably be used in practice.

Motivation & Objective

• Address the need for fast, near-optimal power allocation in ZF OFDMA-SDMA systems supporting both best-effort and real-time users with minimum rate constraints.
• Reduce computation time for power allocation under rate constraints, which is critical in large-scale systems like LTE-Advanced where iterative user selection requires repeated power allocation.
• Develop heuristics that outperform constant power allocation and prior water-filling schemes by enabling dynamic power redistribution to meet real-time user demands.
• Balance feasibility and performance by proposing a non-iterative heuristic that trades off minor infeasibility for significant speed gains.

Proposed method

• Solve the unconstrained power allocation problem using a zero-finding algorithm over a finite number of intervals, ensuring convergence to the exact optimal solution in O(log₂(NK)) steps.
• Propose a faster, non-guaranteed-convergent fixed-point iteration method based on rewriting optimality conditions, which converges quickly in practice.
• For the constrained problem, use dual decomposition with Lagrange multipliers for power and rate constraints, exploiting linearity of rate boundaries in the (θ, δ) plane.
• Develop an iterative boundary-based algorithm that finds a feasible solution on the rate constraint boundary by solving only for the dual variable θ.
• Introduce a non-iterative, one-step heuristic that adjusts dual multipliers in a single step, parameterized to prioritize either feasibility or spectral efficiency.
• Use pseudo-inverse beamforming (ZF precoding) to cancel inter-user interference, enabling convex reformulation of the power allocation problem.

Experimental results

Research questions

• RQ1 How can power allocation be accelerated in ZF OFDMA-SDMA systems with minimum rate constraints without sacrificing too much performance?
• RQ2 Can a non-iterative heuristic achieve feasible or near-feasible solutions significantly faster than exact solvers or iterative methods?
• RQ3 What is the trade-off between computational speed and solution feasibility in power allocation under rate constraints?
• RQ4 How does the performance of boundary-based and non-iterative heuristics compare to the optimal solution in terms of sum rate and constraint satisfaction?

Key findings

• The non-iterative heuristic achieves computation times of approximately 10 ms, representing an order of magnitude speedup over the iterative boundary method and two orders of magnitude faster than exact solvers.
• The iterative boundary-based algorithm produces solutions that are significantly suboptimal compared to the true optimum, especially when minimum rate constraints are tight.
• The non-iterative heuristic yields solutions with low infeasibility—typically small deviations below required minimum rates—making it viable for practical deployment.
• For the third group of users with high rate requirements (16 Mbps), the non-iterative heuristic’s infeasibility is minimal, despite the problem being barely feasible.
• The zero-finding method for unconstrained power allocation converges to the exact optimal solution in O(log₂(NK)) steps, ensuring optimality with low complexity.
• The fixed-point iteration method, while not guaranteed to converge, consistently converges in fewer than 10 iterations across all tested scenarios and is significantly faster than zero-finding.