[Paper Review] Scalable Coordinated Beamforming for Dense Wireless Cooperative Networks

Yuanming Shi, Jun Zhang+1 more|arXiv (Cornell University)|May 13, 2014

Advanced MIMO Systems Optimization9 references3 citations

TL;DR

This paper proposes a scalable, ADMM-based coordinated beamforming framework for dense wireless networks using matrix stuffing to transform the optimization problem into an ADMM-compliant form, enabling closed-form, parallelizable subproblem solutions. The method achieves orders-of-magnitude speedup over interior-point solvers and optimal beamforming significantly outperforms zero-forcing beamforming in spectral efficiency and fairness.

ABSTRACT

To meet the ever growing demand for both high throughput and uniform coverage in future wireless networks, dense network deployment will be ubiquitous, for which co- operation among the access points is critical. Considering the computational complexity of designing coordinated beamformers for dense networks, low-complexity and suboptimal precoding strategies are often adopted. However, it is not clear how much performance loss will be caused. To enable optimal coordinated beamforming, in this paper, we propose a framework to design a scalable beamforming algorithm based on the alternative direction method of multipliers (ADMM) method. Specifically, we first propose to apply the matrix stuffing technique to transform the original optimization problem to an equivalent ADMM-compliant problem, which is much more efficient than the widely-used modeling framework CVX. We will then propose to use the ADMM algorithm, a.k.a. the operator splitting method, to solve the transformed ADMM-compliant problem efficiently. In particular, the subproblems of the ADMM algorithm at each iteration can be solved with closed-forms and in parallel. Simulation results show that the proposed techniques can result in significant computational efficiency compared to the state- of-the-art interior-point solvers. Furthermore, the simulation results demonstrate that the optimal coordinated beamforming can significantly improve the system performance compared to sub-optimal zero forcing beamforming.

Motivation & Objective

• To address the high computational complexity of optimal coordinated beamforming in dense wireless cooperative networks.
• To reduce the runtime of large-scale beamforming optimization without sacrificing solution quality.
• To enable practical deployment of optimal beamforming in networks with up to 100 access points.
• To demonstrate the superiority of optimal beamforming over suboptimal strategies like zero-forcing in dense, high-capacity scenarios.

Proposed method

• The matrix stuffing technique is applied to reformulate the original coordinated beamforming problem into an equivalent ADMM-compliant form, enabling efficient solution via ADMM.
• The ADMM algorithm is used to solve the transformed problem, with subproblems solved in closed-form and in parallel at each iteration.
• The method decouples the optimization problem by introducing auxiliary variables based on the Smith form, allowing distributed and scalable computation.
• The framework pre-generates and stores the fixed ADMM structure for a given network size, enabling fast parameter copying for new realizations.
• The implementation uses the SCS solver for ADMM, leveraging conic optimization with parallelized projections.
• The approach avoids reliance on general-purpose modeling tools like CVX, reducing transformation overhead by over 200x.

Experimental results

Research questions

• RQ1 Can a scalable, low-complexity algorithm achieve optimal coordinated beamforming in dense wireless networks with hundreds of APs?
• RQ2 How does the proposed matrix stuffing and ADMM-based method compare in runtime to CVX and SeDuMi for large-scale problems?
• RQ3 What performance gain does optimal beamforming provide over zero-forcing beamforming in terms of minimum user rate and spectral efficiency?
• RQ4 How does the performance gap between optimal and suboptimal beamforming scale with network density and SNR?

Key findings

• The proposed matrix stuffing technique reduces problem transformation time from ~18 seconds (CVX) to under 0.3 seconds, achieving a 200x speedup.
• The ADMM-based solver (SCS) achieves a 1000x speedup over SeDuMi, reducing runtime from ~2600 seconds to ~1 second for a 100-AP network.
• Optimal coordinated beamforming improves the minimum network-wide achievable rate by 2.0 bps/Hz compared to zero-forcing beamforming at low to medium SNR.
• The performance gap between optimal and zero-forcing beamforming increases with user density, highlighting the necessity of optimal beamforming in ultra-dense networks.
• The proposed framework achieves solutions within modest accuracy of the optimal value, as confirmed by matching results between CVX+SeDuMi and matrix stuffing+SCS.
• The method enables scalable, real-time beamforming optimization for networks with up to 100 access points, making optimal coordination practical.