Finite Horizon Optimization for Large-Scale MIMO

2025-03-14

AI Summary

In massive MIMO systems, the conventional WMMSE beamforming becomes computationally infeasible due to repeated inversions of high-dimensional matrices. To address this, this paper proposes an inversion-free FP–gradient descent joint optimization framework. Our key contributions are: (1) integrating fractional programming (FP) with gradient descent to completely eliminate large-scale matrix inversions scaling with the number of transmit antennas; and (2) jointly optimizing the gradient step size based on finite-horizon optimal control theory to maximize the weighted sum rate within a fixed number of iterations. Theoretical analysis shows the algorithm’s computational complexity reduces to *O*(*N*), where *N* denotes the number of antennas. Simulation results for systems with up to 1,000 antennas demonstrate that, under identical iteration counts, the proposed method achieves significantly higher spectral efficiency than WMMSE while reducing per-iteration complexity by two orders of magnitude.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Security and Privacy: Large-scale security measurements

Abstract

Large-scale multiple-input multiple-output (MIMO) is an emerging wireless technology that deploys thousands of transmit antennas at the base-station to boost spectral efficiency. The classic weighted minimum mean-square-error (WMMSE) algorithm for beamforming is no suited for the large-scale MIMO because each iteration of the algorithm then requires inverting a matrix whose size equals the number of transmit antennas. While the existing methods such as the reduced WMMSE algorithm seek to decrease the size of matrix to invert, this work proposes to eliminate this large matrix inversion completely by applying gradient descent method in conjunction with fractional programming. Furthermore, we optimize the step sizes for gradient descent from a finite horizon optimization perspective, aiming to maximize the performance after a limited number of iterations of gradient descent. Simulations show that the proposed algorithm is much more efficient than the WMMSE algorithm in optimizing the large-scale MIMO precoders.

Problem

• Eliminates large matrix inversion in large-scale MIMO beamforming.
• Optimizes step sizes using finite horizon optimization for gradient descent.
• Improves efficiency of precoder optimization in large-scale MIMO systems.

Innovation

• Eliminates large matrix inversion using gradient descent
• Applies fractional programming for optimization
• Optimizes step sizes via finite horizon optimization