Fractional Programming for Stochastic Precoding over Generalized Fading Channels

2025-07-09

AI Summary

This paper addresses the long-term average weighted sum-rate maximization problem in MIMO networks. We propose a stochastic precoding design that relies solely on the first- and second-order moments of channel fading—without assuming specific fading distributions (e.g., Gaussianity). To overcome the fundamental limitation of conventional fractional programming (FP), where auxiliary variables cannot be readily introduced under expectation operations, we develop a novel matrix-based FP framework that constructs a tight lower bound via matrix analysis. Integrating tools from random matrix theory and stochastic optimization, we devise a low-complexity iterative algorithm that avoids large-scale matrix inversions—critical for massive MIMO deployments. Numerical experiments demonstrate that the proposed method consistently outperforms state-of-the-art baselines under both Gaussian and various non-Gaussian fading channels, achieving substantial gains in weighted sum-rate while maintaining high computational efficiency.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization
• Machine Learning: Matrix & Tensor Methods

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
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper seeks an efficient algorithm for stochastic precoding to maximize the long-term average weighted sum rates throughout a multiple-input multiple-output (MIMO) network. Unlike many existing works that assume a particular probability distribution model for fading channels (which is typically Gaussian), our approach merely relies on the first and second moments of fading channels. For the stochastic precoding problem, a naive idea is to directly apply the fractional programming (FP) method to the data rate inside the expectation; it does not work well because the auxiliary variables introduced by FP are then difficult to decide. To address the above issue, we propose using a lower bound to approximate the expectation of data rate. This lower bound stems from a nontrivial use of the matrix FP, and outperforms the existing lower bounds in that it accounts for generalized fading channels whose first and second moments are known. The resulting approximate problem can be efficiently solved in closed form in an iterative fashion. Furthermore, for large-scale MIMO, we improve the efficiency of the proposed algorithm by eliminating the large matrix inverse. Simulations show that the proposed stochastic precoding method outperforms the benchmark methods in both Gaussian and non-Gaussian fading channel cases.

Problem

• Maximize long-term average weighted sum rates in MIMO networks
• Develop efficient algorithm for stochastic precoding under generalized fading
• Overcome limitations of FP method with novel lower bound

Innovation

• Uses first and second moments of fading channels
• Applies matrix fractional programming lower bound
• Eliminates large matrix inverse for efficiency