Surrogate-Enhanced Fractional Programming for MIMO Device-to-Device Interference Networks

2026-09-28

AI Summary

This study addresses the challenge of extending scalar sum-of-exponentials fractional programming (SEFP) to MIMO D2D networks, where the non-commutativity of matrix ratios impedes direct generalization. By leveraging Hermitian functional calculus, this work extends the scalar ratio information transform (RIT) to its matrix counterpart, establishing a matrix SEFP framework for weighted sum-rate maximization. The primary contributions include formulating matrix SEFP and unifying it with the XMMSE perspective, demonstrating that the latter constitutes a special case of the former. Furthermore, an algorithm termed SEFPLinQ is developed by integrating fractional programming with minimax optimization techniques. Experimental results confirm that the proposed approach consistently yields performance gains in joint scheduling and beamforming optimization for MIMO D2D networks under flexible association strategies.

Abstract

Interference management in multi-stream multi-input multi-output (MIMO) device-to-device (D2D) networks often leads to weighted sum-rate maximization with sum-log-determinant involving matrix-valued signal-to-interference-plus-noise ratios. The state-of-the-art paradigms, including weighted minimum mean-square error (WMMSE) and fractional programming (FP), have achieved tremendous success in link scheduling, power control, and beamforming problems. Recently, an upgraded FP approach, named surrogate-enhanced FP (SEFP) in a scalar form, has attained improved performance in joint uplink scheduling and power control in coordinated multicell SISO networks. The proposed SEFP improves the surrogate construction of the classical Lagrangian dual transform plus quadratic transform for logarithmic fractional objectives with a novel reciprocal-inverse transform (RIT), yet its extension to the matrix form for MIMO settings does not seem straightforward because the matrix ratio and the auxiliary matrix generally do not commute. In this paper, by leveraging mathematical tools from Hermitian functional calculus, we extend RIT to matrix ratios by lifting the scalar RIT along the eigendirections of an auxiliary matrix and recasting the resulting directional construction in an operator form. Following, we develop a matrix SEFP framework for weighted sum-log-determinant maximization. Further, we establish a unified view of SEFP and the recently proposed XMMSE method, specify when the two algorithms attribute to identical minorization-maximization (MM) surrogates and variable update trajectories, and prove XMMSE can be considered as a special case of SEFP under the algorithmic family perspective.Inspired by the unified view, we develop SEFPLinQ for the joint scheduling and beamforming optimization in flexible-association MIMO D2D networks. Numerical results demonstrate consistent performance gains.

Problem

• MIMO D2D networks
• interference management
• fractional programming
• weighted sum-rate maximization
• joint scheduling and beamforming

Innovation

• Surrogate-Enhanced Fractional Programming
• Reciprocal-Inverse Transform
• Hermitian Functional Calculus
• MIMO D2D Networks
• Joint Scheduling and Beamforming