Quantization Noise as an Asset: Optimizing Physical Layer Security With Sigma-Delta Modulation

Massive multiple-input multiple-output (MIMO) technology has revolutionized wireless communication by significantly enhancing spectral efficiency, however its high energy consumption has become a key concern. There is increasing research interest in implementing massive MIMO systems using low-resolution digital-to-analog converters (DACs) to reduce the hardware cost and energy consumption. Meanwhile, the broadcast nature of wireless communications systems poses security risks, exposing user information to potential eavesdroppers (Eve), and this issue has been studied less in the context of low-resolution massive MIMO systems. This paper investigates the potential of low-resolution massive MIMO systems to enhance physical layer security (PLS) without relying on artificial noise (AN). We propose a novel spatial Sigma-Delta modulation technique that strategically leverages quantization noise to obscure confidential communications from Eve, even with limited channel state information. Our design shifts quantization noise away from legitimate users while maintaining its presence near Eve, thus improving PLS. We formulate the resulting non-convex, semi-infinite design problem and apply a proximal majorization-minimization (PMM) algorithm, ensuring convergence to a Karush–Kuhn–Tucker (KKT) point. To enhance computational efficiency, we introduce a proximal distance algorithm (PDA) that addresses the constraints independently, yielding closed-form solutions for projections and proximal operators. Extensive numerical experiments validate our approach, demonstrating effective noise shaping for both users and Eve. Our findings illustrate that quantization noise can be a valuable asset in securing communications in low-resolution massive MIMO systems.