Pseudo-Noise Superposition for Finite-Alphabet Physical Layer Security

Abstract

Physical-layer security based on pseudo-noise (PN) superposition is a promising approach for mitigating eavesdropping in future wireless systems. However, under Shannon's capacity formulation with Gaussian signaling, achieving secrecy typically requires allocating substantial transmit power to PN, resulting in a significant reduction in achievable information rate and limiting practical applicability. This limitation is alleviated when finite-alphabet modulation schemes, such as M-ary Quadrature Amplitude Modulation ($M$-QAM), are employed, as expected in practical 6G transceivers. In this work, we analyze the information rate performance of PN-assisted systems under $M$-QAM signaling using mutual information and derive the corresponding achievable secrecy rate. The impact of PN power allocation on both the legitimate user and the eavesdropper is investigated across different modulation orders and channel conditions. Monte Carlo simulations are conducted to evaluate system behavior under varying user and eavesdropper channel conditions and to examine how PN power allocation influences secrecy performance. The results show that, at sufficiently high signal-to-noise ratio (SNR), the information rate becomes largely insensitive to PN power allocation, enabling near-perfect secrecy with $M$-QAM modulation-highlighting a key departure from Shannon-capacity-based secrecy analyses and underscoring the practicality of finite-alphabet security mechanisms for 6G wireless systems.