Single-Channel Blind Source Separation in Wireless Communications: A Bayesian Approach

Abstract

In non-cooperative communications, single-antenna receivers often face a fundamentally underdetermined problem when separating multiple signals that overlap in the time domain and alias in the frequency. Existing blind separation methods often rely heavily on precise prior knowledge of physical parameters such as carrier frequency offset (CFO) and timing offset, leading to significant performance degradation under parameter uncertainty and mismatch, especially in the presence of highly correlated observations induced by spectral aliasing. To address this challenge, this paper proposes a Bayesian framework for single-channel blind source separation (SCBSS). First, we formulate SCBSS as a Structured Sparse Recovery (SSR) problem with uncertain physical parameters and a highly coherent sensing matrix induced by spectral aliasing. Second, to solve this SSR problem, a periodic support prior is introduced to accurately capture the structural properties of oversampled baseband symbols and mitigate the effect of strong column correlation, while an EM-based Turbo-VBI algorithm is developed for joint symbol inference and parameter estimation in a unified framework. Finally, a lightweight post-processing scheme is designed to resolve residual ambiguities. Simulation results demonstrate that the proposed algorithm outperforms existing model-driven and data-driven approaches under low SNR and CFO mismatch conditions.