MCMC-Based Sparse Bayesian Learning for Super-Resolution Receiver in ISAC Systems

This paper presents a Markov chain Monte Carlo (MCMC)-based sparse Bayesian learning (SBL) algorithm for super-resolution receiver design, aimed at joint target detection and parameter estimation in integrated sensing and communication (ISAC) systems. Unlike traditional compressed sensing (CS) approaches that rely on large sensing matrices and are limited by on-grid estimation accuracy, our proposed method treats both sparse variables and their associated parameters as random variables, enabling gridless estimation with super-resolution and high precision. By leveraging MCMC techniques, our approach avoids the computational burden of matrix inversion while enhancing estimation performance in high-dimensional parameter spaces. Additionally, we introduce a refined MCMC proposal distribution that leverages mini-batch gradients and the Adam optimizer, significantly enhancing convergence while ensuring robust target detection and parameter estimation across varying SNR conditions. Simulation results demonstrate that the proposed algorithm accomplishes an estimation accuracy on the order of 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> m for range, 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> m/s for velocity, and 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> degree for angle, under conditions where the SNR exceeds 10 dB. It achieves superior accuracy and efficiency compared to traditional CS methods, especially in low-SNR ISAC environments.