Bayesian Learning for Double-RIS Aided ISAC Systems with Superimposed Pilots and Data

Reconfigurable intelligent surface (RIS) has great potential to improve the performance of integrated sensing and communication (ISAC) systems, especially in scenarios where line-of-sight paths between the base station and users are blocked. However, the spectral efficiency (SE) of RIS-aided ISAC uplink transmissions may be drastically reduced by the heavy burden of pilot overhead for realizing sensing capabilities. In this paper, we tackle this bottleneck by proposing a superimposed symbol scheme, which superimposes sensing pilots onto data symbols over the same time-frequency resources. Specifically, we develop a structure-aware sparse Bayesian learning framework, where decoded data symbols serve as side information to enhance sensing performance and increase SE. To meet the low-latency requirements of emerging ISAC applications, we further propose a low-complexity simultaneous communication and localization algorithm for multiple users. This algorithm employs the unitary approximate message passing in the Bayesian learning framework for initial angle estimate, followed by iterative refinements through reduced-dimension matrix calculations. Moreover, the sparse code multiple access technology is incorporated into this iterative framework for accurate data detection which also facilitates localization. Numerical results show that the proposed superimposed symbol-based scheme empowered by the developed algorithm can achieve centimeter-level localization while attaining up to <inline-formula><tex-math notation="LaTeX">$96\%$</tex-math></inline-formula> of the SE of conventional communications without sensing capabilities. Moreover, compared to other typical ISAC schemes, the proposed superimposed symbol scheme can provide an effective throughput improvement over <inline-formula><tex-math notation="LaTeX">$133\%$</tex-math></inline-formula>.