Dual-Blind Deconvolution in ISAC Receiver Using Multi-Dimensional Beurling-Selberg Functions

Recent interest in integrated sensing and communications (ISAC) systems has led to the development of innovative signal processing techniques to extract information from a shared radar-communications spectrum setup. We focus on a dual-blind deconvolution (DBD) problem, where the ISAC receiver admits a multi-carrier wireless communications signal overlaid with the radar signal reflected off multiple targets. Here, apart from the unknown radar and communications transmit signals, their channels are characterized by continuous-valued range-time delays, and Doppler velocities are also unknown. Previous efforts tackled the recovery of unknown channels and signals in this highly ill-posed DBD problem through atomic norm minimization. However, they lacked theoretical guarantees for joint minimum separation conditions for radar and communications channels and performed poorly in the presence of noise. In this paper, we introduce an optimal joint separation condition through a novel approach of extremal functions derived from the Beurling-Selberg interpolation theory. Subsequently, we formulate DBD as a low-rank modified Hankel matrix retrieval problem and solve it through nuclear norm minimization. The joint separation condition provides a better bound on the conditional number of the resulting Vandermonde matrix, thereby providing a noise stability guarantee. Our numerical experiments demonstrate the effectiveness of the proposed approach in a shared radar-communications spectrum environment.