Recent interest in integrated sensing and communications has led to the design of novel signal processing techniques to recover information from an overlaid radar-communications signal. Here, we focus on a spectral coexistence scenario, wherein the channels and transmit signals of both radar and communications systems are unknown to the common receiver. In this dual-blind deconvolution (DBD) problem, the receiver admits a multi-carrier wireless communications signal that is overlaid with the radar signal reflected off multiple targets. The communications and radar channels are represented by continuous-valued range-times or delays corresponding to multiple transmission paths and targets, respectively. Prior works addressed recovery of unknown channels and signals in this ill-posed DBD problem through atomic norm minimization but contingent on individual minimum separation conditions for radar and communications channels. In this paper, we provide an optimal joint separation condition using extremal functions from the Beurling-Selberg interpolation theory. Thereafter, we formulate DBD as a low-rank modified Hankel matrix retrieval and solve it via nuclear norm minimization. We estimate the unknown target and communications parameters from the recovered low-rank matrix using multiple signal classification (MUSIC) method. We show that the joint separation condition also guarantees that the underlying Vandermonde matrix for MUSIC is well-conditioned. Numerical experiments validate our theoretical findings.

翻译：近年来，集成感知与通信领域的研究兴趣推动了新型信号处理技术的发展，旨在从叠加的雷达-通信信号中恢复信息。本文聚焦于一种频谱共存场景，其中雷达与通信系统的信道及发射信号对公共接收机均为未知。在此双盲解卷积（DBD）问题中，接收机接收到的多载波无线通信信号与经多个目标反射的雷达信号相互叠加。通信信道与雷达信道分别由对应多径传输路径及目标的连续值距离-时间（或时延）表示。先前工作通过原子范数最小化解决了这一不适定DBD问题中未知信道与信号的恢复，但依赖于雷达与通信信道各自的最小分离条件。本文利用Beurling-Selberg插值理论中的极值函数，提出了最优联合分离条件。随后，将DBD问题建模为低秩修正Hankel矩阵的恢复问题，并通过核范数最小化求解。通过多重信号分类（MUSIC）方法从恢复的低秩矩阵中估计未知目标与通信参数。研究表明，该联合分离条件同时保证了MUSIC方法中底层Vandermonde矩阵的良好条件性。数值实验验证了我们的理论结果。