联合雷达通信中双盲反卷积恢复的Beurling-Selberg极值化方法
Beurling-Selberg Extremization for Dual-Blind Deconvolution Recovery in Joint Radar-Communications
AI总结：
本文针对联合雷达通信中信道与信号均未知的双盲反卷积问题，利用Beurling-Selberg极值函数建立最优联合分离条件，并通过核范数最小化恢复低秩修正Hankel矩阵，结合MUSIC方法实现参数估计。
摘要：
近年来，对集成感知与通信的兴趣推动了新型信号处理技术的设计，以从叠加的雷达通信信号中恢复信息。本文关注频谱共存场景，其中雷达和通信系统的信道与发射信号对公共接收机而言均未知。在该双盲反卷积（DBD）问题中，接收机接收一个多载波无线通信信号，该信号与经多个目标反射的雷达信号叠加。通信信道和雷达信道分别由对应多条传输路径和目标的连续值距离时间或时延表示。此前的工作通过原子范数最小化解决这一不适定DBD问题中的未知信道与信号恢复，但依赖于雷达信道和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，给出了最优的联合分离条件。随后，我们将DBD建模为低秩修正Hankel矩阵恢复问题，并通过核范数最小化求解。我们使用多重信号分类（MUSIC）方法从恢复的低秩矩阵中估计未知目标参数和通信参数。我们证明该联合分离条件同时保证了MUSIC所依赖的Vandermonde矩阵具有良好的条件数。数值实验验证了我们的理论结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
