Joint radar-communications (JRC) has emerged as a promising technology for efficiently using the limited electromagnetic spectrum. In JRC applications such as secure military receivers, often the radar and communications signals are overlaid in the received signal. In these passive listening outposts, the signals and channels of both radar and communications are unknown to the receiver. The ill-posed problem of recovering all signal and channel parameters from the overlaid signal is terms as dual-blind deconvolution (DBD). In this work, we investigate a more challenging version of DBD with a multi-antenna receiver. We model the radar and communications channels with a few (sparse) continuous-valued parameters such as time delays, Doppler velocities, and directions-of-arrival (DoAs). To solve this highly ill-posed DBD, we propose to minimize the sum of multivariate atomic norms (SoMAN) that depends on the unknown parameters. To this end, we devise an exact semidefinite program using theories of positive hyperoctant trigonometric polynomials (PhTP). Our theoretical analyses show that the minimum number of samples and antennas required for perfect recovery is logarithmically dependent on the maximum of the number of radar targets and communications paths rather than their sum. We show that our approach is easily generalized to include several practical issues such as gain/phase errors and additive noise. Numerical experiments show the exact parameter recovery for different JRC

翻译：联合雷达通信（JRC）已成为高效利用有限电磁频谱的一项有前景技术。在安全军事接收机等JRC应用中，雷达与通信信号通常在接收信号中叠加。在这些被动监听站点中，接收方对雷达和通信的信号及信道均未知。从叠加信号中恢复所有信号与信道参数的病态问题被称为双盲解卷积（DBD）。本文研究更具挑战性的多天线接收机DBD版本。我们采用少量（稀疏）连续值参数（如时延、多普勒速度及到达角）对雷达与通信信道进行建模。为解决这一高度病态的DBD问题，我们提出最小化依赖于未知参数的多元原子范数之和（SoMAN）。为此，我们利用正超象限三角多项式（PhTP）理论设计了一种精确的半定规划方案。理论分析表明，实现完美恢复所需的最小样本数与天线数，与雷达目标数与通信路径数中的最大值呈对数关系，而非两者之和。本文方法可轻松推广至包含增益/相位误差及加性噪声等实际场景。数值实验验证了不同JRC场景下的精确参数恢复能力。