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)已成为有效利用有限电磁谱的一种有前途的技术。在诸如安全军用接收器之类的JRC应用中,雷达和通信信号通常在接收信号中重叠。在这些被动监听岗位中,雷达和通信的信号和信道都对接收器不知情。从叠加信号中恢复所有信号和信道参数的不适定问题被称为双盲反卷积(DBD)。在本研究中,我们研究了一个更具挑战性的版本,在多天线接收器中进行DBD。我们用少数(稀疏)连续值参数(例如时间延迟、多普勒速度和到达方向(DoAs))对雷达和通信信道进行建模。为了解决这个高度不适定的DBD问题,我们提出了最小化取决于未知参数的多元原子范数(SoMAN)的方法。为此,我们使用正超八面体三角多项式(PhTP)的理论设计了一个精确的半定规划。我们的理论分析表明,所需的完美恢复样本数和天线数对最大雷达目标数和通信路径数取对数依赖性,而不是它们的总和。我们表明,我们的方法很容易推广到包括多个实际问题,如增益/相位误差和加性噪声。数值实验显示了不同JRC中的精确参数恢复