The increasingly crowded spectrum has spurred the design of joint radar-communications systems that share hardware resources and efficiently use the radio frequency spectrum. We study a general spectral coexistence scenario, wherein the channels and transmit signals of both radar and communications systems are unknown at the receiver. In this dual-blind deconvolution (DBD) problem, a common 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-time and Doppler velocities of multiple transmission paths and multiple targets. We exploit the sparsity of both channels to solve the highly ill-posed DBD problem by casting it into a sum of multivariate atomic norms (SoMAN) minimization. We devise a semidefinite program to estimate the unknown target and communications parameters using the theories of positive-hyperoctant trigonometric polynomials (PhTP). Our theoretical analyses show that the minimum number of samples required for near-perfect recovery is dependent on the logarithm of the maximum of number of radar targets and communications paths rather than their sum. We show that our SoMAN method and PhTP formulations are also applicable to more general scenarios such as unsynchronized transmission, the presence of noise, and multiple emitters. Numerical experiments demonstrate great performance enhancements during parameter recovery under different scenarios.

翻译：日益拥挤的频谱资源推动了共享硬件资源并高效利用射频频谱的联合雷达通信系统设计。本文研究通用频谱共存场景，其中雷达与通信系统的信道及发射信号在接收端均未知。针对此双盲解卷积（DBD）问题，公共接收机接收与多目标雷达反射信号叠加的多载波无线通信信号。通信与雷达信道分别由多传输路径和多目标的连续值距离-时间与多普勒速度表示。通过将高度病态的DBD问题转化为多元原子范数之和（SoMAN）最小化，我们利用两种信道的稀疏性进行求解。基于正超象限三角多项式（PhTP）理论，我们设计半正定规划以估计未知目标及通信参数。理论分析表明，实现近完美恢复所需最小样本数取决于雷达目标数与通信路径数最大值（而非两者之和）的对数。实验证明，所提SoMAN方法与PhTP公式同样适用于非同步传输、噪声环境及多发射机等更通用场景。数值实验展示了不同场景下参数恢复性能的显著提升。