Off-Grid Multi-Snapshot Spectrum Sensing for Cognitive Radar

Spectrum sensing is a key aspect of next-generation cognitive radars that make use of the perception-action cycle to improve their performance while endowing cohabitation with other systems. Awareness of the electromagnetic (EM) environment surrounding the radar is demanded to adapt its behavior to the changing scene. 2-D spectrum sensing is usually carried-out on uniformly-spaced grids, over which the angle of arrival (AOA) of diverse (unknown) sources is estimated along with their frequency occupancy. To mitigate the performance degradations of on-grid methods, this paper proposes an off-grid 2-D profile recovery strategy where the atoms are no longer fixed according to a given pool of nominal AOAs, but some flexibility is allowed to infer off-grid angle displacements. Hence, the angle-frequency profile recovery process is formalized as a regularized maximum likelihood (RML) estimation capable of exploiting the inherent block-sparsity of the overall profile. The resulting challenging optimization problem is handled through a maximum block improvement (MBI) based method, which provides an estimate of the three variable blocks involved in the process, viz., noise power, 2-D profile, and angular displacements. Furthermore, in order to enhance the reliability of determining the space-frequency occupancy map and accurately estimating the angle displacements, three refinement strategies for the 2-D spectrum profile are suggested, suitably leveraging Bayesian information criterion (BIC) and false discovery rate (FDR) paradigms. The proposed framework is then validated through numerical simulations in some realistic EM environments, also comparing the three proposed refinement strategies.