Phase Transition in Frequency Agile Radar Using Compressed Sensing

Frequency Agile Radar (FAR) has improved anti-jamming performance over traditional pulse-Doppler radars under complex electromagnetic circumstances. To reconstruct the range-Doppler information in FAR, many compressed sensing (CS) methods including standard and block sparse recovery have been applied. In this paper, we study phase transitions of range-Doppler recovery in FAR using CS. In particular, we derive the closed-form phase transition curves associated with block sparse recovery and complex Gaussian matrices, based on prior results of standard sparse recovery under real Gaussian matrices. Empirical simulations validate the obtained curves, which lead to tight bounds on the radar and target parameters that guarantee exact recovery of targets' range-Doppler information.