Here is an application of compressive sensing to a specific type of radar. The description of the approach is given in Step-Frequency Radar with Compressive Sampling (SFR-CS) by Sagar Shah, Yao Yu, Athina Petropulu. The abstract reads:
Step-frequency radar (SFR) is a high resolution radar approach, where multiple pulses are transmitted at different frequencies, covering a wide spectrum. The obtained resolution directly depends on the total bandwidth used, or equivalently, the number of transmitted pulses. This paper proposes a novel SFR system, namely SFR with compressive sampling (SFRCS), that achieves the same resolution as a conventional SFR, while using significantly reduced bandwidth, or equivalently, transmitting significantly fewer pulses. This bandwidth reduction is accomplished by employing compressive sampling ideas and exploiting the sparseness of targets in the range velocity space.
I'll add it to the Compressive Sensing Hardware page shortly.