The optimal interception of frequency-hopped waveforms via a compressive receiver

The synthesis and performance evaluation of detectors of frequency-hopped waveforms based to the compressive receiver are carried out. The interference is assumed to be stationary, colored Gaussian noise, and a complete model of the compressive receiver is presented. Optimal detection is achieved by taking the compressive receiver output as an observation and applying likelihood ratio theory. This approach guarantees the greatest probability of detection for a given probability of error, and therefore yields a reference against which simplified or ad hoc schemes can be compared. Since the optimal detector has an unwieldy structure, a simplified, suboptimal scheme is developed that trades off duty-cycle for performance. The performance of the optimal compressive receiver scheme is evaluated and compared to that of the optimal filter bank scheme showing the exact loss incurred by using a compressive receiver. The performance of the suboptimal scheme is analyzed, and the trade-off with duty-cycle is studied