Analysis of Compressive Receivers for the Optimal Interception of Frequency-Hopped Waveforms

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This paper establishes that the compressive receiver is a practical interceptor of high performance. Given a signal of a particular duration, a compressive receiver can estimate simultaneously all frequency components within a set wide band. This processing is similar to a parallel bank of narrowband filters, which is the optimal detector of frequency-hopped signals. Furthermore, hop frequency is estimated to yield performance equal to the parallel filter configuration. We assume interference to be stationary, colored Gaussian noise and present a model of the compressive receiver that contains all its salient features. Locally optimal detection is achieved by taking the compressive receiver output as an observation and applying likelihood ratio theory at small signal-to-noise ratios. For small signals, this approach guarantees the largest probability of correct detection for a given probability of false alarm and thus provides a reference, to which simplified or ad hoc schemes can be compared. Since the locally optimal detector has an unwieldy structure, a simplified suboptimal detector structure is developed that consists of simple filter followed by a sampler and a square-envelope detector. Several candidates for the filter's response are presented. The performance of the locally optimal detector based on compressive receiver observations is compared to the optimal filter-bank detector based on direct observations, thus showing the exact loss incurred when a compressive receiver is used. The performance of various simplified schemes based on compressive receiver observations is analyzed and compared with that of the locally optimal detector.