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. The authors assume interference to be stationary, colored Gaussian noise, and present a model of the compressive receiver that contains all its salient features. Low energy coherence 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 low energy coherence detector has an unwieldy structure, a simplified suboptimal detector structure is developed that consists of a simple filter, followed by a sampler and a square-envelope detector. Several candidates for the filter's response are presented. The performance of the low energy coherence 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.>

The channelized receiver, which is optimal for the detection of unknown noncoherent frequency-hopped waveforms, bases its decisions on a fixed-length block of input data. A sequential method of interception is presented according to which whenever a new data element is collected, a decision is made as to the presence or nonpresence of a frequency-hopped waveform. If that decision is indeterminate, another data element is collected. An optimal sequential test is derived, under the assumption that the waveform signal-to-noise ratio (SNR) is known. It is shown that this sequential test requires less data, on average, than the fixed-length method to make a decision with the same reliability. A truncated sequential test is also derived where a decision is forced, if still indeterminate, after some fixed amount of data is collected. The truncated test is shown to improve the number of samples needed for a decision when the input SNR differs greatly from that assumed in the derivation of the test. Furthermore, it is shown that the truncated test yields a limited degree of robustness when the input SNR differs from that assumed.>