The cumulative distribution of the filtered output of a quadratic rectifier whose input is either narrow-band Gaussian noise or Gaussian noise with a low-pass spectral density is to be computed by numerical quadrature of a Laplace inversion integral along a contour in the complex plane chosen to economize the number of steps. The integrand contains the moment-generating function (mgf) of the output. It is expressed in terms of the Fredholm determinant and the resolvent kernel associated with an integral equation involving the autocovariance function of the input and the impulse response of the output filter. A special case is the power of a mean-zero Gaussian process averaged over a finite interval, and when this process has a rational spectral density, the mgf can be expressed as the ratio of certain finite determinants. By this method distributions are calculated for low-pass noise with RLC and second- and fourth-order Chebyshev spectral densities. For rational input spectral densities but arbitrary positive output filtering and an arbitrary additive input signal, the mgf can be calculated by integrating differential equations of the Kalman-Bucy type.

Distribution of the filtered output of a quadratic rectifier computed by numerical contour integration

: Three new methods for the detection and interception of frequency - hopped waveforms are presented. First presented are two types of sequential detectors: a purely sequential test that requires less data for a decision and a truncated sequential test that requires less data even while opeating under poor signal-to-noise ratios. Performances are evaluated via theoretical, numerical, and Monte Carlo analyses. Second, compressive-receiver-based-based interceptors are presented: (1) a locally optimal detector, which is compared against the optimal channelized detectors; (2) a simplified, suboptimal scheme, which trades off duty cycle against performance; (3) and a technique for estimating hop frequency. Quantified are the performances of the optimal and suboptimal detectors. Third, a detector based on the Amplitude Distribution Function (ADF) is presented. Given is a technique for deconvolving the ADF, enabling signal and noise separation. From this, a detection statistic is defined and statistically characterized, yielding a new class of detectors. The detectors are performance analyzed. Keywords: Spread spectrum, Frequency-hopped, Electronic counter measures, Interception, Probability, Detection, Statistics.

New Methods for the Detection and Interception of Frequency-Hopped Waveforms

In the domain of electronic warfare, jamming is an eavesdropping application. A lot of effort has recently been directed into developing practical algorithms for spectral estimation of target modems. Spread Spectrum systems spread the information bearing digital signal across a broad bandwidth. Spreading the energy of a bounded energy data signal across a very wide bandwidth causes the energy present at any particular frequency or small frequency band to be insignificant. Often, it is too small and can be modeled as thermal noise at that frequency. In this context, this paper presents an innovative architecture of a jammer for efficient jamming of DSSS signals. This work includes a complete design and simulation of Jammer and compares the effect of innovative jamming technique on the performance of a DSSS signal with those available in the literature. Effectiveness of jamming is also visible in our comparison.

Effect of jamming technique on the performance of Direct Sequence Spread Spectrum Modem

A numerical method is described for predicting the detection probability of a frequency compressive pulse receiver. The approach is general; i.e., input pulse envelope shapes, pulse offset frequencies, and filter magnitude responses are arbitrary. The performance of the frequency compressive receiver is analyzed and compared to that of a crystal video receiver for a specific case.

Calculation of Detection Probability for Frequency Compressive Receivers

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. >

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Analysis of compressive receivers for the optimal interception of frequency-hopped waveforms

A numerical method is described for predicting the detection probability performance of a pulse receiver which uses square-law detection. The method is useful for receivers where the ratio of RF bandwidth to video bandwidth is in the range from 2 to 40; a range where numerical results have previously been hard to obtain. A key feature of the approach is that it takes into account the actual filter transfer functions, pulse envelope shape, and pulse frequency.

Filter Selection for Receivers Using Square-Law Detection

A numerical method is described for analyzing the performance of an acoustooptic receiver. The method provides output waveforms, probability density functions for samples of the output, and detection probabilities for output samples. The approach is general in that input pulse envelope shapes, pulse offset frequencies, and output rilter magnitude responses are arbitrary. The basic analysis is also independent of the shape of the optical beam and of the photodiode windows.

B.K. Harms

Papers

Calculation of Detection Probability for Frequency Compressive Receivers

Filter Selection for Receivers Using Square-Law Detection

Analysis of Detection Probability for the Acoustooptic Receiver