Institute for Systems Research
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Item Signal Detection Games with Power Constraints(1993) Sauder, D.; Geraniotis, Evaggelos A.; ISRIn this paper we formulate mathematically and solve maximin and minimax detection problems for signals with power constraints. These problems arise whenever it is necessary to distinguish between a genuine signal and a spurious on designed by an adversary with the principal goal of deceiving the detector. The spurious (or deceptive) signal is usually subject to certain constraints, such as limited power, which preclude it from replicating the genuine signal exactly.The detection problem is formulated as a zero-sum game involving two players: the detector designer and the deceptive signal designer. The payoff is the probability of error of the detector which the detector designer tries to minimize and the deceptive signal designer to maximize. For this detection game, saddle point solutions --- whenever possible --- or otherwise maximin and minimax solutions are derived under three distinct constraints on the deceptive signal power; these distinct constraints involves bounds on (i) the peak power, (ii) the probabilistic average power, and (iii) the time average power. The cases of i.i.d. and correlated signals are both considered.
Item One-Step Memory Nonlinearities for Signal Detection and Discrimination from Correlated Observations(1992) Sauder, D.; Geraniotis, Evaggelos A.; ISRNew detectors employing test statistics which are formed by passing pairs of consecutive observations through one-step memory nonlinearities g(x, y) and summing the resulting terms are introduced. Problems of discrimination between two arbitrary stationary m-dependent or mixing noise are considered in this context. For each problem, the nonlinearity g is optimized for performance criteria, such as the generalized signal-to-noise ratio and the efficacy and is obtained as the solution to an appropriate linear integral equation. Moreover, the schemes considered can be robustified to statistical uncertainties determined by 2-alternating capacity classes, for the second- order joint pdfs of the observations, and by bounds on the correlation coefficients of time-shifts of the observation sequence, for the third - and fourth-order joint pdfs. Evaluation of the performance of the new schemes via simulation reveals significant gains over that of detectors employing memoryless nonlinearities or the i.i.d. nonlinearity.Item The Interception of Spread Spectrum Waveforms with the Amplitude Distribution Function(1992) Snelling, W.E.; Geraniotis, Evaggelos A.; ISRWithin the research effort related to unfriendly detection and interception of secure communications, an innovative concept called the Amplitude Distribution Function (ADF) is used to construct a detector that is an enhancement to the radiometer. The ADF is introduced and shown to be roughly the average probability distribution of a random process. The significance of ADF in the is that, under most spreading modulations, e.g. phase and frequency, the ADF is invariant. This suggests that a detector built around the ADF idea would be robust and of general purpose.To develop the ADF methodology, a mathematical foundation is laid consisting of a sequence of definitions, lemmas, and theorems, an outline of which is included in the paper. The most significant result is that the ADF of signal plus noise is the convolution of the ADF of signal and the ADF of noise taken separately. These ideas are applicable through the definition of the Amplitude Moment Statistic (AMS), a statistical transform that converges to the moment generating function of the ADF. Hence, the AMS is the vehicle for indirectly estimating the ADF from observations. For the particular problem of detecting a modulated sinusoid in stationary Gaussian noise, a detector is developed around the AMS. The detector's performance is analyzed, compared with that of a radiometer, and shown superior for small (10) time-bandwidth products.
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Item Analysis of Compressive Receivers for the Optimal Interception of Frequency-Hopped Waveforms(1991) Snelling, W.E.; Geraniotis, Evaggelos A.; ISRThis 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.Item Neural Networks for Sequential Discrimination of Radar Targets(1991) Haimerl, Joseph A.; Geraniotis, Evaggelos A.; ISRIn this paper, perceptron neural networks are applied to the problem of discriminating between two classes of radar returns. The perceptron neural networks are used as nonlinearities in two threshold sequential discriminators which act upon samples of the radar return. The test statistic compared to the n - K + 1, thresholds is of the form T n (Z) = j = 1 g ( Z j , Z J + 1, ...., Z j + K - 1 ) where, Z i, i = 1, 2, 3, ..... are the radar samples and g () is the nonlinearity formed by the neural network. Numerical results are presented and compared to existing discrimination schemes.Item Robust Sequential Tests for Memoryless Discrimination from Dependent Observations(1991) Geraniotis, Evaggelos A.; ISRThe problem of robust sequential discrimination from two dependent observation sequences with uncertain statistics is addressed. As in Part I ([1]) of this study, which treated asymptotically optimal sequential discrimination for stationary observations characterized by m - dependent or mixing type of dependence, sequential tests based on memoryless nonlinearities are employed. In particular, the sequential tests robustified in this paper employ linear test _ n _ n, statistics of the form Sn = A g (Xi ) + Bn, , where {Xi } i = 1 is the observation _ i = 1 _, sequence, the coefficients A and B are selected so that the normalized drifts of S n are antipodal under the two hypotheses, and the nonlinearity g solves a linear integral equation. As shown in Part I, the performance of these tests is very close to that of the asymptotically optimal memoryless sequential tests when the statistics of the observations are known. The above tests are robustified in terms of the error probabilities and the expected sample numbers under the two hypotheses, for statistical uncertainty determined by 2-alternating capacity classes for the marginal (univariate) pdfs and upper bounds on the correlation coefficients of time-shifts of the observations sequence for the bivariate pdfs. Finally, the robustification of sequential tests based on a test statistic similar to Sn defined above is carried out for detecting a weak-signal in stationary m - dependent or mixing noise with uncertainty in the univariate and bivariate pdfs.