Institute for Systems Research
Permanent URI for this communityhttp://hdl.handle.net/1903/4375
Browse
7 results
Search Results
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.
T
Item Multi-Sensor Correlation and Quantization in Distributed Detection Systems(1991) Chau, Yawgeng A.; Geraniotis, Evaggelos A.; ISRQuantization and fusion schemes are derived for multi-sensor correlation in distributed K- sensor systems that are used for the detection of weak signals or general signal discrimination from dependent observations. The dependence in the observations across time and sensors is modeled via stationary m - dependent, f - mixing, or r - mixing processes. The observation sequences of the various sensors have identical individual statistics and identical pairwise statistics (symmetric conditions). Each sensor observation is passed through a memoryless non-linearity or quantizer (the same one for all sensors) to form the sensor test statistic; the decision statistics of the various sensors are then passed to the fusion center in an unquantized or binary quantized manner to form the final decision statistic of the fusion center. Based on a common large sample size for each sensor that is necessary for achieving high-quality performance, an asymptotic analysis is applied for the error probabilities of the fusion center. This provides design criteria for the optimal memoryless nonlinearity and quantizer. Optimization of these design criteria yields the optimal nonlinearity or quantizer as solutions to linear integral equations involving the first - and second-order pdfs of the sensor observations describing the individual and pairwise dependence. the analytical results obtained are valid for any number of sensors K. Numerical results based on the simulation of the performance of our schemes with different number of sensors are presented. The performance of the optimal nonlinearities and quantizers is shown to outperform that of nonlinearities or quantizers obtained by ignoring the dependence in sensor observations and to improve as the number of sensors increases.Item Quantization and Fusion for Multi-Sensor Discrimination from Dependent Observations(1991) Chau, Yawgeng A.; Geraniotis, Evaggelos A.; ISRSchemes for quantization and fusion in multi-sensor systems used for discriminating between two sequences of dependent observations are introduced and analyzed. The observation sequences of each sensor under the two hypotheses are arbitrary stationary dependent sequences that can not be modeled as signal in additive noise; the objective of the fusion center is to discriminate between the two hypotheses. These observation models are well motivated by practical multi-sensor target discrimination problems. Two cases are considered: in the first, the observation sequences of the sensors are individually dependent but jointly mutually independent; in the second case, the observation sequences are dependent across both time and sensors. The dependence in the observations across time and/or sensors is modeled by m - dependent, j - mixing or r - mixing processes. The following four quantization/fusion schemes are considered: (a) forming test statistics at the sensors by passing the observations through memoryless nonlinearities, summing them up, and fusing these test statistics without previous quantization; (b) quantizing uniformally (with equidistant breakpoints) each sensor observation and then fusing; (c) quantizing optimally each sensor observation and then fusing; and (d) using the sensor test statistic of (a) to make binary decisions and then fusing the binary decisions. To guarantee high-quality performance, a common large sample size is employed by each sensor and an asymptotic analysis is pursued. Design criteria are developed from the bayesian cost of the fusion center for deriving the optimal memoryless nonlinearities of the sensor test statistics and the sensor quantizer parameters (quantization levels and breakpoints). These design criteria are shown to involve an extension of the generalized signal-to-noise ratio used in single-sensor detection and quantization. The optimal nonlinearities and quantizers are obtained as the solutions of linear coupled or uncoupled integral equations involving the univariate and bivariate probability densities of the sensor observations. Numerical results based on simulation are presented for specific cases of practical interest to compare the relative performance of the four quantization/fusion schemes described above and to establish their superiority to schemes that ignore the dependence across time and/or sensors in the observations.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.