Browsing by Author "Sauder, D."
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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 Optimal and Robust Memoryless Discrimination from Dependent Observations.(1989) Sauder, D.; Geraniotis, Evaggelos A.; ISRIn this paper we consider discrimination between two possible sources based on observations of their output. The discrimination problem is modeled by means of a general binary hypothesis test, the main emphasis being on situations that cannot be modeled as signals in additive noise. The structure of the discriminator is such that the observations are passed through a memoryless nonlinearity and summed up to form a test statistic, which is then compared to a threshold. In this paper we consider only fixed sample size tests. Four different performance measures, which resemble the signal-to-noise ratios encountered in the signal in additive noise problems, are derived under different problem formulations. The optimal non-linearities for each of the performance measures are derived as solutions to various integral equations. For three of the four performance measures, we have successfully obtained robust nonlinearities for uncertainty in the marginal and the pint probaWlity density functions of the observations. Computer simulation results which demonstrate the advantage of using our non-linearities over the i.i.d. nonlinearity under the probability of error criterion are presented.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.