On the Improvability and Nonimprovability of Detection via Additional Independent Noise

Cataloged from PDF version of article.Addition of independent noise to measurements can improve performance of some suboptimal detectors under certain conditions. In this letter, sufficient conditions under which the performance of a suboptimal detector cannot be enhanced by additional independent noise are derived according to the Neyman–Pearson criterion. Also, sufficient conditions are obtained to specify when the detector performance can be improved. In addition to a generic condition, various explicit sufficient conditions are proposed for easy evaluation of improvability. Finally, a numerical example is presented and the practicality of the proposed conditions is discussed

Noise enhanced hypothesis-testing according to restricted Neyman-Pearson criterion

Cataloged from PDF version of article.Noise enhanced hypothesis-testing is studied according to the restricted Neyman-Pearson (NP) criterion. First, a problem formulation is presented for obtaining the optimal probability distribution of additive noise in the restricted NP framework. Then, sufficient conditions for improvability and nonimprovability are derived in order to specify if additive noise can or cannot improve detection performance over scenarios in which no additive noise is employed. Also, for the special case of a finite number of possible parameter values under each hypothesis, it is shown that the optimal additive noise can be represented by a discrete random variable with a certain number of point masses. In addition, particular improvability conditions are derived for that special case. Finally, theoretical results are provided for a numerical example and improvements via additive noise are illustrated. © 2013 Elsevier Inc

Noise Enhanced Hypothesis-Testing in the Restricted Bayesian Framework

Cataloged from PDF version of article.Performance of some suboptimal detectors can be enhanced by adding independent noise to their observations. In this paper, the effects of additive noise are investigated according to the restricted Bayes criterion, which provides a generalization of the Bayes and minimax criteria. Based on a generic M-ary composite hypothesis-testing formulation, the optimal probability distribution of additive noise is investigated. Also, sufficient conditions under which the performance of a detector can or cannot be improved via additive noise are derived. In addition, simple hypothesis-testing problems are studied in more detail, and additional improvability conditions that are specific to simple hypotheses are obtained. Furthermore, the optimal probability distribution of the additive noise is shown to include at most mass points in a simple M-ary hypothesis-testing problem under certain conditions. Then, global optimization, analytical and convex relaxation approaches are considered to obtain the optimal noise distribution. Finally, detection examples are presented to investigate the theoretical results

Noise enhanced detection in restricted Neyman-Pearson framework

Ankara : The Department of Electrical and Electronics Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Master's) -- Bilkent University, 2013.Includes bibliographical references leaves 37-40.Hypothesis tests frequently arise in many different engineering problems. Among the most frequently used tests are Bayesian, minimax, and Neyman-Pearson. Even though these tests are capable of addressing many real-life problems, they can be insufficient in certain scenarios. For this reason, developing new hypothesis tests is an important objective. One such developed test is the restricted NeymanPearson test, where one tries to maximize the average detection probability while keeping the worst-case detection and false-alarm probabilities bounded. Finding the best hypothesis testing approach for a problem-at-hand is an important point. Another important one is to employ a detector with an acceptable performance. In particular, if the employed detector is suboptimal, it is crucial that it meets the performance requirements. Previous research has proven that performance of some suboptimal detectors can be improved by adding noise to their inputs, which is known as noise enhancement. In this thesis we investigate noise enhancement according to the restricted Neyman-Pearson framework. To that aim, we formulate an optimization problem for optimal additive noise. Then, generic improvability and nonimprovability conditions are derived, which specify if additive noise can result in performance improvements. We then analyze the special case in which the parameter space is discrete and finite, and show that the optimal noise probability density function is discrete with a certain number of point masses. The improvability results are also extended and more precise conditions are derived. Finally, a numerical example is provided which illustrates the theoretical results and shows the benefits of applying noise enhancement to a suboptimal detector.Gültekin, ŞanM.S

Noise enhanced detection in restricted Neyman-Pearson framework

Noise enhanced detection is studied for binary composite hypothesis-testing problems in the presence of prior information uncertainty. The restricted Neyman-Pearson (NP) framework is considered, and a formulation is obtained for the optimal additive noise that maximizes the average detection probability under constraints on worst-case detection and false-alarm probabilities. In addition, sufficient conditions are provided to specify when the use of additive noise can or cannot improve performance of a given detector according to the restricted NP criterion. A numerical example is presented to illustrate the improvements obtained via additive noise. © 2012 IEEE

Alternative approaches and noise benefits in hypothesis-testing problems in the presence of partial information

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2011.Thesis (Ph. D.) -- Bilkent University, 2011.Includes bibliographical references leaves 153-164.Performance of some suboptimal detectors can be enhanced by adding independent noise to their observations. In the first part of the dissertation, the effects of additive noise are studied according to the restricted Bayes criterion, which provides a generalization of the Bayes and minimax criteria. Based on a generic M-ary composite hypothesis-testing formulation, the optimal probability distribution of additive noise is investigated. Also, sufficient conditions under which the performance of a detector can or cannot be improved via additive noise are derived. In addition, simple hypothesis-testing problems are studied in more detail, and additional improvability conditions that are specific to simple hypotheses are obtained. Furthermore, the optimal probability distribution of the additive noise is shown to include at most M mass points in a simple M-ary hypothesis-testing problem under certain conditions. Then, global optimization, analytical and convex relaxation approaches are considered to obtain the optimal noise distribution. Finally, detection examples are presented to investigate the theoretical results. In the second part of the dissertation, the effects of additive noise are studied for M-ary composite hypothesis-testing problems in the presence of partial prior information. Optimal additive noise is obtained according to two criteria, which assume a uniform distribution (Criterion 1) or the least-favorable distribution (Criterion 2) for the unknown priors. The statistical characterization of the optimal noise is obtained for each criterion. Specifically, it is shown that the optimal noise can be represented by a constant signal level or by a randomization of a finite number of signal levels according to Criterion 1 and Criterion 2, respectively. In addition, the cases of unknown parameter distributions under some composite hypotheses are considered, and upper bounds on the risks are obtained. Finally, a detection example is provided to illustrate the theoretical results. In the third part of the dissertation, the effects of additive noise are studied for binary composite hypothesis-testing problems. A Neyman-Pearson (NP) framework is considered, and the maximization of detection performance under a constraint on the maximum probability of false-alarm is studied. The detection performance is quantified in terms of the sum, the minimum and the maximum of the detection probabilities corresponding to possible parameter values under the alternative hypothesis. Sufficient conditions under which detection performance can or cannot be improved are derived for each case. Also, statistical characterization of optimal additive noise is provided, and the resulting false-alarm probabilities and bounds on detection performance are investigated. In addition, optimization theoretic approaches for obtaining the probability distribution of optimal additive noise are discussed. Finally, a detection example is presented to investigate the theoretical results. Finally, the restricted NP approach is studied for composite hypothesistesting problems in the presence of uncertainty in the prior probability distribution under the alternative hypothesis. A restricted NP decision rule aims to maximize the average detection probability under the constraints on the worstcase detection and false-alarm probabilities, and adjusts the constraint on the worst-case detection probability according to the amount of uncertainty in the prior probability distribution. Optimal decision rules according to the restricted NP criterion are investigated, and an algorithm is provided to calculate the optimal restricted NP decision rule. In addition, it is observed that the average detection probability is a strictly decreasing and concave function of the constraint on the minimum detection probability. Finally, a detection example is presented, and extensions to more generic scenarios are discussed.Bayram, SuatPh.D

Noise Enhanced M-ary Composite Hypothesis-Testing in the Presence of Partial Prior Information

Cataloged from PDF version of article.In this correspondence, noise enhanced detection is studied for M-ary composite hypothesis-testing problems in the presence of partial prior information. Optimal additive noise is obtained according to two criteria, which assume a uniform distribution (Criterion 1) or the least-favorable distribution (Criterion 2) for the unknown priors. The statistical characterization of the optimal noise is obtained for each criterion. Specifically, it is shown that the optimal noise can be represented by a constant signal level or by a randomization of a finite number of signal levels according to Criterion 1 and Criterion 2, respectively. In addition, the cases of unknown parameter distributions under some composite hypotheses are considered, and upper bounds on the risks are obtained. Finally, a detection example is provided in order to investigate the theoretical results. © 2010 IEEE

Stochastic signaling in the presence of channel state information uncertainty

Cataloged from PDF version of article.In this paper, stochastic signaling is studied for power-constrained scalar valued binary communications systems in the presence of uncertainties in channel state information (CSI). First, stochastic signaling based on the available imperfect channel coefficient at the transmitter is analyzed, and it is shown that optimal signals can be represented by a randomization between at most two distinct signal levels for each symbol. Then, performance of stochastic signaling and conventional deterministic signaling is compared for this scenario, and sufficient conditions are derived for improvability and nonimprovability of deterministic signaling via stochastic signaling in the presence of CSI uncertainty. Furthermore, under CSI uncertainty, two different stochastic signaling strategies, namely, robust stochastic signaling and stochastic signaling with averaging, are proposed. For the robust stochastic signaling problem, sufficient conditions are derived for reducing the problem to a simpler form. It is shown that the optimal signal for each symbol can be expressed as a randomization between at most two distinct signal values for stochastic signaling with averaging, as well as for robust stochastic signaling under certain conditions. Finally, two numerical examples are presented to explore the theoretical results. (C) 2012 Elsevier Inc. All rights reserve

Stochastic signaling for power constrained communication systems

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Science of Bilkent University, 2011.Thesis (Master's) -- Bilkent University, 2011.Includes bibliographical references leaves 93-97.In this thesis, optimal stochastic signaling problem is studied for power constrained communications systems. In the first part, optimal stochastic signaling problem is investigated for binary communications systems under second and fourth moment constraints for any given detector structure and noise probability distribution. It is shown that an optimal signal can be represented by randomization among at most three signal levels for each symbol. Next, stochastic signaling problem is studied in the presence of an average power constraint instead of second and fourth moment constraints. It is shown that an optimal signal can be represented by randomization between at most two signal levels for each symbol in this case. For both scenarios, sufficient conditions are obtained to determine the improvability and nonimprovability of conventional deterministic signaling via stochastic signaling. In the second part of the thesis, the joint design of optimal signals and optimal detector is studied for binary communications systems under average power constraints in the presence of additive non-Gaussian noise. It is shown that the optimal solution involves randomization between at most two signal levels and the use of the corresponding maximum a posteriori probability (MAP) detector. In the last part of the thesis, stochastic signaling is investigated for power-constrained scalar valued binary communications systems in the presence of uncertainties in channel state information (CSI). First, stochastic signaling is performed based on the available imperfect channel coef- ficient at the transmitter to examine the effects of imperfect CSI. The sufficient conditions are derived for improvability and nonimprovability of deterministic signaling via stochastic signaling in the presence of CSI uncertainty. Then, two different stochastic signaling strategies, namely, robust stochastic signaling and stochastic signaling with averaging, are proposed for designing stochastic signals under CSI uncertainty. For the robust stochastic signaling problem, sufficient conditions are derived to obtain an equivalent form which is simpler to solve. In addition, it is shown that optimal signals for each symbol can be written as randomization between at most two signal levels for stochastic signaling using imperfect channel coefficient and stochastic signaling with averaging as well as for robust stochastic signaling under certain conditions. The solutions of the optimal stochastic signaling problems are obtained by using global optimization techniques, specifically, Particle Swarm Optimization (PSO), and by employing convex relaxation approaches. Numerical examples are presented to illustrate the theoretical results at the end of each part.Göken, ÇağrıM.S

Noise benefits in joint detection and estimation problems

Adding noise to inputs of some suboptimal detectors or estimators can improve their performance under certain conditions. In the literature, noise benefits have been studied for detection and estimation systems separately. In this study, noise benefits are investigated for joint detection and estimation systems. The analysis is performed under the Neyman-Pearson (NP) and Bayesian detection frameworks and according to the Bayesian estimation criterion. The maximization of the system performance is formulated as an optimization problem. The optimal additive noise is shown to have a specific form, which is derived under both NP and Bayesian detection frameworks. In addition, the proposed optimization problem is approximated as a linear programming (LP) problem, and conditions under which the performance of the system can or cannot be improved via additive noise are obtained. With an illustrative numerical example, performance comparison between the noise enhanced system and the original system is presented to support the theoretical analysis. © 2015 Elsevier B.V. All rights reserved