Suat Bayram

Noise Enhanced Hypothesis-Testing in the Restricted Bayesian Framework

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 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.

Stochastic resonance in binary composite hypothesis-testing problems in the Neyman-Pearson framework

Performance of some suboptimal detectors can be enhanced by adding independent noise to their inputs via the stochastic resonance (SR) effect. In this paper, the effects of SR are studied for binary composite hypothesis-testing problems. A Neyman-Pearson 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 to obtaining the probability distribution of optimal additive noise are discussed. Finally, a detection example is presented to investigate the theoretical results.

Optimum Power Allocation for Average Power Constrained Jammers in the Presence of Non-Gaussian Noise

We study the problem of determining the optimum power allocation policy for an average power constrained jammer operating over an arbitrary additive noise channel, where the aim is to minimize the detection probability of an instantaneously and fully adaptive receiver employing the Neyman-Pearson (NP) criterion. We show that the optimum jamming performance can be achieved via power randomization between at most two different power levels. We also provide sufficient conditions for the improvability and nonimprovability of the jamming performance via power randomization in comparison to a fixed power jamming scheme. Numerical examples are presented to illustrate theoretical results.

Noise Enhanced

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.

M

In this study, the effects of adding independent noise to observations of a suboptimal detector are studied for M-ary hypothesis-testing problems according to the minimax criterion. It is shown that the optimal additional noise can be represented by a randomization of at most M signal values under certain conditions. In addition, a convex relaxation approach is proposed to obtain an accurate approximation to the noise probability distribution in polynomial time. Furthermore, sufficient conditions are presented to determine when additional noise can or cannot improve the performance of a given detector. Finally, a numerical example is presented.

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

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 M-ary hypothesis-testing in the minimax framework

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.

On the Improvability and Nonimprovability of Detection via Additional Independent Noise

The restricted Neyman-Pearson (NP) approach is studied for composite hypothesis-testing 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 worst-case 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. In this study, optimal decision rules according to the restricted NP criterion are investigated. Also, an algorithm is provided to calculate the optimal restricted NP decision rule. In addition, it is shown 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 to investigate the theoretical results, and extensions to more generic scenarios are provided.

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

In this paper, the optimal jamming of wireless localization systems is investigated. Two optimal power allocation schemes are proposed for jammer nodes in the presence of total and peak power constraints. In the first scheme, power is allocated to jammer nodes in order to maximize the average Cramér-Rao lower bound (CRLB) of target nodes, whereas in the second scheme, the power allocation is performed for the aim of maximizing the minimum CRLB of target nodes. Both the schemes are formulated as linear programs, and a closed-form solution is obtained for the first scheme. For the second scheme, under certain conditions, the property of full total power utilization is specified, and a closed-form solution is obtained when the total power is lower than a specific threshold. In addition, it is shown that non-zero power is allocated to at most NT jammer nodes according to the second scheme in the absence of peak power constraints, where NT is the number of target nodes. In the presence of parameter uncertainty, robust versions of the power allocation schemes are proposed. Simulation results are presented to investigate the performance of the proposed schemes and to illustrate the theoretical results.

On the Restricted Neyman–Pearson Approach for Composite Hypothesis-Testing in Presence of Prior Distribution Uncertainty

In this study, optimal jamming of wireless localization systems is investigated. Two optimal power allocation schemes are proposed for jammer nodes in the presence of total and peak power constraints. In the first scheme, power is allocated to jammer nodes in order to maximize the average Cramér-Rao lower bound (CRLB) of target nodes whereas in the second scheme the power allocation is performed for the aim of maximizing the minimum CRLB of target nodes. Both schemes are formulated as linear programs, and a closed-form expression is obtained for the first scheme. Also, the full total power utilization property is specified for the second scheme. Simulation results are presented to investigate performance of the proposed schemes.