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ABSTRACT: 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.
IEEE Transactions on Signal Processing 11/2011; · 2.63 Impact Factor
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ABSTRACT: 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.
IEEE Transactions on Signal Processing 04/2011; · 2.63 Impact Factor
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ABSTRACT: Optimal stochastic signaling is studied under second and fourth moment constraints for the detection of scalar-valued binary signals in additive noise channels. Sufficient conditions are obtained to specify when the use of stochastic signals instead of deterministic ones can or cannot improve the error performance of a given binary communications system. Also, statistical characterization of optimal signals is presented, and it is shown that an optimal stochastic signal can be represented by a randomization of at most three different signal levels. In addition, the power constraints achieved by optimal stochastic signals are specified under various conditions. Furthermore, two approaches for solving the optimal stochastic signaling problem are proposed; one based on particle swarm optimization (PSO) and the other based on convex relaxation of the original optimization problem. Finally, simulations are performed to investigate the theoretical results, and extensions of the results to M-ary communications systems and to other criteria than the average probability of error are discussed.
IEEE Transactions on Wireless Communications 01/2011; · 2.59 Impact Factor
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ABSTRACT: In this paper, probability of error performance of single-threshold detectors is studied for binary communications systems in the presence of Gaussian mixture noise. First, sufficient conditions are proposed to specify when the sign detector is (not) an optimal detector among all the single-threshold detectors. Then, a monotonicity property of the error probability is derived for the optimal single-threshold detector. In addition, a theoretical limit is obtained on the maximum ratio between the average probabilities of error for the sign detector and the optimal single-threshold detector. Finally, numerical examples are presented to investigate the theoretical results.
IEEE Transactions on Communications 12/2010; · 1.68 Impact Factor
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ABSTRACT: In this paper, stochastic signaling is studied for scalar valued binary communications systems over additive noise channels in the presence of an average power constraint. For a given decision rule at the receiver, the effects of using stochastic signals for each symbol instead of conventional deterministic signals are investigated. First, sufficient conditions are derived to determine the cases in which stochastic signaling can or cannot outperform the conventional signaling. Then, statistical characterization of the optimal signals is provided and it is obtained that an optimal stochastic signal can be represented by a randomization of at most two different signal levels for each symbol. In addition, via global optimization techniques, the solution of the generic optimal stochastic signaling problem is obtained, and theoretical results are investigated via numerical examples.
Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on; 11/2010
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ABSTRACT: Stochastic signaling is investigated under second and fourth moment constraints for the detection of scalar-valued binary signals in additive noise channels. Sufficient conditions are derived to determine when the use of stochastic signals instead of deterministic ones can or cannot enhance the error performance of a given binary communications system. Also, a convex relaxation approach is employed to obtain approximate solutions of the optimal stochastic signaling problem. Finally, numerical examples are presented, and extensions of the results to M-ary communications systems and to other criteria than the average probability of error are discussed.
Signal Processing Advances in Wireless Communications (SPAWC), 2010 IEEE Eleventh International Workshop on; 07/2010
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ABSTRACT: In this letter, optimal additive noise is characterized for parameter estimation based on quantized observations. First, optimal probability distribution of noise that should be added to observations is formulated in terms of a Cramer-Rao lower bound (CRLB) minimization problem. Then, it is proven that optimal additive ??noise?? can be represented by a constant signal level, which means that randomization of additive signal levels is not needed for CRLB minimization. In addition, the results are extended to the cases in which there exists prior information about the unknown parameter and the aim is to minimize the Bayesian CRLB (BCRLB). Finally, a numerical example is presented to explain the theoretical results.
IEEE Signal Processing Letters 06/2010; · 1.39 Impact Factor
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ABSTRACT: In this letter, joint optimization of signal structures and detectors is studied for binary communications systems under average power constraints in the presence of additive non-Gaussian noise. First, it is observed that the optimal signal for each symbol can be characterized by a discrete random variable with at most two mass points. Then, optimization over all possible two mass point signals and corresponding maximum a posteriori probability (MAP) decision rules are considered. It is shown that the optimization problem can be simplified into an optimization over a number of signal parameters instead of functions, which can be solved via global optimization techniques, such as particle swarm optimization. Finally, the improvements that can be obtained via the joint design of the signaling and the detector are illustrated via an example.
IEEE Communications Letters 03/2010; · 0.98 Impact Factor
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ABSTRACT: 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.
IEEE Signal Processing Letters 12/2009; · 1.39 Impact Factor
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ABSTRACT: 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.
Signal Processing and Communication Systems, 2009. ICSPCS 2009. 3rd International Conference on; 10/2009
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ABSTRACT: Performance of some suboptimal detectors can be improved by adding independent noise to their observations. In this paper, the effects of adding independent noise to observations of a detector are investigated for binary composite hypothesis-testing problems in a generalized Neyman-Pearson framework. Sufficient conditions are derived to determine when performance of a detector can or cannot be improved via additional independent noise. Also, upper and lower limits are derived on the performance of a detector in the presence of additional noise, and statistical characterization of optimal additional noise is provided. In addition, two optimization techniques are proposed to calculate the optimal additional noise. Finally, simulation results are presented to investigate the theoretical results.
Signal Processing and Communication Systems, 2009. ICSPCS 2009. 3rd International Conference on; 10/2009
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ABSTRACT: In this paper, theoretical limits on estimation of respiration rates via pulse-based ultra-wideband (UWB) signals are studied in the presence of prior information about respiration related signal parameters. First, a generalized Cramer-Rao lower bound (G-CRLB) expression is derived, and then simplified versions of the bound are obtained for sinusoidal displacement functions. In addition to the derivation of the theoretical limits, a two-step suboptimal estimator based on matched filter (correlation) processing and maximum a posteriori probability (MAP) estimation is proposed. It is shown that the proposed estimator performs very closely to the theoretical limits under certain conditions. Simulation results are presented to investigate the theoretical results.
Ultra-Wideband, 2009. ICUWB 2009. IEEE International Conference on; 10/2009
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S. Gezici
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ABSTRACT: In this paper, mean acquisition time (MAT) analysis of fixed-step serial search (FSSS) algorithms is presented. First, it is shown that the MAT of an FSSS algorithm can be obtained from that of a conventional serial search (CSS) algorithm after a certain mapping of the uncertainty region. Then, a generic formula for the MAT of FSSS algorithms is derived, which is valid for both dense and sparse channel environments. In addition, MAT formulas for high signal-to-noise ratio scenarios, for large uncertainty regions, and for dense channels are obtained as special cases of the generic solution. Finally, simulation results are presented to verify the analysis and to investigate the factors that affect the optimal step size for FSSS algorithms.
IEEE Transactions on Wireless Communications 04/2009; · 2.59 Impact Factor
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S. Gezici
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ABSTRACT: Transmitted-reference (TR) and frequency-shifted reference (FSR) ultra-wideband (UWB) systems employ pairs of reference and data signals, which are shifted in the time and frequency domains, respectively, to facilitate low-to-medium data rate communications without the need for complex channel estimation and template signal generation. On the other hand, the recently proposed coded-reference (CR) UWB systems provide orthogonalization of the reference and data signals in the code domain, which has advantages in terms of performance and/or implementation complexity. In this paper, CR UWB systems are investigated. First, it is shown that a CR UWB system can be considered as a generalized non-coherent pulse-position modulated system. Then, an optimal receiver according to the Bayes decision rule is derived for CR UWB systems. In addition, the asymptotic optimality properties of the conventional CR UWB receivers are investigated. Finally, simulation results are presented to compare the performance of the optimal and conventional CR UWB receivers.
Ultra-Wideband, 2008. ICUWB 2008. IEEE International Conference on; 10/2008
