An optimal decision framework is proposed for joint detection and decoding when the prior information is available with some uncertainty. The proposed framework provides tradeoffs between the average inclusive error probability (computed using estimated prior probabilities) and the worst case inclusive error probability according to the amount of uncertainty while satisfying constraints on the probability of false alarm and the maximum probability of miss-detection. Theoretical results that characterize the structure of the optimal decision rule according to the proposed criterion are obtained. The proposed decision rule reduces to some well-known detectors in the case of perfect prior information or when the constraints on the probabilities of miss-detection and false alarm are relaxed. Numerical examples are provided to illustrate the theoretical results.

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 NTjammer nodes according to the second scheme in the absence of peak power constraints, where NTis 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.

Effects of additive independent noise are investigated for suboptimal detectors according to the restricted Bayes criterion. The statistics of optimal additive noise are characterized. Also, sufficient conditions for improvability or nonimprovability of detection via additive noise are obtained. A detection example is presented to study the theoretical results.

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.

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.