Convexity properties of detection probability under additive Gaussian noise: optimal signaling and jamming strategies

Date
2013
Advisor
Instructor
Source Title
IEEE Transactions on Signal Processing
Print ISSN
1053-587X
Electronic ISSN
Publisher
IEEE
Volume
61
Issue
13
Pages
3303 - 3310
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

In this correspondence, we study the convexity properties for the problem of detecting the presence of a signal emitted from a power constrained transmitter in the presence of additive Gaussian noise under the Neyman-Pearson (NP) framework. It is proved that the detection probability corresponding to the α-level likelihood ratio test (LRT) is either strictly concave or has two inflection points such that the function is strictly concave, strictly convex, and finally strictly concave with respect to increasing values of the signal power. In addition, the analysis is extended from scalar observations to multidimensional colored Gaussian noise corrupted signals. Based on the convexity results, optimal and near-optimal time sharing strategies are proposed for average/peak power constrained transmitters and jammers. Numerical methods with global convergence are also provided to obtain the parameters for the proposed strategies.

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Book Title
Keywords
Convexity, Gaussian noise, Neyman-Pearson (NP), Convexity, Neyman-pearson, Power constraints, Stochastic signaling, Time-sharing, Error detection, Gaussian noise (electronic), Jamming, Optimization, Transmitters, Signal detection
Citation
Published Version (Please cite this version)