Convexity Properties of Detection Probability Under Additive Gaussian Noise: Optimal Signaling and Jamming Strategies


Creative Commons License

Dulek B. , Gezici S., Arikan O.

IEEE TRANSACTIONS ON SIGNAL PROCESSING, cilt.61, ss.3303-3310, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 61 Konu: 13
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1109/tsp.2013.2259820
  • Dergi Adı: IEEE TRANSACTIONS ON SIGNAL PROCESSING
  • Sayfa Sayıları: ss.3303-3310

Özet

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 alpha-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.