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      Convexity properties of detection probability for noncoherent detection of a modulated sinusoidal carrier

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      Author
      Ozturk, C.
      Dulek, B.
      Gezici, Sinan
      Date
      2018
      Source Title
      IEEE Transactions on Vehicular Technology
      Print ISSN
      0018-9545
      Publisher
      Institute of Electrical and Electronics Engineers
      Volume
      67
      Issue
      12
      Pages
      12410 - 12415
      Language
      English
      Type
      Article
      Item Usage Stats
      157
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      104
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      Abstract
      In this correspondence paper, the problem of noncoherent detection of a sinusoidal carrier is considered in the presence of Gaussian noise. The convexity properties of the detection probability are characterized with respect to the signal-To-noise ratio (SNR). It is proved that the detection probability is a strictly concave function of SNR when the false alarm probability α satisfies α > e-2, and it is first a strictly convex function and then a strictly concave function of SNR for α < e-2. In addition, optimal power allocation strategies are derived under average and peak power constraints. It is shown that on-off signaling can be optimal for α < e-2 depending on the power constraints, whereas transmission at a constant power level that is equal to the average power limit is optimal in all other cases.
      Keywords
      convexity
      Detection
      Neyman-Pearson
      Noncoherent
      Power allocation
      Probability of detection
      Permalink
      http://hdl.handle.net/11693/50291
      Published Version (Please cite this version)
      https://doi.org/10.1109/TVT.2018.2876516
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      • Department of Electrical and Electronics Engineering 3524
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