Convexity Properties of Detection Probability for Noncoherent Detection of a Modulated Sinusoidal Carrier

Ozturk C., DÜLEK B. , GEZİCİ S.

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, cilt.67, sa.12, ss.12410-12415, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 67 Konu: 12
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1109/tvt.2018.2876516
  • Sayfa Sayıları: ss.12410-12415


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 alpha satisfies alpha > e(-2), and it is first a strictly convex function and then a strictly concave function of SNR for alpha < 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 alpha < 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.