Öztürk, CüneydDülek, B.Gezici, Sinan2019-02-212019-02-2120180018-9545http://hdl.handle.net/11693/50291In 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.EnglishconvexityDetectionNeyman-PearsonNoncoherentPower allocationProbability of detectionArticle10.1109/TVT.2018.2876516