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


Ozturk C., DÜLEK B., GEZİCİ S.

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, vol.67, no.12, pp.12410-12415, 2018 (SCI-Expanded) identifier identifier

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 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.