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

Series

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.

Source Title

IEEE Transactions on Vehicular Technology

Publisher

Institute of Electrical and Electronics Engineers

Course

Other identifiers

Book Title

Degree Discipline

Degree Level

Degree Name

Citation

Published Version (Please cite this version)

Language

English