Capacity and capacity-achieving input distribution of the energy detector

Abstract

This paper presents the channel capacity and capacity-achieving input distribution of an energy detection receiver structure. A proper statistical model is introduced which makes it possible to treat the energy detector as a constrained continuous communication channel. To solve this non-linear optimization we used the Blahut-Arimoto algorithm extended with a particle method, so that also continuous channels can be handled. To get a better convergence behavior of the algorithm, we also implement two new methods, which are called “fuse particles” and “kick particles” [1]. The results we present show that the capacity of the energy detector decreases with increasing integration time and decreasing peak-to-average power ratio. It is shown that the capacity-achieving input distribution is discrete with a finite number of mass points.