The autocorrelation function of a peak-power-limited process (Q1180380)

This paper is concerned with the properties of the autocorrelation function (acf) and power spectral density (psd) function of a stationary, real-valued peak power limited (PPL) process. First, the necessary conditions satisfied by the act of a stationary PPL process is given. Using this, it is shown that the average power is strictly less than the peak power for processes with a finite second moment bandwidth. Then the authors explore the restrictions on the psd function of a continuous PPL process. These restrictions are used to establish a property of the class of corner-positive matrices. Moreover, they are applied to tighten the upper bound on the Shannon capacity of the additive Gaussian channel with peak constraints on the power and slope of the channel input. Finally, the difference between real- and complex-valued PPL processes is pointed out briefly.