Convolutional Noise Analysis via Large Deviation Technique

Abstract

Due to non-ideal coefficients of the adaptive equalizer used in the system, a convolutional noise arises at the output of the deconvolutional process in addition to the source input. A higher convolutional noise may make the recovering process of the source signal more difficult or in other cases even impossible. In this paper we deal with the fluctuations of the arithmetic average (sample mean) of the real part of consecutive convolutional noises which deviate from the mean of order higher than the typical fluctuations. Typical fluctuations are those fluctuations that fluctuate near the mean, while the other fluctuations that deviate from the mean of order higher than the typical ones are considered as rare events. Via the large deviation theory, we obtain a closed-form approximated expression for the amount of deviation from the mean of those fluctuations considered as rare events as a function of the system’s parameters (step-size parameter, equalizer’s tap length, SNR, input signal statistics, characteristics of the chosen equalizer and channel power), for a pre-given probability that these events may occur.