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.

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