In the communication field, during
transmission, a source signal undergoes a convolutive distortion between its
symbols and the channel impulse response. This distortion is referred to as
Intersymbol Interference (ISI) and can be reduced significantly by applying a
blind adaptive deconvolution process (blind adaptive equalizer) on the distorted
received symbols. But, since the entire blind deconvolution process is carried
out with no training symbols and the channel’s coefficients are obviously
unknown to the receiver, no actual indication can be given (via the mean square
error (MSE) or ISI expression) during the deconvolution process whether the
blind adaptive equalizer succeeded to remove the heavy ISI from the transmitted
symbols or not. Up to now, the output of a convolution and deconvolution
process was mainly investigated from the ISI point of view. In this paper, the
output of a convolution and deconvolution process is inspected from the leading
digit point of view. Simulation results indicate that for the 4PAM (Pulse
Amplitude Modulation) and 16QAM (Quadrature Amplitude Modulation) input case,
the number “1” is the leading digit at the output of a convolution and
deconvolution process respectively as long as heavy ISI exists. However, this
leading digit does not follow exactly Benford’s Law but follows approximately
the leading digit (digit 1) of a Gaussian process for independent identically
distributed input symbols and a channel with many coefficients.
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