On the statistics of the companding noise in T1 carrier systems

In modern voiceband data communication using T1 carrier systems the received signal is subject to nonlinear quantization noise due to companding. Under certain conditions this quantization noise may become dominant and cause serious degradation in performance. In order to design better signal constellations for this environment it is of interest to characterize this noise. In this work we obtain an analytical expression for the probability density function (pdf) of the nonlinear quantization noise and a numerical result for the pdf of the filtered noise, which is the actual noise at the slicer input of the linear receiver. We compare the results to a gaussian pdf and conclude that a gaussian approximation, although not entirely accurate, is not unreasonable.