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. In order to design better signal constellations for this environment, it is of interest to characterize this noise. 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, are obtained. The results are compared to a Gaussian PDF. It is concluded that a Gaussian approximation, although not entirely accurate, is not unreasonable