Bussgang revisited: effect of quantization on signal to distortion plus noise ratio with non-Gaussian signals

Quantization plays an important role in the physical layer (PHY) disaggregation which is fundamental to the Open Radio Access Network (O-RAN) architecture, since digitized signals must be transmitted over fronthaul connections. In this paper we explore the effect of quantization on PHY performance, drawing on the Bussgang decomposition and the implications of the Bussgang theorem and extending it to the case of non-Gaussian signals. We first prove several theorems regarding the signal to distortion plus noise ratio for a general non-linearity, applicable to both the Gaussian and the non-Gaussian case, showing that the decomposition can be applied to the non-Gaussian case, but that formulae previously introduced should be amended. We then apply these results to the non-linearity created by quantization, both for Gaussian and non-Gaussian signal distributions, and give numerical results derived from both theory and simulation.