On the detrimental effect of assuming a linear model for non-linear AWGN channels

Abstract

In communication theory, one of the best understood and commonly adopted channel model is the average-power constrained linear AWGN channel, the capacity of which is given by the expression 1 over 2 log(1 + SNR). But what if the channel is not linear? How bad is it to adopt a linear model for a non-linear channel?