High-SNR mutual information of dense constellations

In this paper, we consider the asymptotic (for high signal-to-noise ratio, SNR) behavior of the mutual information (MI) between the input and the output of a two-dimensional additive white Gaussian noise (AWGN) channel with continuous input distributions. In particular, the obtained results apply to modulation formats with dense constellations. The accuracy of the presented results is the higher the denser are the considered constellations. We find two simple expressions relating the MI of the considered continuous input distribution, as a function of the SNR, to that of the Gaussian input distribution, in one- and two-dimensional cases, respectively.