Characterization and optimization of the constrained capacity of coherent fading channels driven by arbitrary inputs: A Mellin transform based asymptotic approach

We unveil asymptotic characterizations of the average minimum mean-squared error (MMSE) and the average mutual information in scalar fading coherent channels, where the receiver knows the exact fading channel state but the transmitter knows only the fading channel distribution, driven by a range of inputs both in the regimes of low-SNR - and at the heart of the novelty of the contribution - high-SNR. We also unveil connections to and generalizations of the MMSE dimension. By capitalizing on the characterizations, we conclude with applications of the results to the optimization of the constrained capacity of a bank of parallel independent coherent fading channels.