Fading Channels With Arbitrary Inputs: Asymptotics of the Constrained Capacity and Information and Estimation Measures

We consider the characterization of the asymptotic behavior of the average minimum mean-squared error (MMSE) in scalar and vector 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. In particular, we construct expansions of the quantities that are asymptotic in the signal-to-noise ratio (snr) for coherent channels subject to Rayleigh, Ricean or Nakagami fading and driven by discrete inputs and continuous inputs. The construction of these expansions leverages the fact that the average MMSE can be seen as an ψ-transform with a kernel of monotonic argument: this offers the means to use a powerful asymptotic expansion of integrals technique-the Mellin transform method-that leads immediately to the expansions of the average MMSE and- via the I-MMSE relationship-to expansions of the average mutual information, in terms of the so called canonical MMSE of a standard additive white Gaussian noise (AWGN) channel. We conclude with applications of the results to the optimization of the constrained capacity of a bank of parallel independent coherent fading channels driven by arbitrary discrete inputs.