Near-optimal input distributions in fading channels with large coherent dimension

The fundamental tradeoff between bandwidth and rate for wideband additive Gaussian channels, when there is a constraint in the error exponent is investigated in the previous paper. This paper extends these results to fading channels. Specifically, we consider fading channels with large coherent dimension D. which is the defined to be the product of coherent time and coherent bandwidth. The behavior of R_z(1/D) which is the maximum rate at which one can communicate when the coherent dimension is D and the error exponent is constrained to be at least equal to z is considered and calculates two quantities: R_z(0) and R˙_z(0), which together partially characterize the behavior of R_z(1/D) when D is large. We show that QPSK is near-optimal for fading channels with large coherent dimension, in the sense that both R_z(0) and R˙_z(0) can be achieved.