Near-optimal input distributions for fading channels in the wideband regime

In this paper, we will investigate the fundamental tradeoff between bandwidth and rate for a coherent fading channel in the wideband regime, when a constraint on the error exponent is imposed. In an earlier paper [1], we computed optimal values of R(0) and Ṙ(0) for a non-fading channel, where R(·) is the maximum rate at which information can be transmitted as a function of the inverse of bandwidth B. given a lower bound on the error exponent. Based on this calculation, we defined an input distribution to be near-optimal or second-order optimal if both optimal values for R(0) and Ṙ(0) can be achieved. In this paper, we extend this result to coherent fading channels. We show that, although both BPSK and QPSK are first-order optimal, only QPSK is second-order optimal.