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 (X. Wu, et al., (2003)), we computed optimal values of R(0) and R˙(0) for a nonfading 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 R˙(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.