Error Exponents for Capacity-Achieving Signaling on Wideband Rayleigh Fading Channels

We have previously presented the exponent for an upper bound on the error probability of a “peaky” signaling scheme that achieves the capacity of the Rayleigh fading channel under an average power constraint in the limit of infinite bandwidth. In the present work, we complement this result with a lower bound. We find that the exponents of the upper and lower bounds coincide in the wideband limit and therefore yield the reliability function of the Rayleigh fading channel using peaky signaling. We illustrate the behavior of the reliability function and the upper and lower error probability bounds with some numerical examples.