An Upper Bound on the Error Probability of Capacity-Achieving Signaling on Broadband Rayleigh Fading Channels

We present an upper bound on the probability of error of a signaling scheme that achieves the capacity of the multipath fading channel under an average power constraint in the limit of infinite bandwidth. The bound is derived under the assumption of Rayleigh block fading. We are therefore able to determine the performance of the scheme when a given finite bandwidth is available. We evaluate the bound numerically for some reasonable parameters and study its interplay with other parameters of interest.