A closed-form approximation for the error probability of BPSK fading channels

Abstract — This letter presents a simple closed-form expression to evaluate the error probability of binary fully-interleaved fading channels. The proposed expression does not require a numerical Laplace transform inversion, numerical integration or similar techniques, and captures the role of the relevant system parameters in the overall error performance. The expression has the same asymptotic behavior as the Bhattacharyya (Chernoff)-union bound but closes the gap with the simulation results. Its precision is numerically validated for coded and uncoded transmission over generic Nakagami-m fading channels. Index Terms — BPSK modulation, AWGN channel, fading channel, error probability, saddlepoint approximation. I. INTRODUCTION AND MAIN RESULT THE computation of error probabilities in fading channelssuffers from the absence of a simple formula akin to the Q(·) function in pure additive white Gaussian noise (AWGN