Effect of timing error on the performance of BPSK modulation over a fading channel

In this letter, a closed form expression for the conditional bit error probability (BEP) with static timing errors of binary phase shift keying (BPSK) modulation over a Rayleigh fading channel is presented. The expressions for average BEP are then given for dynamic timing errors assuming the normalized timing error has either a Gaussian probability density function (pdf) or a Tikhonov pdf. Numerical results to corroborate the derived analytic expressions are presented for average BEP obtained by averaging the conditional error probability over the pdf of normalized timing errors.