Data transmission between a satellite and an aircraft is investigated in the case of a multiphase DPSK system operating in the L‐band. The error rate characteristics of matched filter detection are analyzed exactly on the basis of a multipath model consisting of a direct path wave and a relatively delayed, high‐speed, diffuse‐path Rayleigh wave due to reflection at the Earth's surface. On the basis of this model, concrete error rate (Pe) computations are performed in the case of 4‐phase DPSK (symbol rate 1/Ts) as a function of the Doppler spread (BD) and average relative delay (T) of the reflected wave. Considering the influence of varying duration of the reflected wave, the results show that the error rate Pe is maximum (worst case) for BDTs ≒ 0.40 independently of the powers of the direct wave, reflected wave and noise. Furthermore, in the range BDTs ⩽ 0.17 the diffusion wave can be treated as an AC vector. Next considering the influence of the relative delay of the reflected wave, the value of Pe is given for the 16 cases of phase difference in the delay range 0 ≦ T ≦ Ts and it is shown that the effect of relative delay is negligible for T/Ts ⩽ 1/40 and that the minimum average error rate (best case) is obtained for τ/Ts ≒ 1/5.