In this paper, the time‐varying transfer function of the surface scattering channel is computed from first principles, using an extended Eckart model for the scattering mechanism. By assuming that the probability distribution of the surface is Gaussian with a correlation function having Gaussian form, first and second moments of the transfer function are computed. The effect of various surface parameters, particularly the relative surface roughness, on the channel autocorrelation function can then be easily demonstrated.