A model of an angle-spread source is described, termed the "Gaussian channel model" (GCM). This model is used to represent signals transmitted between a user equipment and a cellular base station. It assumes a Gaussian law of the scatterer occurrence probability, depending upon the scatterer distance from the user. The probability density function of the angle of arrival (AoA) of the multipath components is derived for an arbitrary angle spread. The "wandering" of the "centre of gravity" of the scattering source realisation is investigated, which is in turn due to the nonergodicity of the angle-scatter process. Numerical results obtained with the help of the sum-difference bearing method show the dependence of the AoA estimation accuracy on the spread-source model.