In this paper, the case considered is a planar microphone array placed in front of a wall of the room so that the microphone array plane is perpendicular to that of the wall. For this arrangement, a so-called half-space propagation model has been recently proposed, which accounts for the joint contribution of the direct path and the earliest reflection introduced by the adjacent wall. Based on this propagation model, a numerical process to estimate a model of the diffuse noise spatial coherence, which accounts for the presence of the reflecting surface, is proposed. The suggested noise covariance model is used in order to extend the superdirective beamformer in half-space, achieving notable improvements in performance in comparison to a more typical implementation that involves the spherical isotropic coherence model.