In many adaptive signal processing applications, it is assumed that the direction of arrival of (DOA) of the signals is known. For a radar problem, this is true as we know along which direction we transmitted the beam, and therefore, we expect the radar return to be arriving from that direction. However, this assumption is questionable when there are material bodies near or along its path. Here, we address the question as to what happens to the direction of propagation when the electromagnetic wave encounters a material body near or along its path for the noise free case. Thus, the objective is to calculate the error associated with the prediction of DOA when the free space is not empty. We illustrate the error associated with the estimation of the DOA when there is a perfect electric conducting (PEC) sphere and a dielectric sphere along/near the path of propagation. A PEC and dielectric will diffract the incident electromagnetic energy. We evaluate the scattered far fields at a few points away from the obstacle. From the measured field points, we predict the DOA of the signal of interest. The simulations have been carried out using an electromagnetic simulator and a DOA estimation algorithm using the Matrix Pencil method. The examples deal with the case of both one- and two-dimensional antenna arrays and how they interpret the diffracted signals.