On the multipath effects due to wall reflections for wave reception in a corner

Abstract Multipath effects occur when receiving a wave near a corner, for example, the noise of an helicopter or an aircraft or a drone or other forms of urban air mobility near a building, or a telecommunications receiver antenna near an obstacle. The total signal received in a corner consists of four parts: (i) a direct signal from source to observer; (ii) a second signal reflected on the ground; (iii) a third signal reflected on the wall; (iv) a fourth signal reflected from both wall and ground. The problem is solved in two-dimensions to specify the total signal, whose ratio to the direct signal specifies the multipath factor. The amplitude and phase of the multipath factor are plotted as functions of the frequency over the audible range, for various relative positions of observer and source, and for several combinations of the reflection coefficients of the ground and wall. It is shown that the received signal consists of a double series of spectral bands, in other words: (i) the interference effects lead to spectral bands with peaks and zeros; (ii) the successive peaks also go through zeros and “peaks of the peaks”. The results apply not only to sound, but also to other waves, e.g., electromagnetic waves using the corresponding frequency band and reflection factors.