N-multipath performance of GPS receivers

A wide majority of studies on the effect of multipath focused on the analysis of the code and phase tracking errors when only two rays enter the tracking loops, namely the direct ray plus one diffracted ray. Unfortunately, this condition does not correspond to the most frequent situations, where the received signal can be the discrete sum of several powerful replicas of the direct signal. The aim of this paper is to present the theoretical results of a study that identifies the performance of the GPS receivers in the case where more than two powerful rays enter the tracking loops. The theoretical analysis assuming a triangular autocorrelation function with an infinite receiver bandwidth shows that in the case of continuous tracking, if the summed amplitudes of the reflected signals is lower than the amplitude of the direct signal, the code error envelope of the composite signal can be approximated as the sum of the code error envelope for each individual ray, except in its transition zones. The deviation with respect to the linear superposition assumption is negligible in the ideal case of a triangular autocorrelation function with an infinite receiver bandwidth for the narrow correlator DLLs and the DLLs controlled by linear combinations of correlator outputs. As the receiver bandwidth decreases, the nonlinear effects become more important and the deviation is increased. These results are confirmed by experiments on real receivers