Analytical Derivation of the False Alarm and Detection Probability for NLOS Detection

This paper presents a novel analytical derivation of the false alarm probability (FAP) and detection probability (DP) for non-line-of-sight (NLOS) detection of GNSS signals. In navigation systems, the NLOS propagation in for example urban environments causes positioning errors in the order of hundreds of meters. Thus, detection and mitigation of NLOS signals is a critical task for high accuracy navigation receivers. In this paper, we derive the FAP and DP of power-scaled detectors based on the multipath signals. The derivation considers frequency-selective fading channels taking sub-chip multipath interference, channel dynamics and initial frequency offsets into account. The results show a simple way to calculate the DP versus FAP. Simulation results verify the analytical probabilities and show the trade-off between temporal non-coherent versus temporal coherent averaging. Clearly, the optimum noise averaging depends on the length of the symbol sequence and channel dynamics. Additionally, the simulations show the improved DP of an antenna array at the receiver. Furthermore we see the influence of sub-chip interference in the simulation results.