Comparison of the sensitivity limits for GPS and Galileo receivers in multipath scenarios

The global navigation satellite systems (GNSS) market is anticipated by most market researchers to experience exponential growth in the consumer segment, to the largest extend through the introduction of location based services (LBS). LBS - including the U.S. E-911 mandate - require position fixes at demanding rural sites, such as urban canyon, moderate indoor, and in vehicles without external antennae. The satellite signals are not only attenuated, but also subjected to strong multipath fading. Developing GPS/Galileo receivers for high-volume markets requires support for LBS, which in turn necessitates enhanced receiver sensitivity and multipath robustness. Which business cases are feasible is therefore partially determined by the maximally achievable sensitivity under various multipath scenarios. These sensitivity limits form a baseline for the receiver design. This paper algebraically derives the sensitivity limits for acquisition (i.e. synchronization) of direct sequence spread spectrum positioning signals under multipath propagation conditions. The derived formulas are then evaluated exemplarily for the parameters of the openly accessible L1-band GPS and Galileo signals, while they are also valid for other positioning signals. As commonly applied in wireless communications, the multipath environment is modelled with stochastic Ricean fading processes. The derived sensitivity limits are based on the stochastic models for multipath and noise, being transformed by RF-downconversion, despreading, coherent integration, envelope detection, noncoherent integration, and Neyman-Pearson detection. These results are also provided as plots of probability of detection versus carrier power to noise power spectral density, parameterized for various noncoherent integration times and Ricean factors.