Theses: Advanced Signal Processing Techniques For Global Navigation Satellite Systems Receivers
C. Fernandez Prades

Abstract

This dissertation addresses the synchronization problem using an array of antennas in the general framework of Global Navigation Satellite Systems (GNSS) receivers. Positioning systems are based on time delay and frequency-shift estimation of the incoming signals in the receiver side, in order to compute the user's location. Sources of accuracy degradation in satellite-based navigation systems are well-known, and their mitigation has deserved the attention of a number of researchers in latter times. While atmospheric-dependant sources (delays that depend on the ionosphere and troposphere conditions) can be greatly mitigated by differential systems external to the receiver's operation, the multipath effect is location-dependant and remains as the most important cause of accuracy degradation in time delay estimation, and consequently in position estimation, becoming a signal processing challenge.

Traditional approaches to time delay estimation are often embodied in a communication systems framework. Indeed, in DS-CDMA systems many techniques are driven to minimize the probability of error in the symbol detection by taking advantage of several incoming replicas in order to increase the signal-to-noise ratio (SNR) in the detection stage. This is not the case of GNSS, where the parameter of interest is the time delay of the line-of-sight signal (LOSS), and the rest of replicas are nuisance signals that jeopardize the LOSS time estimation accuracy. Although a number of multipath mitigation techniques have been proposed in the recent years, most of them are based in single-antenna receivers, an approach that has inherent drawbacks. In this dissertation, we propose the use of the spatial diversity provided by an antenna array as a possible solution for the mitigation of reflections that are correlated with the direct signal, denoted as coherent multipath along this dissertation.

After an analysis of the state-of-the-art in GNSS receiver design and providing some details about the signal structure of the GPS and Galileo systems, we propose a signal model for the reception of several scaled, time-delayed and Doppler-shifted signals by an antenna array. In a first instance, the front-end is assumed perfectly calibrated, and thus the model includes a spatial signature, unique for each direction of arrival. Due to the technologic challenge that perfect calibration demands, an unstructured version of the signal model where the array is randomly calibrated is also provided. The particularity of both versions is a noise term which is considered statistically white in the time dimension but colored in the space dimension. This approach tries to characterize in a very simple manner the statistical behavior of multipath and interferences exploiting the spatial diversity provided by antenna arrays. In order to establish a theoretical limit of accuracy in parameter estimation, we provide the derivation of the Cramér-Rao bounds for the estimation of directions of arrival, complex amplitudes, time delays and Doppler shifts of a set of signals. The computation of the theoretical lower bound of variance for unbiased estimators is completed with the proof of uncoupling between the direction of arrival and the synchronization parameters.

The Dissertation follows with the application of the Maximum Likelihood (ML) approach to the proposed array signal model. The result is a new cost function whose minimization leads to the ML joint estimation of time delays and Doppler shifts. This cost function is independent of the directions of arrival and allows its implementation in an unstructured array. Although the formulation of the problem is rather general and allows its use in a number of different applications, the peculiarities of navigation signals leads to some adaptations of the algorithms to better suite the problem at hand and reduce their computational cost. Some iterative algorithms based on the obtained cost function are derived and tested in computer simulations.

Then, the problem of synchronization with antenna arrays is attacked from a completely different point of view. If the ML procedure was based on statistical assumptions about multipath and interferences, now we take the beamforming approach, free from statistical assumptions, exploiting the electronic manipulation of the radiation pattern that allows an antenna array. We propose the combination of temporal and spatial references to avoid the multipath effect, the so-called space-time hybrid beamforming. The result is a beamforming algorithm which requires a reasonable computation cost and is surprisingly linked to the ML approach. Different pointing strategies are proposed, including the derivation of a robust version which copes with array miscalibration resorting to convex optimization theory.

As another original contribution of this Dissertation, the theory of beamforming has been applied for first time to the satellite-based Search And Rescue system named COSPAS-SARSAT. Nowadays, the system works with four satellites that are unable to ensure global coverage, among other serious drawbacks. The European Space Agency (ESA) is evaluating the possibility to equip the forthcoming Galileo satellite constellation with Search And Rescue transponders. The tight power budget constraints and the accuracy requirements for emergency beacon positioning greatly complicates the receiver design, withdrawing the use of a single-antenna system. In this dissertation, we provide the analysis of the current emergency beacon and another signal structure proposed by the Centre National d'Etudes Spatiales (CNES) for a new generation of emergency beacons. Then, we propose the use of an antenna array in the receiver design and provide suitable, specially designed algorithms and extensive simulation results.

Last part of this dissertation describes the design and implementation of an antenna array devoted to the civil signal provided by GPS on the L1 link. We have decided to implement an antenna array in order to apply the theory explained in the previous chapters of this dissertation and provide a testbed for evaluation of the developed algorithms in conditions of real data. We provide details about the hardware architecture, the requirements and measurements of each block and some results working with real GPS data, drawing a link between signal processing theory and its actual hardware and Software-Defined Radio (SDR) implementation.


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