Theses: Dispersive Source Models in Wireless Communications Subscriber Location
R. Jativa


Mobile subscriber positioning is an issue in permanent revision due to the new possibilities of relation that the knowledge of the position introduces, among users and an increasing number of devices. Being this a relevant problem, it is frequently boarded under diverse perspectives and contexts. This thesis studies it in the context of wireless communications and from the perspective of the statistical signal processing. This research provides a quite complete description of this task both from the theoretical viewpoint and through intensive simulations, by using stochastic models than conceive signal as a dispersive source characterized for their spatial and temporal probability density functions. These models are justified from experimental measurements and they are very suited for studying the problem of positioning, not just because they reduce the mathematical complexity and use a fewer number of parameters, but also because these parameters are in fact those required for these positioning techniques. Signal is studied in the framework of Direct Sequence – Spread Spectrum (DS –SS), but once that channel estimation has been performed, the subsequent processes are quite general and could be applied with other infrastructures. This document introduces the positioning technologies, and discusses the problems and possible solutions appearing when these schemes are applied to wireless communications systems, and also some mechanisms for the evaluation of the positioning accuracy. Furthermore, it particularly studies the degradation associated with the Non Line Of Sight (NLOS) condition between the transmitter and the receiver, and possible mechanisms for its mitigation. In order to achieve realistic simulation scenarios, the Greenstein's gaindelay propagation model has been used, and a simulation platform to evaluate positioning accuracy has been developed. Furthermore, the use of some important statistics to perform NLOS mitigation on timing – based positioning algorithms have been proposed. As a result of the derivation of these statistics from the Greenstein's model, it was concluded that the quality of the timing measures decays more strongly with the link distances between transmitter and receiver than the suggested when the propagation model has not been taken account. Therefore, the proper weightings have been provided. Moreover, the weighted linear least squares algorithm has been revisited and a new two-stage solution that includes geometrical restrictions has been proposed and successfully implemented.
Since the signal in a wireless channel is affected by scattering, the use of dispersive models for the theoretical study of these signals in the context of the positioning problem is justified. Therefore the use of Cramer-Rao bounds derived from these models is proposed to extract pondered conclusions about the quality of timing estimates. This research includes a detailed description of Cramer-Rao Bounds derivation for Time of Arrival estimation for both Rice and Rayleigh propagation.
Particularly, to the best of our knowledge, it is in fact the most complete model of its kind in the literature, since it incorporates a way to take into account spatial and temporal correlation among channel estimates, the impact of the roll-off factor, the number of sensors and the number of channel estimates, and also because it assumes an exponential dispersion from delays, which it is characteristic of mobile channels, instead of two or three paths, typical in literature. Moreover, this information model that provides the lower limits of the error variance in the estimation of the first arrival has
been integrated to the simulation platform providing a useful approach to evaluate both qualitative and quantitative the benefits of using space-time diversity in terms of the positioning accuracy.
Finally, this thesis proposes a two-stage procedure to acquire the required improved timing estimates for enhancing the positioning accuracy of the wireless mobile subscribers. Therefore, signal is discriminated from noise at the first stage using a Generalized Likelihood Ratio Test (GLRT) derived from notions of the Statistical Theory of Decision. Signal detectability is evaluated using a novel model developed to put in evidence the optimum operation point from the viewpoint of the quality of the timing detection. This model has been used to evaluate different configurations of the proposed GLRT, but it can be used to evaluate other detectors once provided their receiver operating characteristics. Moreover, a high resolution timing estimation has been proposed for the second stage to reduce timing uncertainty from a chip time at the first stage to a small fraction of this value. From the two candidates methods proposed to be part of this second stage, this research has shown that the NMV approach is suitable to perform this task. Eventually, the operational results from this two-stage detection-estimation approach have been incorporated to the simulation platform to assess their application to the subscriber positioning problem in realistic conditions. The final results show the benefits of using this two-stage procedure, as well as the
advantage of counting with space-time diversity in the solution of the positioning problem. Furthermore, they show as subscriber location may be performed with a high
degree of accuracy from network-based architectures.

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