Browsing by Subject "Quasiconvex Feasibility"

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Open Access
Visible light positioning systems: fundamental limits, algorithms and resource allocation approaches
(2018-08) Keskin, Musa Furkan
Visible light communication (VLC) is an emerging paradigm that enables multiple functionalities to be accomplished concurrently, including illumination, highspeed data communications, and localization. Based on the VLC technology, visible light positioning (VLP) systems aim to estimate locations of VLC receivers by utilizing light-emitting diode (LED) transmitters at known locations. VLP presents a viable alternative to radio frequency (RF)-based positioning systems by providing inexpensive and accurate localization services. In this dissertation, we consider the problem of localization in visible light systems and investigate distance and position estimation approaches in synchronous and asynchronous scenarios, focusing on both theoretical performance characterization and algorithm development aspects. In addition, we design optimal resource allocation strategies for LED transmitters in VLP systems for improved localization performance. Moreover, we propose a cooperative localization framework for VLP systems, motivated by vehicular VLC networks involving vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications. First, theoretical limits and estimators are studied for distance estimation in synchronous and asynchronous VLP systems. Specifically, the Cram er-Rao lower bounds (CRLBs) and maximum likelihood estimators (MLEs) are investigated based on time-of-arrival (TOA) and/or received signal strength (RSS) parameters. Hybrid TOA/RSS based distance estimation is proposed for VLP systems, and its CRLB is compared analytically against the CRLBs of TOA based and RSS based distance estimation. In addition, to investigate e ects of sampling, asymptotic performance results are obtained under sampling rate limitations as the noise variance converges to zero. A modified hybrid TOA/RSS based distance estimator is proposed to provide performance improvements in the presence of sampling rate limitations. Moreover, the Ziv-Zakai bound (ZZB) is derived for synchronous VLP systems. The proposed ZZB extracts ranging information from the prior information, the time delay parameter, and the channel attenuation factor based on the Lambertian pattern. In addition to the ZZB, the Bayesian Cram er-Rao bound (BCRB) and the weighted CRB (WCRB) are calculated for synchronous VLP systems. Furthermore, a closed-form expression is obtained for the expectation of the conditional CRB (ECRB). Numerical examples are presented to compare the bounds against each other and against the maximum a-posteriori probability (MAP) estimator. It is observed that the ZZB can provide a reasonable lower limit on the performance of MAP estimators. On the other hand, the WCRB and the ECRB converge to the ZZB in regions of low and high source optical powers, respectively; however, they are not tight in other regions. Second, direct and two-step positioning approaches are investigated for both synchronous and asynchronous VLP systems. In particular, the CRLB and the direct positioning based ML estimator are derived for three-dimensional localization of a VLC receiver in a synchronous scenario by utilizing information from both time delay parameters and channel attenuation factors. Then, a two-step position estimator is designed for synchronous VLP systems by exploiting the asymptotic properties of TOA and RSS estimates. The proposed two-step estimator is shown to be asymptotically optimal, i.e., converges to the direct estimator at high signal-to-noise ratios (SNRs). In addition, the CRLB and the direct and two-step estimators are obtained for positioning in asynchronous VLP systems. It is proved that the two-step position estimation is optimal in asynchronous VLP systems for practical pulse shapes. Various numerical examples are provided to illustrate the improved performance of the proposed estimators with respect to the current state-of-the-art and to investigate their robustness against model uncertainties in VLP systems. Third, the problem of optimal power allocation among LED transmitters in a VLP system is considered for the purpose of improving localization performance of VLC receivers. Specifically, the aim is to minimize the CRLB on the localization error of a VLC receiver by optimizing LED transmission powers in the presence of practical constraints such as individual and total power limitations and illuminance constraints. The formulated optimization problem is shown to be convex and thus can efficiently be solved via standard tools. We also investigate the case of imperfect knowledge of localization parameters and develop robust power allocation algorithms by taking into account both overall system uncertainty and individual parameter uncertainties related to the location and orientation of the VLC receiver. In addition, we address the total power minimization problem under predefined accuracy requirements to obtain the most energy-efficient power allocation vector for a given CRLB level. Numerical results illustrate the improvements in localization performance achieved by employing the proposed optimal and robust power allocation strategies over the conventional uniform and nonrobust approaches. In the final part of the dissertation, we propose to employ cooperative localization for visible light networks by designing a VLP system configuration that involves multiple LED transmitters with known locations and VLC units equipped with both LEDs and photodetectors (PDs) for the purpose of cooperation. In the proposed cooperative scenario, we derive the CRLB and the MLE for the localization of VLC units. To tackle the nonconvex structure of the MLE, we adopt a set-theoretic approach by formulating the problem of cooperative localization as a quasiconvex feasibility problem, where the aim is to find a point inside the intersection of convex constraint sets constructed as the sublevel sets of quasiconvex functions resulting from the Lambertian formula. Then, we devise two feasibility-seeking algorithms based on iterative gradient projections to solve the feasibility problem. Both algorithms are amenable to distributed implementation, thereby avoiding high-complexity centralized approaches. Capitalizing on the concept of quasi-Fej er convergent sequences, we carry out a formal convergence analysis to prove that the proposed algorithms converge to a solution of the feasibility problem in the consistent case. Numerical examples illustrate the improvements in localization performance achieved via cooperation among VLC units and evidence the convergence of the proposed algorithms to true VLC unit locations in both the consistent and inconsistent cases.