Browsing by Subject "Cramer-Rao lower bound"
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Item Open Access CRLB based optimal noise enhanced parameter estimation using quantized observations(IEEE, 2010-02-22) Balkan, G. O.; Gezici, SinanIn this letter, optimal additive noise is characterized for parameter estimation based on quantized observations. First, optimal probability distribution of noise that should be added to observations is formulated in terms of a CramerRao lower bound (CRLB) minimization problem. Then, it is proven that optimal additive noise can be represented by a constant signal level, which means that randomization of additive signal levels is not needed for CRLB minimization. In addition, the results are extended to the cases in which there exists prior information about the unknown parameter and the aim is to minimize the Bayesian CRLB (BCRLB). Finally, a numerical example is presented to explain the theoretical results.Item Open Access Noise enhanced parameter estimation using quantized observations(Bilkent University, 2010) Balkan, Gökçe OsmanIn this thesis, optimal additive noise is characterized for both single and multiple parameter estimation based on quantized observations. In both cases, first, optimal probability distribution of noise that should be added to observations is formulated in terms of a Cramer-Rao lower bound (CRLB) minimization problem. In the single parameter case, it is proven that optimal additive “noise” can be represented by a constant signal level, which means that randomization of additive signal levels (equivalently, quantization levels) are not needed for CRLB minimization. In addition, the results are extended to the cases in which there exists prior information about the unknown parameter and the aim is to minimize the Bayesian CRLB (BCRLB). Then, numerical examples are presented to explain the theoretical results. Moreover, performance obtained via optimal additive noise is compared to performance of the commonly used dither signals. Furthermore, mean-squared error (MSE) performances of maximum likelihood (ML) and maximum a-posteriori probability (MAP) estimates are investigated in the presence and absence of additive noise. In the multiple parameter case, the form of the optimal random additive noise is derived for CRLB minimization. Next, the theoretical result is supported with a numerical example, where the optimum noise is calculated by using the particle swarm optimization (PSO) algorithm. Finally, the optimal constant noise in the multiple parameter estimation problem in the presence of prior information is discussed.Item Open Access Optimal power allocation techniques for vector parameter estimation with Fisher information based objectives(Bilkent University, 2021-06) Gürgünoğlu, DoğaIn this thesis, optimal power allocation problems are investigated for vector parameter estimation according to various Fisher information based optimality criteria. By considering a generic observation model involving a linear/nonlinear transformation of the parameter vector and an additive noise component with an arbitrary joint probability distribution, six different optimal power allocation problems are formulated based on Fisher information based objective functions. Various closed-form solutions are derived for the proposed problems using opti-mization theoretic approaches for the cases in which the transformation acting on the parameter vector is linear. Also, the results are extended to cases in which nuisance parameters exist in the system model, and to the cases when the transformation acting on the parameter vector is nonlinear. It is shown that the proposed methods are also valid for the provided extensions under certain conditions. Numerical examples are presented to investigate performance of the proposed power allocation strategies, and it is shown that they provide significant performance gains over the equal power allocation strategy.Item Open Access Optimal signal design for visible light positioning under power and illumination constraints(Bilkent University, 2021-11) Yazar, OnurcanThe optimal design of transmit signals for light-emitting diodes (LEDs) in a visible light positioning (VLP) system is analyzed with the objectives of im-provements in localization accuracy and power efficiency. Specifically, the lo-calization performance maximization problem is addressed for asynchronous and synchronous VLP systems where certain system limitations including power con-sumption, illumination, and effective bandwidth are considered, and the localiza-tion performance is quantified using the Cram´er-Rao lower bound (CRLB). The formulated signal design problems are demonstrated to be convex optimization problems and some properties of the optimal signal design parameters are found. On the other hand, the signal design problem is also formulated for achieving the lowest possible power consumption while guaranteeing a certain localization ac-curacy. Then, the optimal signal design parameters resulted from the solution of these optimization problems are used to construct the optimal transmit signals in the LEDs. The advantages of the optimal signal design approach is demonstrated through the numerical experiments while also presenting a comparison with the state-of-the-art optimal power allocation method in the literature.Item Open Access Time delay estimation in cognitive radio systems(IEEE, 2009-12) Koçak, Fatih; Çelebi, H.; Gezici, Sinan; Qaraqe, K. A.; Arslan, H.; Poor, H. V.In cognitive radio systems, secondary users can utilize multiple dispersed bands that are not used by primary users. In this paper, time delay estimation of signals that occupy multiple dispersed bands is studied. First, theoretical limits on time delay estimation are reviewed. Then, two-step time delay estimators that provide trade-offs between computational complexity and performance are investigated. In addition, asymptotic optimality properties of the two-step time delay estimators are discussed. Finally, simulation results are presented to explain the theoretical results. © 2009 IEEE.