Browsing by Subject "Fisher information"

Now showing 1 - 7 of 7

Open Access
Average Fisher information maximisation in presence of cost-constrained measurements
(The Institution of Engineering and Technology, 2011) Dulek, B.; Gezici, Sinan
An optimal estimation framework is considered in the presence of cost-constrained measurements. The aim is to maximise the average Fisher information under a constraint on the total cost of measurement devices. An optimisation problem is formulated to calculate the optimal costs of measurement devices that maximise the average Fisher information for arbitrary observation and measurement statistics. In addition, a closed-form expression is obtained in the case of Gaussian observations and measurement noise. Numerical examples are presented to explain the results.
Open Access
Average fisher information optimization for quantized measurements using additive independent noise
(IEEE, 2010) Balkan, Gokce Osman; Gezici, Sinan
Adding noise to nonlinear systems can enhance their performance. Additive noise benefits are observed also in parameter estimation problems based on quantized observations. In this study, the purpose is to find the optimal probability density function of additive noise, which is applied to observations before quantization, in those problems. First, optimal probability density function of noise is formulated in terms of an average Fisher information maximization problem. Then, it is proven that optimal additive "noise" can be represented by a constant signal level. This result, which means that randomization of additive signal levels is not needed for average Fisher information maximization, is supported with two numerical examples. ©2010 IEEE.
Open Access
Optimal parameter encoding based on worst case fisher information under a secrecy constraint
(Institute of Electrical and Electronics Engineers Inc., 2017) Göken, Ç.; Gezici, Sinan
In this letter, optimal deterministic encoding of a uniformly distributed scalar parameter is performed in the presence of an eavesdropper. The objective is to maximize the worst case Fisher information of the parameter at the intended receiver while keeping the mean-squared error (MSE) at the eavesdropper above a certain level. The eavesdropper is modeled to employ the linear minimum MSE estimator based on the encoded version of the parameter. First, the optimal encoding function is derived when there exist no secrecy constraints. Next, to obtain the solution of the problem in the presence of the secrecy constraint, the form of the encoding function that maximizes the MSE at the eavesdropper is explicitly derived for any given level of worst case Fisher information. Then, based on this result, a low-complexity algorithm is provided to calculate the optimal encoding function for the given secrecy constraint. Finally, numerical examples are presented.
Open Access
Optimal power allocation and optimal linear encoding for parameter estimation in the presence of a smart eavesdropper
(IEEE, 2022-08-11) Abadi, Erfan Mehdipour; Göken, Çağrı; Öztürk, Cüneyd; Gezici, Sinan
In this article, we consider secure transmission of a deterministic vector parameter from a transmitter to an intended receiver in the presence of a smart eavesdropper. The aim is to determine the optimal power allocation and optimal linear encoding strategies at the transmitter to maximize the estimation performance at the intended receiver under constraints on the estimation performance at the eavesdropper and on the transmit power. First, the A-optimality criterion is adopted by utilizing the Cramér-Rao lower bound as the estimation performance metric, and the optimal power allocation and optimal linear encoding strategies are characterized theoretically. Then, corresponding to the D-optimality criterion, the determinant of the Fisher information matrix is considered as the estimation performance metric. It is shown that the optimal linear encoding and optimal power allocation strategies lead to the same solution for this criterion. In addition, extensions of the theoretical results are provided to cases with statistical knowledge of systems parameters. Numerical examples are provided to investigate the optimal power allocation and optimal linear encoding strategies in different scenarios.
Open Access
Optimal power allocation for secure estimation of multiple parameters
(IEEE, 2021-08-11) Gürgünoğlu, Doğa; Göken, Ç.; Gezici, Sinan
Optimal power allocation for secure estimation of multiple deterministic parameters is investigated under a total power constraint. The goal is to minimize the Cramér-Rao lower bound (CRLB) at an intended receiver while keeping estimation errors at an eavesdropper above specified target levels. To that end, an optimization problem is formulated by considering measurement models involving linear transformation of the parameter vector and additive Gaussian noise. Although the proposed optimization problem is nonconvex, it is decomposed into convex sub-problems by utilizing the structure of the secrecy constraints. Then, optimal solutions to the sub-problems are characterized via optimization theoretic approaches. An algorithm utilizing that characterization is developed to obtain the optimal solution of the proposed problem.
Open Access
Optimal power allocation techniques for vector parameter estimation with Fisher information based objectives
(2021-06) Gürgünoğlu, Doğa
In 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.
Open Access
Power adaptation for vector parameter estimation according to Fisher information based optimality criteria
(Elsevier BV, 2022-03) Gürgünoğlu, Doğa; Dülek, Berkan; Gezici, Sinan
The optimal power adaptation problem is investigated for vector parameter estimation according to various Fisher information based optimality criteria. By considering an observation model that involves a linear transformation of the parameter vector and an additive noise component with an arbitrary probability distribution, six different optimal power allocation problems are formulated based on Fisher information based objective functions. Via optimization theoretic approaches, various closed-form solutions are derived for the proposed problems. Also, the results are extended to cases in which nuisance parameters exist in the system model or certain types of nonlinear transformations are applied on the parameter vector. Numerical examples are presented to investigate performance of the proposed power allocation strategies.