Browsing by Subject "Secrecy"

Now showing 1 - 10 of 10

Open Access
Eavesdropper and jammer selection in wireless source localization networks
(IEEE, 2021-07-26) Öztürk, Cüneyd; Gezici, Sinan
We consider a wireless source localization network in which a target node emits localization signals that are used by anchor nodes to estimate the target node position. In addition to target and anchor nodes, there can also exist eavesdropper nodes and jammer nodes which aim to estimate the position of the target node and to degrade the accuracy of localization, respectively. We first propose the problem of eavesdropper selection with the goal of optimally placing a given number of eavesdropper nodes to a subset of possible positions to estimate the target node position as accurately as possible. As the performance metric, the Cramér-Rao lower bound (CRLB) related to the estimation of the target node position by eavesdropper nodes is derived, and its convexity and monotonicity properties are investigated. By relaxing the integer constraints, the eavesdropper selection problem is approximated by a convex optimization problem and algorithms are proposed for eavesdropper selection. Then, the problem of jammer selection is proposed where the aim is to optimally place a given number of jammer nodes to a subset of possible positions for degrading the localization accuracy of the network as much as possible. A CRLB expression from the literature is used as the performance metric, and its concavity and monotonicity properties are derived. Also, a convex optimization problem is derived after relaxation. Finally, the joint eavesdropper and jammer selection problem is proposed with the goal of placing certain numbers of eavesdropper and jammer nodes to a subset of possible positions.
Open Access
ECRB-based optimal parameter encoding under secrecy constraints
(Institute of Electrical and Electronics Engineers, 2018) Göken, Çağrı; Gezici, Sinan
In this paper, optimal deterministic encoding of a scalar parameter is investigated in the presence of an eavesdropper. The aim is to minimize the expectation of the conditional Cramér-Rao bound at the intended receiver while keeping the mean-squared error (MSE) at the eavesdropper above a certain threshold. First, optimal encoding functions are derived in the absence of secrecy constraints for any given prior distribution on the parameter. Next, an optimization problem is formulated under a secrecy constraint and various solution approaches are proposed. Also, theoretical results on the form of the optimal encoding function are provided under the assumption that the eavesdropper employs a linear minimum mean-squared error (MMSE) estimator. Numerical examples are presented to illustrate the theoretical results and to investigate the performance of the proposed solution approaches.
Open Access
Estimation theoretic analyses of location secrecy and ris-aided localization under hardware impairments
(2022-06) Öztürk, Cüneyd
In this thesis, we present estimation theoretic analyses of location secrecy and reconfigurable intelligent surface (RIS) aided localization under hardware impairments. First, we consider a wireless source localization network in which a target node emits localization signals that are used by anchor nodes to estimate the target node position. In addition to target and anchor nodes, there can also exist eavesdropper nodes and jammer nodes which aim to estimate the position of the target node and to degrade the accuracy of localization, respectively. We propose the problem of eavesdropper selection with the goal of optimally placing a given number of eavesdropper nodes to a subset of possible positions in the network to estimate the target node position as accurately as possible. As the performance metric, the Cramér-Rao lower bound (CRLB) related to the estimation of the target node position by eavesdropper nodes is derived, and its convexity and monotonicity properties are investigated. By relaxing the integer constraints, the eavesdropper selection problem is approximated by a convex optimization problem and algorithms are proposed for eavesdropper selection. Moreover, in the presence of parameter uncertainty, a robust version of the eavesdropper selection problem is developed. Then, the problem of jammer selection is proposed where the aim is to optimally place a given number of jammer nodes to a subset of possible positions for degrading the localization accuracy of the network as much as possible. A CRLB expression from the literature is used as the performance metric, and its concavity and monotonicity properties are derived. Also, a convex optimization problem and its robust version are derived after relaxation. Moreover, the joint eavesdropper and jammer selection problem is proposed with the goal of placing certain numbers of eavesdropper and jammer nodes to a subset of possible positions. Simulation results are presented to illustrate performance of the proposed algorithms. Second, a wireless source localization network consisting of synchronized target and anchor nodes is considered. An anchor placement problem is formulated to minimize the CRLB on estimation of target node positions by anchor nodes. It is shown that the anchor placement problem can be approximated as a minimization problem of the ratio of two supermodular functions. Due to the lack of a polynomial time algorithm for such problems, an anchor selection problem is proposed to solve the anchor placement problem. Via relaxation of integer constraints, the anchor selection problem is approximated by a convex optimization problem, which is used to propose two algorithms for anchor selection. Furthermore, extensions to quasi-synchronous wireless localization networks are discussed. To examine the performance of the proposed algorithms, various simulation results are presented. Third, we investigate the problem of RIS-aided near-field localization of a user equipment (UE) served by a base station (BS) under phase-dependent amplitude variations at each RIS element. Through a misspecified Cramér -Rao bound (MCRB) analysis and a resulting lower bound (LB) on localization, we show that when the UE is unaware of amplitude variations (i.e., assumes unit-amplitude responses), severe performance penalties can arise, especially at high signal-to-noise ratios (SNRs). Leveraging Jacobi-Anger expansion to decouple range-azimuth-elevation dimensions, we develop a low-complexity approximated mismatched maximum likelihood (AMML) estimator, which is asymptotically tight to the LB. To mitigate performance loss due to model mismatch, we propose to jointly estimate the UE location and the RIS amplitude model parameters. The corresponding Cramér -Rao bound (CRB) is derived, as well as an iterative refinement algorithm, which employs the AMML method as a subroutine and alternatingly updates individual parameters of the RIS amplitude model. Simulation results indicate fast convergence and performance close to the CRB. The proposed method can successfully recover the performance loss of the AMML under a wide range of RIS parameters and effectively calibrate the RIS amplitude model online with the help of a user that has an a-priori unknown location. Fourth, we consider RIS-aided localization scenarios with RIS pixel failures, where individual RIS elements can become faulty due to hardware imperfections. We explore the impact of such failures on the localization performance. To that aim, an MCRB analysis is conducted and numerical results indicate that performance loss for estimating the UE position can be significant in the presence of pixel failures. To remedy this issue, we develop two different diagnosis strategies to determine which pixels are failing, and design robust methods to perform localization in the presence of faulty elements. One strategy is based on the l_1-regularization method, the second one employs a successive approach. Both methods significantly reduce the performance loss due to pixel failures. The successive one performs very close to the theoretical bounds at high SNRs even though it has a higher computational cost than the l_1-regularization based method. In the final part of the dissertation, the optimal encoding strategy of a scalar parameter is performed in the presence of jamming based on an estimation theoretic criterion. Namely, the aim is to obtain the optimal encoding function at the transmitter that minimizes the expectation of the conditional Cramér -Rao bound (ECRB) at the receiver when the jammer has access to the parameter and alters the received signal by sending an encoded version of the parameter. Via calculus of variations, the optimal encoding function at the transmitter is characterized explicitly, and an algorithm is proposed to calculate it. Numerical examples demonstrate benefits of the proposed optimal encoding approach.
Open Access
Estimation theoretic optimal encoding design for secure transmission of multiple parameters
(IEEE, 2019-08-15) Göken, Çağrı; Gezici, Sinan; Arıkan, Orhan
In this paper, optimal deterministic encoding of a vector parameter is investigated in the presence of an eavesdropper. The objective is to minimize the expectation of the conditional Cramér-Rao bound at the intended receiver, while satisfying an individual secrecy constraint on the mean-squared error of estimating each parameter at the eavesdropper. The eavesdropper is modeled to employ the linear minimum mean-squared error estimator based on the noisy observation of the encoded parameter without being aware of encoding. First, the problem is formulated as a constrained optimization problem in the space of vector-valued functions. Then, two practical solution strategies are developed based on nonlinear individual encoding and affine joint encoding of parameters. Theoretical results on the solutions of the proposed strategies are provided for various scenarios on channel conditions and parameter distributions. Finally, numerical examples are presented to illustrate the performance of the proposed solution approaches.
Open Access
Estimation theoretic secure communication via encoder randomization
(IEEE, 2019-12-01) Göken, Çağrı; Gezici, Sinan
Estimation theoretic secure transmission of a scalar random parameter is investigated in the presence of an eavesdropper. The aim is to minimize the estimation error at the receiver under a secrecy constraint at the eavesdropper; or, alternatively, to maximize the estimation error at the eavesdropper for a given estimation accuracy limit at the receiver. In the considered setting, the encoder at the transmitter is allowed to use a randomized mapping between two one-to-one and continuous functions and the eavesdropper is fully aware of the encoding strategy at the transmitter. For small numbers of observations, both the eavesdropper and the receiver are modeled to employ linear minimum mean-squared error (LMMSE) estimators, and for large numbers of observations, the expectation of the conditional Cramér-Rao bound (ECRB) metric is employed for both the receiver and the eavesdropper. Optimization problems are formulated and various theoretical results are provided in order to obtain the optimal solutions and to analyze the effects of encoder randomization. In addition, numerical examples are presented to corroborate the theoretical results. It is observed that stochastic encoding can bring significant performance gains for estimation theoretic secrecy problems.
Open Access
Optimal parameter design for estimation theoretic secure broadcast
(IEEE, 2020) Göken, Çağrı; Gezici, Sinan
In this letter, estimation theoretic secure broadcast of a random parameter is investigated. In the considered setting, each receiver device employs a fixed estimator and carries a certain security risk such that its decision can be available to a malicious third party with a certain probability. The encoder at the transmitter is allowed to use a random mapping to minimize the weighted sum of the conditional Bayes risks of the estimators under secrecy and average power constraints. After formulating the optimal parameter design problem, it is shown that the optimization problem can be solved individually for each parameter value and the optimal mapping at the transmitter involves a randomization among at most three different signal levels. Sufficient conditions for improvability and non-improvability of the deterministic design via stochastic encoding are obtained. Numerical examples are provided to corroborate the theoretical results.
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 parameter encoding strategies for estimation theoretic secure communications
(2019-12) Göken, Çağrı
Physical layer security has gained a renewed interest with the advances in modern wireless communication technologies. In estimation theoretic security, secrecy levels are measured via estimation theoretic tools and metrics, such as mean-squared error (MSE), where the objective is to perform accurate estimation of the parameter at the intended receiver while keeping the estimation error at the eavesdropper above a certain level. This framework proves useful both for analyzing the achievable performance under security constraints in parameter estimation problems, and for designing low-complexity, practical methods to enhance security in communication systems. In this dissertation, we investigate optimal deterministic encoding of random scalar and vector parameters in the presence of an eavesdropper, who is unaware of the encoding operation. We also analyze optimal stochastic encoding of a random parameter under secrecy constraints in a Gaussian wiretap channel model, where the eavesdropper is aware of the encoding strategy at the transmitter. In addition, we perform optimal parameter design for secure broadcast of a parameter to multiple receivers with fixed estimators. First, optimal deterministic encoding of a scalar parameter is investigated in the presence of an eavesdropper. The aim is to minimize the expectation of the conditional Cram´er-Rao bound (ECRB) at the intended receiver while keeping the MSE at the eavesdropper above a certain threshold. The eavesdropper is modeled to employ the linear minimum mean-squared error (LMMSE) estimator based on the encoded version of the parameter. First, the optimal encoding function is derived in the absence of secrecy constraints for any given prior distribution on the parameter. Next, an optimization problem is formulated under a secrecy constraint and various solution approaches are proposed. Also, theoretical results on the form of the optimal encoding function are provided. Furthermore, a robust parameter encoding approach is developed. In this case, the objective is to maximize the worst-case Fisher information of the parameter at the intended receiver while keeping the MSE at the eavesdropper above a certain level. 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. Numerical examples are presented to illustrate the theoretical results for both the ECRB and worst-case Fisher information based designs. Second, optimal deterministic encoding of a vector parameter is investigated in the presence of an eavesdropper. The objective is to minimize the ECRB at the intended receiver while satisfying an individual secrecy constraint on the MSE of estimating each parameter at the eavesdropper. The eavesdropper is modeled to employ the LMMSE estimator based on the noisy observation of the encoded parameter without being aware of encoding. First, the problem is formulated as a constrained optimization problem in the space of vector-valued functions. Then, two practical solution strategies are developed based on nonlinear individual encoding and affine joint encoding of parameters. Theoretical results on the solutions of the proposed strategies are provided for various scenarios on channel conditions and parameter distributions. Finally, numerical examples are presented to illustrate the performance of the proposed solution approaches. Third, estimation theoretic secure transmission of a scalar random parameter is investigated in the presence of an eavesdropper. The aim is to minimize the estimation error at the receiver under a secrecy constraint at the eavesdropper; or, alternatively, to maximize the estimation error at the eavesdropper for a given estimation accuracy limit at the receiver. In the considered setting, the encoder at the transmitter is allowed to use a randomized mapping between two one-to-one and continuous functions and the eavesdropper is fully aware of the encoding strategy at the transmitter. For small numbers of observations, both the eavesdropper and the receiver are modeled to employ LMMSE estimators, and for large numbers of observations, the ECRB metric is employed for both the receiver and the eavesdropper. Optimization problems are formulated and various theoretical results are provided in order to obtain the optimal solutions and to analyze the effects of encoder randomization. In addition, numerical examples are presented to corroborate the theoretical results. It is observed that stochastic encoding can bring significant performance gains for estimation theoretic secrecy problems. Finally, estimation theoretic secure broadcast of a random parameter is investigated. In the considered setting, each receiver device employs a fixed estimator and carries a certain security risk such that its decision can be available to a malicious third party with a certain probability. The encoder at the transmitter is allowed to use a random mapping to minimize the weighted sum of the conditional Bayes risks of the estimators under secrecy and average power constraints. After formulating the optimal parameter design problem, it is shown that the optimization problem can be solved individually for each parameter value and the optimal mapping at the transmitter involves a randomization among at most three different signal levels. Sufficient conditions for improvability and nonimprovability of the deterministic design via stochastic encoding are obtained. Numerical examples are provided to corroborate the theoretical results.
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.
Embargo
Optimal signal design for coherent detection of binary signals in Gaussian noise under power and secrecy constraints
(Elsevier, 2023-04-13) Dulek, B.; Gezici, Sinan
The problem of optimal signal design for coherent detection of binary signals in Gaussian noise is revisited under power and secrecy constraints. In particular, the aim is to select the binary transmitted signals in an optimal manner so that the probability of error is minimized at an intended receiver while the probability of error at an eavesdropper is maintained above a threshold value and the signal powers are limited. It is shown that an optimal solution exists in the form of antipodal signaling along the eigenvector corresponding to the solution of a maximum (possibly generalized) eigenvalue problem, which is specified explicitly based on the channel coefficient matrices and the noise covariance matrices at the intended receiver and the eavesdropper. Furthermore, optimal signal design can be performed in an efficient manner by solving a semidefinite programming (SDP) relaxation followed by a matrix rank-one decomposition. Numerical examples are provided to illustrate optimal solutions for three different but exhaustive cases.