Time and power allocation for the Gaussian wiretap channel with feedback of secret keys

This paper solves the time and power allocation problem for the simplest feedback scheme for the Gaussian wiretap channel, which is based on the transmission of random secret keys to be used in a one time pad manner. Specifically, the optimal transmission powers at Alice and Bob, as well as the time sharing factor between the feedback and feedforward channels, are given by the solution of a non-convex optimization problem, which is found by means of the golden section algorithm and the sequential solution of several convex optimization problems. Additionally, an specific and highly efficient procedure for the solution of the inner convex optimization problems is provided, which avoids the need for general purpose optimization packages. Finally, several simulation results illustrate the potential secrecy gains achievable with a feedback scheme as simple as the one considered in this paper

Robust secret key capacity for the MIMO induced source model

This paper considers the problem of distilling a secret key in a Gaussian multiple-input multiple-output (MIMO) scenario with two legitimate nodes and an eavesdropper. Focusing on the realistic case without perfect knowledge of the eavesdropper channel, and following a conservative practical approach based on the maximization of the worst case secret key capacity (SKC), the problem of designing the optimal transmit covariance matrix is reformulated as a convex optimization problem. In the limiting case in which the eavesdropper channel can not be estimated, or when the estimate is highly unreliable, the optimal covariance matrix can be obtained by means of waterfilling or matched filtering like algorithms. Additionally, we illustrate the benefits of allowing time sharing between transmissions of the two legitimate nodes, and provide an efficient algorithm for obtaining the optimal transmit covariance matrices and time-sharing factor.This work was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under projects COSIMA (TEC2010-19545-C04-03) and COMONSENS (CSD2008-00010, CONSOLIDER INGENIO 2010 Program)

Antenna grouping for general discriminatory channel estimation

Discriminatory channel estimation emerges as a promising method of not only increasing the secrecy rates in conventional wiretap channels, but also providing a valuable tool for solving the authentication problem. In this paper, we revisit the discriminatory channel estimation method by Chang et al. and propose a generalization to the challenging scenario in which the number of antennas at the legitimate receiver equals or exceeds those of the transmitter. The proposed method is based on the simple idea of dividing the receiver antennas into smaller groups. However, the direct application of previous approaches would result into security problems due to the multiple observations of the eavesdropper, and therefore the transmission system needs to be designed taking this fact into account. The performance of the proposed technique is illustrated by means of some numerical examples, which clearly show the feasibility of discriminatory channel estimation even in the case of systems with more antennas at the receiver side.This work has been supported by the Spanish Government, Ministerio de Ciencia e Innovación, under project RACHEL (TEC2013-47141-C4-3-R)

Sparse multivariate Gaussian mixture regression

Fitting a multivariate Gaussian mixture to data represents an attractive, as well as challenging problem, in especial when sparsity in the solution is demanded. Achieving this objective requires the concurrent update of all parameters (weight, centers, and precisions) of all multivariate Gaussian functions during the learning process. Such is the focus of this paper, which presents a novel method founded on the minimization of the error of the generalized logarithmic utility function (GLUF). This choice, which allows us to move smoothly from the mean square error (MSE) criterion to the one based on the logarithmic error, yields an optimization problem that resembles a locally convex problem and can be solved with a quasi-Newton method. The GLUF framework also facilitates the comparative study between both extremes, concluding that the classical MSE optimization is not the most adequate for the task. The performance of the proposed novel technique is demonstrated on simulated as well as realistic scenarios

Balanced Least Squares: Linear model estimation with noisy inputs

This paper focuses on a linear model with noisy inputs in which the performance of the conventional Total Least Squares (TLS) approach is (maybe surprisingly) far from satisfactory. Under the typical Gaussian assumption, we obtain the maximum likelihood (ML) estimator of the system response. This estimator promotes a reasonable balance between the empirical and theoretical variances of the residual errors, which suggests the name of Balanced Least Squares (BLS). The solution of the associated optimization problem is based on its reformulation as a rank constrained semidefinite program (SDP), for which we show that the relaxation is tight with probability one. Both TLS and BLS can be seen as regularized LS estimators, but the (possibly negative) regularization in BLS is softer than its TLS counterpart, which avoids the inconsistency of TLS in our particular model.This work has been supported by the Spanish Government, Ministerio de Ciencia e Innovación, under project RACHEL (TEC2013-47141-C4-3-R)

Testing quaternion properness: generalized likelihood ratios and locally most powerful invariants

This paper considers the problem of determining whether a quaternion random vector is proper or not, which is an important problem because the structure of the optimal linear processing depends on the specific kind of properness. In particular, we focus on the Gaussian case and consider the two main kinds of quaternion properness, which yields three different binary hypothesis testing problems. The testing problems are solved by means of the generalized likelihood ratio tests (GLRTs) and the locally most powerful invariant tests (LMPITs), which can be derived even without requiring an explicit expression for the maximal invariant statistics. Some simulation examples illustrate the performance of the proposed tests, which allows us to conclude that, for moderate sample sizes, it is advisable to use the LMPITs.This work was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under projects COSIMA (TEC2010-19545-C04-03) and COMONSENS (CSD2008-00010, CONSOLIDERINGENIO 2010 Program)

Balanced least squares: estimation in linear systems with noisy inputs and multiple outputs

This paper revisits the linear model with noisy inputs, in which the performance of the total least squares (TLS) method is far from acceptable. Under the assumption of Gaussian noises, the maximum likelihood (ML) estimation of the system response is reformulated as a general balanced least squares (BLS) problem. Unlike TLS, which minimizes the trace of the product between the empirical and inverse theoretical covariance matrices, BLS promotes solutions with similar values of both the empirical and theoretical error covariance matrices. The general BLS problem is reformulated as a semidefinite program with a rank constraint, which can be relaxed in order to obtain polynomial time algorithms. Moreover, we provide new theoretical results regarding the scenarios in which the relaxation is tight, as well as additional insights on the performance and interpretation of BLS. Finally, some simulation results illustrate the satisfactory performance of the proposed method.This work has been supported by the Spanish Government, Ministerio de Ciencia e Innovación, under project RACHEL (TEC2013-47141-C4-3-R

Node activity monitoring in heterogeneous networks using energy sensors

In Heterogeneous Networks, small cells are usually deployed without operator supervision. Their proper operation highly depends on their self-adaptation capability, especially in dense HetNets where various small cells coexist in the same macrocell. This capability requires the small-cell base stations to continuously sense the radio environment, so they can dynamically adapt their operational setting (e.g. transmission power, carrier/channel selection, etc.) to the environmental conditions. In this work we propose a new method for a small base station to monitor the activity of the rest of nodes in the macrocell. We consider a centralized sensing procedure based on the fusion of the energy levels measured by the users of the small cell at their locations. In particular, we present an efficient algorithm that enables the small base station to monitor the activity of the rest of nodes. In addition, the algorithm also provides the gain of the channels between the nodes and the users of the small cell.This work has been funded by the Ministerio de Economía, Industria y Competitividad (MINECO) of Spain under grant TEC2017-86921-C2-1-R (CAIMAN) and under the KERMES Network (TEC2016-81900-REDT/AEI)

Adaptive EM-based algorithm for cooperative spectrum sensing in mobile environments

In this work we propose a new adaptive algorithm for cooperative spectrum sensing in dynamic environments where the channels are time varying. We assume a cooperative sensing procedure based on the soft fusion of the signal energy levels measured at the sensors. The detection problem is posed as a composite hypothesis testing problem. Then, we consider the Generalized Likelihood Ratio Test approach where the maximum likelihood estimate of the unknown parameters (which are the signal-to-noise ratio under the different hypotheses) are obtained from the most recent energy levels at the sensors by means of the Expectation-Maximization algorithm. We derive simple closed-form expressions for both, the E and the M steps. The algorithm can operate even when only a subset of sensors report their energy estimates, which makes it suited to be used with any sensor selection strategy (active sensing). Simulation results show the feasibility and efficiency of the method in realistic slow-fading environments.This work has been funded by SODERCAN and Programa Operativo FEDER under grant CAIMAN - 12.JU01.64661, and by the Ministerio de Economía, Industria y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U., under grants TEC2017-86921-C2-1-R (CAIMAN), TEC2013-47141-C4-R (RACHEL) and TEC2016-75067- C4-4-R (CARMEN)

Adaptive kernel canonical correlation analysis algorithms for nonparametric identification of Wiener and Hammerstein systems

This paper treats the identification of nonlinear systems that consist of a cascade of a linear channel and a nonlinearity, such as the well-known Wiener and Hammerstein systems. In particular, we follow a supervised identification approach that simultaneously identifies both parts of the nonlinear system. Given the correct restrictions on the identification problem, we show how kernel canonical correlation analysis (KCCA) emerges as the logical solution to this problem.We then extend the proposed identification algorithm to an adaptive version allowing to deal with time-varying systems. In order to avoid overfitting problems, we discuss and compare three possible regularization techniques for both the batch and the adaptive versions of the proposed algorithm. Simulations are included to demonstrate the effectiveness of the presented algorithm