Future wireless systems are envisioned to utilize the large spectra available at THz bands for wireless communications. Extremely massive multiple-input multiple-output (MIMO) antennas can be costly and power inefficient for wideband THz communications. An alternative antenna technology, which can achieve low-cost and power-efficient THz signaling, is based on leaky wave antennas (LWAs). In this paper, we explore the usage of the LWAs for wideband downlink multi-user THz communications. We propose a model for LWA-aided communication systems that faithfully captures the antenna operations. We show that LWAs yield frequency-dependent beams, where the equivalent wideband channel induces a dependence between angle, frequency, and spectral lobe width. We identify the LWA’s inherent frequency-selective beamsteering capabilities as motivating multi-band THz communications, in which subbands are allocated among users based on their relative angles. Then, we propose an alternating optimization algorithm for jointly optimizing the LWA configuration along with the spectral division and power allocation to maximize the achievable sum rate performance. Our numerical results show that a single LWA can generate diverse beampatterns, exhibiting performance comparable to costly MIMO architectures in wideband THz multi-user systems.

Integrating deep neural networks (DNNs) into wireless receivers can enhance reliability in the presence of hard-to-model channels. However, in order to successfully deploy deep receivers, one must address the rapid channel variations while accounting for the limited availability of data and computing resources. This paper presents a novel framework for rapid online learning of deep receivers that builds on continual Bayesian learning. By modeling the channel variations as a dynamic system in the space of DNN model parameters, we enable efficient single-step updates, supporting the rapid training of Bayesian DNNs using limited data. We propose two online learning algorithms based on extended Kalman filtering and on Bayesian gradients. Unlike typical approaches that avoid catastrophic forgetting, our methods prioritize adapting to current channel realization. Numerical results show that the proposed continual Bayesian learning formulation yields deep receivers that can effectively adapt to varying channels with minimal computational overhead.

In this paper, we consider Bayesian parameter estimation in systems incorporating both analog and 1-bit quantized measurements. We develop a tractable form of the Bayesian Cram$\acute{\text{e}}$r-Rao Bound (BCRB) tailored for the linear-Gaussian mixed-resolution scheme. We discuss the properties of the BCRB and examine its limitations as a system design tool. In addition, we present the partially-numeric minimum-mean-squared-error (MMSE) and linear MMSE (LMMSE) estimators with a general quantization threshold. In our simulations, the BCRB is compared with the mean-squared-errors (MSEs) of the estimators for channel estimation with mixed analog-to-digital converters. The results demonstrate that the BCRB is not a tight lower bound, and it fails to accurately capture the non-monotonic behavior of the estimators' MSEs versus signal-to-noise-ratio (SNR) and their behavior regarding different resource allocations. Consequently, while the BCRB provides some valuable insights on the quantization threshold, our results demonstrate that it is not suitable as a practical tool for system design in mixed-resolution settings.

Sparse graph signals have recently been utilized in graph signal processing (GSP) for tasks such as graph signal reconstruction, blind deconvolution, and sampling. In addition, sparse graph signals can be used to model real-world network applications across various domains, such as social, biological, and power systems. Despite the extensive use of sparse graph signals, limited attention has been paid to the derivation of theoretical guarantees on their recovery. In this paper, we present a novel theoretical analysis of the problem of recovering a node-domain sparse graph signal from the output of a first-order graph filter. The graph filter we study is the Laplacian matrix, and we derive upper and lower bounds on its mutual coherence. Our results establish a connection between the recovery performance and the minimal graph nodal degree. The proposed bounds are evaluated via simulations on the Erdős-Rényi graph.

The Laplacian-constrained Gaussian Markov Random Field (LGMRF) is a common multivariate statistical model for learning a weighted sparse dependency graph from given data. This graph learning problem can be formulated as a maximum likelihood estimation (MLE) of the precision matrix, subject to Laplacian structural constraints, with a sparsity-inducing penalty term. This paper aims to solve this learning problem accurately and efficiently. First, since the commonly used $\ell_1$-norm penalty is inappropriate in this setting and may lead to a complete graph, we employ the nonconvex minimax concave penalty (MCP), which promotes sparse solutions with lower estimation bias. Second, as opposed to existing first-order methods for this problem, we develop a second-order proximal Newton approach to obtain an efficient solver, utilizing several algorithmic features, such as using conjugate gradients, preconditioning, and splitting to active/free sets. Numerical experiments demonstrate the advantages of the proposed method in terms of both computational complexity and graph learning accuracy compared to existing methods.

In this paper, we address the problem of tracking dynamic changes in graph topology under a linear graph filtering random process. We propose a graph-based state-space model (SSM), where the measurements are graph signals and the underlying evolving topology serves as the state variable. The proposed approach is based on representing the graphical process as a graph filtering process, and leveraging the incidence matrix-based representation of the Laplacian to formulate the linear SSMs associated with the Kalman filter. We explore two scenarios. In the first scenario, we have a known edge set, and we aim to track the network weights. We show that under suitable reformulation, this scenario can be solved by the classical Kalman filter. In the second scenario, we assume an unknown edge set, where the goal is to track both network connectivity changes and the weights. We discuss three Kalman-filter-based approaches for this scenario by incorporating sparsity-driven techniques: 1) an ignorant Kalman filter that processes the entire signal; 2) a Kalman filter with thresholding of the predicted graph at each iteration; and 3) partial-thresholding, where the estimator update occurs without thresholding. The simulation results demonstrate the performance of the proposed approaches in tracking changes in graph topologies.

THz communications are expected to play a profound role in future wireless systems. The current trend of the extremely massive multiple-input multiple-output (MIMO) antenna architectures tends to be costly and power inefficient when implementing wideband THz communications. An emerging THz antenna technology is leaky wave antenna (LWA), which can realize frequency selective beamforming with a single radiating element. In this work, we explore the usage of LWAs technology for wideband multi-user THz communications. We propose a model for the LWA signal processing that is physically compliant facilitating studying LWA-aided communication systems. Focusing on downlink systems, we propose an alternating optimization algorithm for jointly optimizing the LWA configuration along with the signal spectral power allocation to maximize the sum-rate performance. Our numerical results show that a single LWA can generate diverse beampatterns at THz exhibiting performance comparable to costly fully digital MIMO arrays.

In this paper, we consider the problem of estimating the admittance matrix in power systems, accounting for Laplacian and physical constraints. We assume the nonlinear alternating current (AC) model, which accurately represents the power flow model. We develop a closed-form expression for the oracle Cramér-Rao bound (CRB) on the mean-squared-error (MSE) of any unbiased estimator of the admittance matrix. The proposed oracle CRB takes into account the Laplacian parametric equality constraints, including symmetry and the null space property, through a reparametrization of the estimation problem as an unconstrained optimization. The oracle CRB assumes knowledge of the locations of the nonzero entries of the Laplacian matrix, and, thus, provides a valid lower bound. We evaluate and compare the oracle CRB with the MSE of: 1) the constrained maximum likelihood estimator (CMLE), which integrates the equality, inequality, and jointsparsity Laplacian constraints; and 2) the oracle CML estimator, which knows the location of the nonzero entries of the Laplacian matrix. It is shown that for data from the IEEE 33-bus power system, the MSEs of the estimators converge to the oracle CRB for a sufficient number of measurements.

In many practical parameter estimation problems, the observation model is periodic with respect to the unknown parameters. In these cases, the appropriate estimation criterion is periodic in the parameter space, and cyclic performance bounds should be used. However, existing cyclic performance bounds do not account for the common scenario of model misspecification. The misspecified Cramér-Rao bound (MCRB) provides a lower bound on the mean-squared-error (MSE) for estimation problems under model misspecification. However, the MCRB does not provide a valid bound for periodic problems. In this paper, we close this gap by developing the cyclic MCRB, which is a lower bound on the mean cyclic error (MCE) of any Lehmann unbiased estimator under model misspecification in periodic estimation problems. Thus, it can be seen as a generalization of the cyclic CRB for cases where the assumed model (observations distribution) may be different from the true one. The proposed cyclic MCRB and the performance of the misspecified maximum likelihood (MML) estimator are compared in terms of MCE in direction-of-arrival (DOA) estimation under the misspecified assumption of white additive noise, where the true covariance is colored.

In many practical parameter estimation problems, such as phase, frequency, and direction-of-arrival (DOA) estimation, the observation model is periodic with respect to the unknown parameters, and thus, the appropriate estimation criterion is periodic in the parameter space. However, iterative estimation methods, such as the Fisher-Scoring method, do not take into consideration the periodic information in order to improve the accuracy of the estimation. In this paper, we present a new iterative method - periodic Fisher-Scoring, which takes into account the signal’s periodic properties through the utilization of the cyclic Cramér-Rao bound (CRB). The cyclic CRB is a lower bound on the mean cyclic error (MCE) of unbiased estimators and, thus, is more appropriate for the derivation of the iterative method. In addition, the periodic Fisher-Scoring method uses the modulo $2 \pi$ operator at each iteration. Simulation results for DOA estimation in seismic arrays show that the proposed periodic Fisher-Scoring estimator has a lower MCE compared to the conventional Fisher-Scoring estimator. The performance improvement is more significant around the edges of the range $[-\pi,\pi]$ and under the misspecified model, i.e. under the mismatched assumption of white noise. We also show that the periodic Fisher-Scoring estimator achieves the cyclic CRB much faster than the CRB.

The Kalman filter (KF) is a widely-used algorithm for tracking dynamical systems that can be faithfully captured by state space (SS) models. The need to fully describe an SS model limits its applicability under complex settings, e.g., when tracking based on visual or graphical data. This challenge can be treated by mapping the measurements into latent features obeying some postulated closed-form SS model, and applying the KF in the latent space. However, the validity of this approximated SS model may constitute a limiting factor. In this work we tackle the challenges associated with tracking from high-dimensional measurements by jointly learning the KF along with the latent space mapping. Our proposed approach combines a learned encoder while tracking in the latent space using the recently proposed data-driven Kalman-Net, and having both modules jointly tuned from data. Our empirical results demonstrate that the proposed approach achieves improved performance over both model-based and data-driven techniques, by learning a surrogate latent representation that most facilitates tracking.

We consider the problem of recovering random, time-varying graph processes in a nonlinear dynamic system. The Extended Kalman filter (EKF) is a suitable estimator for such dynamics, but its implementation tends to be complex and possibly unstable when tracking high-dimensional graph signals. To tackle this, we propose the graph signal processing (GSP)-EKF, which replaces the Kalman gain in the EKF with a graph filter that aims to minimize the computed prediction error. The resulting structure of the GSP-EKF Kalman gain increases the numerical stability and reduces the computational burden compared with the standard EKF, particularly when dealing with bandlimited graph processes. We show that for a measurement model with orthogonal graph frequencies, the GSP-EKF coincides with the EKF. The GSP-EKF is evaluated for graph signal tracking in power system state estimation. It is shown that in this case, the proposed GSP-EKF 1) attains the EKF under the accurate model; and 2) outperforms the EKF under a model mismatch, while being notably less complex in both cases.

We consider the task of estimating a network cascade as fast as possible. The cascade is assumed to spread according to a general Susceptible-Infected process with heterogeneous transmission rates from an unknown source in the network. While the propagation is not directly observable, noisy information about its spread can be gathered through multiple rounds of error-prone diagnostic testing. We propose a novel adaptive procedure which quickly outputs an estimate for the cascade source and the full spread under this observation model. Remarkably, under mild conditions on the network topology, our procedure is able to estimate the full spread of the cascade in an n-vertex network, before poly log n vertices are affected by the cascade. We complement our theoretical analysis with simulation results illustrating the effectiveness of our methods.

Admittance matrix estimation in power networks enables faster control actions following emergency scenarios, energy-saving, and other economic and security advantages. In this paper, our goal is to estimate the network admittance matrix, i.e. to learn connectivity and edge weights in the graph representation, under physical and Laplacian constraints. We use the nonlinear AC power flow measurement model, which is based on Kirchhoff’s and Ohm’s laws, with power and voltage phasor measurements. In order to recover the complex-valued admittance matrix, we formulate the associated constrained maximum likelihood (CML) estimator as the solution of a constrained optimization problem with Laplacian and sparsity constraints. We develop an efficient solution using the associated alternating direction method of multipliers (ADMM) algorithm with an ℓ1relaxation. The ADMM algorithm is shown to outperform existing methods in the task of recovering the IEEE 14-bus test case.

The Cramér-Rao bound (CRB) has been extensively used as a benchmark for estimation performance in both Bayesian and non-Bayesian frameworks. In many practical periodic parameter estimation problems, such as phase, frequency, and direction-of-arrival estimation, the observation model is periodic with respect to the unknown parameters and thus, the appropriate criterion is periodic in the parameter space. Consequently, the widely-used Bayesian lower bounds on the mean-squared-error (MSE) are not valid bounds for periodic estimation problems. In addition, many Bayesian MSE lower bounds cannot be derived in the periodic case due to their restrictive regularity conditions. For example, the regularity conditions of the Bayesian CRB (BCRB) are not satisfied for parameters with uniform prior distribution. In this letter, we derive a Bayesian Cramér-Rao-type lower bound on the mean-squared-periodic-error (MSPE). The proposed periodic BCRB (PBCRB) is a lower bound on the MSPE of any estimator and has less restrictive regularity conditions compared to the BCRB. The PBCRB is compared with the MSPE of the minimum MSPE estimator for phase estimation in Gaussian noise and it is shown that the PBCRB is a valid and tight lower bound for this problem.

In this letter, we consider Bayesian parameter estimation using mixed-resolution data consisting of both analog and 1-bit quantized measurements. We investigate the use of the partially linear minimum mean-squared-error (PL-MMSE) estimator for this mixed-resolution scheme. The use of the PL-MMSE estimator, proposed for general models with ``straightforward" and ``complicated" parts, has not been demonstrated for quantized data. We derive closed-form analytic expressions for the linear minimum mean-squared-error (LMMSE) and for the PL-MMSE estimator for the mixed-resolution scheme with linear Gaussian orthonormal measurements. We discuss the properties of the proposed PL-MMSE estimator and show that in this case, the PL-MMSE is the sum of a linear function of the quantized measurements and a general Borel measurable function of the analog measurements. In the simulations, we show that the PL-MMSE estimator outperforms the LMMSE estimator for the problem of channel estimation in multiple-input-multiple-output (MIMO) communication systems with mixed analog-to-digital converters (ADCs).

Estimation after model selection refers to the problem where the exact observation model is unknown and is assumed to belong to a set of candidate models. Thus, a data-based model-selection stage is performed prior to the parameter estimation stage, which affects the performance of the subsequent estimation. In this letter, we investigate post-model-selection Bayesian parameter estimation of a random vector with an unknown deterministic support set, where this support set represents the model. First, we present different estimators, including the oracle minimum mean-squared-error (MMSE), the coherent MMSE, the selected MMSE, and the full model MMSE. Then, we develop the selective Bayesian Cramer-Rao bound (BCRB) and selective tighter BCRB, which are lower bounds on the mean-squared-error (MSE) for any coherent estimator.

The constrained Cramér-Rao bound (CCRB) is a benchmark for constrained parameter estimation. However, the CCRB unbiasedness conditions are too strict and thus, the CCRB may not be a lower bound for estimators under constraints. The recently developed Lehmann-unbiased-CCRB (LU-CCRB) was shown to be a lower bound for the commonly used constrained maximum likelihood (CML) estimator performance in cases where the CCRB is not. In constrained parameter estimation, the estimator is usually required to satisfy the constraints. However, the LU-CCRB is a lower bound for Lehmann-unbiased estimators that do not necessarily satisfy the constraints. In this letter, we consider the norm constraint and derive a novel bound, called norm-constrained CCRB (NC-CCRB), which is a lower bound on the mean-squared-error matrix trace of Lehmann-unbiased estimators that satisfy the norm constraint. The NC-CCRB is shown to be tighter than the LU-CCRB. In the simulations, we consider a linear estimation problem under norm constraint in which the proposed NC-CCRB better predicts the performance of the CML estimator than the CCRB trace and the LU-CCRB.

In many stochastic filtering problems, some of the states have periodic nature, i.e. the observation model is periodic with respect to these states. For estimation of these periodic states, we are interested in the modulo- T error and not in the plain error value. Thus, in this case, the commonly-used Bayesian mean-squared-error (MSE) lower bounds are inappropriate for performance analysis, since the MSE risk is based on the plain error and is inappropriate for periodic state estimation. In contrast, the mean-cyclic-error (MCE) is an appropriate risk for estimation of periodic states. In a mixed periodic and nonperiodic setting, a mixed MCE and MSE lower bound can be useful for performance analysis and design of filters. In this paper, we present the mixed Bayesian Cramér-Rao bound (BCRB) for stochastic filtering. The mixed BCRB is composed of a cyclic part and a noncyclic part for estimation of the periodic and the nonperiodic states, respectively. Direct computation of the mixed BCRB is not practical, since it requires matrix inversion, whose dimensions increase with time. Therefore, we propose a recursive method with low computational complexity for computation of the mixed BCRB at each time step. The mixed BCRB is examined for direction-of-arrival tracking scenarios and compared to the performance of a particle filter. It is shown that in the considered scenarios the mixed BCRB is informative and can be approached by the particle filter. In addition, the inappropriateness of MSE bounds for estimation of periodic states is demonstrated.

Mean-squared-error (MSE) lower bounds are commonly used for performance analysis and system design. Recursive algorithms have been derived for computation of Bayesian bounds in stochastic filtering problems. In this letter, we consider stochastic filtering with a mixture of periodic and nonperiodic states. For periodic states, the modulo- T estimation error is of interest and the MSE lower bounds are inappropriate. Therefore, in this case, the mean-cyclic error and the MSE risks are used for estimation of the periodic and nonperiodic states, respectively. We derive a Bobrovsky-Zakai-type bound for mixed periodic and nonperiodic stochastic filtering. Then, we derive a recursive computation method for this bound in order to allow its computation in dynamic settings. The proposed recursively-computed mixed Bobrovsky-Zakai bound is useful for the design and performance analysis of filters in stochastic filtering problems with both periodic and nonperiodic states. This bound is evaluated for a target tracking example and is shown to be a valid and informative bound for particle filtering performance.

This paper deals with non-Bayesian parameter estimation under the mean-squared-error (MSE), which is a topic of great interest in various engineering fields. Although the unbiasedness condition is commonly used in non-Bayesian MSE estimation, in many cases biased estimation may result in better performance. However, no method for determining the optimal bias function in general cases is available. We propose a new approach for uniform minimum MSE biased estimation, where the optimal bias is chosen in accordance with Lehmann-unbiasedness definition. The proposed approach is based on modifying the MSE risk by its multiplication with a weighting function of the unknown parameter, g2. Under this modified risk, Lehmann's definition of unbiasedness provides a condition referred to as g-unbiasedness. By using the g-unbiasedness, we derive a novel Cramér-Rao-type lower bound on the MSE of locally g-unbiased estimators. In addition, we show that if there exists an estimator that achieves the new bound, then it is produced by the penalized maximum likelihood estimator with a penalty function log g. Simulations show that the proposed approach can lead to non-trivial estimators with lower MSE than existing mean-unbiased estimators.

In many practical parameter estimation problems, a model selection is made prior to estimation. In this paper, we consider the problem of estimating an unknown parameter of a selected population, where the population is chosen from a population set by using a predetermined selection rule. Since the selection step may have an important impact on subsequent estimation, ignoring it could lead to biased-estimation and an invalid Cramér-Rao bound (CRB). In this work, the mean-square-selected-error (MSSE) criterion is used as a performance measure. The concept of Ψ-unbiasedness is introduced for a given selection rule, Ψ, by using the Lehmann-unbiasedness definition. We derive a non-Bayesian Cramér-Rao-type bound on the MSSE of any Ψ-unbiased estimator. The proposed Ψ-CRB is a function of the conditional Fisher information and is a valid bound on the MSSE. Finally, we examine the Ψ-CRB for different selection rules for mean estimation in a linear Gaussian model.

The problem of joint off-nominal frequency and phasor estimation in an unbalanced three-phase power system using a phasor measurement unit (PMU) is considered. Voltage unbalance arises when magnitudes are different from each other or when phases are unequally spaced. A general model for the zero, positive, and negative sequences from a PMU measurement at off-nominal frequencies is presented. Then, the maximum likelihood (ML) estimator is developed under an unbalanced condition for joint symmetrical components phasors and frequency estimation. Finally, a low complexity technique is developed for the estimation of frequency deviation based a new autoregressive (AR) representation of the innovation process for the symmetrical component.

We consider the problem of estimating two deterministic vectors in a linear Gaussian model where one of the unknown vectors is subject to a sparsity constraint. We derive the maximum likelihood estimator for this problem and develop the Projected Orthogonal Matching Pursuit (POMP) algorithm for its practical implementation. The corresponding constrained Cramér-Rao bound (CCRB) on the mean-square-error is developed under the sparsity constraint. We then show that estimation in linear dynamical systems with a sparse control can be formulated as a special case of this problem.

In this letter, we consider the problem of joint off-nominal frequency and phasor estimation that incorporates Kirchhoff's Current Law (KCL) as a constraint. We develop the constrained maximum likelihood (CML) and constrained weighted least-squares (CWLS) estimators for this problem and derive the corresponding constrained Cramér-Rao bound. The KCL constraint is shown to behave as a noise cancellation factor for the phasors estimation. We show that the KCL CML is based on the classical periodogram subtracting the average current periodogram. The results indicate significant performance improvement compared to the unconstrained maximum likelihood (ML) and unconstrained weighted least-squares (WLS).

In many practical parameter estimation problems, the appropriate criterion is periodic in the parameter space. This paper considers the mean square periodic error (MSPE) criterion combined with periodic unbiasedness for which the conventional Cramer-Rao bound (CRB) does not provide a valid bound. The periodic unbiasedness is defined using the Lehmann-unbiasedness concept, and a Cramer-Rao type bound on the MSPE of any periodic unbiased estimator is derived. The proposed bound and performance of some periodic unbiased estimators for phase estimation problem are compared in terms of MSPE in a phase estimation problem with Gaussian noise.

The problem of blind source separation (BSS) for multiple-input multiple-output (MIMO) autoregressive (AR) mixtures is addressed in this paper. A new time-domain method for system identification and BSS is proposed based on the Gaussian mixture model (GMM) for sources distribution. The algorithm is based on the generalized expectation-maximization (GEM) method for joint estimation of the AR model parameters and the GMM parameters of the sources. The method is tested via simulations of synthetic and real audio signals. The results show that the proposed algorithm outperforms the well-known multidimensional linear predictive coding (LPC), and it achieves higher signal-to-interference ratio (SIR) in the BSS problem.