In this paper we introduce a highly adaptive continuous wavelet transform using Gaussian wavelets multiplied by an appropriate rational term. The zeros and poles of this rational modifier act as free parameters and their choice highly influences the shape of the mother wavelet. This allows the proposed construction to approximate signals with complex morphology using only a few wavelet coefficients. We show that the proposed rational Gaussian wavelets are admissible and provide numerical approximations of the wavelet coefficients using variable projection operators. In addition, we show how the proposed variable projection based rational Gaussian wavelet transform can be used in neural networks to obtain a highly interpretable feature learning layer. We demonstrate the effectiveness of the proposed scheme through a number of numerical experiments including biomedical applications, and the detection of abnormal road surface based on tire sensor signals.

This paper addresses the distributed dissipative estimation problem subject to partial nodes measurements over sensor networks. A novel partial-nodes-based distributed estimation algorithm is proposed to accurately estimate the states across the entire network, even when measurements are only available from a subset of nodes. Moreover, the consensus protocol is employed as the information fusion strategy, enabling local communication among neighboring nodes to drive their estimates toward consensus. Sufficient conditions are derived to guarantee that the estimation error system is asymptotically stable and satisfies the predefined dissipativity performance by applying dynamic stability theory and linear matrix inequality (LMI) technique. Within the established two-dimensional system framework, the consensus update is interpreted into an additional dimension, accompanied by the fundamental estimator update dimension. Therefore, the estimator gain and the consensus gain are decoupled, which can be further designed effectively by making use of the LMI technique. In addition, an adaptive consensus weight scheme is developed to enhance the overall estimation accuracy of the proposed partial-nodes-based estimation algorithm. Finally, simulation examples are provided to demonstrate the validity and applicability of the proposed distributed estimation strategy.

Grant-free transmission and cell-free communication are vital in improving coverage and quality-of-service for massive machine-type communication. This paper proposes a novel framework of joint active user detection, channel estimation, and data detection (JACD) for massive grant-free transmission in cell-free wireless communication systems. We formulate JACD as an optimization problem and solve it approximately using forward-backward splitting. To deal with the discrete symbol constraint, we relax the discrete constellation to its convex hull and propose two approaches that promote solutions from the constellation set. To reduce complexity, we replace costly computations with approximate shrinkage operations and approximate posterior mean estimator computations. To improve active user detection (AUD) performance, we introduce a soft-output AUD module that considers both the data estimates and channel conditions. To jointly optimize all algorithm hyper-parameters and to improve JACD performance, we further deploy deep unfolding together with a momentum strategy, resulting in two algorithms called DU-ABC and DU-POEM. Finally, we demonstrate the efficacy of the proposed JACD algorithms via extensive system simulations.

Independent vector analysis (IVA) is an attractive solution to address the problem of joint blind source separation (JBSS), that is, the simultaneous extraction of latent sources from several datasets implicitly sharing some information. Among IVA approaches, we focus here on the celebrated IVA-G model, that describes observed data through the mixing of independent Gaussian source vectors across the datasets. IVA-G algorithms usually seek the values of demixing matrices that maximize the joint likelihood of the datasets, estimating the sources using these demixing matrices. Instead, we write the likelihood of the data with respect to both the demixing matrices and the precision matrices of the source estimates. This allows us to formulate a cost function whose mathematical properties enable the use of a proximal alternating algorithm based on closed form operators with provable convergence to a critical point. After establishing the convergence properties of the new algorithm, we illustrate its desirable performance in separating sources with covariance structures that represent varying degrees of difficulty for JBSS.

We introduce a nonparametric data-driven classifier that harnesses the statistical properties of the data through the cumulant generating function of the training data. Its implementation is straightforward, requiring only a single tuning parameter. Moreover, it ensures global solutions due to inherent convex optimization. The classifier is explainable, where unexpected or poor results can be interpreted and ameliorated. We derive the properties of the classification statistic, offering insightful observations. We apply the classifier to real-world datasets. The simulation results demonstrate the efficacy of the proposed classifier in signal classification, even in scenarios with mismatched training and testing datasets. Moreover, the results demonstrate that the CGFC has lower computational complexity compared to neural networks.

Over-the-air computation (AirComp) integrates analog communication with task-oriented computation, serving as a key enabling technique for communication-efficient federated learning (FL) over wireless networks. However, owing to its analog characteristics, AirComp-enabled FL (AirFL) is vulnerable to both unintentional and intentional interference. In this paper, we aim to attain robustness in AirComp aggregation against interference via reconfigurable intelligent surface (RIS) technology to artificially reconstruct wireless environments. Concretely, we establish performance objectives tailored for interference suppression in wireless FL systems, aiming to achieve unbiased gradient estimation and reduce its mean square error (MSE). Oriented at these objectives, we introduce the concept of phase-manipulated favorable propagation and channel hardening for AirFL, which relies on the adjustment of RIS phase shifts to realize statistical interference elimination and reduce the error variance of gradient estimation. Building upon this concept, we propose two robust aggregation schemes of power control and RIS phase shifts design, both ensuring unbiased gradient estimation in the presence of interference. Theoretical analysis of the MSE and FL convergence affirms the anti-interference capability of the proposed schemes. It is observed that computation and interference errors diminish by an order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf{\mathcal{O}}\left(\frac{\textbf{1}}{\boldsymbol{N}}\right)$</tex-math></inline-formula> where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> is the number of RIS elements, and the ideal convergence rate without interference can be asymptotically achieved by increasing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula>. Numerical results confirm the analytical results and validate the superior performance of the proposed schemes over existing baselines.

Sensing information can be leveraged to reduce the overheads associated with establishing and maintaining multiple-input and multiple-output (MIMO) communication links. Such information can be acquired from integrated sensing and communication (ISAC) capabilities. In this paper, we use sensing information to make precoding for spatial multiplexing more robust in high-dynamic environments with both quasi-static and mobile scattering objects. The significant variability of scattered paths requires frequent reconfigurations of the precoding matrices. To address this, we propose a sensing-aided precoding scheme for channels with high dynamics, leveraging the identification and localization of moving targets to concentrate energy mainly on slow-varying paths. Specifically, the geometric structure of the time-varying channel matrix is analyzed to uncover deviations in the location parameters of moving targets. A channel division criterion is then devised to partition the channel matrix into two matrices characterizing the paths of background scatterers and moving targets, respectively. Exploiting the digital-analog dual orthogonality between these matrices, precoding and combining matrices are jointly designed to suppress transmission leakage over mobile paths in both analog and digital domains. Numerical simulations validate that the proposed method achieves high spectral efficiency without requiring explicit channel tracking, thereby reducing complexity and overheads compared to conventional MIMO precoding methods.

In this paper, the channel estimation problem for extremely large-scale multi-input multi-output (XL-MIMO) systems is investigated with the considerations of near-field (NF) spherical wavefront effects and spatially non-stationary (SnS) properties. Due to the diversity of SnS characteristics across different propagation paths, the concurrent channel estimation of multiple paths becomes intractable. To address this challenge, we propose a two-phase estimation scheme that decouples the problem into multiple subchannel estimation tasks. To solve these sub-tasks, we introduce a novel three-layer Bayesian inference scheme, exploiting the correlations and sparsity of the SnS subchannels in both the spatial and angular domains. Specifically, the first layer captures block sparsity in the angular domain, the second layer promotes SnS properties in the spatial domain, and the third layer effectively decouples each subchannel from the observed signal. To enable efficient Bayesian inference, we develop a three-layer generalized approximate message passing (TL-GAMP) algorithm that combines structured variational message passing with belief propagation rules. Simulation results validate the convergence and effectiveness of the proposed TL-GAMP algorithm, demonstrating its robustness across various channel environments, including NF-SnS, NF spatially stationary (NF-SS), and far-field spatially stationary (FF-SS) scenarios.

We revisit two fundamental decentralized optimization methods, Decentralized Gradient Tracking (DGT) and Decentralized Gradient Descent (DGD), with multiple local updates. We consider two settings and demonstrate that incorporating local update steps can reduce communication complexity. Specifically, for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>-strongly convex and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L$</tex-math></inline-formula>-smooth loss functions, we proved that local DGT achieves communication complexity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\tilde{\mathcal{O}}\Big{(}\frac{L}{\mu(K+1)}+\frac{\delta+{}{\mu}}{\mu(1-\rho)}+\frac{\rho}{(1-\rho)^{2}}\cdot\frac{L+\delta}{\mu}\Big{)}$</tex-math></inline-formula>, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> is the number of additional local update, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\rho$</tex-math></inline-formula> measures the network connectivity and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> measures the second-order heterogeneity of the local losses. Our results reveal the tradeoff between communication and computation and show increasing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> can effectively reduce communication costs when the data heterogeneity is low and the network is well-connected. We then consider the over-parameterization regime where the local losses share the same minimums. We proved that employing local updates in DGD, even without gradient correction, achieves exact linear convergence under the Polyak-Łojasiewicz (PL) condition, which can yield a similar effect as DGT in reducing communication complexity. Customization of the result to linear models is further provided, with improved rate expression. Numerical experiments validate our theoretical results.

In this paper, we generalize the concepts of kernels, weak stationarity and white noise from undirected to directed graphs (digraphs) based on the Jordan decomposition of the shift operator. We characterize two types of kernels (type-I and type-II) and their corresponding localization operators for digraphs. We analytically study the interplay of these types of kernels with the concept of stationarity, specially the filtering properties. We also generalize graph Wiener filters and the related optimization framework to digraphs. For the special case of Gaussian processes, we show that the Wiener filtering again coincides with the MAP estimator. We further investigate the linear minimum mean-squared error (LMMSE) estimator for the non-Gaussian cases; the corresponding optimization problem simplifies to a Lyapunov matrix equation. We propose an algorithm to solve the Wiener optimization using proximal splitting methods. Finally, we provide simulation results to verify the provided theory.