While it becomes more challenging to improve the energy efficiency of incremental delta-sigma data converters (IDCs) from the analog circuit design perspective, we propose two novel linear reconstruction filters for IDCs to enhance their performance in a digital way, including the L ${}_{\mathbf{2}}$ min ${}^{\mathbf{2}}$ filter and its symmetric version, the L ${}_{\mathbf{2}}$ min ${}^{\mathbf{2s}}$

Multichannel frequency estimation with incomplete data and miscellaneous noises arises in array signal processing, modal analysis, wireless communications, and so on. In this paper, we consider maximum-likelihood(-like) optimization methods for frequency estimation in which proper objective functions are adopted subject to observed data patterns and noise types. We propose a universal signal-domain

A multiple distributed subarray (MDS) system usually transmits the raw data to the fusion center (FC), where the target detection and localization can be processed. Transmitting raw data requires large bandwidth and is power-consuming, so that technologies such as one-bit analog-to-digital converters (ADCs) have been applied to reduce the volume of data. This paper focuses on the detection and localization

In this article, we present a maximum a posteriori (MAP) based framework to deal with the challenging problem of joint fundamental frequency and order estimation for harmonic signal corrupted by impulsive noise, which is modeled as Gaussian noise contaminated by outliers. In the proposed method, parameters including the fundamental frequency (subject to possible scaling), noise variance, signal waveform

To solve the estimation problem in three-dimensional space, the quaternion Kalman filter (QKF) is developed for quaternion-valued signals using the well-known minimum mean square error (MMSE) criterion under the Gaussian assumption. However, when the system is disturbed by some non-Gaussian impulsive noises, the performance of QKF will be degraded significantly. To address this issue, this paper first

We consider probabilistic models for sequential observations which exhibit gradual transitions among a finite number of states. We are particularly motivated by applications such as human activity analysis where observed accelerometer time series contains segments representing distinct activities, which we call pure states , as well as periods characterized by continuous transition among these pure

Counter-adversarial system design problems have lately motivated the development of inverse Bayesian filters. For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary’s Kalman-filter-tracked estimates and hence, predict the adversary’s future steps. The purpose of this paper and the companion paper (Part I) is to address the inverse filtering problem in non-linear

We consider adaptive detection of a Gaussian rank-one component known up to a scaling factor buried in Gaussian noise with unknown statistics, a problem which arises when detecting Swerling I targets in radar systems. From the joint distribution of the samples under test and the training samples, the score function and the Fisher information matrix are derived, which enables us to formulate the Rao

Recent advances in counter-adversarial systems have garnered significant research attention to inverse filtering from a Bayesian perspective. For example, interest in estimating the adversary’s Kalman filter tracked estimate with the purpose of predicting the adversary’s future steps has led to recent formulations of inverse Kalman filter (I-KF). In this context of inverse filtering, we address the

We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian processes that are implemented via random feature-based Gaussian processes. In these models, we have two sets of unknowns, highly nonlinear unknowns (the values

Scattering networks on Euclidean domains are capable of analytically realizing signal representation invariant to transformations such as translation, rotation and scaling with wavelets. However, existing scattering networks defined on the sphere and Riemannian manifolds only consider axisymmetric wavelets and are restricted in representation by the isotropic filter structures. In this paper, we propose

This paper considers the problem of cooperative lidar sensing in vehicular networks. We focus on the task of associating the vehicle-generated measurements by lidars to enable a cooperative detection of vulnerable road users. The considered measurements are the three-dimensional bounding boxes extracted from the lidar point cloud. Focusing on a centralized architecture which aggregates and processes

With the increase in the number of antennas at base stations (BSs), centralized multi-antenna architectures have encountered scalability problems from excessive interconnection bandwidth to the central processing unit (CPU), as well as increased processing complexity. Thus, research efforts have been directed towards finding decentralized receiver architectures where a part of the processing is performed

This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of motifs of the unknown graph to enhance the inference of classical Gaussian graphical models. Directly dealing with the density of motifs constitutes a challenging

In wideband joint communications and sensing (JCAS) systems, the waveforms are often designed and optimized over the entire bandwidth. This significantly limits the degrees of freedom in beamforming and causes severe communications performance loss, especially under a strict radar sensing constraint. In this work, we consider a downlink of a wideband multiuser (MU) multiple-input multiple-output (MIMO)

Reconfigurable intelligent surface (RIS) is a promising solution to enhance the spectral and energy efficiencies of future wireless networks. In this paper, we aim to maximize the sum rate of the RIS-assisted multiuser system with different availabilities of channel state information (CSI) by jointly optimizing the transmit precoding matrix and the RIS reflection matrix. Considering the large-scale

The $\boldsymbol{\ell_{p}}$ null space property ( $\boldsymbol{\ell_{p}}$ -NSP) and restricted isometry property (RIP) are two important frames for sparse signal recovery. New sufficient conditions in terms of $\boldsymbol{\ell_{p}}$ -NSP and RIP are respectively developed in this paper. Firstly, we characterize the $\boldsymbol{\ell_{p}}$ robust null space property ( $\boldsymbol{\ell_{p}}$ -RNSP)

The main aim of this paper is to study quaternion phase retrieval (QPR), i.e., the recovery of quaternion signal from the magnitude of quaternion linear measurements. We show that all $\boldsymbol{d}$ -dimensional quaternion signals can be reconstructed up to a global right quaternion phase factor from $\boldsymbol{O(d)}$ phaseless measurements. We also develop the scalable algorithm quaternion Wirtinger

In this paper, we propose a novel framework that aims to jointly design the reflection coefficients of multiple reconfigurable intelligent surfaces and the precoding strategy of a single base station (BS) to optimize the self-tracking of the position and the velocity of a single multi-antenna user equipment (UE) that moves either in the far- or near-field region. Differently from the literature, and

This article focuses on decentralized stochastic optimization in the presence of Byzantine attacks. During the optimization process, an unknown number of malfunctioning or malicious workers, termed as Byzantine workers, disobey the algorithmic protocol and send arbitrarily wrong messages to their neighbors. Even though various Byzantine-resilient algorithms have been developed for distributed stochastic

The decentralized stochastic gradient method emerges as a promising solution for solving large-scale machine learning problems. This paper studies the decentralized Markov chain gradient descent (DMGD), a variant of the decentralized stochastic gradient method, which draws random samples along the trajectory of a Markov chain. DMGD arises when obtaining independent samples is costly or impossible,

In this paper, we study the high-dimensional multiple-measurement-vector (MMV) problem, which typically arises in massive machine-type communications (mMTC) that operates with massive multiple-input multiple-output (MIMO) in a grant-free manner. We derive an expression for the mutual information (MI) of the MMV channel, considering an input that has i.i.d. rows and a row-wise output that is randomly

Several sparse linear array structures have recently been proposed to enhance the identifiability of direction-of-arrival estimation by using second-order or higher even-order statistics under the co-array equivalence. This paper aims to explore non-conventional odd-order statistics, namely third-order cumulants, to design a sparse linear array under the co-array equivalence for enhancing the identifiability

In 5G networks, Device-to-Device (D2D) communications aim to provide dense coverage without relying on the cellular network infrastructure. To achieve this goal, the D2D links are expected to be capable of self-organizing and allocating finite, interfering resources with limited inter-link coordination. We consider a dense ad-hoc D2D network and propose a decentralized time-frequency allocation mechanism

Stochastic Approximation ( SA ) is a classical algorithm that has had since the early days a huge impact on signal processing, and nowadays on machine learning, due to the necessity to deal with a large amount of data observed with uncertainties. An exemplar special case of SA pertains to the popular stochastic (sub)gradient algorithm which is the working horse behind many important applications. A

The traditional centralized baseband processing architecture is faced with the bottlenecks of high computation complexity and excessive fronthaul communication, especially when the number of antennas at the base station (BS) is large. To cope with these two challenges, the decentralized baseband processing (DBP) architecture has been proposed, where the BS antennas are partitioned into multiple clusters

Compressed sensing (CS) model of complex-valued data can represent the signal recovery process of many types of radar systems, especially when the measurement matrix is row-orthogonal. Based on debiased least absolute shrinkage and selection operator (LASSO), the detection problem under the Gaussian random design model, i.e. the elements of the measurement matrix are drawn from a Gaussian distribution

This paper considers frequency division duplexing massive multiple-input multiple-output systems in which the base station (BS) is equipped with either a uniform linear antenna array (ULA) or a uniform rectangular antenna array (URA). For these systems, we develop novel uplink-to-downlink channel covariance mapping schemes. These schemes can be expressed in the form of easy-to-implement affine transformations

Uplink sensing in perceptive mobile networks (PMNs), which uses uplink communication signals for sensing the environment around a base station, faces challenging issues of clock asynchronism and the requirement of a line-of-sight (LOS) path between transmitters and receivers. The channel state information (CSI) ratio has been applied to resolve these issues, however, current research on the CSI ratio

Federated learning (FL) is a collaborative machine learning (ML) paradigm based on persistent communication between a central server and multiple edge devices. However, frequent communication of large ML models can incur considerable communication resources, especially costly for wireless network nodes. In this paper, we develop a communication-efficient protocol to reduce the number of communication

The mean and variance of portfolio returns are the standard quantities to measure the expected return and risk of a portfolio. Efficient portfolios that provide optimal trade-offs between mean and variance warrant consideration. To express a preference among these efficient portfolios, investors have put forward many mean-variance portfolio (MVP) formulations which date back to the classical Markowitz

Location privacy leakage in cooperative localization is receiving increasing attention. Geo-indistinguishability (GI) protects location privacy by adding random noise to an actual location, which inevitably degrades localization accuracy. This work considers a cooperative localization scenario with mobile nodes, where the cooperative nodes (CNs) share their locations under GI. We investigate the tradeoff

In this paper we introduce and study the algebraic generalization of non commutative convolutional neural networks. We leverage the theory of algebraic signal processing to model convolutional non commutative architectures, and we derive concrete stability bounds that extend those obtained in the literature for commutative convolutional neural networks. We show that non commutative convolutional architectures

This work examines a social learning problem, where dispersed agents connected through a network topology interact locally to form their opinions ( beliefs ) as regards certain hypotheses of interest. These opinions evolve over time, since the agents collect observations from the environment, and update their current beliefs by accounting for: their past beliefs, the innovation contained in the new

Graph wavelet transforms allow for the effective representation of signals that are defined over irregular domains. The transform coefficients should be sparse, and encode salient features of a signal. In many situations, these salient features appear as discontinuities in the signal, e.g. physical edges in natural images. The transforms facilitate the development of various graph signal processing

Introducing adaptiveness to federated learning has recently ushered in a new way to optimize its convergence performance. However, adaptive learning strategies originally designed in centralized machine learning are in naїve extended to federated learning in existing works, which does not necessarily improve convergence performance and further reduce communication overhead as expected. In this paper

The challenging problem of distribution-agnostic linear (weighted) unbiased estimation of a global parameter from heterogeneous and unbalanced data is addressed. This setup may originate in different signal processing contexts involving the joint processing of non-homogeneous groups of data whose statistical distribution is unknown, with (possibly highly) diverse sample sizes. Since sample estimators

Suppose $\boldsymbol{L}$ simultaneous independent stochastic systems generate observations, where the observations from each system depend on the underlying model parameter of that system. The observations are unlabeled (anonymized), in the sense that an analyst does not know which observation came from which stochastic system. How can the analyst estimate the underlying model parameters of the $\boldsymbol{L}$

As a widely-used tool to resist outliers, the correntropy criterion or Welsch function has recently been exploited for robust matrix recovery. However, it down-weighs all observations including uncontaminated data. On the other hand, its implicit regularizer (IR) cannot achieve sparseness, which is a desirable property in many practical scenarios. To address these two issues, we devise a novel M-estimator

In an active sensing system, waveforms with good auto-correlations are preferred for accurate parameter estimation. Furthermore, spectral compatibility is required to avoid mutual interference between devices as the electromagnetic environment becomes increasingly crowded. Waveforms should also be unimodular due to hardware limits. In this article, a new approach to generating a unimodular sequence

The block-term decompositions (BTD) represent tensors as a linear combination of low multilinear rank terms and can be explicitly related to the Canonical Polyadic decomposition (CPD). In this paper, we introduce the SECSI-BTD framework, which exploits the connection between two decompositions to estimate the block-terms of the rank- $(L_{r},L_{r},1)$ BTD. The proposed SECSI-BTD algorithm includes

This article considers the problem of radar target detection in compound Gaussian clutter background. Different from the existing detector design criteria, we propose two new detection schemes for the detection problem from the optimization perspective. Specifically, in the first scheme, the detection problem is firstly studied by introducing an auxiliary variable and transforming it into a maximum

Finite Rate of Innovation (FRI) sampling theory enables reconstruction of classes of continuous non-bandlimited signals that have a small number of free parameters from their low-rate discrete samples. This task is often translated into a spectral estimation problem that is solved using methods involving estimating signal subspaces, which tend to break down at a certain peak signal-to-noise ratio (PSNR)

Proportional-type algorithms have attracted much attention because of their fast convergence ability for sparse system identification. To overcome the drawbacks of existing block proportional methods stemming from inadequate block partitioning, this article develops tap-amplitude-based block partitioning methods. In the procedure, we present two block proportional normalized least-mean-square (PNLMS)

An important preliminary procedure in multi-sensor data fusion is sensor registration , and the key step in this procedure is to estimate sensor biases from their noisy measurements. There are generally two difficulties in this bias estimation problem: one is the unknown target states which serve as the nuisance variables in the estimation problem, and the other is the highly nonlinear coordinate transformation

This article focuses on a challenging class of inverse problems that is often encountered in applications. The forward model is a complex non-linear black-box, potentially non-injective, whose outputs cover multiple decades in amplitude. Observations are supposed to be simultaneously damaged by additive and multiplicative noises and censorship. As needed in many applications, the aim of this work is

Deep neural networks (DNNs) with noisy weights, which we refer to as noisy neural networks (NoisyNNs), arise from the training and inference of DNNs in the presence of noise. NoisyNNs emerge in many new applications, including the wireless transmission of DNNs, the efficient deployment or storage of DNNs in analog devices, and the truncation or quantization of DNN weights. This article studies a fundamental

This article studies the statistical model of the non-centered mixture of scaled Gaussian distributions (NC-MSG). Using the Fisher-Rao information geometry associated with this distribution, we derive a Riemannian gradient descent algorithm. This algorithm is leveraged for two minimization problems. The first is the minimization of a regularized negative log-likelihood (NLL). The latter makes the trade-off

This article deals with the detection of range and Doppler distributed targets imbedded in non-Gaussian clutter. The clutter is modeled as a spherically invariant random process with unknown texture components and a covariance matrix structure. We also assume a set of secondary signal-free data is available to estimate the correlation properties of the clutter. Moreover, the target signal at each range

In this article, we propose a new low-rank matrix factorization model dubbed bounded simplex-structured matrix factorization (BSSMF). Given an input matrix $X$ and a factorization rank $r$ , BSSMF looks for a matrix $W$ with $r$ columns and a matrix $H$ with $r$ rows such that $X \approx WH$ where the entries in each column of $W$ are bounded, that is, they belong to given intervals, and the columns

In this article, the problem of estimating and tracking a subspace signal in the presence of non-Gaussian noise is addressed. In contrast to non-robust methods such as PAST, NIC, and NP3, which are based on restrictive noise models, we use the popular $\epsilon -$ contamination noise model employed in robust statistics with Gaussian density as the nominal model to estimate the subspace that the target

Group testing can help maintain a widespread testing program using fewer resources amid a pandemic. In a group testing setup, we are given $n$ samples, one per individual. Each individual is either infected or uninfected. These samples are arranged into $m < n$ pooled samples, where each pool is obtained by mixing a subset of the $n$ individual samples. Infected individuals are then identified using

This article focuses on greedy approaches to select the most informative $k$ sensors from $N$ candidates to maximize the Fisher information, i.e., the determinant of the Fisher information matrix (FIM), which indicates the volume of the information ellipsoid (VIE) constructed by the FIM. However, it is a critical issue for conventional greedy approaches to quantify the Fisher information properly when

In this article, we consider decentralized optimization problems where agents have individual cost functions to minimize subject to subspace constraints that require the minimizers across the network to lie in low-dimensional subspaces. This constrained formulation includes consensus or single-task optimization as special cases, and allows for more general task relatedness models such as multitask

In this article, a new class of global mean-squared-error (MSE) lower bound for Bayesian parameter estimation is derived. First, it is shown that under the non-Bayesian framework, the Hammersley-Chapman-Robbins (HCR) for the problem of single-source parameter estimation, is related to the corresponding ambiguity function. This result is achieved by judicious choice of signal test-point. This result

The airborne coherent multi-input multi-output (MIMO) radar benefiting from coherent integration (including intra-channel integration and inter-channel integration) of multi-channel echoes can obtain superior detection performance for high-speed maneuvering targets. However, due to the coupling motion characteristic between multiple airborne platforms and high-speed targets, the range walk (RW) and

Convergent cross mapping is a principled causal discovery technique for signals, but its efficacy depends on a number of assumptions about the systems that generated the signals. In this work, we present a self-contained introduction to the theory of causality in state-spaces, Takens' theorem, and cross maps, and we propose conditions to check if a signal is appropriate for cross mapping. Further,

A method for multi-frequency notch filtering is described. The approach is based on quadratic programming, which leads to projecting the signal vector onto the orthogonal complement of the subspace spanned by a set of sinusoidal basis vectors, each corresponding to a notch frequency. The projection matrix uses a weighted inner product whose weights are samples of a standard spectral analysis window

Elementary chirp signals can be found in various fields of science and engineering. We propose two computationally efficient algorithms based on the choice of two different initial estimators to estimate the parameters of the elementary chirp model. It is observed that the proposed efficient estimators are consistent; they have the identical asymptotic distribution as that of the least squares estimators

A novel and computationally efficient source enumeration algorithm is proposed for large-scale arrays with a small number of samples, by employing a two-step difference operation of linear shrinkage (LS) coefficients of sample covariance matrix (SCM) in large-dimensional scenarios. It is firstly proved that the difference between noise LS coefficients tends to zero and there exists a clear gap between