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This paper focuses on optimal time-of-arrival (TOA) sensor placement for multiple target localization simultaneously. In previous work, different solutions only using non-shared sensors to localize multiple targets have been developed. Those methods localize different targets one-by-one or use a large number of mobile sensors with many limitations, such as low effectiveness and high network complexity. In this paper, firstly, a novel optimization model for multi-target localization incorporating shared sensors is formulated. Secondly, the systematic theoretical results of the optimal sensor placement are derived and concluded using the A-optimality criterion, i.e., minimizing the trace of the inverse Fisher information matrix (FIM), based on rigorous geometrical derivations. The reachable optimal trace of Cramér-Rao lower bound (CRLB) is also derived. It can provide optimal conditions for many cases and even closed form solutions for some special cases. Thirdly, a novel numerical optimization algorithm to quickly find and calculate the (sub-)optimal placement and achievable lower bound is explored, when the model becomes complicated with more practical constraints. Then, a hybrid method for solving the most general situation, integrating both the analytical and numerical solutions, is proposed. Finally, the correctness and effectiveness of the proposed theoretical and mathematical methods are demonstrated by several simulation examples. [ABSTRACT FROM AUTHOR]

The problem of range estimation based on noisy measurements with phase ambiguity can be solved using signals across multiple frequencies by existing algorithms based on either the Chinese Remainder Theorem or lattice theory. The performances of these algorithms are constrained by the trade-off between SNR of measurements and required estimation accuracy. In this paper, we firstly propose an algorithm to find a set of wavelengths satisfying the conditions to apply the closed-form lattice algorithm from a given interval. Then we propose an enhanced lattice algorithm for range estimation based on existing lattice approaches. In the conventional lattice algorithm, the selection of an integer vector by the estimator often fails to be the ground truth because of noise. As a result, the true value can be a neighbouring lattice point of the estimated point where neighbours are defined in terms of a distance depending on the noise characteristics. In this paper, all neighbouring lattice points of the estimated point obtained by a conventional lattice algorithm are regarded as candidates for the new estimate. Then an efficient estimator is presented to choose one of those candidates to be the new estimate. The performance of the proposed algorithm, i.e. the successful probability of reconstruction, is derived mathematically. Additionally, a computation-reduced algorithm is presented to reduce the overhead of computation. The calculated probability and simulation results demonstrate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Distributed or decentralized estimation of covariance, and distributed principal component analysis have been introduced and studied in the signal processing community in recent years, and applications in array processing have been indicated in some detail. Inspired by these, this paper provides a detailed development of several distributed algorithms for array processing. New distributed algorithms are proposed for DOA estimation methods like root-MUSIC, total least squares-ESPRIT, and FOCUSS. Other contributions include distributed design of the Capon beamformer from data, and distributed implementation of the spatial smoothing method for coherent sources. A distributed implementation of a recently proposed beamspace method called the convolutional beamspace (CBS) is also proposed. The proposed algorithms are fully distributed – an average consensus (AC) is used to avoid the need for a fusion center. The algorithms are based on a recently reported finite-time version of AC which converges to the exact solution in a finite number of iterations. Numerical examples are given throughout the paper to show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The recent criteria of a preferable linear sparse array for a robust direction of arrival (DOA) estimation are: the closed-form expression for its sensor locations; the large central uniform linear array (ULA) segment in its resulting co-array; and the fewer sensor pairs with small separations in its arrangement. These features, in turn, will lead to a straightforward array design process, more sources being resolved and strong helpful performance for the array within a real-world mutual coupling environment. This paper introduces a new array called the dilated nested array (DNA), which takes into account all these considerations. The sensors of the DNA are arranged in a way that yields an effective difference co-array with a central virtual ULA part larger than that of the co-prime array and equal to that of the nested array, and in an equivalent importance, a physical arrangement with smaller numbers of sensor pairs with small separations than those of the super nested array, so that the array can notably reduce the mutual coupling effects in comparison. A displaced arrangement obtained from the DNA geometry is also introduced to further increase the co-array total number of DOFs and at the same time to decrease the numbers of sensor pairs with small separations. Extensive numerical simulations are included to demonstrate the effectiveness of the proposed DNAs over other sparse arrays. [ABSTRACT FROM AUTHOR]

This paper studies distributed diffusion adaptation over clustered multi-task networks in the presence of impulsive interferences and Byzantine attacks. We develop a robust resilient diffusion least mean Geman-McClure-estimation (RDLMG) algorithm based on the cost function used by the Geman-McClure estimator, which can reduce the sensitivity to large outliers and make the algorithm robust under impulsive interferences. Moreover, the mean sub-sequence reduced method, in which each node discards the extreme value information of cost contributions received from its neighbors, can make the network resilient against Byzantine attacks. In this regard, the proposed RDLMG algorithm ensures that all normal nodes converge to their ideal states with cooperation among nodes. A statistical analysis of the RDLMG algorithm is also carried out in terms of mean and mean-square performances. Numerical results evaluate the proposed RDLMG algorithm in applications to multi-target localization and multi-task spectrum sensing. [ABSTRACT FROM AUTHOR]

Covariance matrix tapers have a long history in signal processing and related fields. Examples of applications include autoregressive models (promoting a banded structure) or beamforming (widening the spectral null width associated with an interferer). In this paper, the focus is on high-dimensional setting where the dimension $p$ is high, while the data aspect ratio $n/p$ is low. We propose an estimator called Tabasco (TApered or BAnded Shrinkage COvariance matrix) that shrinks the tapered sample covariance matrix towards a scaled identity matrix. We derive optimal and estimated (data adaptive) regularization parameters that are designed to minimize the mean squared error (MSE) between the proposed shrinkage estimator and the true covariance matrix. These parameters are derived under the general assumption that the data is sampled from an unspecified elliptically symmetric distribution with finite 4th order moments (both real- and complex-valued cases are addressed). Simulation studies show that the proposed Tabasco outperforms all competing tapering covariance matrix estimators in diverse setups. An application to space-time adaptive processing (STAP) also illustrates the benefit of the proposed estimator in a practical signal processing setup. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of joint direction-of-arrival (DoA) and range estimation using frequency diverse coprime array (FDCA). By incorporating the coprime array structure and coprime frequency offsets, a two-dimensional space-frequency virtual difference coarray corresponding to uniform array and uniform frequency offset is considered to increase the number of degrees-of-freedom (DoFs). However, the reconstruction of the doubly-Toeplitz covariance matrix is computationally prohibitive. To solve this problem, we propose an interpolation algorithm based on decoupled atomic norm minimization (DANM), which converts the coarray signal to a simple matrix form. On this basis, a relaxation-based optimization problem is formulated to achieve joint DoA-range estimation with enhanced DoFs. The reconstructed coarray signal enables application of existing subspace-based spectral estimation methods. The proposed DANM problem is further reformulated as an equivalent rank-minimization problem which is solved by cyclic rank minimization. This approach avoids the approximation errors introduced in nuclear norm-based approach, thereby achieving superior root-mean-square error which is closer to the Cramér-Rao bound. The effectiveness of the proposed method is confirmed by theoretical analyses and numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a federated online training framework for deep neural network (DNN)-based channel estimation (CE) in frequency-division duplexing (FDD) multi-user massive multiple-input multiple-output (MU-MIMO) systems. The proposed DNN consists of two stages, where Stage-I explores the partial common sparsity structure among the users, while Stage-II estimates the channel state information (CSI) with reduced pilot overhead leveraging the common support information provided by Stage-I. To realize online training, we first propose three axioms for a legitimate online loss function, based on which we develop the federated online training algorithm with convergence analysis. The proposed two-tier DNN is trained online at the base station (BS) based on real-time pilot measurements distributively fed back from the users without the need of true channel labels, and the estimates for the CSI at the transmitter (CSIT) can be simultaneously generated in real-time. Meanwhile, the weights of Stage-II can be broadcasted to the users for real-time estimation of the CSI at the receiver (CSIR) at each user. Simulation shows that the proposed solution achieves higher CE performance than traditional compressive sensing (CS)-based algorithms while enjoying much faster computation. The solution is also robust to the channel model mismatches induced by the change of propagation environment, and is able to track the time-varying channel model. [ABSTRACT FROM AUTHOR]

In this paper, we propose and implement blind multiuser carrier frequency offsets (CFOs) estimation for multi-input multi-output (MIMO) single carrier frequency division multiple access (SC-FDMA) uplink system using orthogonal propagator method (OPM) over a noisy frequency-selective channel. The performance of typical OPM is limited at low signal-to-noise ratio (SNR) due to its noise-free signal model. The additive white Gaussian noise mainly impacts the diagonal elements of the data covariance matrix (DCM) of the received signal. First, the proposed fractional CFOs estimator minimizes the noise effect by reconstructing the denoised diagonal elements of the DCM for the received signal through cubic Hermite interpolation. Therefore, we use modified OPM to estimate multiple CFOs for MIMO SC-FDMA systems. Second, we have used an iterative method based on the first-order Taylor series approximation of the CFO vector to avoid peak ambiguity and reduce the number of iterations required in the grid search. The mean square error of the proposed CFO estimator considerably improves compared with the existing methods at a low SNR regime. The bit error rate performance of the proposed method for MIMO SC-FDMA is also compared with the existing methods. Finally, the proposed estimator is validated by implementing it on radio frequency hardware testbed over an indoor propagation environment. [ABSTRACT FROM AUTHOR]

This paper presents a low-complexity linear minimum mean-squared-error-based iterative soft interference cancellation (LMMSE-ISIC) scheme for multiple-input multiple-output (MIMO) systems. To avoid direct matrix inversion in the conventional LMMSE-ISIC scheme, expressions are derived to obtain the filtering vector and estimate of the conventional scheme; the direct inverse operation is then replaced by the vector-based operations in the proposed scheme. Thus, for the worst-case scenario in the proposed scheme, the complexity of estimating each transmit symbol is approximately proportional to the square of the number of receive antennas; in the conventional scheme, it is approximately proportional to the cube of the number of receive antennas. In addition, because there are no approximations for deriving the filtering vector and estimate, the proposed LMMSE-ISIC scheme achieves near-optimum performance identical to that of the conventional scheme, which is close to the matched filter bound of the channel. Further, the extension of the proposed scheme for iterative detection and decoding is developed for coded systems. The simulated results confirm that the conventional and proposed schemes outperform the approximated matrix inversion based schemes and achieve the identical error performance in both uncoded and coded systems, while the complexity order of the proposed scheme is similar to or even lower than those of the approximation schemes. Therefore, the proposed scheme can be considered an effective near-optimum LMMSE-based iterative detection approach for MIMO systems, especially for massive MIMO systems with a high load factor. [ABSTRACT FROM AUTHOR]

This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain of the optimization variable, which are difficult to project onto; and (b) deterministic or stochastic constraints that admit efficient projection. Problems of this form arise frequently in the context of semidefinite programming as well as when various NP-hard problems are solved approximately via semidefinite relaxation. Since projection onto the first set of constraints is difficult, it becomes necessary to explore projection-free algorithms, such as the stochastic Frank-Wolfe (FW) algorithm. On the other hand, the second set of constraints cannot be handled in the same way, and must be incorporated as an indicator function within the objective function, thereby complicating the application of FW methods. Similar problems have been studied before; however, they suffer from slow convergence rates. This work, equipped with momentum based gradient tracking technique, guarantees fast convergence rates on par with the best-known rates for problems without the second set of constraints. Zeroth-order variants of the proposed algorithms are also developed and again improve upon the state-of-the-art rate results. We further propose the novel trimmed FW variants that enjoy the same convergence rates as their classical counterparts, but are empirically shown to require significantly fewer calls to the linear minimization oracle speeding up the overall algorithm. The efficacy of the proposed algorithms is tested on relevant applications of sparse matrix estimation, clustering via semidefinite relaxation, and uniform sparsest cut problem. [ABSTRACT FROM AUTHOR]

We consider the problem of recovering random graph signals from nonlinear measurements. For this setting, closed-form Bayesian estimators are usually intractable and even numerical evaluation may be difficult to compute for large networks. In this paper, we propose a graph signal processing (GSP) framework for random graph signal recovery that utilizes information on the structure behind the data. First, we develop the GSP-linear minimum mean-squared-error (GSP-LMMSE) estimator, which minimizes the mean-squared-error (MSE) among estimators that are represented as an output of a graph filter. The GSP-LMMSE estimator is based on diagonal covariance matrices in the graph frequency domain, and thus, has reduced complexity compared with the LMMSE estimator. This property is especially important when using the sample-mean estimators that are based on a training dataset. We then state conditions under which the low-complexity GSP-LMMSE estimator coincides with the optimal LMMSE estimator. Next, we develop an approximate parametrization of the GSP-LMMSE estimator by graph filters. We present three implementations of the parametric GSP-LMMSE estimator for typical graph filters. These parametric graph filters are more robust to outliers and to network topology changes. In our simulations, we evaluate the performance of the proposed GSP-LMMSE estimators for the problem of state estimation in power systems, which can be interpreted as a graph signal recovery task. We show that the proposed sample-GSP estimators outperform the sample-LMMSE estimator for a limited training dataset and that the parametric GSP-LMMSE estimators are more robust to topology changes in the form of adding/removing vertices/edges. [ABSTRACT FROM AUTHOR]

Conventionalliterature on array signal processing (ASP) is based on the “capture first, process later” philosophy and to this end, signal processing algorithms are typically decoupled from the hardware. This poses fundamental limitations because if the sensors result in information loss, the algorithms may no longer be able to achieve their guaranteed performance. In this paper, our goal is to overcome the barrier of information loss via sensor saturation and clipping. This is a significant problem in application areas including physiological monitoring and extra-terrestrial exploration where the amplitudes may be unknown or larger than the dynamic range of the sensor. To overcome this fundamental bottleneck, we propose “computational arrays” which are based on a co-design approach so that a collaboration between the sensor array hardware and algorithms can be harnessed. Our work is inspired by the recently introduced unlimited sensing framework. In this context, our computational arrays encode the high-dynamic-range information by folding the signal amplitudes, thus introducing a new form of information loss in terms of the modulo measurements. On the decoding front, we develop mathematically guaranteed recovery algorithms for spatio-temporal array signal processing tasks that include DoA estimation, beamforming and signal reconstruction. Numerical examples corroborate the applicability of our approach and pave a path for the development of novel computational arrays for ASP. [ABSTRACT FROM AUTHOR]

Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality. This paper proposes a joint dimensionality reduction and non-parametric density estimation framework, using a novel estimator that can explicitly capture the underlying distribution of appropriate reduced-dimension representations of the input data. The idea is to jointly design a nonlinear dimensionality reducing auto-encoder to model the training data in terms of a parsimonious set of latent random variables, and learn a canonical low-rank tensor model of the joint distribution of the latent variables in the Fourier domain. The proposed latent density model is non-parametric and “universal,” as opposed to the predefined prior that is assumed in variational auto-encoders. Joint optimization of the auto-encoder and the latent density estimator is pursued via a formulation which learns both by minimizing a combination of the negative log-likelihood in the latent domain and the auto-encoder reconstruction loss. We demonstrate that the proposed model achieves very promising results on toy, tabular, and image datasets on regression tasks, sampling, and anomaly detection. [ABSTRACT FROM AUTHOR]

Effective non-parametric density estimation is a key challenge in high-dimensional multivariate data analysis. In this paper, we propose a novel approach that builds upon tensor factorization tools. Any multivariate density can be represented by its characteristic function, via the Fourier transform. If the sought density is compactly supported, then its characteristic function can be approximated, within controllable error, by a finite tensor of leading Fourier coefficients, whose size depends on the smoothness of the underlying density. This tensor can be naturally estimated from observed and possibly incomplete realizations of the random vector of interest, via sample averaging. In order to circumvent the curse of dimensionality, we introduce a low-rank model of this characteristic tensor, which significantly improves the density estimate especially for high-dimensional data and/or in the sample-starved regime. By virtue of uniqueness of low-rank tensor decomposition, under certain conditions, our method enables learning the true data-generating distribution. We demonstrate the very promising performance of the proposed method using several toy, measured, and image datasets. [ABSTRACT FROM AUTHOR]

In this paper, two types of linear estimators are considered for three related estimation set-ups involving set-theoretic uncertainty pertaining to $ \mathcal {H}_{2}$ and $ \mathcal {H}_{\infty }$ balls of frequency-responses. The problems at stake correspond to robust $ \mathcal {H}_{2}$ and $ \mathcal {H}_{\infty }$ estimation in the face of non-parametric “channel-model’ uncertainty and to a nominal $ \mathcal {H}_{\infty }$ estimation problem. The estimators considered here are defined by minimizing the worst-case estimation error magnitude over the “uncertainty set” or by minimizing an average cost under the constraint that the worst-case error of any admissible estimator does not exceed a prescribed value. The main point is to explore the derivation of estimators which may be viewed as less conservative alternatives to minimax estimators, or in other words, that allow for trade-offs between worst-case performance and better performance over “large” subsets of the uncertainty set. The “average costs” over $ \mathcal {H}_{2}-$ signal balls are obtained as limits of averages over sets of finite impulse responses, as their length grows unbounded. The estimator design problems for the two types of estimators and the three set-ups addressed here are recast as semi-definite programming problems (SDPs, for short). These SDPs are solved in the case of simple examples to illustrate the potential of the “average cost/worst-case constraint” estimators to mitigate the inherent conservatism of the minimax estimators. [ABSTRACT FROM AUTHOR]

The state estimation problem of heterogeneous multi-agent systems with random transport protocol is investigated in this paper. Due to the dependency of the agent dynamics and the random sparse structure induced by the random transport protocol, the optimal state estimation design becomes complex and challenging. An optimal state estimator is successfully designed by the Hadamard product and gradient method. Based on the analysis of the matrix functions, a sufficient condition is established to guarantee that the average estimate error covariance is limited. Finally, a numerical example and a smart grid model are utilized to demonstrate the effectiveness of the deigned estimator. [ABSTRACT FROM AUTHOR]

Sensor placement methods for field estimation based on Gaussian processes are proposed. Generally, sensor placement methods determine the appropriate placement positions by selecting them from predefined candidate positions. Many criteria for the selection have been proposed, with which the quality of the placements is evaluated with regard to the field at the candidate positions. This means that these sensor placement methods seek to find the positions that can estimate the field at the candidate positions accurately. In practical situations, however, the candidate sensor placement region can be different from the target region for field estimation. In this paper, to make sensor placement methods applicable to this situation, we propose two sensor placement methods based on the mean squared error and on conditional entropy that can be applied to cases in which the sensor placement region is arbitrarily restricted. After formulating the sensor placement problems, two approximate algorithms are derived: the greedy algorithm and the convex-relaxation-based algorithm. The application of the proposed methods to sound field estimation is also illustrated, and their effectiveness was confirmed through numerical experiments. [ABSTRACT FROM AUTHOR]

For direction-of-arrival (DOA) estimation of heterogeneous wideband sources, we propose a new adaptive space-frequency joint processing algorithm. The algorithm is implemented in the sparse Bayesian learning (SBL) DOA framework, which is named as ASF-SBL algorithm in this paper. The traditional SBL-based DOA methods suffer from the problem of erroneous DOA estimation due to the structural mismatch between the invariant prior and the sparse coefficients. To solve this problem, the ASF-SBL algorithm employs a new space-frequency correlation prior model that can be adaptively changed to fit heterogeneous DOA scenarios. Specifically, nine alternative space-frequency structural patterns are constructed to represent the joint space-frequency characteristics of spatial sparse signals. By evaluating the space-frequency correlation of the sparse coefficients updated in each iteration under SBL framework, a suitable pattern is selected from the nine choices to determine the adaptive prior of each coefficient. This adaptive method leads to accurate DOA estimation in different wideband sources scenarios. In addition, we introduce a distributed processing method to extend the ASF-SBL algorithm to two-dimensional DOA estimation. This extension is achieved by decoupling the DOA estimation into two one-dimensional estimations. The decoupling avoids the problems of a huge redundant dictionary and excessive computational complexity caused by the combination of azimuth and elevation angles. Numerical simulations show that the ASF-SBL algorithm is superior to existing algorithms in DOA estimation of heterogeneous sources. [ABSTRACT FROM AUTHOR]

A key objective of multi-agent surveillance systems is to monitor a much larger region than the limited field-of-view (FoV) of any individual agent by successfully exploiting cooperation among multiple agents. Whenever either a centralized or a distributed approach is pursued, this goal cannot be achieved unless an appropriately designed fusion strategy is adopted. This paper presents a novel information fusion approach by considering for each agent a known limited, and possibly different, FoV. The proposed method, named Bayesian-operation InvaRiance on Difference-sets (BIRD) fusion, relies on Generalized Covariance Intersection (GCI) and exploits a general and exact decomposition of each multi-object posterior by partitioning the global FoV, i.e. the union of the FoVs of the fusing agents, into common and exclusive FoVs. It is shown how BIRD fusion can be used to perform multi-object estimation based on random finite sets on both a centralized and a distributed peer-to-peer sensor network. Simulation experiments on realistic multi-object tracking scenarios demonstrate the effectiveness of BIRD fusion. [ABSTRACT FROM AUTHOR]

Robust spectral analysis of the sinusoidal signals corrupted by impulsive noise poses a big challenge in the signal processing community. In this paper, we address the issue of robust spectral analysis for multi-channel sinusoidal signals, including order detection and parameter estimation. The successive robust low-rank decomposition is firstly designed to extract the common signal subspace from the multi-channel data matrix. Subsequently, the number of sinusoidal poles is determined with a model order selection criterion, based on the so-obtained subspace. With the signal order information, the sinusoidal parameters and outliers are jointly estimated according to the maximum a posteriori criterion. To find a robust initial guess of the sinusoidal parameters, an estimator based on robust weighted linear prediction is developed. Additionally, the performance analysis is provided, which includes computational complexity, convergence verification of the sinusoidal parameter estimation, and asymptotic consistency of the signal order detection. Simulation results demonstrate the advantages of the proposed robust spectral analysis framework compared to state-of-the-art schemes. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to extend the semiparametric inference methodology, recently investigated for Real Elliptically Symmetric (RES) distributions, to Complex Elliptically Symmetric (CES) distributions. The generalization to the complex field is of fundamental importance in all practical applications that exploit the complex representation of the acquired data. Moreover, the CES distributions has been widely recognized as a valuable and general model to statistically describe the non-Gaussian behaviour of datasets originated from a wide variety of physical measurement processes. The paper is divided in two parts. In the first part, a closed form expression of the constrained semiparametric Cramér-Rao Bound (CSCRB) for the joint estimation of complex mean vector and complex scatter matrix of a set of CES-distributed random vectors is obtained by exploiting the so-called Wirtinger or $\mathbb {C}\mathbb {R}$ -calculus. The second part deals with the derivation of the semiparametric version of the Slepian-Bangs formula in the context of the CES model. Specifically, the proposed semiparametric Slepian-Bangs (SSB) formula provides us with a useful and ready-to-use expression of the semiparametric Fisher Information Matrix (SFIM) for the estimation of a parameter vector parametrizing the complex mean and the complex scatter matrix of a CES-distributed vector in the presence of unknown, nuisance, density generator. Furthermore, we show how to exploit the derived SSB formula to obtain the semiparametric counterpart of the Stochastic CRB for Direction of Arrival (DOA) estimation under a random signal model assumption. Simulation results are also provided to clarify the theoretical findings and to demonstrate their usefulness in common array processing applications. [ABSTRACT FROM AUTHOR]

The posterior Cramr-Rao lower bound (PCRLB) and a number of its extensions including the unconditional PCRLB (U-PCRLB) and the conditional PCRLB (C-PCRLB) have been widely studied in multi-sensor target tracking (MSTT). Previous MSTT works assume that the measurements are conditionally independent, which is often not the case in practice. When the correlations of the measurements are unknown, the standard Bayes update and PCRLB computations cannot be performed. Inspired by geometric average (GA) fusion that implements data fusion with unknown data correlations by employing exponential mixture density (EMD) to compute the global posterior, EMD-based approximations to U-PCRLB and C-PCRLB are derived in this paper for two classic distributed fusion architectures, namely the hierarchical and consensus architectures. The PCRLB can be decomposed into two parts, one coming from the prior information and the other from the information contained in the data. The data information part of PCRLB is approximated via EMD-based posterior, leading to the approximation of the PCRLB. We present a sequential Monte Carlo solution to recursively compute the proposed approximation to the PCRLB for nonlinear non-Gaussian estimation problems. Numerical simulations are provided to show that the proposed approximation to the bound on the estimation mean square error (MSE) is tighter compared to the existing bounds based on likelihood fusion obtained under the measurement independence assumption. [ABSTRACT FROM AUTHOR]

This paper presents a convex recovery method for block-sparse signals whose block partitions are unknown a priori. We first introduce a nonconvex penalty function, where the block partition is adapted for the signal of interest by minimizing the mixed $\ell _{2}/\ell _{1}$ norm over all possible block partitions. Then, by exploiting a variational representation of the $\ell _{2}$ norm, we derive the proposed penalty function as a suitable convex relaxation of the nonconvex one. For a block-sparse recovery model designed with the proposed penalty, we develop an iterative algorithm which is guaranteed to converge to a globally optimal solution. Numerical experiments demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The conventional direction of arrival (DOA) estimation methods are performed with multiple receiving channels. In this paper, a changeling DOA estimation problem is addressed in a different scenario with only one full-functional receiving channel. A new unmanned aerial vehicle (UAV) swarm system using multiple lifted reconfigurable intelligent surface (RIS) is proposed for the DOA estimation. The UAV movement degrades the DOA estimation performance significantly, and the existing atomic norm minimization (ANM) methods cannot be used in the scenario with array perturbation. Specifically, considering the position perturbation of UAVs, a new atomic norm-based DOA estimation method is proposed, where an atomic norm is defined with the parameter of the position perturbation. Then, a customized semi-definite programming (SDP) method is derived to solve the atomic norm-based method, where different from the traditional SDP method, an additional transforming matrix is formulated. Moreover, a gradient descent method is applied to refine the estimated DOA and the position perturbation further. Simulation results show that the proposed method achieves much better DOA estimation performance in the RIS-aided UAV swarm system with only one receiving channel than various benchmark schemes. [ABSTRACT FROM AUTHOR]

Random matrices are widely used to estimate the extent of an elliptically contoured object. Usually, it is assumed that the measurements follow a normal distribution, with its standard deviation being proportional to the object’s extent. However, the random matrix approach can filter the center of gravity and the covariance matrix of measurements independently of the measurement model. This work considers the whole chain from data acquisition to the linear Kalman Filter with extension estimation as a reference plant. The input is the (unknown) ground truth (position and extent). The output is the filtered center of gravity and the filtered covariance matrix of the measurement distribution. A virtual measurement model emulates the behavior of the reference plant. The input of the virtual measurement model is adapted using the proposed algorithm until the output parameters of the virtual measurement model match the result of the reference plant. After the adaptation, the input to the virtual measurement model is considered an estimation for position and extent. The main contribution of this paper is the reference model concept and an adaptation algorithm to optimize the input of the virtual measurement model. [ABSTRACT FROM AUTHOR]

In this paper, we propose multi-input multi-output (MIMO) beamforming designs towards joint radar sensing and multi-user communications. We employ the Cramér-Rao bound (CRB) as a performance metric of target estimation, under both point and extended target scenarios. We then propose minimizing the CRB of radar sensing while guaranteeing a pre-defined level of signal-to-interference-plus-noise ratio (SINR) for each communication user. For the single-user scenario, we derive a closed form for the optimal solution for both cases of point and extended targets. For the multi-user scenario, we show that both problems can be relaxed into semidefinite programming by using the semidefinite relaxation approach, and prove that the global optimum can be generally obtained. Finally, we demonstrate numerically that the globally optimal solutions are reachable via the proposed methods, which provide significant gains in target estimation performance over state-of-the-art benchmarks. [ABSTRACT FROM AUTHOR]

The large antenna arrays with hybrid analog and digital (HAD) architectures can provide a large aperture with low cost and hardware complexity, resulting in enhanced direction-of-arrival (DOA) estimation and reduced power consumption. This paper investigates the trade-off between DOA estimation and power consumption in large antenna arrays with HAD architectures. Particularly, the DOA estimation problem of fully-connected, sub-connected (SC), and switches-based (SE) hybrid architectures is formulated into a unified expression, with the compression matrix in a time-varying form. Based on this model, we derive a dynamic maximum likelihood (D-ML) estimator that is suitable for both HAD and conventional fully digital (FD) structures, and the closed-form expression of Cramér-Rao bound (CRB) to evaluate the performance limit of the D-ML estimator for different HAD structures. The theoretical CRB analysis in the single-source case reveals that, the SC structure has the ability to achieve approximately the same performance as the FD structures at DOAs around zero, but suffers from the inherent angle ambiguity because of the antenna grouping. In addition, we propose a dynamic SC (D-SC) structure that is proved to eliminate the angle ambiguity with time-varying phase shifters, and a switch optimization (SWO) algorithm to minimize the CRB of SE structures. Finally, we introduce a new metric, DOA efficiency, to measure the trade-off between the DOA estimation performance and power consumption of different structures. Simulation results verify our theoretical analysis and the superiority of the proposed D-SC structure and the SWO algorithm. [ABSTRACT FROM AUTHOR]

In practical hardware platforms such as FPGA orDSP, the FFT operation is based on a length of $2^{L}$. However, due to the system limitation, the length of sampled signal would be not equal to $2^{L}$. Thus, zero-padding is performed on the signal before FFT operation. Most traditional sinusoidal frequency estimation methods are for signals without zero-padding. When applying these methods to the zero-padded signal, the performances would degrade. To solve this problem, a novel frequency estimation method for zero-padded signal is proposed in this paper. In the proposed method, by using the analytical expression of the DFT signal after zero-padding, an amplitude ratio function is defined between the two DFT samples nearest to the true frequency. Based on the monotonic property of the ratio function, Newton-Raphson method or bisection search is used to estimate the residual frequency. Two implementation flows are proposed, with similar performance and computational complexity. Experimental results show that the proposed method achieves better RMSE performance than the traditional methods. More importantly, the proposed estimation method can be applied to both the zero-padded signal and the non-padding signal. [ABSTRACT FROM AUTHOR]

This paper studies a statistical model for heteroscedastic (i.e., power fluctuating) signals embedded in white Gaussian noise. Using the Riemannian geometry theory, we propose an unified approach to tackle several problems related to this model. The first axis of contribution concerns parameters (signal subspace and power factors) estimation, for which we derive intrinsic Cramér-Rao bounds and propose a flexible Riemannian optimization algorithmic framework in order to compute the maximum likelihood estimator (as well as other cost functions involving the parameters). Interestingly, the obtained bounds are in closed forms and interpretable in terms of problem’s dimensions and SNR. The second axis of contribution concerns the problem of clustering data assuming a mixture of heteroscedastic signals model, for which we generalize the Euclidean K-means++ to the considered Riemannian parameter space. We propose an application of the resulting clustering algorithm on the Indian Pines segmentation problem benchmark. [ABSTRACT FROM AUTHOR]

This paper investigates estimation of direction of arrivals (DOAs) and time of arrivals (TOAs) for a multi-user orthogonal frequency-division multiplexing (OFDM) system that is equipped with large-scale arrays and interfered by carrier frequency offsets (CFOs). We propose a novel scheme for joint TOA and DOA estimation with CFO compensation by taking advantages of large-scale receive antenna arrays. The pilot is designed to balance the pilot length and the estimation performance. The proposed CFO estimation scheme is with lower complexity. After analyzing the resolution of joint DOA and TOA estimation, we find a criterion to choose an appropriate smoothing window for the best resolution and provide insights in sub-carrier selection strategy. We also prove that the large-scale array can asymptotically achieve perfect resolution of both TOA and DOA estimation. We reveal the pseudo peak (PP) elimination property of large-scale arrays and exploit it to develop a novel path number estimation algorithm accordingly. Based on our numerical results, the proposed scheme can efficiently eliminate the CFO effect, the optimized smoothing window attains much better performance, and the path number estimation algorithm performs better than the traditional minimum description length (MDL) approach, especially in the low signal-to-noise ratio (SNR) regime. [ABSTRACT FROM AUTHOR]

Sparse Bayesian learning (SBL) has become a popular approach for direction-of-arrival (DOA) estimation, but its computational complexity for Bayesian inference is quite high because calculating inverse of a large complex matrix per iteration is required. It is known that the computational load can be reduced by transforming the complex-valued problem into a real-valued one. However, the commonly used real-valued transformation works for uniform linear arrays (ULAs) only. In this paper, we propose a new real-valued transformation for DOA estimation with arbitrary linear arrays by exploiting the virtual steering of linear arrays. Then, we introduce an alternating optimization algorithm based on the variational Bayesian inference (VBI) methodology to iteratively obtain a stationary solution to the real-valued sparse representation problem. Because of utilizing the additional real-valued structure, the VBI scheme can achieve a better performance in terms of both estimation accuracy and computational complexity. Moreover, we embed the generalized approximate message passing (GAMP) into the VBI-based method for further complexity reduction. Although there may be a performance loss for the GAMP variant, simulation results reveal its substantial performance improvement over existing methods. [ABSTRACT FROM AUTHOR]

To achieve high resolution, orthogonal frequency division multiplex (OFDM) radars deploy two-dimensional multiple signal classification (2D-MUSIC) in the joint range-velocity estimator. However, it is obvious that both of the signal reconstruction and 2D smoothing affect the noise statistical distribution and virtual array aperture in the joint range-velocity estimator with 2D-MUSIC. Therefore, the conventional accuracy analysis methods for the MUSIC are no longer suitable. In this paper, we propose an estimation accuracy analysis for the joint range-velocity estimator with 2D-MUSIC. Firstly, we present that the noise statistical distribution of the signals being reconstructed and 2D smoothed has a 2-fold Hankel structure. Then, the closed-forms of the range and velocity estimation accuracies are derived, respectively, which both show that the estimation accuracies highly depend on the 2D smoothing and could be improved by properly choosing the 2D smoothing window. Further, we formulate the smoothing optimization and propose the quasi-optimal size of the 2D smoothing window. Finally, both theoretical analyses and simulations validate that the proposed smoothing optimization could significantly improve the estimation accuracies with a lower computational burden than the conventional smoothing. [ABSTRACT FROM AUTHOR]

The high precision positioning of global navigation satellite systems (GNSS), which essentially corresponds to solving the integer least-squares (ILS) problem in the integer phase ambiguity estimation, has emerged as a key problem for the development of industrial internet-of-things (IIoT). In this paper, a novel paradigm for solving the ILS problem is introduced to the integer phase ambiguity estimation. Different from the traditional paradigm of ILS which only involves one parameter to characterize the trade-off between performance and complexity, the proposed ILS paradigm entails two parameters named as the initial searching size $K\geq 1$ and the standard deviation $\sigma >0$ , thus introducing extra degrees of freedom to facilitate the system trade-off. Based on it, explicit analysis can be carried out for a mathematically tractable trade-off, where great potentials could be further exploited for the high precision positioning of GNSS. The equivalent searching algorithm (ESA) is proposed, which achieves the same performance as the classic Fincke-Pohst strategy in sphere decoding (SD) but with tractable complexity measured by the number of visited nodes in the searching stage. Moreover, the candidate protection mechanism is given to further upgrade the equivalent searching algorithm, which makes it not only an optimal but also a sub-optimal ILS estimator given the flexible setup of $K$. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of wideband direction of arrival (DoA) estimation with sparse linear arrays (SLAs), where a number of uncorrelated wideband signals impinge on an SLA and the data is collected from multiple frequency bins. To boost the performance and perform underdetermined DoA estimation, the difference co-array response matrices for all frequency bins are constructed first. Then, to merge the data from different frequency bins, we resort to the Jacobi-Anger approximation to transform the co-array response matrices of all frequency bins into a single virtual uniform linear array (ULA) response matrix. The major advantage of this approach is that the transformation matrices are all signal independent. For the special case where all sources share an identical distribution of the power spectrum, we develop two super-resolution off-the-grid DoA estimation approaches based on atomic norm minimization (ANM), one with and one without prior knowledge of the power spectrum. Our solution is able to resolve more sources than the number of antennas but also more than the number of degrees of freedom (DoF) of the difference co-array of the SLA. For the general case where each source has an arbitrary power spectrum, we propose a multi-task ANM method to exploit the joint sparsity from all frequency bins. Simulation results show that our proposed methods present a clear performance advantage over existing methods, and achieve an estimation accuracy close to the associated Cramér-Rao bounds (CRBs). [ABSTRACT FROM AUTHOR]

For stationary signals in time, the weak law of large numbers (WLLN) states that ensemble and realization averages are within $\epsilon$ of each other with a probability of order ${\mathcal O}(1/N\epsilon ^2)$ when considering $N$ signal components. The graph WLLN introduced in this paper shows that the same is essentially true for signals supported on graphs. However, the notions of stationarity, ensemble mean, and realization mean are different. Recent papers have defined graph stationary signals as those that satisfy a form of invariance with respect to graph diffusion. The ensemble mean of a graph stationary signal is not a constant but a node-varying signal whose structure depends on the spectral properties of the graph. The realization average of a graph signal is defined here as an average of successive weighted averages of local signal values with signal values of neighboring nodes. The graph WLLN shows that these two node-varying signals are within $\epsilon$ of each other with probability of order ${\mathcal O}(1/N\epsilon ^2)$ in at least some nodes. In stationary time signals, the realization average is not only a consistent estimator of the ensemble mean but also optimal in terms of mean squared error (MSE). This is not true for graph signals. Optimal MSE graph filter designs are also presented. An example problem concerning the estimation of the mean of a Gaussian random field is presented. [ABSTRACT FROM AUTHOR]

This paper studies linear distributed estimation of an unknown random parameter vector in a bandwidth-constrained multisensor network. To meet the bandwidth limitations, each sensor converts its observation into a low-dimensional datum via a suitable linear transformation. Then, the fusion center estimates the parameter vector by linearly combining all the received low-dimensional data, aiming at minimizing the estimation mean square error. The main purpose of this paper is to jointly determine the compression dimension of each sensor (referred to as dimension assignment) and design the corresponding compression matrix when the total compression dimensions is limited. Such a joint design problem can be formulated as a rank-constrained optimization problem and it is shown to be NP-hard for the first time. In addition, successive quadratic upper-bound minimization (SQUM), SQUM-block coordinate descent (SQUM-BCD) and nuclear norm regularization (NNR) methods are developed to solve it approximately. Furthermore, we show that any accumulation point of the sequence generated by the SQUM method satisfies the Karush-Kuhn-Tucker conditions of the rank-constrained optimization problem, and the Phase II algorithm of the SQUM-BCD and NNR methods (both are two-phase algorithms and have the same Phase II algorithm) guarantees convergence at least to a stationary point. Numerical experiments illustrate the advantages of the proposed methods compared with the existing method. [ABSTRACT FROM AUTHOR]

Estimation of multiple common remainders from a sequence of erroneous residue sets is an important step for the robust generalized Chinese Remainder Theorem (CRT). This paper considers the problem of how to estimate the two common remainders from their residue sets modulo a set of moduli. To measure the errors properly under the modular operation, we introduce two type circular distances. Based on these circular distances, two estimation methods are proposed by properly grouping the erroneous remainders into two ordered clusters. Both of the two methods perform better with lower computational complexities than the existing methods. In this paper, theoretical analysis as well as analytical results for the two proposed methods are obtained. For the first method, the two optimal estimates are proved to be in a finite set with no more than $L$ candidates, where $L$ is the number of the given moduli. The second method have closed forms. Simulation results show that the two proposed methods have nearly the same performance. These optimal estimates can improve the performance of the robust generalized CRT significantly. [ABSTRACT FROM AUTHOR]

This paper considers the problem of network structure manipulation in the absence of a central coordinator that collects network information and makes decisions. The primary focus is on the spectral radius minimization problem by removing/rewiring links to control epidemic spreading over networks. The resulting optimizations are generally combinatorial and NP-hard. The lack of the central base prevents us from solving such problems in a centralized fashion, thus driving the need for distributed computation and collaborative decision-making to support effective topology modification. In this paper, a distributed estimation scheme involving event-based communication and parallel algorithms is developed to enhance network capability against epidemics. Based on this low-complexity estimation algorithm, fully distributed strategies are proposed to enable individuals to sequentially discern the critical in-network contact, and to implement the desired link operation solely. We further extend the acquisitions to a more flexible framework based on a “coevolutionary networks” picture and discuss the optimality of solutions from an algebraic and topological perspective. Extensive simulation examples are presented to demonstrate the effectiveness of the proposed strategies. [ABSTRACT FROM AUTHOR]

In the practical radar with multiple antennas, the antenna imperfections degrade the system performance. In this paper, the problem of estimating the direction of arrival (DOA) in a multiple-input and multiple-output (MIMO) radar system with unknown mutual coupling effect between antennas is investigated. To exploit the target sparsity in the spatial domain, the compressed sensing based methods have been proposed by discretizing the detection area and formulating the dictionary matrix, so an off-grid gap is caused by the discretization processes. In this paper, different from the present DOA estimation methods, both the off-grid gap due to the sparse sampling and the unknown mutual coupling effect between antennas are considered at the same time, and a novel sparse system model for DOA estimation is formulated. Then, a novel sparse Bayesian learning (SBL)-based method named sparse Bayesian learning with the mutual coupling (SBLMC) is proposed, where an expectation-maximum-based method is established to estimate all the unknown parameters including the noise variance, the mutual coupling vectors, the off-grid vector, and the variance vector of scattering coefficients. Additionally, the prior distributions for all the unknown parameters are theoretically derived. With regard to the DOA estimation performance, the proposed SBLMC method can outperform state-of-the-art methods in the MIMO radar with unknown mutual coupling effect, while keeping the acceptable computational complexity. [ABSTRACT FROM AUTHOR]

This paper has a twofold goal. The first aim is to provide a deeper understanding of the family of the real elliptically symmetric (RES) distributions by investigating their intrinsic semiparametric nature. The second aim is to derive a semiparametric lower bound for the estimation of the parametric component of the model. The RES distributions represent a semiparametric model, where the parametric part is given by the mean vector and by the scatter matrix, while the non-parametric, infinite-dimensional, part is represented by the density generator. Since, in practical applications, we are often interested only in the estimation of the parametric component, the density generator can be considered as nuisance. The first part of this paper is dedicated to conveniently place the RES distributions in the framework of the semiparametric group models. In the second part, building on the mathematical tools previously introduced, the constrained semiparametric Cramér–Rao bound (CSCRB) for the estimation of the mean vector and of the constrained scatter matrix of a RES distributed random vector is introduced. The CSCRB provides a lower bound on the mean squared error of any robust $M$ -estimator of mean vector and scatter matrix when no a priori information on the density generator is available. A closed-form expression for the CSCRB is derived. Finally, in simulations, we assess the statistical efficiency of the Tyler's and Huber's scatter matrix $M$ -estimators with respect to the CSCRB. [ABSTRACT FROM AUTHOR]

Low-rank matrix estimation plays a central role in various applications across science and engineering. Recently, nonconvex formulations based on matrix factorization are provably solved by simple gradient descent algorithms with strong computational and statistical guarantees. However, when the low-rank matrices are asymmetric, existing approaches rely on adding a regularization term to balance the scale of the two matrix factors which in practice can be removed safely without hurting the performance when initialized via the spectral method. In this paper, we provide a theoretical justification to this for the matrix sensing problem, which aims to recover a low-rank matrix from a small number of linear measurements. As long as the measurement ensemble satisfies the restricted isometry property, gradient descent—in conjunction with spectral initialization—converges linearly without the need of explicitly promoting balancedness of the factors; in fact, the factors stay balanced automatically throughout the execution of the algorithm. Our analysis is based on analyzing the evolution of a new distance metric that directly accounts for the ambiguity due to invertible transforms, and might be of independent interest. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of classifying clutter returns into statistically homogeneous subsets. The classification procedures are devised assuming latent variables, which represent the classes to which each range bin belongs, and three different models for the structure of the clutter covariance matrix. Then, the expectation-maximization algorithm is exploited in conjunction with cyclic estimation procedures to come up with suitable estimates of the unknown parameters. Finally, the classification is performed by maximizing the posterior probability that a range bin belongs to a specific class. The performance analysis of the proposed classifiers is conducted over synthetic data as well as real recorded data and highlights that they represent a viable means to cluster clutter returns with respect to their range. [ABSTRACT FROM AUTHOR]

The estimation of mutual information (MI) or conditional mutual information (CMI) from a set of samples is a long-standing problem. A recent line of work in this area has leveraged the approximation power of artificial neural networks and has shown improvements over conventional methods. One important challenge in this new approach is the need to obtain, given the original dataset, a different set where the samples are distributed according to a specific product density function. This is particularly challenging when estimating CMI. In this paper, we introduce a new technique, based on k nearest neighbors (k-NN), to perform the resampling and derive high-confidence concentration bounds for the sample average. Then the technique is employed to train a neural network classifier and the CMI is estimated accordingly. We propose three estimators using this technique and prove their consistency, make a comparison between them and similar approaches in the literature, and experimentally show improvements in estimating the CMI in terms of accuracy and variance of the estimators. [ABSTRACT FROM AUTHOR]

Causality graphs are routinely estimated in social sciences, natural sciences, and engineering due to their capacity to efficiently represent the spatiotemporal structure of multi-variate data sets in a format amenable for human interpretation, forecasting, and anomaly detection. A popular approach to mathematically formalize causality is based on vector autoregressive (VAR) models and constitutes an alternative to the well-known, yet usually intractable, Granger causality. Relying on such a VAR causality notion, this paper develops two algorithms with complementary benefits to track time-varying causality graphs in an online fashion. Their constant complexity per update also renders these algorithms appealing for big-data scenarios. Despite using data sequentially, both algorithms are shown to asymptotically attain the same average performance as a batch estimator which uses the entire data set at once. To this end, sublinear (static) regret bounds are established. Performance is also characterized in time-varying setups by means of dynamic regret analysis. Numerical results with real and synthetic data further support the merits of the proposed algorithms in static and dynamic scenarios. [ABSTRACT FROM AUTHOR]

Inferring network topologies from observed graph-structured data (also known as graph signals) is a crucial task in many applications of network science. Existing papers on network topology inference typically assume that the observations at all nodes are available. However, there are many situations where only partial observations can be collected due to application-specific constraints. To handle the missing data problem, we propose a framework that relies on heterogeneous incomplete data from a collection of related networks to identify multiple network topologies simultaneously. This work advocates the Gaussian graphical model (GGM) and casts the topology inference problem in terms of estimating the precision matrix that has a form of graph Laplacian. Firstly, an unbiased estimator for the covariance matrix of incomplete data is established and then algorithms based on the alternating direction method of multipliers (ADMM) are developed to jointly estimate graph topologies, rather than estimate each graph topology separately. So that we can borrow information across the multiple related networks to eliminate the impact of missing data. Moreover, non-asymptotic statistical analysis is provided, which proves the consistency of the graph estimator and enables us to investigate the effect of several key factors on the graph estimation error bound. Furthermore, based on the consistent graph estimator, an adaptive algorithm that utilizes the reweighting scheme is proposed to improve the estimation accuracy of the graph-edge structure. Finally, we evaluate our method on both real and synthetic datasets, and the experimental results demonstrate the advantage of our method in comparison with benchmarking algorithms. [ABSTRACT FROM AUTHOR]

In this paper, using the shrinkage-based approach for portfolio weights and modern results from random matrix theory we construct an effective procedure for testing the efficiency of the expected utility (EU) portfolio and discuss the asymptotic behavior of the proposed test statistic under the high-dimensional asymptotic regime, namely when the number of assets p increases at the same rate as the sample size n such that their ratio p/n approaches a positive constant c ∈ (0,1) as n → ∞. We provide an extensive simulation study where the power function and receiver operating characteristic curves of the test are analyzed. In the empirical study, the methodology is applied to the returns of S&P 500 constituents. [ABSTRACT FROM AUTHOR]

The paper presents a communication efficient distributed algorithm, $\mathcal {CIRFE}$ of the consensus+innovations type, to estimate a high-dimensional parameter in a multi-agent network, in which each agent is interested in reconstructing only a few components of the parameter. This problem arises, for example, when monitoring the high-dimensional distributed state of a large-scale infrastructure with a network of limited capability sensors and where each sensor is tasked with estimating some local components of the state. At each observation sampling epoch, each agent updates its local estimate of the parameter components in its interest set by simultaneously processing the latest locally sensed information (innovations) and the parameter estimates from agents (consensus) in its communication neighborhood given by a time-varying possibly sparse graph. Under minimal conditions, on the interagent communication network and the sensing models, almost sure convergence of the estimate sequence at each agent to the components of the true parameter in its interest set is established. Furthermore, the paper establishes the performance of $\mathcal {CIRFE}$ in terms of asymptotic covariance of the estimate sequences and specifically characterizes the dependencies of the component wise asymptotic covariance in terms of the number of agents tasked with estimating it. Finally, simulation experiments demonstrate the efficacy of $\mathcal {CIRFE}$. [ABSTRACT FROM AUTHOR]

Linear beamformers are optimal, in a mean square (MS) sense, when the signal of interest (SOI) and observations are jointly Gaussian and circular. Otherwise, linear beamformers become suboptimal. When the SOI and observations are zero-mean, jointly Gaussian and noncircular, optimal beamformers become widely linear (WL). They become nonlinear with a structure depending on the unknown joint probability distribution of the SOI and observations when the latter are jointly nonGaussian, assumption which is very common in radiocommunications. In this context, the paper aims at introducing, for small-scale systems, third-order Volterra minimum variance distortionless response (MVDR) beamformers, for the reception of an SOI, whose waveform is unknown but whose steering vector is known, corrupted by nonGaussian and potentially noncircular interference, omnipresent in practical situations. Properties, performance, complexity, and adaptive implementation of these beamformers in the presence of nonGaussian and potentially noncircular interference are analyzed in this paper. These new beamformers are shown to always improve, in the steady state, the performance of Capon beamformer for nonGaussian/circular interference, whereas some of them improve the performance of the WL MVDR beamformer for nonGaussian/noncircular interference. These new beamformers open new perspectives for spectrum monitoring of nonGaussian signals and for radiocommunication networks using such signals. [ABSTRACT FROM AUTHOR]

Estimating the joint probability mass function (PMF) of a set of random variables lies at the heart of statistical learning and signal processing. Without structural assumptions, such as modeling the variables as a Markov chain, tree, or other graphical model, joint PMF estimation is often considered mission impossible—the number of unknowns grows exponentially with the number of variables. But who gives us the structural model? What if we only observe random subsets of the variables, can we still reliably estimate the joint PMF of all? This paper shows, perhaps surprisingly, that if the joint PMF of any three variables can be estimated, then the joint PMF of all the variables can be provably recovered under relatively mild conditions. The result is reminiscent of Kolmogorov's extension theorem – consistent specification of lower-dimensional distributions induces a unique probability measure for the entire process. The difference is that for processes of limited complexity (rank of the high-dimensional PMF) it is possible to obtain complete characterization from only three-dimensional distributions. In fact not all three-dimensional PMFs are needed; and under more stringent conditions even two-dimensional will do. Exploiting multilinear (tensor) algebra, this paper proves that such higher-dimensional PMF completion can be guaranteed—several pertinent identifiability results are derived. It also provides a practical and efficient algorithm to carry out the recovery task. Judiciously designed simulations and real-data experiments on movie recommendation and data classification are presented to showcase the effectiveness of the approach. [ABSTRACT FROM AUTHOR]