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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]

Synchrophasor estimators are nowadays evaluated with the Total Vector Error (TVE) using the synchrophasor representations of the few benchmark signals. This synchrophasor dependence prevents its application to power signals of real events. A new method to obtain the synchrophasor of real signals is proposed in this paper. A finite impulse response (FIR) filter, designed with the nonic O-spline is proposed to obtain phasor estimates asymptotically close to those of an ideal bandpass filter. The phasor estimation accuracy of one or several Phasor Measurement Units (PMUs) can be then assessed using the standard. In addition, it is possible to design two FIR differentiators to obtain frequency and ROCOF estimates close enough to those of ideal differentiator filters, and largely compliant with the standard. This new set of filters opens the way to apply the synchrophasor standard to assess estimates of PMUs of different brands when they process the same signals of a power system event. In this paper, the erratic phasor and frequency estimates produced by a SEL-351 A PMU from a real distributed generation system are assessed to corroborate that the synchrophasor standard can be opened to this new application based on real signals from the field, previously considered as impossible. [ABSTRACT FROM AUTHOR]

Channel estimation is one of the main challenges for implementing reconfigurable intelligent surface (RIS)-aided communication system with a large number of antennas at the base station (BS) because RIS is equipped with many passive reflective elements without active transmitting/receiving and signal processing abilities. In this paper, we focus on the channel estimation in a general RIS-aided multi-user mmWave communication system. Specifically, a novel two-phase channel estimation scheme consisting of on-line and off-line phases is proposed to estimate the BS-RIS channel, RIS-user channel, and BS-user channel, respectively. Inspired by the characteristics of few scatterers in mmWave communication systems, the antenna domain channels are converted into the virtual angular domain channels by using the discrete Fourier transform (DFT) matrix. Thus, the estimation problem can be formulated as a compressed sensing (CS) problem, and solved by using efficient vector approximate message passing (VAMP) algorithm with expectation-maximization (EM) to learn unknown parameters and obtain the estimates simultaneously. Simulation results show that, the above algorithm with two choices of prior distributions in the proposed mmWave RIS-aided multi-user system has fast convergence speed and desirable estimation performance. [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]

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]

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]

In this paper, we investigate the problem of joint direction of departure (DoD) and direction of arrival (DoA) estimation with bistatic MIMO radar. Specifically, a weaved co-prime array (WCA) bistatic MIMO (WCA-bMIMO) radar is proposed to produce a hole-free sum-difference co-array, which enables to offer significantly increased degrees of freedom (DoFs) and enlarged array aperture. Moreover, the two-dimensional spatial smoothing method is introduced to construct a smoothed received signal, which helps to tackle the rank deduction problem rooted in the equivalent one-snapshot received signal from the sum-difference co-array. Subsequently, the joint DoD and DoA estimates can be obtained by extracting the three-way tensor model. Furthermore, co-array Cramer-Rao Bound (CRB) for the bistatic co-prime MIMO radar is provided. Finally, the superiorities of the proposed bistatic co-prime MIMO radar in accuracy and resolution are proved by numerical simulation results. [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]

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]

Hybrid antenna array consisting of analog subarrays provides a low-cost solution to achieving high beamforming gain in millimeter-wave/terahertz communication systems. For beam adjustment, beam scanning can be readily applied to find the line-of-sight (LoS) path. Conventionally, the beam scanning process is inefficient because the number of grids, together with the scanning period, has to be large to achieve high resolution. To improve the beam scanning efficiency, in this paper we propose an off-gird direction-of-arrival (DoA) estimation method utilizing unequal-sized subarrays. Specifically, we first provide a new solution to overcome the ambiguity problem, i.e., the hybrid antenna array may render the DoA estimate non-unique. That new solution is formed by designing the antenna numbers in the subarrays and can be easily combined with the beam scanning process. We then propose a three-stage beam scanning strategy. At the first stage, coarse scanning is applied to roughly steer the subarrays along the LoS path. At the second stage, a simple DoA estimator is employed to obtain the candidate DoAs. Finally, beam scanning is performed again on the candidate DoAs to obtain the final DoA estimate. Simulation results demonstrate that the proposed method can achieve higher DoA estimation accuracy in shorter scanning period than the conventional beam scanning method; and compared with existing methods developed for equal-sized subarrays, the proposed method is more robust against multi-path interference. [ABSTRACT FROM AUTHOR]

Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the theoretical understanding of this problem is still elusive. In this paper, we introduce and quantitatively characterize the two resolution limits for the line spectral estimation problem under deterministic noise: one is the minimum separation distance between the line spectra that is required for exact detection of their number, and the other is the minimum separation distance between the line spectra that is required for a stable recovery of their supports. The quantitative results imply a phase transition phenomenon in each of the two recovery problems, and also the subtle difference between the two. We further propose a sweeping singular-value-thresholding algorithm for the number detection problem and conduct numerical experiments. The numerical results confirm the phase transition phenomenon in the number detection problem. [ABSTRACT FROM AUTHOR]

Recently, maximum correntropy criterion (MCC) has been widely and successfully used in robust signal processing and machine learning, in which the correntropy is maximized instead of minimizing the popular mean square error (MSE) to improve the robustness with respect to outliers or impulsive noises. A lot of efforts have been devoted to derive different adaptive algorithms under MCC, but to date, little insight has been gained as to how the MCC solution will be influenced by outliers. In this paper, we investigate this problem and our focus is mainly on the parameter estimation of a simple linear errors-in-variables (EIVs) model with scalar variables. Under some conditions, we derive an upper bound on the absolute value of the estimation error and show that the MCC solution can get very close to the true value of the unknown parameter even with arbitrarily large outliers in both the input and output variables. Illustrative examples are provided to verify and clarify the theory. [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]

In the scope of vehicular communication networks, the nature of exchanged safety/warning messages renders itself highly location dependent, as it is usually for incident reporting. Vehicles are required to periodically exchange beacon messages that include speed, time, and GPS location information. Reported position information must be accurate and authentic. To mitigate the potential risk of location spoofing/falsifying attack, this paper presents Angle-of-Arrival (AoA) estimation as a physical layer authentication scheme for cross verification of the reported location information. We consider a multi-antenna road side unit under location spoofing attack. Within the considered vehicular communication settings, fundamental limits of AoA estimation are developed in terms of its Cramer–Rao Bound and existence of efficient estimator. The problem of deciding whether the received signal originated from the claimed GPS location is formulated as a two-sided hypotheses testing problem whose solution is given by Wald test statics. We give correct decision $P_D$ and false alarm $P_F$ probabilities in a closed form. To offset the gap between information theoretical studies and practical implementations of physical layer security architectures, theoretical results presented in this paper are further supported by detailed hardware implantation using software-defined radios and field experimental results. We show that the keystone for obtaining reliable AoA measurements is the accurate characterization of the array response vector. Our hardware measurements showed that, unlike idealized models, hardware imperfections leave the actual array response vector of non-structured form. To address this problem, we introduce the method for obtaining the actual array response vector empirically, which led to accurate and stable AoA measurements. Field experimental results shows the feasibility of the proposed AoA authentication scheme. [ABSTRACT FROM AUTHOR]

This paper presents the design and the experimental demonstration of transmission of spectrally efficient frequency division multiplexing (SEFDM) signals, using a single 5-GHz channel, from 81 to 86 GHz in the E-band frequency allocation. A purpose-built E-band SEFDM experimental demonstrator, consisting of transmitter and receiver GaAs microwave integrated circuits, along with a complete chain of digital signal processing is explained. Solutions are proposed to solve the channel and phase offset estimation and equalization issues, which arise from the well-known intercarrier interference between the SEFDM signal subcarriers. This paper shows the highest transmission rate of 12 Gb/s over a bandwidth varying between 2.67 to 4 GHz depending on the compression level of the SEFDM signals, which results in a spectral efficiency improvement by up to 50%, compared to the conventional orthogonal frequency division multiplexing modulation format. [ABSTRACT FROM AUTHOR]

This paper is an extension of the procedure pointed out to evaluate the distortion of the exponential signal, modeled as multiexponential signal with different amplitudes and time constants. This procedure evaluates the distortion by applying the Prony-like method to the signal reconstructed by zero-crossing time evaluated on the difference between the exponential original signal and the reference sinusoidal one. The extension proposed in this paper concerns with the use of the low-chirp signal as reference instead of the sinusoidal signal. The low-chirp signal permits to increase the number of the zero-crossing time in the section of exponential signal with the higher slope and decreasing in the section with the lower slope. This setting permits to estimate the distortion of the exponential signal with higher accuracy and precision. The parameters’ amplitude, phase, and start frequency of the reference low-chirp signal are used to reconstruct the exponential signal in the zero-crossing time in order to overcome the problem of the high-resolution sampling. Their estimation is carried out by the time-varying sine-fitting algorithm that processes the resulting signal that is the difference between the exponential original signal and the low-chirp signal. Advantages of the proposed extended procedure regard the direct estimation of the reference low-chirp signal parameters from the resulting signal over-sampled at low resolution, and the use of only one input acquisition channel that permits to overcome the synchronization problem between the reference and the resulting signal. The numerical and experimental tests validate the extended procedure. [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]

Timing skews among channels degrade seriously the time-interleaved analog-to-digital converter (TIADC) performance, which can be improved by the blind timing skew estimation (TSE) technique. In this paper, we proposed the all-phase fast Fourier transform (ApFFT) based on spectrum sparsity signal phase relationship blind TSE (ApFFT-SSPR-BLTSE) algorithm. The ApFFT-SSPR-BLTSE algorithm reduces computational complexity based on the phase relationship of the total output from TIADC and the corresponding reference channel output compared with the existing spectrum sparsity blind TSE (SS-BLTSE) algorithm. We also utilized the ApFFT technique to increase the accuracy of phase spectral estimation. Simulation results show that the proposed ApFFT-SSPR-BLTSE algorithm, which as a reduced number of fast Fourier transforms (FFTs) and low hardware complexity, has higher accuracy for blind TSE compared to the existing SS-BLTSE algorithm. In addition, this paper presents an efficient hardware architecture of the ApFFT-SSPR-BLTSE algorithm on the Xilinx Virtex-6 vlx550tff1759 field-programmable gate array (FPGA) chip for the blind TSE of the four-channel 400-MHz 14-bit TIADC real system. The validation results show that the proposed algorithm uses only a few percent of the hardware resources of the FPGA chip, and the mismatch spurs were suppressed to better than −81.54 dB. [ABSTRACT FROM AUTHOR]

This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A distribution-free analysis shows that by observing just a single linear measurement of each vector, one can consistently estimate the covariance matrix, in both infinity and spectral norm, and this analysis leads to precise rates of convergence in both norms. Through information-theoretic techniques, lower bounds showing that this estimator is minimax-optimal for both infinity and spectral norm estimation problems are established. These results are also specialized to give matching upper and lower bounds for estimating the population covariance of a collection of Gaussian vectors, again in the compressive measurement model. The analysis conducted in this paper shows that the effective sample complexity for this problem is scaled by a factor of $m^{2}/d^{2}$ , where $m$ is the compression dimension and $d$ is the ambient dimension. Applications to subspace learning (principal components analysis) and learning over distributed sensor networks are also discussed. [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]

In this paper, the problem of estimating the unknown degree of sparsity from compressive measurements without the need to carry out a sparse recovery step is investigated. While the sparsity order can be directly inferred from the effective rank of the observation matrix in the multiple snapshot case, this appears to be impossible in the more challenging single snapshot case. It is shown that specially designed measurement matrices allow to rearrange the measurement vector into a matrix such that its effective rank coincides with the effective sparsity order. In fact, it is proven that matrices that are composed of a Khatri–Rao product of smaller matrices generate measurements that allow to infer the sparsity order. Moreover, if some samples are used more than once, one of the matrices needs to be Vandermonde. These structural constraints reduce the degrees of freedom in choosing the measurement matrix, which may incur in a degradation in the achievable coherence. Thus, this paper also addresses suitable choices of the measurement matrices. In particular, Khatri–Rao and Vandermonde matrices are analyzed in terms of their coherence and a new design for Vandermonde matrices that achieves a low coherence is proposed. [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]

Most existing phasor measurement units (PMUs) are noncausal PMUs and they compensate for the group delay in PMU applications by shifting time stamps, which may result in high latency that will impair performance of PMU applications. This paper presents causal PMUs to reduce the group delay caused latency without shifting time stamps, and studies the impact of causality on performance of PMU algorithms. The paper first analyzes how causal and noncausal PMUs compensate for the group delay caused by digital filters and it is found that causal PMUs normally reduce latency by the group delay, whereas noncausal PMU will not. Then, the impact of causality on performance of PMU algorithms is investigated and analyzed by using the Hydro Quebec Research Institute (IREQ) PMU model and the IEEE PMU model. Finally, the simulation results carried out on two test systems highlight the difference between the causal method and the noncausal method under fault conditions in realistic multimachine setups. [ABSTRACT FROM AUTHOR]

Bilinear and Volterra models are important when dealing with nonlinear systems which arise in several signal processing applications. The former can approximate a large class of systems affine in the input with relatively low parametric complexity. Such an approximate bilinear model can be derived by means of Carleman bilinearization (CB). Then, a Volterra model can be computed from it, having the advantage of being linear in the parameters, but often involving a large number of them. In this paper, we develop efficient routines for CB and for computing the Volterra kernels of a bilinear system. We argue that they are useful for studying a class of systems for which a reference physical model is known. In particular, the so-derived kernels allow assessing the suitability of a Volterra filter and of other alternatives for modeling the system of interest. Techniques exploiting sparsity and low rank of involved matrices are proposed for alleviating computing cost. Several examples are given along the paper to illustrate their use, based on existing physical models of loudspeakers. [ABSTRACT FROM AUTHOR]

In dipole-antenna array signal-processing algorithm development, research has focused on “short dipoles” whose physical length ( $L$ ) is under (1/10) of a wavelength \lambda $ . Such electrically “short” dipoles have very small input impedances, rendering such “short” dipoles to be inefficient radiators. Practical dipoles, with an electrical length of ({L}/{\lambda }) \in [{0.1, 1}] , have notably larger input impedance, hence making them better radiators. Of such practical dipoles, this paper investigates their use for azimuth-polar direction finding and for polarization estimation. This paper will first present the measurement model (i.e., array manifold) of a triad of such practical dipoles, collocated in space and orthogonally oriented. This paper will then develop the corresponding closed-form algorithms to estimate the bivariate azimuth–elevation direction-of-arrival or the bivariate polarization. Such closed-form algorithms previously have been unavailable in the existing literature for such a triad of electrically “long” dipoles of pragmatic radiation efficiency. [ABSTRACT FROM AUTHOR]

This paper proposes a new acoustic vector sensor array geometry containing a sparse right triangular subarray with three guiding vector sensors plus an additional subarray with arbitrarily placed vector sensors at unknown locations and develops a new cumulant-based algorithm for two-dimensional direction estimation (CADE) of multiple non-Gaussian signals. In the CADE algorithm, three cumulant matrices are defined to form a third-order tensor, using which the direction cosines of the signal are recovered by utilizing parallel factor (PARAFAC) fitting. Furthermore, the PARAFAC model is extended to multiple cumulant matrices and a fourth-order tensor framework to enhance the identifiability issues and to improve the performance of the algorithm. Unlike most of the existing acoustic vector sensor direction estimation algorithms, the proposed algorithm imposes less geometric constraint on the array shape and requires no open-form two-dimensional searching and parameter pairing. Simulation results demonstrate the superiority of the CADE algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a threshold signal detector is proposed to improve the state estimation accuracy of an extended Kalman filter (EKF) and is validated experimentally with a microelectromechanical system electrostatic microscanner. A first-order derivative of Gaussian filter is used to detect and locate rapid changes in voltage signal caused by crossing of a threshold angle determined by maximum overlap of capacitive electrodes. The event-triggered measurement is used in the update step of the EKF to provide intermittent but more accurate angle measurements than those of the capacitive sensor's continuous output. Experiments on the electrostatic microscanner show that with the threshold signal detector incorporated; the average position estimation accuracy of the EKF is improved by 15.1% with largest improvement (30.3%) seen under low signal-to-noise ratio conditions. A parametric study is conducted to examine sampling frequency and capacitance profile, among other factors that may affect detection error and EKF accuracy. [ABSTRACT FROM AUTHOR]

This paper is focused on noncooperative target position estimation via the joint use of two-dimensional (2-D) hyperbolic and elliptic passive location techniques based on time difference of arrival (TDOA) and passive coherent locator (PCL) measurements, respectively. A fusion strategy is laid down at the signal processing level to obtain a reliable estimate of the current target position. With reference to the scenario with a single transmitter of opportunity, the mathematical model for joint exploitation of TDOA and PCL strategies is formulated. Then, the Cramer–Rao lower bound (CRLB) for the Cartesian coordinates of the target is established and the theoretical performance gains achievable over the localization technique using only TDOA or PCL observations are assessed. Finally, TDOA-PCL hybrid 2-D localization algorithms are provided and their performance in terms of root-mean-square error is compared with the square root of the CRLB. [ABSTRACT FROM AUTHOR]

Rapid voltage changes (RVCs) are power quality (PQ) events characterized by small and fast transitions between two steady-state root-mean-square (rms) voltage levels. RVCs occur quite often at the distribution level and are expected to be even more frequent in the future due to the increasing penetration of dynamic loads and renewable-based generators in the smart grid. Unlike other PQ events, RVCs are less critical, but also more difficult to detect than dips/sags and swells, due to their smaller voltage variations. Nevertheless, they can be harmful to generators’ control systems and electronic equipment in general. Moreover, they strongly affect flicker. The IEC Standard 61000-4-3:2015 clearly describes an algorithm for RVC detection. However, this approach is poorly characterized in the scientific literature. In fact, it suffers from some drawbacks. In this paper, some of them (e.g., rate-dependent detection limits and detection delays) are analyzed in depth. In addition, an alternative approach based on the estimation of the rate of change of rms voltage is proposed. Multiple simulation results show that the approach considered is more sensitive to noise, but also faster, especially when not so fast RVCs occur. Moreover, it allows measuring the rate of change of rms voltage, which is currently disregarded in the IEC Standard. [ABSTRACT FROM AUTHOR]

A novel control scheme is proposed in this paper for the sensorless control of interior permanent magnet synchronous machines (IPMSMs) with the automatic tracking of the maximum-torque-per-ampere (MTPA) trajectory. Differing from the conventional method that the estimation of the rotor position and the tracking of MTPA trajectory are two separate processes, the proposed control scheme can achieve sensorless MTPA control of IPMSMs in one step by defining and constructing a proper virtual q-axis inductance to directly calculate the current space vector angle along the MTPA trajectory rather than the rotor position, which greatly simplifies the whole implementation process. Meanwhile, considering that the virtual q-axis inductance is changing with the machine parameters and the applied load, a simple signal processing technique based on the virtual high-frequency signal injection is developed for the real time and accurate acquisition of the virtual q-axis inductance. Furthermore, in order to ensure the reliability and stability of the proposed control scheme, the effective range of the virtual q-axis inductance is analyzed in detail. Finally, the experimental results on an IPMSM demonstrate the proposed control scheme can achieve the high-performance sensorless control with accurate MTPA self-tracking operation. [ABSTRACT FROM AUTHOR]

This paper proposes a novel on-line rotor position estimation method for an aircraft wound-field synchronous starter/generator (WFSSG) in the low-speed region. The method is based on the fact that mutual inductance between stator and rotor windings of the main machine (MM) varies with the rotor position, so it is independent of magnetic saliency. High-frequency (HF) rotating voltage is imposed in the stator windings of the MM, and the rotor position information is extracted from the HF response current signals in the stator windings of the main exciter (ME) in WFSSG. Theoretical expressions of the HF response current signals containing rotor position information in the rotor and stator windings of the ME are derived. Then, harmonics in the ME stator windings are analyzed, and optimum frequencies of the injected HF voltage for MM and excited voltage for the ME are obtained. Also, a novel signal processing method without time delay is adopted to improve the signal-to-noise ratio of the extracted rotor position information. The performance of the proposed method is verified by the experimental results, and accurate rotor position can be estimated even if the magnetic saliency of the MM changes greatly during the start-up process. [ABSTRACT FROM AUTHOR]

This paper introduces a self-interference cancellation (SIC) technique for data over cable service interface specification (DOCSIS) 3.1 uplink system with full duplex. At DOCSIS 3.1 uplink environment with full duplex, cable modems (CMs) transmit their request information (upstream) to CM termination system (CMTS), and CMTS transmits its broadcasting data (downstream) through the same frequency band at the same time. Therefore, the upstream becomes a signal of interest (SoI), and consequently the high-power feedback downstream causes self-interference (SI) signal against SoI. However, under the practical DOCSIS 3.1 uplink environment, achieving time and frequency synchronization between upstream and downstream is a challenging problem and additional signal processing technique should be applied. Therefore, in order to improve the processing efficiency and to reflect practical communication environment, the time-domain SIC technique, which does not require any synchronization between upstream and downstream is proposed. Furthermore, since the proposed scheme can consider various practical signal processing aspects, such as multi-path fading channel estimation and nonlinear element estimation of SI signal, it can be efficiently applied for the practical DOCSIS 3.1 uplink system. Test results indicate that the uplink system with 1024QAM (mandatory maximum constellation) can be operated in the case that there is SI estimation interval with two OFDM symbols. [ABSTRACT FROM AUTHOR]

In this paper, we construct two tests for the weights of the global minimum variance portfolio (GMVP) in a high-dimensional setting, namely, when the number of assets $p$ depends on the sample size $n$ such that $\frac{p}{n}\rightarrow c \in (0,1)$ as $n$ tends to infinity. In the case of a singular covariance matrix with rank equal to $q$ we assume that $q/n\rightarrow \tilde{c}\in (0, 1)$ as $n\rightarrow \infty$. The considered tests are based on the sample estimator and on the shrinkage estimator of the GMVP weights. We derive the asymptotic distributions of the test statistics under the null and alternative hypotheses. Moreover, we provide a simulation study where the power functions and the receiver operating characteristic curves of the proposed tests are compared with other existing approaches. We observe that the test based on the shrinkage estimator performs well even for values of $c$ close to one. [ABSTRACT FROM AUTHOR]

This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and nonsmooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and proximal updates, respectively. The proposed algorithm is closely related to a previous algorithm, PG-EXTRA (W. Shi, Q. Ling, G. Wu, and W. Yin, “A proximal gradient algorithm for decentralized composite optimization,” IEEE Trans. Signal Process., vol. 63, no. 22, pp. 6013–6023, 2015), but has a few advantages. First of all, agents use uncoordinated step-sizes, and the stable upper bounds on step-sizes are independent of network topologies. The step-sizes depend on local objective functions, and they can be as large as those of the gradient descent. Second, for the special case without nonsmooth terms, linear convergence can be achieved under the strong convexity assumption. The dependence of the convergence rate on the objective functions and the network are separated, and the convergence rate of the new algorithm is as good as one of the two convergence rates that match the typical rates for the general gradient descent and the consensus averaging. We provide numerical experiments to demonstrate the efficacy of the introduced algorithm and validate our theoretical discoveries. [ABSTRACT FROM AUTHOR]

This paper concerns the sparse Bayesian learning (SBL) problem for group sparse signals. Group sparsity means that the signal coefficients can be divided into groups and that the entries in one group are simultaneously zero or nonzero. In SBL, each group is controlled by a hyperparameter, which is estimated by solving the marginal likelihood maximization (MLM) problem. MLM is used to maximize the marginal likelihood of a given hyper-parameter by fixing all others. The main contribution of this paper is to extend the fast marginal likelihood maximization (FMLM) method to the group sparsity case. The key process of realizing FMLM in the group sparsity case is solved by finding the roots of a polynomial. Hence, the local maximum of the marginal likelihood can be found exactly, and the final estimation is obtained more efficiently. Furthermore, most large matrix inverses involved in MLM are replaced with the eigenvalue decompositions of much smaller matrices, which substantially reduces the computational complexity. Numerical results with both simulated and real data demonstrate the excellent performance and relatively high computational efficiency of the proposed method. [ABSTRACT FROM PUBLISHER]

In this paper, we derive closed-form and near closed-form solutions for joint source and sensor localization from time-difference-of-arrival (TDOA) measurements. In our previous works, we derived closed-form and near closed-form solutions for joint source and sensor localization from time-of-arrival (TOA) measurements. On the basis of these results, the main idea in this paper is to recover the TOA information only from the given TDOA measurements. We show that the TOA information can be recovered by using the low-rank property of the difference of square TOA-distance matrix in a closed-form or a near closed-form based on the linear method of solving polynomial equations. Since the low-rank property is reliable even in noisy cases, the TOA recovery works well under both small and large amounts of noise. The root-mean-squared errors achieved by our proposed algorithms are compared with the Cramér–Rao lower bound in synthetic experiments. The results show that the proposed methods work well for both small and large amounts of noise and for small and large numbers of sources and sensors. [ABSTRACT FROM PUBLISHER]

This paper is Part I of a series of two papers where we address sequential estimation of wide-sense stationary autoregressive moving average (ARMA) state processes by particle filtering. In Part I, we present estimation methods for ARMA processes of known model order, where the parameters are first known and then unknown. The driving noise of the ARMA process is Gaussian with unknown variance. We derive the transition density of the ARMA state for settings that correspond to different assumptions of a priori knowledge. Instead of estimating all the unknown parameters of the model, we treat them by Rao-Blackwellization. We propose a particle filtering method, with appropriate variations according to available information, for sequential estimation of the unknown state as it evolves with time. We demonstrate the performance of the proposed methods by extensive computer simulations. [ABSTRACT FROM PUBLISHER]

This is Part II of a series of two papers where we address sequential estimation of wide-sense stationary autoregressive moving average (ARMA) state processes by particle filtering. In Part I, we considered a state-space model where the state was an ARMA process of known order and where the parameters of the process could be known or unknown. In this paper, we extend our work from Part I by considering the same type of models, with the added complexity that the ARMA processes are now of unknown order. Instead of working on a scheme that first tracks the state by operating with different assumed models, and then selects the best model by using a predefined criterion, we present a method that directly estimates the state without the need of knowing the model order. We derive the transition density of the state for unknown ARMA model order, and propose a particle filter based on that density and the empirical Bayesian methodology. We demonstrate the performance of the proposed method with computer simulations and compare it with the methods from Part I. [ABSTRACT FROM PUBLISHER]

In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., DOA). Sparse arrays such as nested arrays, coprime arrays, and minimum redundancy arrays (MRA) have reduced mutual coupling compared to uniform linear arrays (ULAs). These arrays also have a difference coarray with O\left(N^2\right) virtual elements, where $N$ is the number of physical sensors, and can therefore resolve O\left(N^2\right) uncorrelated source directions. But these well-known sparse arrays have disadvantages: MRAs do not have simple closed-form expressions for the array geometry; coprime arrays have holes in the coarray; and nested arrays contain a dense ULA in the physical array, resulting in significantly higher mutual coupling than coprime arrays and MRAs. In a companion paper, a sparse array configuration called the (second-order) super nested array was introduced, which has many of the advantages of these sparse arrays, while removing most of the disadvantages. Namely, the sensor locations are readily computed for any $N$ (unlike MRAs), and the difference coarray is exactly that of a nested array, and therefore hole-free. At the same time, the mutual coupling is reduced significantly (unlike nested arrays). In this paper, a generalization of super nested arrays is introduced, called the $Q$th-order super nested array. This has all the properties of the second-order super nested array with the additional advantage that mutual coupling effects are further reduced for $Q > 2$. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of these arrays. [ABSTRACT FROM PUBLISHER]

In this paper, we address the problem of subspace averaging, with special emphasis placed on the question of estimating the dimension of the average. The results suggest that the enumeration of sources in a multi-sensor array, which is a problem of estimating the dimension of the array manifold, and as a consequence the number of radiating sources, may be cast as a problem of averaging subspaces. This point of view stands in contrast to conventional approaches, which cast the problem as one of identifiying covariance models in a factor model. We present a robust formulation of the proposed order fitting rule based on majorization–minimization algorithms. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. By means of simulation examples, we show that the proposed SA criterion is especially effective in high-dimensional scenarios with low sample support. [ABSTRACT FROM AUTHOR]

Spike estimation from calcium (Ca $^{2+}$) fluorescence signals is a fundamental and challenging problem in neuroscience. Several models and algorithms have been proposed for this task over the past decade. Nevertheless, it is still hard to achieve accurate spike positions from the Ca $^{2+}$ fluorescence signals. While existing methods rely on data-driven methods and the physiology of neurons for modeling the spiking process, this paper exploits the nature of the fluorescence responses to spikes using signal processing. We first motivate the problem by a novel analysis of the high-resolution property of minimum-phase group delay (GD) functions for multi-pole resonators. The resonators could be connected either in series or in parallel. The Ca $^{2+}$ indicator responds to a spike with a sudden rise, that is followed by an exponential decay. We interpret the Ca $^{2+}$ signal as the response of an impulse train to the change in Ca $^{2+}$ concentration, where the Ca $^{2+}$ response corresponds to a resonator. We perform minimum-phase GD-based filtering of the Ca $^{2+}$ signal for resolving spike locations. The performance of the proposed algorithm is evaluated on nine datasets spanning various indicators, sampling rates, and mouse brain regions. The proposed approach, GDspike, is compared with other spike estimation methods, including MLspike, Vogelstein de-convolution algorithm, and data-driven spike-triggered mixture model. The performance of GDspike is superior to that of the Vogelstein algorithm and is comparable to that of MLspike. It can also be used to post-process the output of MLspike, which further enhances the performance. [ABSTRACT FROM AUTHOR]

Timing advance (TA) estimation at the base station (BS) and reliable decoding of random access response (RAR) at the users are important steps in the initial random access (RA) procedure. However, due to limited availability of physical resources dedicated for RA, successful completion of RA requests would become difficult in high user density scenarios, due to contention among users requesting RA. In this paper, we propose to use the large antenna array at the massive multiple input multiple output BS to jointly group RA requests from different users using the same RA preamble. We then beamform the common RAR of each detected user group onto the same frequency resource, in such a way that most users in the group can reliably decode the RAR. The proposed RAR beamforming therefore automatically resolves the problem of collision between multiple RA requests on the same preamble, which reduces the RA latency significantly as compared to LTE. Analysis and simulations also reveal that for a fixed desired signal-to-interference-and-noise ratio of the received RAR, both the required per-user preamble transmission power and the total RAR beamforming power can be decreased roughly by 1.5 dB with every doubling in the number of BS antennas. [ABSTRACT FROM AUTHOR]

Passive source localization is an important research area with numerous applications in mobile communications and signal processing. This paper presents an analysis of energy-based localization performance with unknown transmit power using received signal strength (RSS) and RSS difference (RSSD) models. These models are widely used because of their low cost and simple implementation. Previous studies were based on the assumption that the source node transmit power is known, which is not practical in many situations. The Cramér–Rao lower bound for the RSS and RSSD models with correlated noise is derived as a performance benchmark for the mean squared error (MSE) of the location and transmit power estimation. It is shown that the MSE can be factored into two independent terms corresponding to the geometric distribution of the sensors and the channel parameters including the noise variance. The effect of the sensor and source node positions on the location accuracy and the MSE is derived via the geometric dilution of precision (GDOP). The GDOP is then used to evaluate the effect of the joint estimation of unknown power and source location on the performance. Lower bounds on the GDOP are derived to obtain the minimum MSE. The RSSD solution is obtained by formulating the nonlinear and nonconvex objective functions into a convex optimization problem through relaxation and semidefinite programming. Simulation results are presented with the source inside or outside the sensor network. [ABSTRACT FROM AUTHOR]

In this paper, we study the low complexity reception of multiuser signals in uplink millimeter wave (mmWave) communications using a partially connected hybrid antenna array. Exploiting the mmWave channel property, we propose a low-complexity user-directed multiuser receiver with three novel schemes for allocating subarrays to users. This receiver only requires the knowledge of angles-of-arrival (AoAs) for dominating paths and a small amount of equivalent channel information instead of perfect channel state information. For comparison, we also derive a successive interference cancellation-based solution as a performance benchmark. We design two types of reference signals with the channel estimation method to enable efficient and simple estimation for AoA and equivalent baseband channel. Also, we provide analytical results for the performance of the AoA estimation, using the lower bounds of mean square errors in line-of-sight dominated mmWave channels. The simulation results validate that the proposed channel estimation method is effective when employed in combination with a zero-forcing equalizer. [ABSTRACT FROM AUTHOR]

In this paper, we consider the uplink channel parameter estimation problem in the presence of pilot contamination for massive multiple-input-multiple-output (MIMO) systems. We propose a parallel factor (PARAFAC)-based estimation scheme, which exploits the low-rank property of massive MIMO channels caused by the finite scattering in a physical environment. Specifically, we first parameterize the channel in terms of three parameters, i.e., fading coefficients, directions of arrival (DOAs), and delays; thereby, the channel is characterized via three equivalent PARAFAC models. Then, the proposed PARAFAC-based scheme is developed, which jointly estimates these three channel parameters using an alternating least squares (ALS) algorithm. Therein, we certify the identifiability of the three channel parameters of the PARAFAC models to mitigate the pilot contamination and state the convergence of the ALS algorithm, which guarantees that the three channel parameters can be uniquely determined with the proposed scheme. Moreover, to further reduce the computational complexity, two advanced schemes are proposed by antenna selection and reducing the estimation frequency of DOAs and delays, respectively. Simulation results show that the proposed schemes can achieve both low computational complexities and close to optimal Cramer–Rao Bound performance. [ABSTRACT FROM AUTHOR]

Atmospheric ice accretion is considered a severe safety issue for technical systems such as communication infrastructure, power lines, blades of wind turbines, and so on in cold climate regions. Among different sensing systems to detect and provide reliable information about the state of ice, capacitive sensing has been reported as a suitable technique. In capacitive sensing, measured capacitances are influenced due to ice accretion. Signal processing for ice sensors requires to estimate parameters for the state of ice from the data. In this paper, we present a model-based estimation approach for capacitive ice sensors. We analyze different electrode topologies for ice sensing and provide a statistical analysis of the sensor behavior. We hereby consider the random nature of natural ice accretion. From simulations, we show how a statistical model for the measurement process can be derived and demonstrate the construction of estimation algorithms within the Bayesian framework. We will demonstrate the capability of our approach for automated ice detection by means of long-term field data showing the ability to estimate ice layers with a precision better than 1 mm. [ABSTRACT FROM AUTHOR]

Covariance matrix estimation concerns the problem of estimating the covariance matrix from a collection of samples, which is of extreme importance in many applications. Classical results have shown that $O(n)$ samples are sufficient to accurately estimate the covariance matrix from $n$ -dimensional independent Gaussian samples. However, in many practical applications, the received signal samples might be correlated, which makes the classical analysis inapplicable. In this paper, we develop a nonasymptotic analysis for the covariance matrix estimation from linearly-correlated Gaussian samples. Our theoretical results show that the error bounds are determined by the signal dimension $n$ , the sample size $m$ , and the shape parameter of the distribution of the correlated sample covariance matrix. Particularly, when the shape parameter is a class of Toeplitz matrices (which is of great practical interest), $O(n)$ samples are also sufficient to faithfully estimate the covariance matrix from correlated samples. Simulations are provided to verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

Global navigation satellite system reflectometry (GNSS-R) is a new remote sensing technique, which can be used to measure a wide range of geophysical parameters. GNSS-R makes use of the simultaneous reception of the direct transmission and the coherent surface reflections of the GNSS signal with either a single antenna or multiple separate antennas. This paper presents a new snow depth estimation method using a combination of pseudorange and carrier phase of GNSS dual-frequency signals. The proposed method is geometry-free and is not affected by ionospheric delays. The formulas of the amplitude attenuation factor of reflected signals, multipath-induced carrier-phase error, and pesudorange error for ground-based GNSS receivers are used to describe the combined signals. Using theoretical formulas instead of in situ measurement data, analytical linear models are established in advance to describe the relationship between snow depth and main frequency of combined signal time series. When the main frequency of the combined measurements is obtained by spectrum analysis, the model is used to determine snow depth. Two experimental data sets recorded in two different environments were used to test the proposed method. The results demonstrate that there exists good agreement between the proposed method and the ground-truth measurements. [ABSTRACT FROM AUTHOR]

Fast and accurate frequency estimation of a complex sinusoidal plays an important role in many applications, including communications, radar, and sonar. This paper presents two methods for the frequency estimation of a complex sinusoidal in noisy environments. The proposed methods interpolate on shifted DFT coefficients to acquire the frequency estimates iteratively. The first method interpolates on the $q$ -shifted DFT coefficients of the signal, whose optimum iteration number is found to be a logarithmic function of the signal length. Furthermore, we also show that by appropriately selecting the value of the shift $q$ , the proposed method becomes asymptotically efficient. In the second method, we use hybrid half-shifted and $q$ -shifted DFT interpolators together, which converges in only two iterations. It is shown that both of the estimators are asymptotically unbiased with their mean square errors performing on the Crámer–Rao lower bound. Theoretical results are validated by extensive computer simulations. [ABSTRACT FROM AUTHOR]

The problem of high range resolution profile (HRRP) estimation is considered in this paper. In particular, stepped frequency waveforms are devised to enhance the target range profile (RP) estimation accuracy. The basic idea relies on the dynamic optimization of the probing waveform accounting for some feedback information to minimize the profile estimation error. The transmitted frequency hopping pattern is selected so as to minimize the predicted Cramer–Rao lower bound (CRLB) associated with the amplitudes and locations of the scattering centers falling in the coarse range bin under test (i.e., the target profile). Specifically, it is assumed that the target imaging is initially performed via a conventional linear stepped frequency transmission, hence, based on the collected data, an initial prediction of the target profile is derived (perception). Then, the RP estimation is enhanced progressively according to the cognitive paradigm, via a specific frequency pattern selection at the next transmission (action). The results highlight the capabilities of the cognitive approach to provide interesting benefits with respect to the classic linear stepped frequency strategy. [ABSTRACT FROM AUTHOR]