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In array processing, sparse arrays are capable of resolving $\mathcal {O}(N^2)$ uncorrelated sources with $N$ sensors. Sparse arrays have this property because they possess uniform linear array (ULA) segments of size $\mathcal {O}(N^2)$ in the difference coarray, defined as the differences between sensor locations. However, the coarray structure of sparse arrays is susceptible to sensor failures and the reliability of sparse arrays remains a significant but challenging topic for investigation. In the companion paper, a theory of the $k$ -essential family, the $k$ -fragility, and the $k$ -essential Sperner family were presented not only to characterize the patterns of $k$ faulty sensors that shrink the difference coarray, but also to provide a number of insights into the robustness of arrays. This paper derives closed-form characterizations of the $k$ -essential Sperner family for several commonly used array geometries, such as ULA, minimum redundancy arrays (MRA), minimum holes arrays (MHA), Cantor arrays, nested arrays, and coprime arrays. These results lead to many insights into the relative importance of each sensor, the robustness of these arrays, and the DOA estimation performance in the presence of sensor failure. Broadly speaking, ULAs are more robust than coprime arrays, while coprime arrays are more robust than maximally economic sparse arrays, such as MRA, MHA, Cantor arrays, and nested arrays. [ABSTRACT FROM AUTHOR]

This paper proposes a novel algorithm to determine the optimal orientation of sensing axes of redundant inertial sensors such as accelerometers and gyroscopes (gyros) for increasing the sensing accuracy. In this paper, we have proposed a novel iterative algorithm to find the optimal sensor configuration. The proposed algorithm utilizes the majorization-minimization (MM) algorithm and the duality principle to find the optimal configuration. Unlike the state-of-the-art approaches which are mainly geometrical in nature and restricted to sensors’ noise being uncorrelated, the proposed algorithm gives the exact orientations of the sensors and can easily deal with the cases of correlated noise. The proposed algorithm has been implemented and tested via numerical simulation in the MATLAB. The simulation results show that the algorithm converges to the optimal configurations and shows the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper considers a low-complexity iterative linear minimum mean square error (LMMSE) multiuser detector for the multiple-input and multiple-output system with nonorthogonal multiple access (MIMO-NOMA), where multiple single-antenna users simultaneously communicate with a multiple-antenna base station (BS). While LMMSE being a linear detector has a low complexity, it has suboptimal performance in multiuser detection scenario due to the mismatch between LMMSE detection and multiuser decoding. Therefore, in this paper, we provide the matching conditions between the detector and decoders for MIMO-NOMA, which are then used to derive the achievable rate of the iterative detection. We prove that a matched iterative LMMSE detector can achieve the optimal capacity of symmetric MIMO-NOMA with any number of users, the optimal sum capacity of asymmetric MIMO-NOMA with any number of users, all the maximal extreme points in the capacity region of asymmetric MIMO-NOMA with any number of users, and all points in the capacity region of two-user and three-user asymmetric MIMO-NOMA systems. In addition, a kind of practical low-complexity error-correcting multiuser code, called irregular repeat-accumulate code, is designed to match the LMMSE detector. Numerical results shows that the bit error rate performance of the proposed iterative LMMSE detection outperforms the state-of-art methods and is within 0.8 dB from the associated capacity limit. [ABSTRACT FROM AUTHOR]

Signal classification problems arise in a wide variety of applications, and their demand is only expected to grow. In this paper, we focus on the wireless sensor network signal classification setting, where each sensor forwards quantized signals to a fusion center to be classified. Our primary goal is to train a decision function and quantizers across the sensors to maximize the classification performance in an online manner. Moreover, we are interested in sparse sensor selection using a marginalized weighted kernel approach to improve network resource efficiency by disabling less reliable sensors with minimal effect on classification performance. To achieve our goals, we develop a multi-sensor online kernel scalar quantization (MSOKSQ) learning strategy that operates on the sensor outputs at the fusion center. Our theoretical analysis reveals how the proposed algorithm affects the quantizers across the sensors. Additionally, we provide a convergence analysis of our online learning approach by studying its relationship to batch learning. We conduct numerical studies under different classification and sensor network settings which demonstrate the accuracy gains from optimizing different components of MSOKSQ and robustness to reduction in the number of sensors selected. [ABSTRACT FROM AUTHOR]

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]

In this two-part paper, we consider the problem of adaptive multidimensional/multichannel signal detection in Gaussian noise with unknown covariance matrix. The test data (primary data) is assumed as a collection of sample vectors, arranged as the columns of a rectangular data array. The rows and columns of the signal matrix are both assumed to lie in known subspaces, but with unknown coordinates. Due to this feature of the signal structure, we name this kind of signal as the double subspace signal. Part I of this paper focuses on the adaptive detection in homogeneous environments, while Part II deals with the adaptive detection in partially homogeneous environments. Precisely, in this part, we derive the generalized likelihood ratio test (GLRT), Rao test, Wald test, as well as their two-step variations, in homogeneous environments. Three types of spectral norm tests (SNTs) are also introduced. All these detectors are shown to possess the constant false alarm rate (CFAR) property. Moreover, we discuss the differences between them and show how they work. Another contribution is that we investigate various special cases of these detectors. Remarkably, some of them are well-known existing detectors, while some others are still new. At the stage of performance evaluation, conducted by Monte Carlo simulations, both matched and mismatched signals are dealt with. For each case, more than one scenario is considered. [ABSTRACT FROM PUBLISHER]

This paper deals with the problem of adaptive multidimensional/multichannel signal detection in homogeneous Gaussian disturbance with unknown covariance matrix and structured (unknown) deterministic interference. The aforementioned problem extends the well-known Generalized Multivariate Analysis of Variance (GMANOVA) tackled in the open literature. In Part I of this paper, we have obtained the Maximal Invariant Statistic (MIS) for the problem under consideration, as an enabling tool for the design of suitable detectors which possess the Constant False Alarm Rate (CFAR) property. Herein, we focus on the development of several theoretically founded detectors for the problem under consideration. First, all the considered detectors are shown to be function of the MIS, thus proving their CFARness property. Second, coincidence or statistical equivalence among some of them in such a general signal model is proved. Third, strong connections to well-known (simpler) scenarios analyzed in adaptive detection literature are established. Finally, simulation results are provided for a comparison of the proposed receivers. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a frequency domain approach for eigenvalue-based detection of a primary user, based on equal gain combining (EGC) and spectrum estimation with Bartlett’s method. This paper considers two techniques for eigenvalue detection which are Maximum Eigenvalue Detection (MED) and the Maximum-Minimum Eigenvalue (MME) detector. We exploit the eigenvalues that are associated with the Hermitian form representation of Bartlett’s estimate to assess the performance of the aforementioned eigenvalue techniques in the frequency domain. For each case, we quantify the performance based on the probabilities of false alarm and missed detection over Rayleigh and Rician fading. A bivariate Mellin transform approach is employed to obtain the probability distribution function for the ratio of the extreme eigenvalues under each hypothesis. All obtained formulas are validated via Monte-Carlo simulations, and the results give a clear insight into the performance of the investigated methods. In frequency domain, MED outperforms both the MME detector and Periodogram-based energy detection even in a worst case scenario of noise uncertainty, while the MME detector exhibits heavy-tailed statistical characteristics and thus its receiver operating characteristics tend to stay on the line of no-discrimination. The performance of MED is further enhanced by careful choice of combinations of the total length of the sensing frame and number of sub-slots. [ABSTRACT FROM PUBLISHER]

In this paper, an approach for the adaptive detection of a hypothesized signal in unknown multivariate Gaussian interference-plus-noise is considered under conditions where the set of signal space eigenvalues of the interference-plus-noise covariance matrix of the training samples and the test vector may be mismatched. The detector is required to have the constant false alarm rate (CFAR) property under these conditions. The proposed approach uses two sets of interference-plus-noise data: First, vectors from a reference set, typically from range cells in the vicinity of the test cell that have the same interference-plus-noise covariance matrix ${\bf C}$ as the test vector, and second, vectors from a training set that are used to compute the weights for interference suppression in the test vector and the reference vectors. Because the matrices ${\bf C}$ and ${\bf \Sigma }$ are unknown, the average power level of the residual interference in the test cell and reference cells after interference suppression is unknown. The adaptive matched filter statistic at the test cell is normalized by the sample mean of similar statistics for the reference cells to evaluate the detection statistic, which is shown to have the CFAR property. The detection performance of the CFAR detector is analyzed and the effect of mismatches in the eigenvalues of the covariance matrices ${\bf C}$ and ${\bf \Sigma }$ is shown to be characterized by a single random variable $\rho$ , defined as the signal-to-interference-plus-noise ratio loss factor. Sample results are provided for purposes of illustration. [ABSTRACT FROM AUTHOR]

The focus of this paper is on detection theory for union of subspaces (UoS). To this end, generalized likelihood ratio tests (GLRTs) are presented for detection of signals conforming to the UoS model and detection of the corresponding “active” subspace. One of the main contributions of this paper is bounds on the performances of these GLRTs in terms of geometry of subspaces under various assumptions on the observation noise. The insights obtained through geometrical interpretation of the GLRTs are also validated through extensive numerical experiments on both synthetic and real-world data. [ABSTRACT FROM AUTHOR]

The framework of this paper is that of adaptive detection in Gaussian noise with unknown covariance matrix when the training samples do not share the same covariance matrix as the vector under test. We consider a class of constant false alarm rate detectors which depend on two statistics (β,t) whose distribution is parameter-free in the case of no mismatch and we analyze the impact of covariance mismatched training samples. More precisely, we provide a statistical representation of these two variables for an arbitrary mismatch. We show that covariance mismatch induces significant variations of the probability of false alarm and we investigate a way to mitigate this effect. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel neural network architecture for MIMO symbol detection, the Recurrent Equivariant MIMO detector (RE-MIMO). It incorporates several important considerations in wireless communication systems, such as robustness to channel misspecification, the ability to handle a varying number of users with a single model, and invariance to the (sequential) order in which the users interact with the system. The decoder consists of three main blocks; one block to inform the decoder of the channel model, one permutation equivariant block based on the successful transformer architecture to model transmitter channel interactions, and one fully connected feedforward network to predict the demodulated symbols for each user. These blocks are chained together into an iterative decoder that is trained through end-to-end backpropagation. RE-MIMO is compared against a broad range of existing methods and the results confirm the ability of the network to achieve the state of the art demodulation accuracy. In particular, RE-MIMO efficiently handles a variable number of transmitters with only a single trained model, is capable of dealing with correlated channels, and is robust to channel misspecification. In terms of computational complexity, RE-MIMO scales favorably with the number of transmitters. [ABSTRACT FROM AUTHOR]

This paper studies how to deploy sensors in the context of detection in adversarial environments. A fusion center is performing a binary hypothesis testing based on measurements from remotely deployed heterogeneous sensors. An attacker may compromise some of the deployed sensors, which send arbitrary measurements to the fusion center. The problems of interest are: to characterize the performance of the system under attack and, thus, develop a performance metric; and to deploy sensors within a cost budget, such that the proposed performance metric is maximized. In this paper, we first present a performance metric by formulating the detection in adversarial environments in a game theoretic way. A Nash equilibrium pair of the detection algorithm and attack strategy, with the deployed sensors given, is provided and the corresponding detection performance is adopted as the performance metric. We then show that the optimal sensor deployment can be determined approximately by solving a group of unbounded knapsack problems. We also show that the performance metric gap between the optimal sensor deployment and the optimal one with sensors being identical is within a fixed constant for any cost budget. The main results are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, cooperative sensor localization using asynchronous time-of-arrival measurements is investigated. It is well known that localization performance in wireless networks using time-based ranging or pseudo-ranging methods is greatly affected by the accuracy of the timing synchronization between the nodes involved in the estimation. Commonly, the original estimation problem is broken down into two subproblems, the synchronization problem and the localization problem, in what is known as a two-step approach. However, in this paper, the joint synchronization and localization problem is considered and examined for use in cooperative networks. It is discussed that the cooperation between the source nodes eliminates the need for high anchor node densities and improves localization performance significantly. Furthermore, the Cramér-Rao lower bounds (CRLB) and the maximum likelihood (ML) estimator are derived. It is shown that the ML estimator is highly nonlinear and nonconvex and must, therefore, be solved by using computationally complex algorithms. In order to reduce the complexity of the estimation, a novel semidefinite programming (SDP) relaxation method is developed by relaxing the original nonconvex ML problem, in such a way as to reformulate the estimation problem as a convex problem. The performance of the proposed SDP method is shown through computer simulations to nearly equal that of the ML estimator. The approach is also applied to the noncooperative case where it is found to be superior in performance than the previously proposed suboptimal estimators. Finally, complexity analyses are included for the estimators under consideration. [ABSTRACT FROM PUBLISHER]

Detecting the presence of signals in noise from multiple sources is a fundamental problem in statistical signal processing. In this paper, we consider multi-antenna signal detection when the noise covariance matrix is assumed to be arbitrary and unknown. We address this problem in the context of cognitive radio, where a multiple-primary-user detector is analyzed. This detector is known as Wilks' detector in statistics literature, which was derived under the generalized likelihood ratio criterion. We calculate the moments of Wilks' detector, which lead to simple and accurate approximate analytical formulae for the false alarm probability, the detection probability and the receiver operating characteristic. From the considered simulation settings, performance gain over existing detection algorithms is observed in scenarios with arbitrary and unknown noise correlation and multiple primary users. [ABSTRACT FROM PUBLISHER]

A system operator asks a group of sensors toexert costly effort to collect accurate measurements of a value of interest over time. At each time, each sensor is asked to report its observation to the operator, and is suitably compensated for the costly effort it exerts. Since both the effort and the observation are private information for the sensor, a naive payment scheme which compensates the sensor based only on its self-reported values of the effort and the measurements will lead to both shirking and falsification of outcomes by the sensor. In this paper, we design an appropriate compensation scheme to incentivize the sensors to both exert costly effort and then reveal the resulting observation truthfully. To this end, we formulate the problem as a repeated game and propose a compensation scheme that employs stochastic verification by the operator coupled with an algorithm to assign a reputation to each sensor. By including the history of the behavior exerted by the sensor in determining present payments, we show that the operator can incentivize higher effort as well as more frequent truthtelling by the sensors. [ABSTRACT FROM AUTHOR]

The estimation of mean matrix for a set of Hermitian positive definite (HPD) matrices can be considered based on a geometric framework. This kind of estimator is closely related to geometric measures, which can be established to measure the dissimilarity between two matrices on the matrix manifold. In this paper, the matrix spectral norm is exploited to derive a new geometric measure on the matrix manifold consisting of all HPD matrices. Correspondingly, the mean matrix associated with the new geometric measure on the matrix manifold is considered via two effective solution techniques. More specifically, the first method transforms the mean matrix estimation into a semidefinite programming problem solved by the interior point method; the second method exploits joint approximate diagonalization to diagonalize the given covariance matrices and then recasts the mean matrix estimation into an optimization problem with linear inequality constraints. Furthermore, two matrix detectors employing the proposed mean matrix estimators are designed for target detection using pulse Doppler radar with a small bunch of pulses. At the analysis stage, we show that the proposed matrix detector can guarantee the bounded constant false alarm rate property in terms of the clutter covariance matrix. Finally, numerical experiments based on simulated clutter data and real sea clutter data are performed to verify the effectiveness and robustness of the proposed matrix detectors. [ABSTRACT FROM AUTHOR]

The common approach to inertial sensor calibration has been to model the stochastic error signals of individual sensors independently, whether as components of a single inertial measurement unit (IMU) in different directions or arrayed in the same direction for redundancy. For this purpose, research in this domain has been focused on the proposal of various methods to improve the estimation of these models both from a computational and a statistical point of view. However, the separate calibration of the individual sensors is unable to take into account the dependence between each of them which can have an important impact on the precision of the navigation systems. In this paper, we develop a new approach to simultaneously model the individual signals and the dependence between them by studying the quantity called Wavelet Cross-Covariance and using it to extend the application of the Generalized Method of Wavelet Moments. This new method can be used in other settings for time series modeling, especially in cases where the dependence among signals may be hard to detect. Moreover, in the field of inertial sensor calibration, this approach can deliver important contributions among which the possibility to test dependence between sensors, integrate their dependence within the navigation filter and construct an optimal virtual sensor that can be used to simplify and improve navigation accuracy. The advantages of this method and its usefulness for inertial sensor calibration are highlighted through a simulation study and an applied example with a small array of XSens MTi-G IMUs. [ABSTRACT FROM AUTHOR]

The paper addresses the problem of designing radar detectors more robust than Kelly's detector to possible mismatches of the assumed target signature, but with no performance degradation under matched conditions. The idea is to model the received signal under the signal-plus-noise hypothesis by adding a random component, parameterized via a design covariance matrix, that makes the hypothesis more plausible in presence of mismatches. Moreover, an unknown power of such component, to be estimated from the observables, can lead to no performance loss, under matched conditions. Derivation of the (one-step) GLRT is provided for two choices of the design matrix, obtaining detectors with different complexity and behavior. A third parametric detector is also obtained by an ad-hoc generalization of one of such GLRTs. The analysis shows that the proposed approach can cover a range of different robustness levels that is not achievable by state-of-the-art with the same performance of Kelly's detector under matched conditions. [ABSTRACT FROM AUTHOR]

The problem of distributed inference with M-ary quantized data at the sensors is investigated in the presence of Byzantine attacks. We assume that the Byzantine nodes attack the inference network by modifying the symbol corresponding to the quantized data to one of the other symbols in the quantization alphabet-set and transmitting falsified symbol to the fusion center (FC). In this paper, we find the optimal Byzantine attack that blinds any distributed inference network. As the quantization alphabet size increases, a tremendous improvement in the security performance of the distributed inference network is observed. In addition to the perfect channel case, in Appendix A , we also analyze the optimal Byzantine attack when the channel between the nodes and the FC is noisy and is modelled as a discrete M-ary channel. We also investigate the optimal attack within the restricted space of highly-symmetric attack strategies, that maximally degrades the performance of the inference network in the presence of resource-constrained Byzantine attacks. A reputation-based scheme for identifying malicious nodes is also presented as the network's strategy to mitigate the impact of Byzantine threats on the inference performance of the distributed sensor network. We also provide asymptotic analysis to find the optimal reputation-based scheme as a function of the fraction of compromised nodes in the network. [ABSTRACT FROM PUBLISHER]

This paper addresses adaptive detection of range spread targets in the presence of thermal noise, jammer, and clutter. After motivating the study, a set of clutter-free training (CFT) data is considered to assist radar detection in absence of conventional secondary data sharing the same spectral properties as the interference of the cells under test. To this end, a maximum likelihood (ML) estimate of the unknown parameters is derived under the alternative hypothesis by leveraging the primary data and the CFT data simultaneously. Subsequently, the ML estimate is used to design decision rules based on generalized likelihood ratio, complex parameter Wald, and complex parameter Gradient test criteria. Furthermore, conditions guaranteeing the constant false alarm rate (CFAR) property of the proposed detectors are discussed. At the analysis stage, numerical examples are presented to evaluate the effectiveness of the proposed detectors in comparison with other detection schemes available in the literature. [ABSTRACT FROM AUTHOR]

The great success of deep learning (DL) has inspired researchers to develop more accurate and efficient symbol detectors for multi-input multi-output (MIMO) systems. Existing DL-based MIMO detectors, however, suffer several drawbacks. To address these issues, in this paper, we develop a model-driven DL detector based on variational Bayesian inference. Specifically, the proposed unrolled DL architecture is inspired by an inverse-free variational Bayesian learning framework which circumvents matrix inversion via maximizing a relaxed evidence lower bound. Two networks are respectively developed for independent and identically distributed (i.i.d.) Gaussian channels and arbitrarily correlated channels. The proposed networks, referred to as VBINet, have only a few learnable parameters and thus can be efficiently trained with a moderate amount of training samples. The proposed VBINet-based detectors can work in both offline and online training modes. An important advantage of our proposed networks over state-of-the-art MIMO detection networks such as OAMPNet and MMNet is that the VBINet can automatically learn the noise variance from data, thus yielding a significant performance improvement over the OAMPNet and MMNet in the presence of noise variance uncertainty. Simulation results show that the proposed VBINet-based detectors achieve competitive performance for both i.i.d. Gaussian and realistic 3GPP MIMO channels. [ABSTRACT FROM AUTHOR]

The theoretical basis for conventional acquisition of bandlimited signals typically relies on uniform time sampling and assumes infinite-precision amplitude values. In this paper, we explore signal representation and recovery based on uniform amplitude sampling with assumed infinite precision timing information. The approach is based on the delta-ramp encoder which consists of applying a one-level level-crossing detector to the result of adding an appropriate sawtooth-like waveform to the input signal. The output samples are the time instants of these level crossings, thus representing a time-encoded version of the input signal. For theoretical purposes, this system can be equivalently analyzed by reversibly transforming through ramp addition a nonmonotonic input signal into a monotonic one, which is then uniformly sampled in amplitude. The monotonic function is then represented by the times at which the signal crosses a predefined and equally-spaced set of amplitude values. We refer to this technique as amplitude sampling. The time sequence generated can be interpreted alternatively as nonuniform time sampling of the original source signal. We derive duality and frequency-domain properties for the functions involved in the transformation. Iterative algorithms are proposed and implemented for recovery of the original source signal. As indicated in the simulations, the proposed iterative amplitude-sampling algorithm achieves a faster convergence rate than frame-based reconstruction for nonuniform sampling. The performance can also be improved by appropriate choice of the parameters while maintaining the same sampling density. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of detection of sparse stochastic signals with quantized measurements in sensor networks. The observed sparse signals are assumed to follow the Bernoulli–Gaussian distribution. Due to the limited bandwidth in sensor networks, the local sensors are required to send quantized measurements to the fusion center. First, we propose a detector using the locally most powerful test (LMPT) strategy, called the quantized LMPT detector, for the problem of distributed detection of sparse signals with quantized measurements. Then, the local quantizers are designed to guarantee the near optimal detection performance of the proposed quantized LMPT detector. When the designed quantization thresholds are applied at the local sensors, we show that 1) the proposed 1-bit LMPT detector with 3.3L sensors achieves approximately the same detection performance as the clairvoyant LMPT detector with L sensors; 2) the proposed LMPT detector with 3-bit measurements can achieve detection performance comparable to the clairvoyant LMPT detector. Simulation results demonstrate the performance of the proposed quantized LMPT detector and corroborate our theoretical analysis. [ABSTRACT FROM AUTHOR]

Coprime sensor arrays (CSAs) can estimate the directions of arrival of O(MN) narrowband planewave sources using only O(M + N) sensors with the CSA product processor. All previous investigations on the product processed CSA's performance for detecting Gaussian signals assumed spatially white Gaussian noise. Considering the product and conventional delay-and-sum beamforming processors applied to the CSA geometry, this paper derives the detection gain for each processor under the deflection metric when the background noise is spatially correlated. The conditional probability distribution functions are also derived in closed form to evaluate and compare the receiver operating characteristic performances. Despite the nonlinear processing, the product processed CSA's detection performance closely rivals its conventional beamforming (CBF) counterpart, while also demonstrating greater robustness than the CBF to spatially correlated Gaussian noise. [ABSTRACT FROM AUTHOR]

The stability of sparse signal reconstruction with respect to measurement noise is investigated in this paper. We design efficient algorithms to verify the sufficient condition for unique \ell1 sparse recovery. One of our algorithms produces comparable results with the state-of-the-art technique and performs orders of magnitude faster. We show that the \ell1-constrained minimal singular value (\ell1-CMSV) of the measurement matrix determines, in a very concise manner, the recovery performance of \ell1-based algorithms such as the Basis Pursuit, the Dantzig selector, and the LASSO estimator. Compared to performance analysis involving the Restricted Isometry Constant, the arguments in this paper are much less complicated and provide more intuition on the stability of sparse signal recovery. We show also that, with high probability, the subgaussian ensemble generates measurement matrices with \ell1-CMSVs bounded away from zero, as long as the number of measurements is relatively large. To compute the \ell1-CMSV and its lower bound, we design two algorithms based on the interior point algorithm and the semidefinite relaxation. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel approach to perform detection of stochastic signals embedded in an additive random noise. Both signal and noise are considered to be realizations of zero mean random processes of which only second-order statistics are known (their covariance matrices). The method proposed, called constrained stochastic matched filter (CSMF), is an extension of the stochastic matched filter itself derived from the matched filter. The CSMF is optimal in the sense that it maximizes the signal-to-noise ratio in a subspace whose dimension is fixed a priori. In this paper, after giving the reasons for our approach, we show that there is neither an obvious nor analytic solution to the problem expressed. Then an algorithm, which is proved to converge, is proposed to obtain the optimal solution. Evaluation of the algorithm's performance is completed through estimation of receiver operating characteristic curves. Experiments on real signals show the improvement brought about by this method and thus its significance. [ABSTRACT FROM AUTHOR]

This paper studies the existence of optimal invariant detectors for determining whether $P$ multivariate processes have the same power spectral density. This problem finds application in multiple fields, including physical layer security and cognitive radio. For Gaussian observations, we prove that the optimal invariant detector, i.e., the uniformly most powerful invariant test, does not exist. Additionally, we consider the challenging case of close hypotheses, where we study the existence of the locally most powerful invariant test (LMPIT). The LMPIT is obtained in the closed form only for univariate signals. In the multivariate case, it is shown that the LMPIT does not exist. However, the corresponding proof naturally suggests an LMPIT-inspired detector that outperforms previously proposed detectors. [ABSTRACT FROM AUTHOR]

Detection of a causal relationship between two or more sets of data is an important problem across various scientific disciplines. The Granger causality index and its derivatives are important metrics developed and used for this purpose. However, the test statistics based on these metrics ignore the effect of practical measurement impairments such as subsampling, additive noise, and finite sample effects. In this paper, we model the problem of detecting a causal relationship between two time series as a binary hypothesis test with the null and alternate hypotheses corresponding to the absence and presence of a causal relationship, respectively. We derive the distribution of the test statistic under the two hypotheses and show that measurement impairments can lead to suppression of a causal relationship between the signals, as well as false detection of a causal relationship, where there is none. We also use the derived results to propose two alternative test statistics for causality detection. These detectors are analytically tractable, which allows us to design the detection threshold and determine the number of samples required to achieve a given missed detection and false alarm rate. Finally, we validate the derived results using extensive Monte Carlo simulations as well as experiments based on real-world data, and illustrate the dependence of detection performance of the conventional and proposed causality detectors on parameters such as the additive noise variance and the strength of the causal relationship. [ABSTRACT FROM AUTHOR]

This paper considers the blind maximum-likelihood (ML) detection problem for orthogonal space-time block codes (OSTBCs) in multiple-input multiple-output flat-fading channels. While the blind ML detection problem for general space-time codes is difficult to solve, it has been shown that for OSTBCs with constant modulus constellations, the blind ML detection problem can be formulated as a discrete quadratic program, and then handled by a powerful convex approximation technique known as semidefinite relaxation (SDR). In this paper, we turn our attention to the case of higher order QAM OSTBCs. Due to the nonconstant modulus nature of higher order QAM signals, the blind ML detection problem turns out to be a discrete Rayleigh quotient maximization problem, and as a result the current SDR technique is no longer directly applicable. We propose a linear fractional SDR (LFSDR) approach to this problem. This approach first relaxes the higher order QAM blind ML detection problem into a quasi-convex problem, followed by a simple solution approximation procedure. In general, quasi-convex problems are computationally more complex to solve than convex problems, but we show that an optimum solution of our quasi-convex problem can be efficiently obtained by solving a convex semidefinite program. The approximation accuracy of the proposed approach relative to other possible relaxation approaches is also studied. Simulation results are presented to demonstrate that the proposed LFSDR-based blind ML detector outperforms some existing suboptimal detectors and can yield promising performance even with a small to moderate number of code blocks. [ABSTRACT FROM AUTHOR]

This paper quantifies the adaptive performance of a blind adaptive multiuser detector (MUD) based on the linearly constrained constant modulus algorithm (LCCMA) in both a stationary and nonstationary channel. A framework is developed to apply the feedback analysis method to analyzing adaptive MUD schemes. A closed-form expression for the excess mean square error (EMSE) of LCCMA blind adaptive MUD in a CDMA communications system is derived for both of the steady-state and tracking cases. The effects of additive noise and multiple access interference are considered. A transient analysis is performed that predicts the learning curve of the adaptive filter. Computer simulation is used to verify the accuracy of the analysis. [ABSTRACT FROM AUTHOR]

In bearings-only tracking applications, the standard bearing model ignores the propagation delay of signal, except in cases where the target speed is comparable to the signal speed. This paper provides a theoretical analysis of the performance degradation suffered by a maximum likelihood estimator (MLE) that neglects the signal propagation delay in the bearings-only fusion of heterogeneous sensors: one with negligible propagation delay and the other with non-negligible delay. By using a higher order Taylor-series based analysis, we derive approximate expressions for the bias and mean square error (MSE) of the MLE. The analysis shows that neglecting the propagation delay of a sensor (with non-negligible delay) in such bearings-only fusion problems leads to severe degradation in performance even when the signal speed is orders of magnitude higher than that of target. Simulation results confirm the validity of the theoretical predictions. Finally, a bias-compensated MLE is proposed that not only takes into account the propagation delay, but also compensates for the estimation bias. This bias-compensated MLE is nearly unbiased and exhibits an RMS error performance close to the Cramer Rao lower bound. [ABSTRACT FROM AUTHOR]

Information divergences are commonly used to measure the dissimilarity of two elements on a statistical manifold. Differentiable manifolds endowed with different divergences may possess different geometric properties, which can result in totally different performances in many practical applications. In this paper, we propose a total Bregman divergence-based matrix information geometry (TBD-MIG) detector and apply it to detect targets emerged into nonhomogeneous clutter. In particular, each sample data is assumed to be modeled as a Hermitian positive-definite (HPD) matrix and the clutter covariance matrix is estimated by the TBD mean of a set of secondary HPD matrices. We then reformulate the problem of signal detection as discriminating two points on the HPD matrix manifold. Three TBD-MIG detectors, referred to as the total square loss, the total log-determinant and the total von Neumann MIG detectors, are proposed, and they can achieve great performances due to their power of discrimination and robustness to interferences. Simulations show the advantage of the proposed TBD-MIG detectors in comparison with the geometric detector using an affine invariant Riemannian metric as well as the adaptive matched filter in nonhomogeneous clutter. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new robust spectrum sensing method for MIMO cognitive radios in the presence of heavy-tailed noise. The proposed sensing technique, called measure-transformed covariance test (MTCT), operates by applying a transform to the probability measure of the data. The considered probability measure transform is structured by a non-negative function, called MT-function, that weights the data points. We show that proper selection of the MT-function, under the class of zero-centered spherically contoured Gaussian functions, can lead to significant mitigation of heavy-tailed noise effects on the sensing performance. Simulation studies illustrate the advantages of the proposed MTCT comparing to other robust MIMO and SIMO spectrum sensing techniques. [ABSTRACT FROM AUTHOR]

In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as matrix-factorization problem arising in relay communication among others. Assuming statistically independent matrix entries with known priors, the new algorithm called ML-BiGAMP could approximate the general sum-product loopy belief propagation (LBP) in the high-dimensional limit enjoying a substantial reduction in computational complexity. We demonstrate that, in large system limit, the asymptotic MSE performance of ML-BiGAMP could be fully characterized via a set of simple one-dimensional equations termed state evolution (SE). We establish that the asymptotic MSE predicted by ML-BiGAMP’ SE matches perfectly the exact MMSE predicted by the replica method, which is well-known to be Bayes-optimal but infeasible in practice. This consistency indicates that the ML-BiGAMP may still retain the same Bayes-optimal performance as the MMSE estimator in high-dimensional applications, although ML-BiGAMP's computational burden is far lower. As an illustrative example of the general ML-BiGAMP, we provide a detector design that could estimate the channel fading and the data symbols jointly with high precision for the two-hop amplify-and-forward relay communication systems. [ABSTRACT FROM AUTHOR]

We consider a modern radar system which has a general antenna array configuration consisting of primary channels with high-gain beams and reference channels with low-gain beams. A generalized likelihood ratio test (GLRT) was proposed in this context for target detection and direction of arrival estimation. However, the analytical performance of the GLRT has not been provided yet. In this paper, we derive finite-sum expressions for the probabilities of false alarm and detection. It is proven that the GLRT exhibits a constant false alarm rate against the overall interference disturbance covariance matrix. Numerical examples show that the detection performance of the GLRT may not necessarily improve when the number of sensors increases [ABSTRACT FROM AUTHOR]

In this paper, we develop a new elegant systematic framework relying on the Kullback-Leibler Information Criterion to approach the design of one-stage adaptive detection architectures for multiple hypothesis testing problems in radar. Specifically, at the design stage, we assume that one out of several alternative hypotheses may be in force and that only one null hypothesis exists. Then, starting from the case where all the parameters are known and proceeding towards the adaptivity with respect to the entire parameter set, we come up with decision schemes for multiple alternative hypotheses consisting of the sum between the compressed log-likelihood ratio based upon the available data and a penalty term accounting for the number of unknown parameters. Such a term arises from suitable approximations of the Kullback-Leibler Divergence between the true and a candidate probability density function. Interestingly, under specific constraints, the proposed decision schemes can share the constant false alarm rate property by virtue of the Invariance Principle. Finally, we also show that the new architectures can be viewed as the result of a suitable regularization of the log-likelihood. [ABSTRACT FROM AUTHOR]

This paper considers the problem of density estimation and clustering in distributed sensor networks. It is assumed that each node in the network senses an environment that can be described as a mixture of some elementary conditions. The measurements are thus statistically modeled with a mixture of Gaussians, where each Gaussian component corresponds to one of the elementary conditions. This paper presents a distributed expectation-maximization (EM) algorithm for estimating the Gaussian components, which are common to the environment and sensor network as a whole, as well as the mixing probabilities that may vary from node to node. The algorithm produces an estimate (in terms of a Gaussian mixture approximation) of the density of the sensor data without requiring the data to be transmitted to and processed at a central location. Alternatively, the algorithm can be viewed as an distributed processing strategy for clustering the sensor data into components corresponding to predominant environmental features sensed by the network. The convergence of the distributed EM algorithm is investigated, and simulations demonstrate the potential of this approach to sensor network data analysis. [ABSTRACT FROM AUTHOR]

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 investigate the design of distributed detection networks in the presence of an eavesdropper (Eve). We consider the problem of designing binary sensor quantizers that maximize the Kullback-Leibler (KL) divergence at the fusion center (FC), when subject to a tolerable constraint on the KL divergence at Eve. We assume that the channels between the sensors and the FC (likewise the channels between the sensors and the Eve) are modeled as binary symmetric channels (BSCs). In the case of i.i.d. received symbols at both the FC and Eve, we prove that the structure of the optimal binary quantizers is a likelihood ratio test (LRT). We also present an algorithm to find the threshold of the optimal LRT, and illustrate it for the case of Additive white Gaussian noise (AWGN) observation models at the sensors. In the case of non-i.i.d. received symbols at both FC and Eve, we propose a dynamic-programming based algorithm to find efficient quantizers at the sensors. Numerical results are presented to illustrate the performance of the proposed network. [ABSTRACT FROM AUTHOR]

An offline sampling design problem for distributed detection is considered in this paper. To reduce the sensing, storage, transmission, and processing costs, the natural choice for the sampler is the sparsest one that results in a desired global error probability. Since the numerical optimization of the error probabilities is difficult, we adopt simpler costs related to distance measures between the conditional distributions of the sensor observations. We design sparse samplers for the Bayesian as well as the Neyman-Pearson setting. The developed theory can be applied to sensor placement/selection, sample selection, and fully decentralized data compression. For conditionally independent observations, we give an explicit solution, which is optimal in terms of the error exponents. More specifically, the best subset of sensors is the one with the smallest local average root-likelihood ratio and largest local average log-likelihood ratio in the Bayesian and Neyman-Pearson setting, respectively. We supplement the proposed framework with a thorough analysis for Gaussian observations, including the case when the sensors are conditionally dependent, and also provide examples for other observation distributions. One of the results shows that, for nonidentical Gaussian sensor observations with uncommon means and common covariances under both hypotheses, the number of sensors required to achieve a desired detection performance reduces significantly as the sensors become more coherent. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the problem of distributed Bayesian detection in the presence of Byzantines in the network. It is assumed that a fraction of the nodes in the network are compromised and reprogrammed by an adversary to transmit false information to the fusion center (FC) to degrade detection performance. The problem of distributed detection is formulated as a binary hypothesis test at the FC based on 1-bit data sent by the sensors. The expression for minimum attacking power required by the Byzantines to blind the FC is obtained. More specifically, we show that above a certain fraction of Byzantine attackers in the network, the detection scheme becomes completely incapable of utilizing the sensor data for detection. We analyze the problem under different attacking scenarios and derive results for different non-asymptotic cases. It is found that existing asymptotics-based results do not hold under several non-asymptotic scenarios. When the fraction of Byzantines is not sufficient to blind the FC, we also provide closed form expressions for the optimal attacking strategies for the Byzantines that most degrade the detection performance. [ABSTRACT FROM PUBLISHER]

The demand for accurate localization in complex environments continues to increase despite the difficulty in extracting positional information from measurements. Conventional range-based localization approaches rely on distance estimates obtained from measurements (e.g., delay or strength of received waveforms). This paper goes one step further and develops localization techniques that rely on all probable range values rather than on a single estimate of each distance. In particular, the concept of soft range information (SRI) is introduced, showing its essential role for network localization. We then establish a general framework for SRI-based localization and develop algorithms for obtaining the SRI using machine learning techniques. The performance of the proposed approach is quantified via network experimentation in indoor environments. The results show that SRI-based localization techniques can achieve performance approaching the Cramér–Rao lower bound and significantly outperform the conventional techniques especially in harsh wireless environments. [ABSTRACT FROM AUTHOR]

Detection with high-dimensional multimodal data is a challenging problem when there are complex inter- and intra- modal dependencies. While several approaches have been proposed for dependent data fusion (e.g., based on copula theory), their advantages come at a high price in terms of computational complexity. In this paper, we treat the detection problem with compressive sensing (CS) where compression at each sensor is achieved via low-dimensional random projections. CS has recently been exploited to solve detection problems under various assumptions on the signals of interest; however, its potential for dependent data fusion has not been explored adequately. We exploit the capability of CS to capture statistical properties of uncompressed data in order to compute decision statistics for detection in the compressed domain. First, a Gaussian approximation is employed to perform likelihood ratio (LR) based detection with compressed data. In this approach, intermodal dependence is captured via a compressed version of the covariance matrix of the concatenated (temporally and spatially) uncompressed data vector. We show that, under certain conditions, this approach with a small number of compressed measurements per node leads to enhanced performance compared to detection with uncompressed data using widely considered suboptimal approaches. Second, we develop a nonparametric approach where a decision statistic based on the second order statistics of uncompressed data is computed in the compressed domain. The second approach is promising over the first approach and the other related nonparametric approaches when multimodal data is highly correlated at the expense of slightly increased computational complexity. [ABSTRACT FROM AUTHOR]

Wireless relay networking has been proposed as a solution to enable communication between disconnected users that otherwise are unable to reliably share information with one another due to distance or obstruction. Instead, a relay forwards a processed version of the data sent from one or more transmitters to one or more receivers. In this paper, we propose an energy efficient distributed relay networking structure where the spatial diversity of distributed multiple-input multiple-output systems is utilized. The distributed relay network consists of several single antenna relay nodes that are spatially distributed to receive transmissions from many users through an uplink. Each of the relay nodes performs a simple quantization operation to send a quantized version of the combination of the received signals through a downlink to a receiver (fusion center). Using the quantized signals broadcast by each relay node, we derive the maximum likelihood detector that can be implemented at each user to detect transmissions from other users. We also introduce suboptimal detectors that are less computationally complex than the maximum likelihood detector while having comparable performance. Analysis on the number of relay nodes required for the relay network to perform properly is also discussed. Our results are verified through simulations. [ABSTRACT FROM AUTHOR]

In this paper, we consider multiuser detection that copes with multiple access interference caused in low-rate wireless communication systems with a large number of nodes, such as machine-to-machine communications. We take account of discreteness of transmitted signals (e.g., binary signals taking values of $\pm 1$), which we utilize as prior information in detection. We first formulate the detection problem as a maximum a posteriori estimation problem. Since this problem is highly nonconvex and discontinuous, we propose convex relaxation based on the sum-of-absolute-values (SOAV) optimization, which can be efficiently solved by proximal splitting. We also derive an upper bound of the relaxation error by the SOAV optimization in noisy cases based on the restricted isometry property. Numerical simulations are shown to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM PUBLISHER]

In this paper, we consider a two-channel multiple-input multiple-output passive detection problem, in which there is a surveillance array and a reference array. The reference array is known to carry a linear combination of broadband noise and a subspace signal of known dimension, but unknown basis. The question is whether the surveillance channel carries a linear combination of broadband noise and a subspace signal of the same dimension, but unknown basis, which is correlated with the subspace signal in the reference channel. We consider a second-order detection problem where these subspace signals are structured by an unknown, but common, $p$-dimensional random vector of symbols transmitted from sources of opportunity, and then received through unknown $M\times p$ matrices at each of the $M$ -element arrays. The noises in each channel have spatial correlation models ranging from arbitrarily correlated to independent with identical variances. We provide a unified framework to derive the generalized likelihood ratio test for these different noise models. In the most general case of arbitrary noise covariance matrices, the test statistic is a monotone function of canonical correlations between the reference and surveillance channels. [ABSTRACT FROM PUBLISHER]

This paper presents a new solution for multi-target tracking over a network of sensors with limited spatial coverage. The proposed solution is based on the centralized data fusion architecture. The main contribution of the paper is the introduction of a new track-to-track fusion approach in which the posterior distributions of multi-target states, reported by various sensor nodes, are fused in a way that the redundant information are combined and the rest complement each other. The proposed solution is formulated within the labeled random finite set framework in which the fused posterior incorporates all the state and label information provided by multiple sensor nodes. The performance of the proposed method is evaluated via simulation experiments that involve challenging tracking scenarios. The proposed method is implemented using sequential Monte Carlo method and the results confirm its effectiveness. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Tobit Kalman filtering problem for a class of discrete time-varying systems subject to censored observations, integral measurements and probabilistic sensor failures under the Round-Robin protocol (RRP). The censored observations are characterized by the Tobit observation model, the integral measurements are described as functions of system states over a certain time interval required for data acquisition, and the sensor failures are governed by a set of uncorrelated random variables. The RRP is employed to decide the transmission sequence of sensors in order to alleviate undesirable data collisions. By resorting to the augmentation technique and the orthogonality projection principle, a protocol-based Tobit Kalman filter (TKF) is developed with the coexistence of integral measurements and sensor failures that lead to a couple of augmentation-induced terms. Moreover, the performance of the proposed filter is analyzed through examining the statistical property of the error covariance of the state estimation. Further analysis shows the existence of self-propagating upper and lower bounds on the estimation error covariance. A case study on ballistic roll rate estimation is presented to illustrate the efficacy of the developed filter. [ABSTRACT FROM AUTHOR]

In this paper, the particle filtering problem is investigated for a class of nonlinear/non-Gaussian systems with energy harvesting sensors subject to randomly occurring sensor saturations (ROSSs). The random occurrences of the sensor saturations are characterized by a series of Bernoulli distributed stochastic variables with known probability distributions. The energy harvesting sensor transmits its measurement output to the remote filter only when the current energy level is sufficient, where the transmission probability of the measurement is recursively calculated by using the probability distribution of the sensor energy level. The effects of the ROSSs and the possible measurement losses induced by insufficient energies are fully considered in the design of filtering scheme, and an explicit expression of the likelihood function is derived. Finally, the numerical simulation examples (including a benchmark example for nonlinear filtering and the applications in moving target tracking problem) are provided to demonstrate the feasibility and effectiveness of the proposed particle filtering algorithm. [ABSTRACT FROM AUTHOR]