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

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]

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 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 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]

Coherent processing in cooperative multi-agent networks can achieve significant performance gain via accurate alignment of observed signals. However, the inaccessibility of phase information in mobile scenes prevents the acquisition of a high degree of coherence for target detection. This paper presents a quasi-coherent mobile detection framework for cooperative multi-agent networks, which exploits the phase information inherent in the carrier wave of direct-path signals. Specifically, we derive the quasi-coherent detector with the aid of phase calibration by incorporating the maximum likelihood estimation of phase-related parameters obtained from direct-path signals. Next, we characterize the detection performance degradation induced by the mismatch of initial phase, transmitter position, orientation and clock. We further demonstrate the near-optimal detection capability of the proposed detector compared with generic coherent detectors and validate the effectiveness of phase information exploitation via numerical simulations. [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]

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 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]

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]

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]

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, 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]

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, 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]

In this paper, the paradigm of expectation propagation (EP) algorithm in large-scale MIMO detection is extended by the sampling decoding in an Markov chain Monte Carlo way to boost the approximation of the target posterior distribution. The proposed EP-based sampling decoding scheme not only theoretically addresses the inherent convergence problem of EP, but also is able to achieve the near-optimal decoding performance with the increment of Markov moves. Specifically, the EP-based independent Metropolis-Hastings (MH) is proposed to guarantee the exponential convergence to the target posterior distribution, thus bridging the EP detector and the sampling decoding as a whole. Meanwhile, the output yielded by the EP detector also provides a good initial setup for the sampling decoding, which results in a better convergence performance in the approximation. To further improve the convergence performance and the decoding efficiency, the EP-based Gibbs sampling is given, where the choice of the standard deviation of the discrete Gaussian distribution in the Markov mixing is also studied for a better decoding performance. Moreover, we extend the proposed EP-based Gibbs sampling decoding to the soft-output decoding in MIMO bit-interleaved coded modulation (BICM) systems, which enjoys a flexible decoding trade-off between performance and complexity by the number of Markov moves. [ABSTRACT FROM AUTHOR]

Minimum-mean-square-error (MMSE) detection is increasingly relevant for massive multiple-input multiple-output (MIMO) systems. MMSE suffers from high computational complexity and low parallelism because of the increasing number of users and antennas in massive MIMO systems. This paper proposes a recursive conjugate gradient (RCG) method to iteratively estimate signals. First, a recursive conjugate gradient detection algorithm is proposed that achieves high parallelism and low complexity through iteration. Second, a quadrant-certain-based initial method that improves detection accuracy without added complexity is proposed. Third, an approximated log likelihood ratio (LLR) computation method is proposed to achieve simplified calculation. The analyses show that compared with related methods, the proposed RCG algorithm reduces computational complexity and exploits the potential parallelism. RCG is mathematically demonstrated to achieve low approximated error. Based on the RCG method, an architecture is proposed in a 128 × 8 64-QAM massive MIMO system. First, a parallel processing element array with single-sided input is adopted; this array eliminates the throughput limitation. Second, a deeply pipelined user-level method based on the recursive conjugate gradient method is proposed. Third, an approximated architecture is proposed to compute the soft output. The architecture is verified on an FPGA and fabricated on 1.87 × 1.87 mm $^2$ silicon with TSMC 65 nm CMOS technology. The chip achieves 2.69 Mbps/mW and 1.09 Mbps/kG energy efficiency (throughput/power) and area efficiency (throughput/area), respectively, which are 2.39 to 10.60× and 1.15 to 8.81× those of the normalized state-of-the-art designs. [ABSTRACT FROM AUTHOR]

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]

This paper deals with near-optimal spectrum sensing of orthogonal frequency division multiplexing (OFDM) signals to achieve reliable detection at low signal-to-noise ratio (SNR). The likelihood ratio test (LRT), a simple hypothesis test, delivers the optimal performance, but it requires that the parameters involved in the test are known. Hence, the generalized likelihood ratio test (GLRT), a composite hypothesis test, has often been employed. However, GLRT-based detectors involve biased parameter estimation, which may lead to inferior performance. In this paper, with proper approximation, the LRT is reduced to a simpler form, which only requires the knowledge of noise power. Then a novel unbiased and consistent estimator of the noise power is developed. This estimator is combined with the approximate LRT, leading to an asymptotic simple hypothesis test (ASHT). Two ASHT-based detectors are presented for cases with and without time synchronization, and their theoretical performances are analyzed. Simulation results show that the ASHT-based detectors deliver performances very close to that of the optimal LRT, and significantly outperform the existing GLRT-based detectors. It is also shown that the ASHT-based detectors exhibit robustness against the influence of multipath channels. [ABSTRACT FROM PUBLISHER]

The Multiple Measurement Vector (MMV) problem is central to sparse signal processing, where the goal is to recover the common support of a set of unknown sparse vectors of size $N$ , from $L$ compressed measurement vectors, each of size $M << N$. Recent advances in correlation-aware and Bayesian techniques for MMV models show promising evidence that under appropriate assumptions, it is possible to recover supports of size ($s$) larger than the dimension ($M$) of each measurement vector. However, these results are primarily asymptotic in $L$ , and cannot provide support recovery guarantees for finite $L$. This paper overcomes such drawback by focusing on a broader family of correlation-aware optimization problems (which include convex problems), and establishing rigorous non-asymptotic probabilistic guarantees in the regime $s>M$ when the measurements are collected using appropriately designed sparse sensor arrays (such as nested and coprime). Assuming the source locations obey a certain “minimum separation” condition, we develop uniform upper bounds on the estimation error that is obeyed by any algorithm belonging to this family, and utilize this bound to ensure probabilistic support recovery in the regime $s>M$. Our results crucially rely upon (i) the unique geometry of the difference co-array of the sparse arrays, and (ii) certain non-negativity constraints on the optimization variable. As a result of independent interest, we also show that this upper bound is tight with respect to the dimension $N$. Extensive numerical simulations (including phase transition plots) are presented to validate the theoretical claims. [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]

This paper deals with adaptive radar detection of targets in the presence of Gaussian disturbance sharing a block-diagonal covariance structure. The problem is formulated according to a very general signal model, which contains the point-like, range-spread, and subspace target (or targets) as special instances. Hence, a unified study on the resulting adaptive detection problem is handled with the use of the invariance theory. The obtained results, including an appropriate transformation group, a maximal invariant and an induced maximal invariant, are proven consistent with those existing in the literature for some simple scenarios. Meanwhile, since the widely-used generalized likelihood ratio detector does not admit a closed form expression, new invariant detectors and their CFAR versions are proposed in this general scenario. Finally, their detection performance is assessed and validated via numerical examples. [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]

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]

In the presence of interference and Gaussian noise with unknown covariance matrix, a generalized likelihood ratio test (GLRT) detector has already been developed for detecting a distributed target. The target signal and interference are described with subspace models, namely, the target signals (or interference) are modeled as linear combinations of the linearly independent columns of a known subspace matrix. In this paper, we obtain statistical properties of this GLRT detector, and prove its constant false alarm rate against the noise covariance matrix. Moreover, we derive analytical expressions for the probability of false alarm of the GLRT detector. Specifically, exact expressions for the probability of false alarm are obtained for six cases where the target subspace dimension (denoted by $p$) is 1, 2, and 3, and the number of range cells (denoted by $H$) the distributed target occupies is 1, 2, and 3. For the general case where $p\geq 4$ and $H\geq 4$ , we derive an approximate expression for the probability of false alarm. Monte Carlo simulations show that the exact expressions are valid, and the accuracy of the approximate expression is acceptable for moderate or large training data size. In practice, these expressions can greatly facilitate the threshold setting for the GLRT detector for any preassigned probability of false alarm. [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 multiple-input-multiple-output detection using deep neural networks. We introduce two different deep architectures: a standard fully connected multi-layer network, and a detection network (DetNet), which is specifically designed for the task. The structure of DetNet is obtained by unfolding the iterations of a projected gradient descent algorithm into a network. We compare the accuracy and runtime complexity of the proposed approaches and achieve state-of-the-art performance while maintaining low computational requirements. Furthermore, we manage to train a single network to detect over an entire distribution of channels. Finally, we consider detection with soft outputs and show that the networks can easily be modified to produce soft decisions. [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]

In this paper, we propose a regular vine copula based methodology for the fusion of correlated decisions. Regular vine copula is an extremely flexible and powerful graphical model to characterize complex dependence among multiple modalities. It can express a multivariate copula by using a cascade of bivariate copulas, the so-called pair copulas. Assuming that local detectors are single threshold binary quantizers and taking complex dependence among sensor decisions into account, we design an optimal fusion rule using a regular vine copula under the Neyman–Pearson framework. In order to reduce the computational complexity resulting from the complex dependence, we propose an efficient and computationally light regular vine copula based optimal fusion algorithm. Numerical experiments are conducted to demonstrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

We deal with the classical problem of testing two simple statistical hypotheses but, as a new element, it is assumed that the data vector is observed after an unknown permutation of its entries. What is the fundamental limit for the detection performance in this case? How much information for detection is contained in the entry values and how much in their positions? In the first part of this paper, we answer these questions. In the second part, we focus on practical algorithms. A low-complexity detector solves the detection problem without attempting to estimate the permutation. A modified version of the auction algorithm is then considered, and two greedy algorithms with affordable worst case complexity are presented. The detection operational characteristics of these detectors are investigated by computer experiments. The problem we address is referred to as unlabeled detection and is motivated by large sensor network applications, but applications are also foreseen in different fields, including image processing, social sensing, genome research, and molecular communication. [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]

In this paper, we consider the distributed target detection problem in Gaussian clutter with unknown covariance matrix. By exploiting the persymmetry of the covariance matrix, an adaptive detector is proposed according to the two-step design method. The probabilities of detection and false alarm of the proposed detector are derived in closed form, which are verified through Monte Carlo simulations. The expression for the probability of false alarm reveals that the proposed detector bears constant false alarm rate against the covariance matrix. Numerical examples illustrate that the proposed detector outperforms its counterparts, especially in the limited training data environment. [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]

In distributed multi-input multi-output (MIMO) systems, antennas may not be able to utilize common oscillators at the transmitter side or the receiver side. Consequently, there are multiple carrier frequency offsets (CFOs) and multiple timing offsets (TOs) due to distributed antennas that may significantly degrade the system performance if not properly addressed. In this paper, we analyze the effect of multiple CFOs and multiple TOs on receiver signal energy at the front end of each receive antenna pulse matched filter output in a distributed MIMO system. We then propose a novel receiver design for distributed MIMO systems that can accommodate multiple CFOs and multiple TOs. The proposed receiver structure utilizes a bank of pulse matched filters at each receive antenna where each filter accommodates one CFO specifically. Each filter output is then sampled at the symbol rate, with sampling timing selected according to the corresponding TO, followed by an information symbol detector. For the proposed receiver configuration, we derive the maximum-likelihood (ML) symbol detector for both space-time block coded and uncoded distributed MIMO systems. In addition, we design sub-optimal detectors and show that under certain conditions, the sub-optimal detectors perform close to the ML-optimal detector with significantly lower complexities. Extensive simulation studies illustrate our theoretical development for distributed MIMO systems with various transceiver configurations and channel conditions. The simulation results indicate that the proposed receiver structure together with the ML detection offers significant performance gains compared to the current state of the art. [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]

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, 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]

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 deals with the problem of detecting a subspace signal in the presence of spatially and temporally colored disturbance. A new subspace parametric signal model that takes into account a multi-rank subspace structure for the target signal and employs a multi-channel auto-regressive process for the disturbance signal is proposed. Following this model, a new subspace parametric Rao detector (SP-Rao) is developed for training-limited scenarios. Unlike conventional parametric detectors that are designed for only rank-one signal detection, the SP-Rao has a new multi-rank structure with a pairwise successive spatio-temporal whitening and cross-correlation process between the observed signal and each subspace basis vector. Additionally, a non-parametric subspace detector (NSD) is derived based upon a frequency-domain representation of the SP-Rao test statistic. The NSD is distinctively different from conventional subspace detectors, in which the former involves pairwise whitening and cross-correlation between the test signal and each subspace basis vector but the latter employs the whole subspace matrix. Numerical results are presented to illustrate the performance of the proposed subspace detectors in comparison with several leading existing methods, especially in the case of limited data. [ABSTRACT FROM AUTHOR]

In sparse recovery, a sparse signal ${\mathbf x}\in \mathbb {R}^N$ with $K$ nonzero entries is to be reconstructed from a compressed measurement $\mathbf y=Ax$ with ${\mathbf A}\in \mathbb {R}^{M\times N}$ ($M

The problem of reconstructing a sparse signal vector from magnitude-only measurements (a.k.a. compressive phase retrieval) emerges in diverse applications, but it is NP-hard in general. Building on recent advances in nonconvex optimization, this paper puts forth a new algorithm that is termed compressive reweighted amplitude flow (CRAF) and abbreviated as CRAF, for compressive phase retrieval. Specifically, CRAF operates in two stages. The first stage seeks a sparse initial guess via a new spectral procedure. In the second stage, CRAF implements a few hard thresholding based iterations using reweighted gradients. When there are sufficient measurements, CRAF provably recovers the underlying signal vector exactly with high probability under suitable conditions. Moreover, its sample complexity coincides with that of state-of-the-art procedures. Finally, numerical tests showcase improved performance of the new spectral initialization, as well as improved exact recovery relative to competing alternatives. Empirically, the number of measurements required for exact recovery by CRAF is about 40% less than those of competing alternatives in our experiments using real images. [ABSTRACT FROM AUTHOR]

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]