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Three-variable chaotic synchronization has been implemented based on DNA chemical reaction networks (CRNs) in previous works. However, it is still difficult to realize the encryption and decryption of continuous signals. A scheme of secure communication is proposed based on chaotic coupling synchronization by DNA CRNs in this paper. Firstly, the CRNs of two three-variable chaotic systems are constructed using bimolecular representation. Secondly, according to the design principle of the coupling term and the theory of stability, the CRNs of the coupling term are designed to realize the synchronization of two chaotic systems. Finally, the oblique wave, square wave, and staircase wave signals are added into chaotic systems to realize encryption and decryption. The dynamic behavior of a three-variable chaotic system is verified by Visual DSD and MATLAB software. The synchronization proof and the experimental results of encryption and decryption are given. The results indicate that the proposed secure communication scheme is effective. This paper provides an application method for studying secure communication in the DNA field. [ABSTRACT FROM AUTHOR]

Angle-based localization of a source at unique coordinates in the three-dimensional (3-D) space utilizes traditionally the two-dimensional (2-D) angle of arrival (AOA) measurements from planar arrays. This paper investigates the positioning performance and develops an optimal solution for the 3-D localization using one-dimensional (1-D) space angle (SA) measurements that has the appeal of involving linear arrays only. The localization performance by SA is less understood and the positioning algorithms from the literature are suboptimal and have restrictions on the altitudes and orientations of the linear array receivers. This paper establishes the basic concept of using SA for localization, and conducts analytical comparison of SA and AOA positionings by cross arrays, where the contrasts in the angle observation accuracy, the geometric dilution effect and overall localization performance are elaborated. A solution that can reach the Cramér-Rao Lower Bound performance under Gaussian noise is also proposed that does not have restriction on the placement of the linear array receivers. It consists of an initial solution by semidefinite relaxation and a refined solution by an algebraic estimator. Simulations validate the theoretical investigation and the algorithm performance. [ABSTRACT FROM AUTHOR]

The dataflow concept has been successfully used for modeling and synthesizing signal processing applications since decades, and recently, dataflow has also been discovered to match the computation model of machine learning applications, leading to extremely successful dataflow based application design frameworks. One of the most attractive features of dataflow, especially for signal processing, is related to its formal nature: when properly defined, a dataflow-based application model can be analytically verified for correctness at the stage of application design. This paper proposes VR-PRUNE, a novel dataflow model of computation that is aimed for design of high-performance signal processing software, together with runtime support that allows efficient application deployment to heterogeneous GPU-equipped platforms. Compared to prior work, VR-PRUNE features variable token rate processing, which enables designing adaptive signal processing applications, and implementing solutions that, e.g., allow trading-off between power consumption and filtering bandwidth at runtime. The paper presents the formal concepts of VR-PRUNE, as well as four application examples from domains related to signal processing, accompanied with quantitative results, which show that using VR-PRUNE enables, for example, application power-performance scaling, and on the other hand describing adaptive application behavior with 59% fewer dataflow graph components compared to previous work. [ABSTRACT FROM AUTHOR]

Superdirective arrays have been extensively studied because of their considerable potential accompanied, unfortunately, by a high sensitivity to random errors that affect the responses and positions of array elements. However, the statistics of their actual beam pattern (BP) has never been systematically investigated. This paper shows that the Rician probability density function (PDF), sometimes adopted to study the impact of errors in conventional arrays, is a valid approximation for superdirective BP statistics only where some mathematical terms are negligible. The paper also shows that this is the case for all linear end-fire arrays considered. A similar study is proposed concerning the correlation between BP lobes, showing that for the superdirective arrays considered the lobes, especially non-adjacent ones, are almost independent. Furthermore, knowledge of the PDF of the actual BP allows one to define quantile BP functions, whose probability of being exceeded, at any point, is fixed. Combining the lobes’ independence with quantile BP functions, an empirical equation for the probability that the entire actual BP will not exceed a quantile function over an interval larger than a given size is obtained. This new knowledge and these tools make it possible to devise new methods to design robust superdirective arrays via optimization goals with clearer and more relevant statistical meaning. [ABSTRACT FROM AUTHOR]

In this paper, two different timing-mismatch compensation strategies for two-channel time-interleaved analog-to-digital converters are comprehensively analyzed and compared. In the first strategy (SA), one channel serves as a reference channel, and the other channel is compensated to match the reference channel using the timing mismatch between the channels. In the second strategy (SB), both channels are compensated to match each other, using half the value of the channel mismatch with different signs. For SB, the paper introduces a novel compensation structure that utilizes parallel differentiator-multiplier (PDM) branches. Expressions for the spurious-free dynamic range (SFDR) after compensation are derived for both strategies. These expressions reveal that the novel PDM structure achieves a remarkably greater SFDR than the existing cascaded differentiator-multiplier (CDM) compensation structure which can be used for both SA and SB. This is because, after compensation, the remaining aliasing distortion in the proposed PDM structure is shown to be of higher approximation order (in terms of the mismatch value) and thus substantially smaller than in the CDM structure. Simulations included in the paper validate the theoretical results. [ABSTRACT FROM AUTHOR]

A reconfigurable intelligent surface (RIS) is a nearly-passive flat layer made of inexpensive elements that can add a tunable phase shift to the impinging electromagnetic wave and are controlled by a low-power electronic circuit. This paper considers the fundamental problem of target detection in a RIS-aided multiple-input multiple-output (MIMO) radar. At first, a general signal model is introduced, which includes the possibility of using up to two RISs (one close to the radar transmitter and one close to the radar receiver) and subsumes both a monostatic and a bistatic radar configuration with or without a line-of-sight view of the prospective target. Upon resorting to a generalized likelihood ratio test (GLRT), the design of the phase shifts introduced by the RIS elements is formulated as the maximization of the probability of detection in the location under inspection for a fixed probability of false alarm, and suitable optimization algorithms are proposed. The performance analysis shows the benefits granted by the presence of the RISs and shed light on the interplay among the key system parameters, such as the radar-RIS distance, the RIS size, and the location of the prospective target. A major finding is that the RISs should be better deployed in the near-field of the radar arrays at both the transmit and the receive side. The paper is concluded by discussing some open problems and foreseen applications. [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]

Anti-eavesdropping channel estimation (ANECE) is useful for a network of cooperative full-duplex radio devices/users. Using ANECE, a secret key can be generated by each pair of users, and additional secret information can be transmitted between a pair of users. This paper analyzes the capacity of the secret key based on ANECE, and compares it with the conventional method for channel training. The paper also analyzes the secrecy capacity of information transmission using an one-way scheme, and compares it with a two-way scheme. It is shown that the total amount of secrecy generated from ANECE can be substantially larger than that based on the conventional method especially when an eavesdropper may have an unlimited number of antennas. The paper also formulates a total secure degree of freedom (TSDoF) of the ANECE based scheme, and compares it with a prior scheme of secret information transmission from a multi-antenna node to another against a multi-antenna eavesdropper where channel state information is unknown everywhere initially. The comparison shows that there is a substantial gain of TSDoF by exploiting full-duplex radios and reciprocal channels via ANECE. Most of the key insights are highlighted in twelve proven properties. [ABSTRACT FROM AUTHOR]

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

The Unlimited Sensing Framework (USF) was recently introduced to overcome the sensor saturation bottleneck in conventional digital acquisition systems. At its core, the USF converts a continuous-time high-dynamic-range (HDR) signal into folded, low-dynamic-range, modulo samples and allows the recovery of the HDR signal via algorithmic unfolding. In hardware, however, implementing ideal modulo folding requires careful calibration, analog design and high precision. At the interface of theory and practice, this paper explores a computational sampling strategy that relaxes strict hardware requirements via a novel, mathematically guaranteed reconstruction. We start with a generalized model for USF with two new parameters modeling hysteresis and folding transients in addition to the modulo threshold. Hysteresis accounts for mismatches between the reset threshold and the amplitude displacement at the folding time and the folding transient is a continuous transition period in the implementation of a reset. Both these effects are motivated by our hardware experiments and also occur in previous, domain-specific applications. We show that hysteresis is beneficial for USF and leverage it to derive the first recovery guarantees in the context of our generalized USF model for a certain sampling rate regime. Additionally, we show how the sampling rate requirement can be greatly reduced via a direct generalization of the proposed recovery. Our theoretical work is corroborated by hardware experiments with a hysteresis enabled, modulo ADC testbed comprising off-the-shelf electronic components. Thus, by capitalizing on a collaboration between hardware and algorithms, our paper enables an end-to-end pipeline for HDR sampling allowing more flexible hardware implementations. [ABSTRACT FROM AUTHOR]

This paper proposes a momentum algorithm based on Borges difference and an adaptive momentum (Adam) algorithm based on Borges difference to update parameters, which can adjust the momentum information more flexibly. The Borges difference is proposed from the definition of Borges derivative to be combined with the gradient algorithm in convolutional neural networks. The proposed momentum algorithm based on Borges difference and Adam algorithm based on Borges difference can be adjusted more flexibly in order to speed up the convergence. The parameter optimization algorithm with the Borges difference presents a better performance compared with the integer-order momentum algorithm and integer-order Adam algorithm, with the proposed nonlinear adjustment method for the parameter tuning of convolutional neural networks. By analyzing experimental results of Fashion-MNIST dataset and CIFAR-10 dataset, the optimization algorithms based on Borges difference proposed in this paper gain better effects on the optimization model compared with the corresponding ones based on the integer-order difference, and can speed up the convergence speed and recognition accuracy of the image recognition. [ABSTRACT FROM AUTHOR]

This paper considers the problem of adaptive group testing for isolating up to $k$ defective items from a population of size $n$. There exist restrictions or preferences which determine how the items can be pooled for testing. A graphical model formalizes the pooling restrictions and preferences. Such graph-constrained group testing is investigated in three settings: populations with defectives, populations facing the potential presence of inhibitors, and populations with community structures. Adaptive group testing frameworks are provided for each setting. In populations without inhibitors, existing non adaptive frameworks can isolate the defective items perfectly with $\Theta(k \log n/k)$ number of tests, where is the $\beta$ -mixing time of a random walk over the underlying graph. This paper provides a two-stage framework that can perfectly isolate up to $k$ defective items for a regular graph using $\Theta(k2 \log n k + k)$ number of tests, thus achieving an approximate gain of a factor of $k$ over the non-adaptive frameworks. This twostage framework's principles are extended to community-structured graphs and graphs with up to $r$ inhibitor items. In particular, when inhibitors are present in the graph, a four-stage group testing framework is proposed. The results show that in the regime $r= O(k)$ for a fully connected graph, $\Theta ((k+r)\log n/(k+r) + r\log n)$ tests are sufficient for isolating the defective items. This matches the corresponding necessary condition on tests which scales $(k+r)\log n$. The adaptive graphconstrained group testing framework is also empirically evaluated. [ABSTRACT FROM AUTHOR]

In this paper, our goal is first to investigate the behavior of reassignment operators used in synchrosqueezing transforms applied to multicomponent signals made of the superposition of amplitude and frequency modulated modes. Indeed, while these operators are associated with instantaneous frequency estimators very accurate on specific types of modes, the quality of the former worsens drastically when the modes depart from the ideal case they are designed for. We show in this paper that this particularly true when the modes interfere in the time-frequency plane or when some noise is present. Based on that analysis, we propose a novel instantaneous frequency estimator that only makes use of some specific points located on the ridges of synchrosqueezing transforms, and compare its performance with state-of-the-art techniques based on the same type of time-frequency representations. [ABSTRACT FROM AUTHOR]

The performance of a single neural network can vary unexpectedly corresponding to different classification tasks, and thus the network with fixed structure may lack flexibility and often lead to overfitting or underfitting. It is urgent, also the main objective of this paper, to deal with the limitation of the fixed neural network structure on classifying radar signals in different electromagnetic environments. We in this paper propose a variable network architecture search (NAS) mechanism, called balanced-NAS framework, and apply it in specific emitter identification (SEI) to greatly improve the flexibility of model searching. In the proposed balanced-NAS framework, a “block-cell” structure and a controller based recurrent neural network (RNN) are utilized to design models automatically according to external environment. In particular, a balance function is also proposed and utilized in the balanced-NAS framework, acting on the RNN controller to take both the validation accuracy and computational budget into consideration while searching for ideal models. The efficiency of the searching process is further enhanced by exploiting a progressive strategy to design simple and complicate child models where unpromising ones after each evaluation process are obsoleted to release searching space. Simulations and experiments indicate that the proposed balanced-NAS framework is extremely efficient and outperforms the conventional algorithms in classifying radar signals in different environments. [ABSTRACT FROM AUTHOR]

Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so degrades when the noise is heteroscedastic across samples, as occurs, e.g., when samples come from sources of heterogeneous quality. This paper develops a probabilistic PCA variant that estimates and accounts for this heterogeneity by incorporating it in the statistical model. Unlike in the homoscedastic setting, the resulting nonconvex optimization problem is not seemingly solved by singular value decomposition. This paper develops a heteroscedastic probabilistic PCA technique (HePPCAT) that uses efficient alternating maximization algorithms to jointly estimate both the underlying factors and the unknown noise variances. Simulation experiments illustrate the comparative speed of the algorithms, the benefit of accounting for heteroscedasticity, and the seemingly favorable optimization landscape of this problem. Real data experiments on environmental air quality data show that HePPCAT can give a better PCA estimate than techniques that do not account for heteroscedasticity. [ABSTRACT FROM AUTHOR]

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

This paper deals with the problem of testing for equality between the location parameters of two unknown symmetric distributions that may belong to different families. Under this framework, we develop a new robust extension of the two-sample Hotelling test (HT). The proposed extension, called measure-transformed HT (MT-HT), operates by applying a transform to the probability measures of some reshaped versions of the two compared data sets. The considered measure transform is structured by a non-negative function, called MT-function, that weights the data points. In the paper we show that proper selection of the involved MT-functions can result in significant enhancement of the decision performance in the presence of non-Gaussian distributions with heavy tails. The advantages of the proposed MT-HT are illustrated in simulation studies that involve synthetic measurements. Additionally, the MT-HT is illustrated for anomaly detection in a blurred and noisy video stream. [ABSTRACT FROM AUTHOR]

This paper studies the device activity detection problem in a multi-cell massive multiple-input multiple-output (MIMO) system, in which the active devices transmit signature sequences to multiple base stations (BSs) that are connected to a central unit (CU), and the BSs cooperate across multiple cells to detect the active devices based on the sample covariance matrices at the BSs. This paper demonstrates the importance of exploiting the knowledge of channel large-scale fadings in this cooperative detection setting through a phase transition analysis, which characterizes the length of signature sequences needed for successful device activity detection in the massive MIMO regime. It is shown that when the large-scale fadings are known, the phase transition for the multi-cell scenario is approximately the same as that of a single-cell system. In this case, the length of the signature sequences required for reliable activity detection in the multi-cell system can be made to be independent of the number of cells through cooperation, in contrast to the case where the large-scale fadings are not known. Further, this paper considers the case in which the fronthaul links between the BSs and the CU have capacity constraints and proposes a novel cooperation scheme based on the quantization of preliminary detection results at the BSs and the reconstruction of the sample covariance matrices at the CU. Simulations show that the proposed method significantly outperforms the scheme of directly quantizing the sample covariance matrices. [ABSTRACT FROM AUTHOR]

This paper deals with adaptive radar detection problems where several alternative hypotheses may be plausible. This kind of problems naturally extends the conventional binary tests that often occur in radar (as well as in other application fields) by including a further uncertainty degree related to the number of unknown signal parameters (model order). Such a modification consequently leads to multiple composite alternative hypotheses. In the companion paper (Addabbo et al., 2021), we have defined a new design framework which allows us to come up with decision schemes for these hypothesis testing problems by exploiting the Kullback-Leibler Information Criterion and without resorting to heuristic design criteria. The architectures devised within the proposed framework consist of the sum between the compressed log-likelihood ratio and a penalty term inherited from model order selection rules. Such a penalty term accounts for the number of unknown parameters to overcome the limitation of the generalized likelihood ratio test in the presence of nested hypotheses. In the present paper, we apply the new design framework to different detection problems related to both real aperture and (polarimetric) synthetic aperture radar. The analysis is carried out in comparison with suitable competitors (possibly based upon heuristic design criteria) and shows that the architectures devised within the proposed theoretically-founded design framework represent an effective means to deal with detection problems where the uncertainty on some parameters leads to multiple alternative hypotheses. [ABSTRACT FROM AUTHOR]

Real-world phenomena that can be formulated as signals are often affected by a number of factors and appear as multi-component modes. To understand and process such phenomena, “divide-and-conquer” is probably the most common strategy to address the problem. In other words, the captured signal is decomposed into signal components for each individual component to be processed. Unfortunately, for signals that are superimposition of non-stationary amplitude-frequency modulated (AM-FM) components, the “divide-and-conquer” strategy is bound to fail, since there is no way to be sure that the decomposed components take on the AM-FM formulations which are necessary for the extraction of their instantaneous frequencies (IFs) and amplitudes (IAs). In this paper, we propose an adaptive signal separation operation (ASSO) for effective and accurate separation of a single-channel blind-source multi-component signal, via introducing a time-varying parameter that adapts locally to IFs and using linear chirp (linear frequency modulation) signals to approximate components at each time instant. We derive more accurate component recovery formulae based on the linear chirp signal local approximation. In addition, a recovery scheme, together with a ridge detection method, is also proposed to extract the signal components one by one, and the time-varying parameter is updated for each component. The proposed method is suitable for engineering implementation, being capable of separating complicated signals into their components or sub-signals and reconstructing the signal trend directly. Numerical experiments on synthetic and real-world signals are presented to demonstrate our improvement over the previous attempts. [ABSTRACT FROM AUTHOR]

Traditional recursive least squares (RLS) adaptive filtering is widely used to estimate the impulse responses (IR) of an unknown system. Nevertheless, the RLS estimator shows poor performance when tracking rapidly time-varying systems. In this paper, we propose a multi-layered RLS (m-RLS) estimator to address this concern. The m-RLS estimator is composed of multiple RLS estimators, each of which is employed to estimate and eliminate the misadjustment of the previous layer. It is shown that the mean squared error (MSE) of the m-RLS estimate can be minimized by selecting the optimum number of layers. We provide a method to determine the optimum number of layers. A low-complexity implementation of m-RLS is discussed and it is indicated that the complexity order of the proposed estimator can be reduced to ${\mathcal O}(M)$ , where $M$ is the IR length. Through simulations, we show that m-RLS outperforms the classic RLS and the RLS methods with a variable forgetting factor. [ABSTRACT FROM AUTHOR]

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

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

In this paper, we introduce a Multilinear Generalized Singular Value Decomposition (ML-GSVD) for two or more matrices with one common dimension. The ML-GSVD extends the Generalized Singular Value decomposition (GSVD) of two matrices to higher orders. The proposed decomposition allows us to jointly factorize a set of matrices with one common dimension. In comparison with other approaches that extend the GSVD, the ML-GSVD preserves the essential properties of the original (matrix-based) GSVD, such as orthogonality of the second-mode factor matrices as well as the subspace structure of the third-mode factor matrices. We introduce an ALS-based algorithm to compute the ML-GSVD, which has been inspired by PARAFAC2 decomposition algorithms. In addition, we present an application of the ML-GSVD for transceiver optimization in multicast and unicast MIMO-OFDM systems. Our numerical results show that the proposed ML-GSVD multicast and unicast beamforming outperforms existing state-of-the-art schemes in terms of the sum rate. [ABSTRACT FROM AUTHOR]

This paper explains how to describe any finite-energy signal through a unique representation consisting of an ordered set of positions and a sparse set of signals. This is obtained by designing an iterative decomposition through a series of mirror operations around those positions. The purpose is to find at any step of the decomposition the location that provides for the maximum decoupling between the even and odd components of the signal with respect to it. By limiting such even and odd components on three separate information bearing support, the algorithm can be iterated at infinity determining a sequence of positions. The per location information determines the optimal energy decoupling strategy at each stage providing remarkable sparsity in the representation. The resulting transformation leads to a 1-to-1 mapping. The approach is easily extended to finite-energy sequences, and in particular for sequences of finite length $N$ , at most $N$ iterations of the decomposition are required. Thanks to the sparsity of the resulting representation, experimental simulations demonstrate superior approximation capabilities of this proposed non-linear Mirror Transform with potential application in many domains such as approximation and coding. Its implementation has been made publicly available. [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]

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

This paper introduces Distributed Stein Variational Gradient Descent (DSVGD), a non-parametric generalized Bayesian inference framework for federated learning. DSVGD maintains a number of non-random and interacting particles at a central server to represent the current iterate of the model global posterior. The particles are iteratively downloaded and updated by a subset of agents with the end goal of minimizing the global free energy. By varying the number of particles, DSVGD enables a flexible trade-off between per-iteration communication load and number of communication rounds. DSVGD is shown to compare favorably to benchmark frequentist and Bayesian federated learning strategies in terms of accuracy and scalability with respect to the number of agents, while also providing well-calibrated, and hence trustworthy, predictions. [ABSTRACT FROM AUTHOR]

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

Phase retrieval (PR) is about reconstructing a signal from the magnitude of a number of its complex-valued linear measurements. Recent rapid progress has been made on the development of neural network (NN) based methods for PR. Most of these methods employ pre-trained NNs for modeling target signals, and they require collecting large-scale datasets with ground-truth signals for pre-training, which can be very challenging in many scenarios. There are a few unsupervised learning methods employing untrained NN priors for PR which avoid using external datasets; however, their performance is unsatisfactory compared to pre-trained-NN-based methods. This paper proposes an unsupervised learning method for PR which does not rely on pre-trained NNs while providing state-of-the-art performance. The proposed method trains a randomly-initialized generative NN for signal reconstruction directly on the magnitude measurements of a target signal, which approximates the minimum mean squared error estimator via dropout-based model averaging. Such a model-averaging-based approach provides a better internal prior for the target signal than existing untrained-NN-based methods. The experiments on image reconstruction demonstrate both the advantage of our method over existing unsupervised methods and its competitive performance to pre-trained-NN-based methods. [ABSTRACT FROM AUTHOR]

Frequency-selective (FS) digital predistortion (DPD), which focuses on suppressing the nonlinear distortion at a specific band, has gained increased interest in recent years. However, there is a lack of a general FS DPD approach that is applicable to most scenarios and is suitable for practical implementation. This paper proposes an FS DPD method based on a generalized indirect learning architecture (GILA). Our work on this GILA-based FS DPD method is composed of two contributions. First, an FS Volterra series model structure, which consists of a basic linear part and a partial-band pre-compensation part, is proposed to construct an FS predistorter. Second, a GILA-based identification method is proposed to extract coefficients of the FS predistorter with the FS Volterra series model structure. The proposed GILA-based FS DPD is a general method with low complexity for implementation. Both simulations and experiments verify that the target band of the DPD linearization is arbitrary for the proposed GILA-based FS DPD method. As a special case, when using the proposed method to focus on suppressing the out-of-band distortion, the adjacent channel power ratio performance of the proposed method can be 7.1 dB better than that of the conventional full-band DPD. [ABSTRACT FROM AUTHOR]

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

This paper considers the integrated waveform design to simultaneously achieve a desired radar beampattern and multi-users communication for a dual-function Multiple-Input Multiple-Output (MIMO) system. To this end, a spatio-spectral modulation strategy via shaping the spatial waveform Energy Spectral Density (ESD) in directions of communication is proposed for the communication function, while beampattern Integrated Sidelobe Level (ISL) is minimized to enhance radar detectability. Meanwhile, Peak-to-Average Ratio (PAR) and power restrictions to comply with the current hardware technique and the mainlobe width constraint to cohere the beampattern main energy on the spatial region of interest are forced, respectively. Exploiting an equivalent reformulation of the original non-convex optimization problem, a Sequential Block Enhancement (SBE) framework that alternately updates each waveform in each emitting antenna is developed to monotonically decrease ISL. Each block involves the Dinkelbach’s procedure, sequential convex approximation and Alternating Direction Method of Multipliers (ADMM) to obtain single waveform, while the analytic proof with the converged block being a Karush-Kuhn-Tucker (KKT) point is provided. Finally, numerical results highlight the effectiveness of both the proposed dual function scheme and the waveform synthesis technique in comparison with some counterparts. [ABSTRACT FROM AUTHOR]

Designing efficient sparse recovery algorithms that could handle noisy quantized measurements is important in a variety of applications – from radar to source localization, spectrum sensing and wireless networking. We take advantage of the approximate message passing (AMP) framework to achieve this goal given its high computational efficiency and state-of-the-art performance. In AMP, the signal of interest is assumed to follow certain prior distribution with unknown parameters. Previous works focused on finding the parameters that maximize the measurement likelihood via expectation maximization – an increasingly difficult problem to solve in cases involving complicated probability models. In this paper, we treat the parameters as unknown variables and compute their posteriors via AMP. The parameters and signal of interest can then be jointly recovered. Compared to previous methods, the proposed approach leads to a simple and elegant parameter estimation scheme, allowing us to directly work with 1-bit quantization noise model. We then further extend our approach to general multi-bit quantization noise model. Experimental results show that the proposed framework provides significant improvement over state-of-the-art methods across a wide range of sparsity and noise levels. [ABSTRACT FROM AUTHOR]

It is an essential technique for the moving user nodes (UNs) with clock offset and clock skew to resolve the joint localization and synchronization (JLAS) problem. Existing iterative maximum likelihood methods using sequential one-way time-of-arrival (TOA) measurements from the anchor nodes’ (AN) broadcast signals require a good initial guess and have a computational complexity that grows with the number of iterations, given the size of the problem. In this paper, we propose a new closed-form JLAS approach, namely CFJLAS, which achieves the asymptotically optimal solution in one shot without initialization when the noise is small, and has a low computational complexity. After squaring and differencing the sequential TOA measurement equations, we devise two intermediate variables to reparameterize the non-linear problem, and convert it to a simpler one of solving two simultaneous quadratic equations. We then solve the equations analytically to obtain a raw closed-form JLAS estimation. Finally, we apply a weighted least squares (WLS) step to optimize the estimation. We derive the Cramér-Rao lower bound (CRLB), analyze the estimation error, and show that the estimation accuracy of the CFJLAS reaches the CRLB under the small noise condition. The complexity of the new CFJLAS is only determined by the size of the problem, unlike the conventional iterative method, whose complexity is additionally multiplied by the number of iterations. Simulations in a 2D scene verify that the estimation accuracies of the new CFJLAS method all reach the CRLB under the small noise condition. Compared with the conventional iterative method, the proposed new CFJLAS method does not require initialization, obtains the optimal solution under the small noise condition, and has a low computational complexity. [ABSTRACT FROM AUTHOR]

In this paper, we present two variations of an algorithm for signal reconstruction from one-bit or two-bit noisy observations of the discrete Fourier transform (DFT). The one-bit observations of the DFT correspond to the sign of its real part, whereas, the two-bit observations of the DFT correspond to the signs of both its real and imaginary parts. We focus on images for analysis and simulations, thus using the sign of the 2D-DFT. This choice of the class of signals is inspired by previous works on this problem. For our algorithm, we show that the expected mean squared error (MSE) in signal reconstruction is asymptotically proportional to the inverse of the sampling rate. The samples are affected by additive zero-mean noise of a known distribution. We solve this signal estimation problem by designing an algorithm that uses contraction mapping, based on the Banach fixed point theorem. Numerical tests with four benchmark images are provided to show the effectiveness of our algorithm. Various metrics for image reconstruction quality assessment such as PSNR, SSIM, ESSIM, and MS-SSIM are employed. On all four benchmark images, our algorithm outperforms the state-of-the-art in all of these metrics by a significant margin. [ABSTRACT FROM AUTHOR]

Classical sampling is based on acquiring signal amplitudes at specific points in time, with the minimal sampling rate dictated by the degrees of freedom in the signal. The samplers in this framework are controlled by a global clock that operates at a rate greater than or equal to the minimal sampling rate. At high sampling rates, clocks are power-consuming and prone to electromagnetic interference. An integrate-and-fire time encoding machine (IF-TEM) is an alternative power-efficient sampling mechanism which does not require a global clock. Here, the samples are irregularly spaced threshold-based samples. In this paper, we investigate the problem of sampling FRI signals using an IF-TEM. We provide theoretical guarantees for a recently proposed recovery method to perfectly recover an FRI input. In addition, we propose a modified sampling approach in the presence of noise that is more robust than existing techniques. This method is also proven to ensure recovery in the noise-free setting. The modified approach requires twice the number of measurements compared to the existing method, however, it results in lower error in the presence of noise for the same number of measurements. Our results enable designing low-cost and energy-efficient analog-to-digital converters for FRI signals. [ABSTRACT FROM AUTHOR]

This paper treats a blind detection problem to identify the central nodes in a graph from filtered graph signals. Unlike prior works which impose strong restrictions on the data model, we only require the underlying graph filter to satisfy a low pass property with a generic low-rank excitation model. We treat two cases depending on the low pass graph filter’s strength. When the graph filter is strong low pass, i.e., it has a frequency response that drops sharply at the high frequencies, we show that the principal component analysis (PCA) method detects central nodes with high accuracy. For general low pass graph filter, we show that the graph signals can be described by a structured factor model featuring the product between a low-rank plus sparse factor and an unstructured factor. We propose a two-stage decomposition algorithm to learn the structured factor model via a judicious combination of the non-negative matrix factorization and robust PCA algorithms. We analyze the identifiability conditions for the model which lead to accurate central nodes detection. Numerical experiments on synthetic and real data are provided to support our findings. We demonstrate significant performance gains over prior works. [ABSTRACT FROM AUTHOR]

Goal-guided behavior and destination-directed motion appear in a wide range of human activities and physical processes. Taking advantage of such predictive information can produce better system models and state estimates. This paper focuses on modeling and filtering issues of linear dynamic systems with linear destination constraints. We examine deficiencies of the existing destination constrained (DC) estimation methods. Basically, they resort to post-treatment by imposing destination constraints on updated states only. Viewing destination constraints as an attribute implicit of the state evolution, we propose to incorporate the destination constraints accordingly, particularly on the predictive distribution of the whole state sequence. We construct a congruous DC dynamic model by sufficiently refining the relaxed dynamics with the destination constraint using the state augmentation technique, and analyze its characterization and properties. Next, for the proposed DC model, we develop an optimal DC state estimator and describe its properties. Finally, in the context of aerial surveillance, the superiority of the proposed estimator to existing DC estimators is verified by simulation results, and the effectiveness of the proposed DC dynamic model is demonstrated using real data. [ABSTRACT FROM AUTHOR]

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

This paper proposes a Poisson multi-Bernoulli mixture (PMBM) filter on the space of sets of tree trajectories for multiple target tracking with spawning targets. A tree trajectory contains all trajectory information of a target and its descendants, which appear due to the spawning process. Each tree contains a set of branches, where each branch has trajectory information of a target or one of the descendants and its genealogy. For the standard dynamic and measurement models with multi-Bernoulli spawning, the posterior is a PMBM density, with each Bernoulli having information on a potential tree trajectory. To enable a computationally efficient implementation, we derive an approximate PMBM filter in which each Bernoulli tree trajectory has multi-Bernoulli branches, obtained by minimising the Kullback-Leibler divergence. The resulting filter improves tracking performance of state-of-the-art algorithms in a simulated scenario. [ABSTRACT FROM AUTHOR]

It is well accepted that acquiring downlink channel state information in frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems is challenging because of the large overhead in training and feedback. In this paper, we propose a deep generative model (DGM)-based technique to address this challenge. Exploiting the partial reciprocity of uplink and downlink channels, we first estimate the frequency-independent underlying channel parameters, i.e., the magnitudes of path gains, delays, angles-of-arrivals (AoAs) and angles-of-departures (AoDs), via uplink training, since these parameters are common in both uplink and downlink. Then, the frequency-specific underlying channel parameters, specifically, the phase of each propagation path, are estimated via downlink training using a very short training signal. In the first step, we incorporate the underlying distribution of the channel parameters as a prior into our channel estimation algorithm. We use DGMs to learn this distribution. Simulation results indicate that our proposed DGM-based channel estimation technique outperforms, by a large gap, the conventional channel estimation techniques in practical ranges of signal-to-noise ratio (SNR). In addition, a near-optimal performance is achieved using only few downlink pilot measurements. [ABSTRACT FROM AUTHOR]

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

Tensor rank learning for canonical polyadic decomposition (CPD) has long been deemed as an essential yet challenging problem. In particular, since thetensor rank controls the complexity of the CPD model, its inaccurate learning would cause overfitting to noise or underfitting to the signal sources, and even destroy the interpretability of model parameters. However, the optimal determination of a tensor rank is known to be a non-deterministic polynomial-time hard (NP-hard) task. Rather than exhaustively searching for the best tensor rank via trial-and-error experiments, Bayesian inference under the Gaussian-gamma prior was introduced in the context of probabilistic CPD modeling, and it was shown to be an effective strategy for automatic tensor rank determination. This triggered flourishing research on other structured tensor CPDs with automatic tensor rank learning. On the other side of the coin, these research works also reveal that the Gaussian-gamma model does not perform well for high-rank tensors and/or low signal-to-noise ratios (SNRs). To overcome these drawbacks, in this paper, we introduce a more advanced generalized hyperbolic (GH) prior to the probabilistic CPD model, which not only includes the Gaussian-gamma model as a special case, but also is more flexible to adapt to different levels of sparsity. Based on this novel probabilistic model, an algorithm is developed under the framework of variational inference, where each update is obtained in a closed-form. Extensive numerical results, using synthetic data and real-world datasets, demonstrate the significantly improved performance of the proposed method in learning both low as well as high tensor ranks even for low SNR cases. [ABSTRACT FROM AUTHOR]

In harmonic radar (HR), the transmitter illuminates a nonlinear target (the tag), causing the return signal to consist of harmonics at multiples of the transmitted carrier frequency. Of them, the second harmonic is usually the strongest and the one to which the receiver is tuned. This frequency difference distinguishes the tag reflection from environmental clutter, which remains at the illuminating frequency. However, the passive nature of HR tags severely limits the reflected power, and therefore the operational range of a HR system. We propose to increase the range and/or signal to noise ratio (SNR) by novel restructuring at the physical and signal levels. For this, we accompany the original transmitter with auxiliary transmitters able to send simple tones that are synchronized to arrive at the tag in phase, and we design the receiver to detect an intermodulation component. The resulting range and SNR are much greater than those of the original, conventional HR system, even if the original system were to transmit with power equal to the aggregate power of the proposed system. Achieving mutually coherent, (in phase), arrival of the tones at the tag is the focus of the present paper. We provide a system framework that models the tag, then present the adaptive phase coherence algorithm and analyze the probabilistic growth of the output signal power. We also account for the effects of frequency shifts due to transmitter mobility and the frequency offset errors in the transmitter local oscillators. [ABSTRACT FROM AUTHOR]

This paper considers the problem of adaptive classification for performing pattern discrimination in varying conditions when new data arrives. A new efficient method is presented to incrementally update features in a Nyström-approximated linearized kernel embedding (LKE). Our method leverages a fast eigendecomposition algorithm for symmetric Arrowhead matrices. The proposed method can also be applied to kernel principal component analysis (KPCA) or similar problems. A mechanism is proposed which allows the incremental linearized kernel embedding to be used for updating of dictionaries in a sparse representation-based classification algorithm. The method is based on transporting the dictionaries into the embedding expanded with new data points and avoids the need to learn new dictionary matrices every time new data becomes available. The effectiveness of the developed methods is illustrated on two handwritten digit image data sets namely MNIST and USPS. Classification performance before and after sequential embedding updates is evaluated and compared. Comparisons are also made between our incremental LKE algorithm and the conventional approach to updating the empirical kernel map in terms of their computational requirements and numerical stability. [ABSTRACT FROM AUTHOR]

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

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

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

This paper considers community inference methods for finding communities on a graph. We treat the setting where the edges are not fully observed. Instead, inference is based on partially observed filtered graph signals where observations from some nodes are missing. Under this setup, we treat two related tasks: $\mathsf{A}$) blind inference which recovers the inherited communities on the sub-graph; $\mathsf{B}$) semi-blind inference which recovers communities on the full graph with additional partial topology information. For task $\mathsf{A}$ , we suggest a spectral method which analyzes the principal components of the data covariance matrix. We prove that it succeeds in finding the ‘true’ communities if the graph filter is low-pass and the nodes are uniformly sampled. For task $\mathsf{B}$ , we propose a method using spectral interpolation with a Nyström extension. The latter approach is proven to succeed in finding the ‘true’ communities for modular graphs and low-pass graph filters. Numerical experiments on synthetic and real data corroborate our results. [ABSTRACT FROM AUTHOR]