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A new dirty paper coding technique that is robust against the gain attack is presented. The performance of dirty coding algorithm is further improved by replacing orthogonal with quasi-orthogonal codes, namely Gold sequences, and by concatenating them with an outer turbo code.

In this paper, we show that the communication channel known as writing in memory with defective cells is a relevant information-theoretical model for a specific case of passive warden steganography when the sender embeds a secret message into a subset C of the cover object X without sharing C with the recipient. The set C, which is also called the selection channel, could be arbitrary, determined by the sender from the cover object using a deterministic, pseudo-random, or a truly random process. We call this steganography "writing on wet paper" and realize it using a simple variable-rate random linear code that gives the sender a convenient flexibility and control over the embedding process and is thus suitable for practical implementation. The importance of the wet paper scenario for covert communication is discussed within the context of adaptive steganography and perturbed quantization steganography. Heuristic arguments supported by tests using blind steganalysis indicate that the wet paper steganography provides improved steganographic security and is less vulnerable to steganalytic attacks compared with existing methods with shared selection channels. [ABSTRACT FROM PUBLISHER]

The reputation of the IEEE TRANSACTIONS ON SIGNAL PROCESSING rests on the high quality of its articles and on the dedicated service and expertise of its editorial board and reviewers. In this yearly column, we are pleased to announce the TRANSACTIONS articles that have been selected to receive 2003 Best Paper Awards. We would also like to encourage our readers to nominate TRANSACTIONS papers for awards. Nominations can be submitted online through the TRANSACTIONS website. [ABSTRACT FROM AUTHOR]

Each year in spring, the IEEE Signal Processing Society, at the International Conference on Acoustics, Speech, and Signal Processing (ICASSP), presents its annual awards. Several of these awards are related to Best Papers, and although this is not a rule, several of these papers have appeared in IEEE TRANSACTIONS ON SIGNAL PROCESSING. In this editorial, we are pleased to announce the articles receiving 2005 awards. For the 2006 awards, readers are encouraged to nominate candidate papers before September 1, 2006 to the Editor-in-Chief. Nominations will be judged by the relevant Society Technical Committees before being forwarded to the Awards Board. [ABSTRACT FROM AUTHOR]

The recipients of the 2006 Best Paper Awards are presented. [ABSTRACT FROM PUBLISHER]

These instructions give guidelines for preparing papers for this publication. Presents information for authors publishing in this journal. [ABSTRACT FROM AUTHOR]

These instructions give guidelines for preparing papers for this publication. Presents information for authors publishing in this journal. [ABSTRACT FROM AUTHOR]

The IEEE TRANSACTIONS ON SIGNAL PROCESSING is fortunate to attract submissions of the highest quality and to publish articles that deal with topics that are at the forefront of what is happening in the field of signal processing and its adjacent areas. In this column, we are pleased to announce the TRANSACTIONS articles that have been selected to receive 2004 best paper awards. We would also like to encourage our readers to nominate TRANSACTIONS papers for awards. Nominations can be submitted online through the TRANSACTIONS website. [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 presents secrecy analyses of a full-duplex MIMOME network which consists of two full-duplex multi-antenna users (Alice and Bob) and an arbitrarily located multi-antenna eavesdropper (Eve). The paper assumes that Eve's channel state information (CSI) is completely unknown to Alice and Bob except for a small radius of secured zone. The first part of this paper aims to optimize the powers of jamming noises from both users. To handle Eve's CSI being unknown to users, the focus is placed on Eve at the most harmful location, and the large matrix theory is applied to yield a hardened secrecy rate to work on. The performance gain of the power optimization in terms of maximum tolerable number of antennas on Eve is shown to be significant. The second part of this paper shows two analyses of anti-eavesdropping channel estimation (ANECE) that can better handle Eve with any number of antennas. One analysis assumes that Eve has a prior statistical knowledge of its CSI, which yields lower and upper bounds on secure degrees of freedom of the system as functions of the number (N) of antennas on Eve and the size (K) of information packet. The second analysis assumes that Eve does not have any prior knowledge of its CSI but performs blind detection of information, which yields an approximate secrecy rate for the case of K being larger than N. [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]

This two-part paper aims to quantify the cost of device activity detection in an uplink massive connectivity scenario with a large number of devices but device activities are sporadic. Part I of this paper shows that in an asymptotic massive multiple-input multiple-output (MIMO) regime, device activity detection can always be made perfect. Part II of this paper subsequently shows that despite the perfect device activity detection, there is nevertheless significant cost due to device detection in terms of overall achievable rate, because of the fact that nonorthogonal pilot sequences have to be used in order to accommodate the large number of potential devices, resulting in significantly larger channel estimation error as compared to conventional massive MIMO systems with orthogonal pilots. Specifically, this paper characterizes each active user's achievable rate using random matrix theory under either maximal-ratio combining (MRC) or minimum mean-squared error (MMSE) receive beamforming at the base station (BS), assuming the statistics of their estimated channels as derived in Part I. The characterization of user rate also allows the optimization of pilot sequences length. Moreover, in contrast to the conventional massive MIMO system, the MMSE beamforming is shown to achieve much higher rate than the MRC beamforming for the massive connectivity scenario under consideration. Finally, this paper illustrates the necessity of user scheduling for rate maximization when the number of active users is larger than the number of antennas at the BS. [ABSTRACT FROM AUTHOR]

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]

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]

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]

A sensor array collects spatial samples of propagating wave fields, and a beamformer performs spatial filtering to preserve the desired signal while suppressing interfering signals and noise arriving from directions other than the direction of interest. Given a signal with wideband frequency, using a uniform array is one of the most common approaches to obtain broadband beamforming. In this work, a function formulating the relations between the sensor coefficients and its beam pattern over frequency is introduced. The function is called inverse beam pattern transform. The inverse beam pattern transform mainly contains the coordinate transform and inverse Fourier transform. From the view of spatial aliasing, the inter-distance of the sensors should be less than half of the minimum wavelength of the signal. However, from the bijection of the new function and broadband beamforming perspective, this paper proposes the other lower and upper bounds for the inter-distance. Within these bounds, the new function is the bijective function which can be applied to design the uniform array with broadband beamforming. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g., sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of non-convex penalty functions (regularizers) constrained so as to ensure the convexity of the total cost function F to be minimized. The method is based on parametric penalty functions, the parameters of which are constrained to ensure convexity of F. It is shown that optimal parameters can be obtained by semidefinite programming (SDP). This maximally sparse convex (MSC) approach yields maximally non-convex sparsity-inducing penalty functions constrained such that the total cost function F is convex. It is demonstrated that iterative MSC (IMSC) can yield solutions substantially more sparse than the standard convex sparsity-inducing approach, i.e., L1 norm minimization. [ABSTRACT FROM PUBLISHER]

The practical application of a new class of coprime arrays based on the Chinese remainder theorem (CRT) over quadratic fields is presented in this paper. The proposed CRT arrays are constructed by ideal lattices embedded from coprime quadratic integers with $\mathbf {B}_1$ and $\mathbf {B}_2$ being their matrix representations, respectively, whereby the degrees of freedom (DOF) surges to $O(|\det {(\mathbf {B}_1\mathbf {B}_2)}|)$ with $|\det (\mathbf {B}_1)| + |\det (\mathbf {B}_2)|$ sensors. The geometrical constructions and theoretical foundations were discussed in the accompanying paper in great detail, while this paper focuses on aspects of the application of the proposed arrays in two-dimensional (2-D) remote sensing. A generalization of CRT arrays based on two or more pairwise coprime ideal lattices is proposed with closed-form expressions on sensor locations, the total number of sensors, and the achievable DOF. The issues pertaining to the coprimality of any two quadratic integers are also addressed to explore all possible ideal lattices. Exploiting the symmetry of lattices, sensor reduction methods are discussed with the coarray remaining intact for economic maximization. In order to extend conventional angle estimation techniques based on uniformly distributed arrays to the method that can exploit any coarray configurations based on lattices, this paper introduces a hexagon-to-rectangular transformation to 2-D spatial smoothing, providing the possibility of finding more compact sensor arrays. Examples are provided to verify the feasibility of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper studies the robust matrix completion (RMC) problem with the objective to recover a low-rank matrix from partial observations that may contain significant errors. If all the observations in one column are erroneous, existing RMC methods can locate the corrupted column at best but cannot recover the actual data in that column. Low-rank Hankel matrices characterize the additional correlations among columns besides the low-rankness and exist in power system monitoring, magnetic resonance imaging (MRI) imaging, and array signal processing. Exploiting the low-rank Hankel property, this paper develops an alternating-projection-based fast algorithm to solve the nonconvex RMC problem. The algorithm converges to the ground-truth low-rank matrix with a linear rate even when all the measurements in a constant fraction of columns are corrupted. The required number of observations is significantly less than the existing bounds for the conventional RMC. Numerical results are reported to evaluate the proposed algorithm. [ABSTRACT FROM AUTHOR]

Provides instructions and guidelines to prospective authors who wish to submit manuscripts. [ABSTRACT FROM AUTHOR]

Provides instructions and guidelines to prospective authors who wish to submit manuscripts. [ABSTRACT FROM AUTHOR]

Provides instructions and guidelines to prospective authors who wish to submit manuscripts. [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]

Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a more general set of convex programs known as semi-definite and second-order cone programs. However, these methods are excessively slow for high dimensions. On the other hand, optimization algorithms on manifolds have shown great abilities in finding solutions to non-convex problems in a reasonable time. This paper suggests using a Riemannian optimization approach to solve a subset of convex optimization problems wherein the optimization variable is a doubly stochastic matrix. Optimization over the set of doubly stochastic matrices is crucial for multiple communications and signal processing applications, especially graph-based clustering. The paper introduces and investigates the geometries of three convex manifolds, namely the doubly stochastic, the symmetric, and the definite multinomial manifolds which generalize the simplex, also known as the multinomial manifold. Theoretical complexity analysis and numerical simulation results testify the efficiency of the proposed method over state-of-the-art algorithms. In particular, they reveal that the proposed framework outperforms conventional generic and specialized approaches, especially in high dimensions. [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]

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 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 considers the detection of a distributed target in a partial observation scenario. A distributed targetmodel is usually adopted when the target size is larger than the range bin, for example, in some high-resolution radars. Based on the distributed target model, joint processing of several consecutive range bins can be adopted to achieve performance improvement with respect to processing just one range bin. In applications in complex electromagnetic environments, the radars may miss some of their observations, a phenomenon that usually caused by interference, spectrum sharing, and so on. This partial observation problem leads to degradation of the estimation accuracy for the disturbance (clutter plus noise) covariance matrix and target amplitude vector, which results in decline of the target detection performance. In this paper, a scheme is proposed by using the low-rank priori knowledge of clutter covariance matrix to estimate the detector's unknown parameters. Specifically, the target amplitude vector is obtained by maximizing the likelihood function, and the disturbance covariance matrix is reconstructed by solving an optimization that considers both the likelihood maximization and low-rank property of the clutter covariance matrix. The simulation results indicate that this algorithm improves the estimation accuracy, and achieves a better detection performance in the partial observation scenarios. [ABSTRACT FROM AUTHOR]

Multiple antenna techniques that allow energy beamforming have been looked upon as a possible candidate for increasing the transfer efficiency between the energy transmitter (ET) and the energy receiver in wireless power transfer. This paper introduces a novel scheme that facilitates energy beamforming by utilizing received signal strength indicator (RSSI) values to estimate the channel. First, in the training stage, the ET will transmit using each beamforming vector in a codebook, which is predefined using a Cramer-Rao lower bound analysis. RSSI value corresponding to each beamforming vector is fed back to the ET, and these values are used to estimate the channel through a maximum likelihood analysis. The results that are obtained are remarkably simple, requires minimal processing, and can be easily implemented. The paper also validates the analytical results numerically, as well as experimentally, and it is shown that the proposed method achieves impressive results. [ABSTRACT FROM AUTHOR]

This paper proposes a new framework for the design of transmit and receive beamformers for interference alignment (IA) without symbol extensions in multi-antenna cellular networks. We consider IA in a G cell network with K users/cell, N antennas at each base station (BS) and M antennas at each user. The proposed framework is developed by recasting the conditions for IA as two sets of rank constraints, one on the rank of interference matrices, and the other on the transmit beamformers in the uplink. The interference matrix consists of all the interfering vectors received at a BS from the out-of-cell users in the uplink. Using these conditions and the crucial observation that the rank of interference matrices under alignment can be determined beforehand, this paper develops two sets of algorithms for IA. The first part of this paper develops rank minimization algorithms for IA by iteratively minimizing a weighted matrix norm of the interference matrix. Different choices of matrix norms lead to reweighted nuclear norm minimization (RNNM) or reweighted Frobenius norm minimization (RFNM) algorithms with significantly different per-iteration complexities. Alternately, the second part of this paper devises an alternating minimization (AM) algorithm where the rank-deficient interference matrices are expressed as a product of two lower-dimensional matrices that are then alternately optimized. Simulation results indicate that RNNM, which has a per-iteration complexity of a semidefinite program, is effective in designing aligned beamformers for proper-feasible systems with or without redundant antennas, while RFNM and AM, which have a per-iteration complexity of a quadratic program, are better suited for systems with redundant antennas. [ABSTRACT FROM PUBLISHER]

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

The task of finding a sparse signal decomposition in an overcomplete dictionary is made more complicated when the signal undergoes an unknown modulation (or convolution in the complementary Fourier domain). Such simultaneous sparse recovery and blind demodulation problems appear in many applications including medical imaging, super resolution, self-calibration, etc. In this paper, we consider a more general sparse recovery and blind demodulation problem in which each atom comprising the signal undergoes a distinct modulation process. Under the assumption that the modulating waveforms live in a known common subspace, we employ the lifting technique and recast this problem as the recovery of a column-wise sparse matrix from structured linear measurements. In this framework, we accomplish sparse recovery and blind demodulation simultaneously by minimizing the induced atomic norm, which in this problem corresponds to the block $\ell _{1}$ norm minimization. For perfect recovery in the noiseless case, we derive near optimal sample complexity bounds for Gaussian and random Fourier overcomplete dictionaries. We also provide bounds on recovering the column-wise sparse matrix in the noisy case. Numerical simulations illustrate and support our theoretical results. [ABSTRACT FROM AUTHOR]

This paper is mainly devoted to the derivation of a new fully orthogonal two-dimensional (2-D) lattice structure for general autoregressive (AR) modeling of random fields. Similar to the 1-D lattice theory, this approach is based on recursive incrementation of the prediction support region by adding a single past observation point at each stage. In addition to developing the basic theory, the presentation includes horizontal and vertical building blocks of the proposed causal 2-D AR lattice filters. The algorithm presented here is useful for high-resolution 2-D spectral analysis applications. It is shown that the new fully orthogonal 2-D lattice structure can be an efficient tool for high-resolution radar imaging. [ABSTRACT FROM AUTHOR]

In this paper, we propose new methodologies to decrease the computational cost of safe screening tests for LASSO. We first introduce a new screening strategy, dubbed “joint screening test,” which allows the rejection of a set of atoms by performing one single test. Our approach enables to find good compromises between complexity of implementation and effectiveness of screening. Second, we propose two new methods to decrease the computational cost inherent to the construction of the (so-called) “safe region.” Our numerical experiments show that the proposed procedures lead to significant computational gains as compared to standard methodologies. [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. Broadly speaking, ULAs whose difference coarrays only have $\mathcal {O}(N)$ elements are more robust than sparse arrays with $\mathcal {O}(N^2)$ coarray sizes. This paper advances a theory for quantifying such robustness by introducing the $k$ -essentialness of sensors and the $k$ -essential family of arrays. The proposed theory is motivated by the coarray MUltiple SIgnal Classification (MUSIC) algorithm, which estimates source directions based on difference coarrays. Furthermore, the concept of essentialness not only characterizes the patterns of $k$ faulty sensors that shrink the difference coarray, but also leads to the notion of $k$ -fragility, which assesses the robustness of array geometries quantitatively. However, the large size of the $k$ -essential family usually complicates the theory. It will be shown that the $k$ -essential family can be compactly represented by the so-called $k$ -essential Sperner family. Finally, the proposed theory is used to provide insights into the probability of change of the difference coarray, as a function of the sensor failure probability and array geometry. In a companion paper, the $k$ -essential Sperner family for several commonly used array geometries will be derived in closed form, resulting in a quantitative comparison of the robustness of these arrays. [ABSTRACT FROM AUTHOR]

This paper introduces a node-asynchronous communication protocol in which an agent in a network wakes up randomly and independently, collects states of its neighbors, updates its own state, and then broadcasts back to its neighbors. This protocol differs from consensus algorithms and it allows distributed computation of an arbitrary eigenvector of the network, in which communication between agents is allowed to be directed. (The graph operator is still required to be a normal matrix). To analyze the scheme, this paper studies a random asynchronous variant of the power iteration. Under this random asynchronous model, an initial signal is proven to converge to an eigenvector of eigenvalue 1 (a fixed point) even in the case of operator having spectral radius larger than unity. The rate of convergence is shown to depend not only on the eigenvalue gap but also on the eigenspace geometry of the operator as well as the amount of asynchronicity of the updates. In particular, the convergence region for the eigenvalues gets larger as the updates get less synchronous. Random asynchronous updates are also interpreted from the graph signal perspective, and it is shown that a non-smooth signal converges to the smoothest signal under the random model. When the eigenvalues are real, second order polynomials are used to achieve convergence to an arbitrary eigenvector of the operator. Using second order polynomials the paper formalizes the node-asynchronous communication model. As an application, the protocol is used to compute the Fiedler vector of a network to achieve autonomous clustering. [ABSTRACT FROM AUTHOR]

This paper utilizes sparse array motion to increase the numbers of achievable both degrees of freedom (DOFs) and consecutive lags in direction-of-arrival (DOA) estimation problems. We use commonly employed environment-independent sparse array configurations. The design of these arrays is not dependent on the sources in the field of view, but rather aims at achieving desirable difference co-arrays. They include structured coprime and nested arrays, minimum redundancy array (MRA), minimum hole array (MHA), and sparse uniform linear array (SULA). Array motion can fill the holes in the spatial autocorrelation lags associated with a fixed platform and, therefore, increases the number of sources detectable by the same number of array sensors. Quasi-stationarity of the environment is assumed where the source locations and waveforms are considered invariant over array motion of half wavelength. Closed-form expressions of the number of DOFs and consecutive spatial correlation lags for coprime and nested arrays as well as SULA, due to array translation motion, are derived. The number of DOFs and consecutive lags for the specific cases of MRA an 5 avaluated. We show the respective DOA estimation performance based on sparse reconstruction techniques. [ABSTRACT FROM AUTHOR]

A coprime antenna array consists of two or more sparse subarrays featuring enhanced degrees of freedom (DOF) and reduced mutual coupling. This paper introduces a new class of planar coprime arrays, based on the theory of ideal lattices. In quadratic number fields, a splitting prime $p$ can be decomposed into the product of two distinct prime ideals, which give rise to the two sparse subarrays. Their virtual difference coarray enjoys a quadratic gain in DOF, thanks to the generalized Chinese remainder theorem (CRT). To enlarge the contiguous aperture of the coarray, we present hole-free symmetric CRT arrays with simple closed-form expressions. The ring of Gaussian integers and the ring of Eisenstein integers are considered as examples to demonstrate the procedure of designing coprime arrays. With Eisenstein integers, our design yields a difference coarray that is a subset of the hexagonal lattice, offering a significant gain in DOF over the rectangular lattice, given the same physical areas. Maximization of CRT arrays in the aspect of essentialness and the superior performance in the context of angle estimation will be presented in the companion paper (Part II). [ABSTRACT FROM AUTHOR]

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