Showing papers in "IEEE Transactions on Signal Processing in 2012"
TL;DR: If unlimited energy can be stored in the battery with harvested energy and the full SI is available, it is proved the optimality of a water-filling energy allocation solution where the so-called water levels follow a staircase function.
Abstract: We consider the use of energy harvesters, in place of conventional batteries with fixed energy storage, for point-to-point wireless communications. In addition to the challenge of transmitting in a channel with time selective fading, energy harvesters provide a perpetual but unreliable energy source. In this paper, we consider the problem of energy allocation over a finite horizon, taking into account channel conditions and energy sources that are time varying, so as to maximize the throughput. Two types of side information (SI) on the channel conditions and harvested energy are assumed to be available: causal SI (of the past and present slots) or full SI (of the past, present and future slots). We obtain structural results for the optimal energy allocation, via the use of dynamic programming and convex optimization techniques. In particular, if unlimited energy can be stored in the battery with harvested energy and the full SI is available, we prove the optimality of a water-filling energy allocation solution where the so-called water levels follow a staircase function.
726 citations
TL;DR: An adaptive diffusion mechanism to optimize global cost functions in a distributed manner over a network of nodes, which endow networks with adaptation abilities that enable the individual nodes to continue learning even when the cost function changes with time.
Abstract: We propose an adaptive diffusion mechanism to optimize global cost functions in a distributed manner over a network of nodes. The cost function is assumed to consist of a collection of individual components. Diffusion adaptation allows the nodes to cooperate and diffuse information in real-time; it also helps alleviate the effects of stochastic gradient noise and measurement noise through a continuous learning process. We analyze the mean-square-error performance of the algorithm in some detail, including its transient and steady-state behavior. We also apply the diffusion algorithm to two problems: distributed estimation with sparse parameters and distributed localization. Compared to well-studied incremental methods, diffusion methods do not require the use of a cyclic path over the nodes and are robust to node and link failure. Diffusion methods also endow networks with adaptation abilities that enable the individual nodes to continue learning even when the cost function changes with time. Examples involving such dynamic cost functions with moving targets are common in the context of biological networks.
672 citations
TL;DR: The generalized OMP (gOMP) as discussed by the authors is a generalization of the OMP in the sense that multiple N indices are identified per iteration, and it is shown that the gOMP algorithm can perfectly reconstruct any K-sparse signals (K >; 1) provided that the sensing matrix satisfies the RIP with δNK <; [(√N)/(√K+3√ N)].
Abstract: As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing efficiency in reconstructing sparse signals. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple N indices are identified per iteration. Owing to the selection of multiple “correct” indices, the gOMP algorithm is finished with much smaller number of iterations when compared to the OMP. We show that the gOMP can perfectly reconstruct any K-sparse signals (K >; 1), provided that the sensing matrix satisfies the RIP with δNK <; [(√N)/(√K+3√N)]. We also demonstrate by empirical simulations that the gOMP has excellent recovery performance comparable to l1-minimization technique with fast processing speed and competitive computational complexity.
517 citations
TL;DR: Simulation results demonstrate that the performance of the proposed adaptive beamforming algorithm is almost always close to the optimal value across a wide range of signal to noise and signal to interference ratios.
Abstract: Adaptive beamformers are sensitive to model mismatch, especially when the desired signal is present in training snapshots or when the training is done using data samples. In contrast to previous works, this correspondence attempts to reconstruct the interference-plus-noise covariance matrix instead of searching for the optimal diagonal loading factor for the sample covariance matrix. The estimator is based on the Capon spectral estimator integrated over a region separated from the desired signal direction. This is shown to be more robust than using the sample covariance matrix. Subsequently, the mismatch in the steering vector of the desired signal is estimated by maximizing the beamformer output power under a constraint that prevents the corrected steering vector from getting close to the interference steering vectors. The proposed adaptive beamforming algorithm does not impose a norm constraint. Therefore, it can be used even in applications where gain perturbations affect the steering vector. Simulation results demonstrate that the performance of the proposed adaptive beamformer is almost always close to the optimal value across a wide range of signal to noise and signal to interference ratios.
472 citations
TL;DR: A new efficient NeNMF solver is presented that applies Nesterov's optimal gradient method to alternatively optimize one factor with another fixed and can be used to solve -norm, -norm and manifold regularized NMF with the optimal convergence rate.
Abstract: Nonnegative matrix factorization (NMF) is a powerful matrix decomposition technique that approximates a nonnegative matrix by the product of two low-rank nonnegative matrix factors. It has been widely applied to signal processing, computer vision, and data mining. Traditional NMF solvers include the multiplicative update rule (MUR), the projected gradient method (PG), the projected nonnegative least squares (PNLS), and the active set method (AS). However, they suffer from one or some of the following three problems: slow convergence rate, numerical instability and nonconvergence. In this paper, we present a new efficient NeNMF solver to simultaneously overcome the aforementioned problems. It applies Nesterov's optimal gradient method to alternatively optimize one factor with another fixed. In particular, at each iteration round, the matrix factor is updated by using the PG method performed on a smartly chosen search point, where the step size is determined by the Lipschitz constant. Since NeNMF does not use the time consuming line search and converges optimally at rate in optimizing each matrix factor, it is superior to MUR and PG in terms of efficiency as well as approximation accuracy. Compared to PNLS and AS that suffer from numerical instability problem in the worst case, NeNMF overcomes this deficiency. In addition, NeNMF can be used to solve -norm, -norm and manifold regularized NMF with the optimal convergence rate. Numerical experiments on both synthetic and real-world datasets show the efficiency of NeNMF for NMF and its variants comparing to representative NMF solvers. Extensive experiments on document clustering suggest the effectiveness of NeNMF.
465 citations
TL;DR: This work proposes the construction of two-channel wavelet filter banks for analyzing functions defined on the vertices of any arbitrary finite weighted undirected graph, and proposes quadrature mirror filters for bipartite graph which cancel aliasing and lead to perfect reconstruction.
Abstract: In this work, we propose the construction of two-channel wavelet filter banks for analyzing functions defined on the vertices of any arbitrary finite weighted undirected graph. These graph based functions are referred to as graph-signals as we build a framework in which many concepts from the classical signal processing domain, such as Fourier decomposition, signal filtering and downsampling can be extended to graph domain. Especially, we observe a spectral folding phenomenon in bipartite graphs which occurs during downsampling of these graphs and produces aliasing in graph signals. This property of bipartite graphs, allows us to design critically sampled two-channel filter banks, and we propose quadrature mirror filters (referred to as graph-QMF) for bipartite graph which cancel aliasing and lead to perfect reconstruction. For arbitrary graphs we present a bipartite subgraph decomposition which produces an edge-disjoint collection of bipartite subgraphs. Graph-QMFs are then constructed on each bipartite subgraph leading to “multi-dimensional” separable wavelet filter banks on graphs. Our proposed filter banks are critically sampled and we state necessary and sufficient conditions for orthogonality, aliasing cancellation and perfect reconstruction. The filter banks are realized by Chebychev polynomial approximations.
418 citations
TL;DR: It is confirmed that under constant step-sizes, diffusion strategies allow information to diffuse more thoroughly through the network and this property has a favorable effect on the evolution of the network: diffusion networks are shown to converge faster and reach lower mean-square deviation than consensus networks, and their mean- square stability is insensitive to the choice of the combination weights.
Abstract: Adaptive networks consist of a collection of nodes with adaptation and learning abilities. The nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a distributed manner. In this work, we compare the mean-square performance of two main strategies for distributed estimation over networks: consensus strategies and diffusion strategies. The analysis in the paper confirms that under constant step-sizes, diffusion strategies allow information to diffuse more thoroughly through the network and this property has a favorable effect on the evolution of the network: diffusion networks are shown to converge faster and reach lower mean-square deviation than consensus networks, and their mean-square stability is insensitive to the choice of the combination weights. In contrast, and surprisingly, it is shown that consensus networks can become unstable even if all the individual nodes are stable and able to solve the estimation task on their own. When this occurs, cooperation over the network leads to a catastrophic failure of the estimation task. This phenomenon does not occur for diffusion networks: we show that stability of the individual nodes always ensures stability of the diffusion network irrespective of the combination topology. Simulation results support the theoretical findings.
414 citations
TL;DR: Applications of CES distributions and the adaptive signal processors based on ML- and M-estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for Direction-of-Arrival estimation and beamforming.
Abstract: Complex elliptically symmetric (CES) distributions have been widely used in various engineering applications for which non-Gaussian models are needed. In this overview, circular CES distributions are surveyed, some new results are derived and their applications e.g., in radar and array signal processing are discussed and illustrated with theoretical examples, simulations and analysis of real radar data. The maximum likelihood (ML) estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness, and for convergence of the iterative fixed point algorithm are established. Specific ML-estimators for several CES distributions that are widely used in the signal processing literature are discussed in depth, including the complex t -distribution, K-distribution, the generalized Gaussian distribution and the closely related angular central Gaussian distribution. A generalization of ML-estimators, the M-estimators of the scatter matrix, are also discussed and asymptotic analysis is provided. Applications of CES distributions and the adaptive signal processors based on ML- and M-estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for Direction-of-Arrival (DOA) estimation and beamforming. Furthermore, experimental validation of the usefulness of CES distributions for modelling real radar data is given.
392 citations
TL;DR: Numerical simulation results verify the validity of the theory and illustrate the promising potentials of the proposed sensing framework, called Structurally Random Matrix (SRM), which has theoretical sensing performance comparable to that of completely random sensing matrices.
Abstract: This paper introduces a new framework to construct fast and efficient sensing matrices for practical compressive sensing, called Structurally Random Matrix (SRM). In the proposed framework, we prerandomize the sensing signal by scrambling its sample locations or flipping its sample signs and then fast-transform the randomized samples and finally, subsample the resulting transform coefficients to obtain the final sensing measurements. SRM is highly relevant for large-scale, real-time compressive sensing applications as it has fast computation and supports block-based processing. In addition, we can show that SRM has theoretical sensing performance comparable to that of completely random sensing matrices. Numerical simulation results verify the validity of the theory and illustrate the promising potentials of the proposed sensing framework.
364 citations
TL;DR: This paper presents a new classifier, kernel sparse representation-based classifier (KSRC), based on SRC and the kernel trick which is a usual technique in machine learning and shows KSRC improves the performance of SRC.
Abstract: Sparse representation-based classifier (SRC), a combined result of machine learning and compressed sensing, shows its good classification performance on face image data. However, SRC could not well classify the data with the same direction distribution. The same direction distribution means that the sample vectors belonging to different classes distribute on the same vector direction. This paper presents a new classifier, kernel sparse representation-based classifier (KSRC), based on SRC and the kernel trick which is a usual technique in machine learning. KSRC is a nonlinear extension of SRC and can remedy the drawback of SRC. To make the data in an input space separable, we implicitly map these data into a high-dimensional kernel feature space by using some nonlinear mapping associated with a kernel function. Since this kernel feature space has a very high (or possibly infinite) dimensionality, or is unknown, we have to avoid working in this space explicitly. Fortunately, we can indeed reduce the dimensionality of the kernel feature space by exploiting kernel-based dimensionality reduction methods. In the reduced subspace, we need to find sparse combination coefficients for a test sample and assign a class label to it. Similar to SRC, KSRC is also cast into an l1-minimization problem or a quadratically constrained l1 -minimization problem. Extensive experimental results on UCI and face data sets show KSRC improves the performance of SRC.
329 citations
TL;DR: This work establishes a general condition that must be satisfied by any degrees of freedom tuple (d1. d2....dK) achievable through linear interference alignment that implies that the total achievable DoF cannot grow linearly with K, and is in fact no more than K(M + N)/(K + 1).
Abstract: Consider a K-user flat fading MIMO interference channel where the kth transmitter (or receiver) is equipped with Mk (respectively Nk) antennas. If an exponential (in K) number of generic channel extensions are used either across time or frequency, Cadambe and Jafar [1] showed that the total achievable degrees of freedom (DoF) can be maximized via interference alignment, resulting in a total DoF that grows linearly with A even if Mk and Nk are bounded. In this work we consider the case where no channel extension is allowed, and establish a general condition that must be satisfied by any degrees of freedom tuple (d1. d2....dK) achievable through linear interference alignment. For a symmetric system with Mk = M, Nk = N, dk = d for all k, this condition implies that the total achievable DoF cannot grow linearly with K, and is in fact no more than K(M + N)/(K + 1). We also show that this bound is tight when the number of antennas at each transceiver is divisible by d, the number of data streams per user.
TL;DR: It is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model, and a less cited version of the EKf based on a second-order Taylor expansion is shown to be quite closely related to UKF.
Abstract: The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The claimed advantages with UKF are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model. We point out several less known links between EKF and UKF in terms of two conceptually different implementations of the Kalman filter: the standard one based on the discrete Riccati equation, and one based on a formula on conditional expectations that does not involve an explicit Riccati equation. First, it is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model. Second, a less cited version of the EKF based on a second-order Taylor expansion is shown to be quite closely related to UKF. The different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications.
TL;DR: This paper addresses the security of a two-way relay network in the presence of an eavesdropper, where each node is only equipped with single antenna, and proposes two-phase distributed analog network coding, or distributed beamforming and power allocation to enhance the secrecy sum rate of the data exchange.
Abstract: In this paper, we address the security of a two-way relay network in the presence of an eavesdropper, where each node is only equipped with single antenna. We propose two-phase distributed analog network coding, or distributed beamforming and power allocation to enhance the secrecy sum rate of the data exchange. In the first phase, the two terminals broadcast their information data simultaneously to all the relay nodes. In the second phase, three different security schemes are proposed: optimal beamforming, null-space beamforming, and artificial noise beamforming. In the first scheme, the objective is to achieve the maximum secrecy sum rate of the two terminals. Mathematically, the objective function is difficult to optimize. In the second scheme, we maximize the total information exchanged while we eliminate the information leakage completely, subject to the total transmission power constraint. We show that the problem has a unique and global optimum, which can be solved using bisection method. When the instantaneous channel state information of the eavesdropper is not available, we propose an artificial noise beamforming in the third scheme. We minimize the information transmission power so that the artificial noise power is maximized to eliminate information leakage, under the constraints of quality of service (QoS) required by terminals. It is a second-order convex cone programming (SOCP) problem, thus can be efficiently solved using interior point methods. Numerical results are provided and analyzed to show the properties and efficiency of the proposed designs.
TL;DR: This paper proposes an efficient approximation method for solving the nonconvex centralized problem, using semidefinite relaxation (SDR), an approximation technique based on convex optimization, and analytically shows the convergence of the proposed distributed robust MCBF algorithm to the optimal centralized solution.
Abstract: Multicell coordinated beamforming (MCBF), where multiple base stations (BSs) collaborate with each other in the beamforming design for mitigating the intercell interference (ICI), has been a subject drawing great attention recently. Most MCBF designs assume perfect channel state information (CSI) of mobile stations (MSs); however CSI errors are inevitable at the BSs in practice. Assuming elliptically bounded CSI errors, this paper studies the robust MCBF design problem that minimizes the weighted sum power of BSs subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on the MSs. Our goal is to devise a distributed optimization method to obtain the worst-case robust beamforming solutions in a decentralized fashion with only local CSI used at each BS and limited backhaul information exchange between BSs. However, the considered problem is difficult to handle even in the centralized form. We first propose an efficient approximation method for solving the nonconvex centralized problem, using semidefinite relaxation (SDR), an approximation technique based on convex optimization. Then a distributed robust MCBF algorithm is further proposed, using a distributed convex optimization technique known as alternating direction method of multipliers (ADMM). We analytically show the convergence of the proposed distributed robust MCBF algorithm to the optimal centralized solution. We also extend the worst-case robust beamforming design as well as its decentralized implementation method to a fully coordinated scenario. Simulation results are presented to examine the effectiveness of the proposed SDR method and the distributed robust MCBF algorithm.
TL;DR: It is shown that the performance of HD based CS is very sensitive to the BEP wall phenomenon while the SD basedCS is more robust in that sense.
Abstract: This paper focuses on the performance analysis and comparison of hard decision (HD) and soft decision (SD) based approaches for cooperative spectrum sensing in the presence of reporting channel errors. For cooperative sensing (CS) in cognitive radio networks, a distributed detection approach with displaced sensors and a fusion center (FC) is employed. For HD based CS, each secondary user (SU) sends a one-bit hard local decision to the FC. For SD based CS, each SU sends a quantized version of a local decision statistic such as the log-likelihood ratio or any suitable sufficient statistic. The decision statistics are sent through channels that may cause errors. The effects of channel errors are incorporated in the analysis through the bit error probability (BEP). For HD based CS, the counting rule or the K-out-of-N rule is used at the FC. For SD based CS, the optimal fusion rule in the presence of reporting channel errors is derived and its distribution is established. A comparison of the two schemes is conducted to show that there is a performance gain in using SD based CS even in the presence of reporting channel errors. In addition, a BEP wall is shown to exist for CS such that if the BEP is above a certain value, then irrespective of the received signal strength corresponding to the primary user, the constraints on false alarm probability and detection probability cannot be met. It is shown that the performance of HD based CS is very sensitive to the BEP wall phenomenon while the SD based CS is more robust in that sense.
TL;DR: The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets, subsuming eight apparently distinct types of analysis filters into a single common form.
Abstract: The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets, subsuming eight apparently distinct types of analysis filters into a single common form. This superfamily of analytic wavelets provides a framework for systematically investigating wavelet suitability for various applications. In addition to a parameter controlling the time-domain duration or Fourier-domain bandwidth, the wavelet shape with fixed bandwidth may be modified by varying a second parameter, called γ. For integer values of γ, the most symmetric, most nearly Gaussian, and generally most time-frequency concentrated member of the superfamily is found to occur for γ = 3. These wavelets, known as “Airy wavelets,” capture the essential idea of popular Morlet wavelet, while avoiding its deficiencies. They may be recommended as an ideal starting point for general purpose use.
TL;DR: This paper presents a random set based approach to tracking of an unknown number of extended targets, in the presence of clutter measurements and missed detections, where the targets' extensions are modeled as random matrices, resulting in the Gaussian inverse Wishart phd (giw-phd) filter.
Abstract: This paper presents a random set based approach to tracking of an unknown number of extended targets, in the presence of clutter measurements and missed detections, where the targets' extensions are modeled as random matrices For this purpose, the random matrix framework developed recently by Koch is adapted into the extended target phd framework, resulting in the Gaussian inverse Wishart phd (giw-phd) filter A suitable multiple target likelihood is derived, and the main filter recursion is presented along with the necessary assumptions and approximations The particularly challenging case of close extended targets is addressed with practical measurement clustering algorithms The capabilities and limitations of the resulting extended target tracking framework are illustrated both in simulations and in experiments based on laser scans
TL;DR: The maximum likelihood estimators (MLE) are derived for motion estimation of a maneuvering target based on joint envelope and phase measurement, phase- only measurement and envelope-only measurement in case of high signal-to-noise ratio (SNR), respectively.
Abstract: The slant range of a radar maneuvering target is usually modeled as a multivariate function in terms of its illumination time and multiple motion parameters. This multivariate range function includes the modulations on both the envelope and the phase of an echo of the coherent radar target and provides the foundation for radar target motion estimation. In this paper, the maximum likelihood estimators (MLE) are derived for motion estimation of a maneuvering target based on joint envelope and phase measurement, phase-only measurement and envelope-only measurement in case of high signal-to-noise ratio (SNR), respectively. It is shown that the proposed MLEs are to search the maximums of the outputs of the proposed generalized Radon-Fourier transform (GRFT), generalized Radon transform (GRT) and generalized Fourier transform (GFT), respectively. Furthermore, by approximating the slant range function by a high-order polynomial, the inherent accuracy limitations, i.e., the Cramer-Rao low bounds (CRLB), and some analysis are given for high order motion parameter estimations in different scenarios. Finally, some numerical experimental results are provided to demonstrate the effectiveness of the proposed methods.
TL;DR: Analysis shows that both methods reduce the bias considerably and achieve the CRLB performance for distant source when the noise is Gaussian and small and the BiasRed method is able to lower the bias to the same level as the Maximum Likelihood Estimator.
Abstract: This paper proposes two methods to reduce the bias of the well-known algebraic explicit solution (Chan and Ho, "A simple and efficient estimator for hyperbolic location," IEEE Trans. Signal Process., vol. 42, pp. 1905-1915, Aug. 1994) for source localization using TDOA. Bias of a source location estimate is significant when the measurement noise is large and the geolocation geometry is poor. Bias also dominates performance when multiple times of independent measurements are available such as in UWB localization or in target tracking. The paper starts by deriving the bias of the source location estimate from Chan and Ho. The bias is found to be considerably larger than that of the Maximum Likelihood Estimator. Two methods, called BiasSub and BiasRed, are developed to reduce the bias. The BiasSub method subtracts the expected bias from the solution of Chan and Ho's work, where the expected bias is approximated by the theoretical bias using the estimated source location and noisy data measurements. The BiasRed method augments the equation error formulation and imposes a constraint to improve the source location estimate. The BiasSub method requires the exact knowledge of the noise covariance matrix and BiasRed only needs the structure of it. Analysis shows that both methods reduce the bias considerably and achieve the CRLB performance for distant source when the noise is Gaussian and small. The BiasSub method can nearly eliminate the bias and the BiasRed method is able to lower the bias to the same level as the Maximum Likelihood Estimator. The BiasRed method is extended for TDOA and FDOA positioning. Simulations corroborate the performance of the proposed methods.
TL;DR: Although cooperative jamming is not necessary for optimal transmission with perfect eavesdropper's CSI, it is shown that robust jamming support can increase the worst-case secrecy rate and lower the signal to interference-plus-noise ratio at the eaves dropper in the presence of channel mismatches between the transmitters and the eavesdroppers.
Abstract: This paper studies robust transmission schemes for multiple-input single-output (MISO) wiretap channels. Both the cases of direct transmission and cooperative jamming with a helper are investigated with imperfect channel state information (CSI) for the eavesdropper links. Robust transmit covariance matrices are obtained based on worst-case secrecy rate maximization, under both individual and global power constraints. For the case of an individual power constraint, we show that the nonconvex maximin optimization problem can be transformed into a quasi-convex problem that can be efficiently solved with existing methods. For a global power constraint, the joint optimization of the transmit covariance matrices and power allocation between the source and the helper is studied. We also investigate the robust wiretap transmission problem for the case with a quality-of-service constraint at the legitimate receiver. Numerical results show the advantage of the proposed robust design. In particular, for the global power constraint scenario, although cooperative jamming is not necessary for optimal transmission with perfect eavesdropper's CSI, we show that robust jamming support can increase the worst-case secrecy rate and lower the signal to interference-plus-noise ratio at the eavesdropper in the presence of channel mismatches between the transmitters and the eavesdropper.
TL;DR: A new MVDR RAB technique, which uses as little as possible and easy to obtain imprecise prior information, is developed and simulation results demonstrate the superiority of the proposed method over other previously developed RAB techniques.
Abstract: A general notion of robustness for robust adaptive beamforming (RAB) problem and a unified principle for minimum variance distortionless response (MVDR) RAB techniques design are formulated. This principle is to use standard MVDR beamformer in tandem with an estimate of the desired signal steering vector found based on some imprecise prior information. Differences between various MVDR RAB techniques occur only because of the differences in the assumed prior information and the corresponding signal steering vector estimation techniques. A new MVDR RAB technique, which uses as little as possible and easy to obtain imprecise prior information, is developed. The objective for estimating the steering vector is the maximization of the beamformer output power, while the constraints are the normalization condition and the requirement that the estimate does not converge to any of the interference steering vectors and their linear combinations. The prior information used is only the imprecise knowledge of the antenna array geometry and angular sector in which the actual steering vector lies. Mathematically, the proposed MVDR RAB is expressed as the well known non-convex quadratically constrained quadratic programming problem with two constraints, which can be efficiently and exactly solved. Some new results for the corresponding optimization problem such as a new algebraic way of finding the rank-one solution from the general-rank solution of the relaxed problem and the condition under which the solution of the relaxed problem is guaranteed to be rank-one are derived. Our simulation results demonstrate the superiority of the proposed method over other previously developed RAB techniques.
TL;DR: In this paper, a matrix factorization formulation and enforcing the low-rank constraint in the estimates as a sparsity constraint are used to determine the correct rank while providing high recovery performance.
Abstract: Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. In this paper, we present novel recovery algorithms for estimating low-rank matrices in matrix completion and robust principal component analysis based on sparse Bayesian learning (SBL) principles. Starting from a matrix factorization formulation and enforcing the low-rank constraint in the estimates as a sparsity constraint, we develop an approach that is very effective in determining the correct rank while providing high recovery performance. We provide connections with existing methods in other similar problems and empirical results and comparisons with current state-of-the-art methods that illustrate the effectiveness of this approach.
TL;DR: The source and relay beamforming is jointly designed to maximize the secrecy rate in the cooperative scheme and the performance of the secure beamforming schemes is compared through extensive numerical simulations.
Abstract: An amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network composed of a source, a relay, and a destination is considered, where transmit beamforming is employed both at the source and at the relay. The relay is a user who is willing to help the communication from the source to the destination. In our paper, however, the relay is untrusted in the sense that it may make a passive security attack; that is, it may decode messages of the source. We consider two ways to transmit confidential information of the source to the destination: noncooperative secure beamforming and cooperative secure beamforming. In the noncooperative scheme, the relay is simply treated as an eavesdropper, and does not participate in communication. In the cooperative scheme, the relay is asked to relay signals from the source to the destination. In this paper, the source and relay beamforming is jointly designed to maximize the secrecy rate in the cooperative scheme. The conditions under which the cooperative scheme achieves a higher secrecy rate than the noncooperative scheme are derived in the low and high signal-to-noise ratio (SNR) regimes of the source-relay and relay-destination links. The performance of the secure beamforming schemes is compared through extensive numerical simulations.
TL;DR: A solution is first presented based on a periodic sampling procedure and a simple least-squares reconstruction method that is able to recover the unknown power spectrum of a wide-sense stationary signal from the obtained sub-Nyquist rate samples and the statistical properties of the estimated power spectrum.
Abstract: In several applications, such as wideband spectrum sensing for cognitive radio, only the power spectrum (a.k.a. the power spectral density) is of interest and there is no need to recover the original signal itself. In addition, high-rate analog-to-digital converters (ADCs) are too power hungry for direct wideband spectrum sensing. These two facts have motivated us to investigate compressive wideband power spectrum sensing, which consists of a compressive sampling procedure and a reconstruction method that is able to recover the unknown power spectrum of a wide-sense stationary signal from the obtained sub-Nyquist rate samples. It is different from spectrum blind sampling (SBS), which aims at reconstructing the original signal instead of the power spectrum. In this paper, a solution is first presented based on a periodic sampling procedure and a simple least-squares reconstruction method. We evaluate the reconstruction process both in the time and frequency domain. Then, we examine two possible implementations for the compressive sampling procedure, namely complex Gaussian sampling and multicoset sampling, although we mainly focus on the latter. A new type of multicoset sampling is introduced based on the so-called minimal sparse ruler problem. Next, we analyze the statistical properties of the estimated power spectrum. The computation of the mean and the covariance of the estimates allows us to calculate the analytical normalized mean squared error (NMSE) of the estimated power spectrum. Further, when the received signal is assumed to contain only circular complex zero-mean Gaussian i.i.d. noise, the computed mean and covariance can be used to derive a suitable detection threshold. Simulation results underline the promising performance of our proposed approach. Note that all benefits of our method arise without putting any sparsity constraints on the power spectrum.
TL;DR: A diffusion Kalman filtering algorithm based on the covariance intersection method, where local estimates are fused by incorporating the covariances information of local Kalman filters, which leads to a stable estimate for each agent.
Abstract: This paper is concerned with distributed Kalman filtering for linear time-varying systems over multiagent sensor networks. We propose a diffusion Kalman filtering algorithm based on the covariance intersection method, where local estimates are fused by incorporating the covariance information of local Kalman filters. Our algorithm leads to a stable estimate for each agent regardless of whether the system is uniformly observable locally by the measurements of its neighbors which include the measurements of itself as long as the system is uniformly observable by the measurements of all the agents and the communication is sufficiently fast compared to the sampling. Simulation results validate the effectiveness of the proposed distributed Kalman filtering algorithm.
TL;DR: This work achieves SNR enhancement, by beamforming the sub-Nyquist samples obtained from multiple elements, by applying this process to cardiac ultrasound data, while achieving a nearly eightfold reduction in sample-rate, compared to standard techniques.
Abstract: Emerging sonography techniques often require increasing the number of transducer elements involved in the imaging process. Consequently, larger amounts of data must be acquired and processed. The significant growth in the amounts of data affects both machinery size and power consumption. Within the classical sampling framework, state of the art systems reduce processing rates by exploiting the bandpass bandwidth of the detected signals. It has been recently shown, that a much more significant sample-rate reduction may be obtained, by treating ultrasound signals within the Finite Rate of Innovation framework. These ideas follow the spirit of Xampling, which combines classic methods from sampling theory with recent developments in Compressed Sensing. Applying such low-rate sampling schemes to individual transducer elements, which detect energy reflected from biological tissues, is limited by the noisy nature of the signals. This often results in erroneous parameter extraction, bringing forward the need to enhance the SNR of the low-rate samples. In our work, we achieve SNR enhancement, by beamforming the sub-Nyquist samples obtained from multiple elements. We refer to this process as “compressed beamforming”. Applying it to cardiac ultrasound data, we successfully image macroscopic perturbations, while achieving a nearly eightfold reduction in sample-rate, compared to standard techniques.
TL;DR: This work proposes a novel approach to extending the applicability of state-space models to a wider range of noise distributions without losing the computational advantages of the associated algorithms.
Abstract: State-space models have been successfully applied across a wide range of problems ranging from system control to target tracking and autonomous navigation. Their ubiquity stems from their modeling flexibility, as well as the development of a battery of powerful algorithms for estimating the state variables. For multivariate models, the Gaussian noise assumption is predominant due its convenient computational properties. In some cases, anyhow, this assumption breaks down and no longer holds. We propose a novel approach to extending the applicability of this class of models to a wider range of noise distributions without losing the computational advantages of the associated algorithms. The estimation methods we develop parallel the Kalman filter and thus are readily implemented and inherit the same order of complexity. We derive all of the equations and algorithms from first principles. In order to validate the performance of our approach, we present specific instances of non-Gaussian state-space models and test their performance on experiments with synthetic and real data.
TL;DR: The algorithm, named D-ADMM, is a decentralized implementation of the alternating direction method of multi- pliers, and it is shown through numerical simulation that the algorithm requires considerably less communications between the nodes than the state-of-the-art algorithms.
Abstract: We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP) BP finds the least l1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction Our algorithm solves BP on a distributed platform such as a sensor network, and is designed to minimize the communication between nodes The algorithm only requires the network to be connected, has no notion of a central processing node, and no node has access to the entire matrix A at any time We consider two scenarios in which either the columns or the rows of A are distributed among the compute nodes Our algorithm, named D-ADMM, is a decentralized implementation of the alternating direction method of multi- pliers We show through numerical simulation that our algorithm requires considerably less communications between the nodes than the state-of-the-art algorithms
TL;DR: The solution of the distributed filter gains is characterized by solving a set of recursive linear matrix inequalities, and a simulation example is provided to show the effectiveness of the proposed filtering scheme.
Abstract: This paper is concerned with the distributed finite-horizon filtering problem for a class of time-varying systems over lossy sensor networks. The time-varying system (target plant) is subject to randomly varying nonlinearities (RVNs) caused by environmental circumstances. The lossy sensor network suffers from quantization errors and successive packet dropouts that are described in a unified framework. Two mutually independent sets of Bernoulli distributed white sequences are introduced to govern the random occurrences of the RVNs and successive packet dropouts. Through available output measurements from not only the individual sensor but also its neighboring sensors according to the given topology, a sufficient condition is established for the desired distributed finite-horizon filter to ensure that the prescribed average filtering performance constraint is satisfied. The solution of the distributed filter gains is characterized by solving a set of recursive linear matrix inequalities. A simulation example is provided to show the effectiveness of the proposed filtering scheme.
TL;DR: This bound offers a substantial improvement over the recent result of Davenport and Wakin and also closes gap between the recovery bound and fundamental limit over which the perfect recovery of the OMP cannot be guaranteed.
Abstract: Orthogonal matching pursuit (OMP) is a greedy search algorithm popularly being used for the recovery of compressive sensed sparse signals. In this correspondence, we show that if the isometry constant δK+1 of the sensing matrix Φ satisfies δK+1 <; 1/(1/√K+1) then the OMP algorithm can perfectly recover K-sparse signals from the compressed measurements y=Φx. Our bound offers a substantial improvement over the recent result of Davenport and Wakin and also closes gap between the recovery bound and fundamental limit over which the perfect recovery of the OMP cannot be guaranteed.