R. C. de Lamare

Y. Yu, L. Lu, Y. Zakharov et al.

This paper proposes a unified sparsity-aware robust recursive least-squares RLS (S-RRLS) algorithm for the identification of sparse systems under impulsive noise. The proposed algorithm generalizes multiple algorithms only by replacing the specified criterion of robustness and sparsity-aware penalty. Furthermore, by jointly optimizing the forgetting factor and the sparsity penalty parameter, we develop the jointly-optimized S-RRLS (JO-S-RRLS) algorithm, which not only exhibits low misadjustment but also can track well sudden changes of a sparse system. Simulations in impulsive noise scenarios demonstrate that the proposed S-RRLS and JO-S-RRLS algorithms outperform existing techniques.

W. Shi, Y. Li, R. C. de Lamare

A novel sparse array (SA) structure is proposed based on the maximum inter-element spacing (IES) constraint (MISC) criterion. Compared with the traditional MISC array, the proposed SA configurations, termed as improved MISC (IMISC) has significantly increased uniform degrees of freedom (uDOF) and reduced mutual coupling. In particular, the IMISC arrays are composed of six uniform linear arrays (ULAs), which can be determined by an IES set. The IES set is constrained by two parameters, namely the maximum IES and the number of sensors. The uDOF of the IMISC arrays is derived and the weight function of the IMISC arrays is analyzed as well. The proposed IMISC arrays have a great advantage in terms of uDOF against the existing SAs, while their mutual coupling remains at a low level. Simulations are carried out to demonstrate the advantages of the IMISC arrays.

S. Mohammadzadeh, V. H. Nascimento, R. C. de Lamare et al.

In this work, a simple and effective robust adaptive beamforming technique is proposed for uniform linear arrays, which is based on the power spectral estimation and uncertainty region (PSEUR) of the interference plus noise (IPN) components. In particular, two algorithms are presented to find the angular sector of interference in every snapshot based on the adopted spatial uncertainty region of the interference direction. Moreover, a power spectrum is introduced based on the estimation of the power of interference and noise components, which allows the development of a robust approach to IPN covariance matrix reconstruction. The proposed method has two main advantages. First, an angular region that contains the interference direction is updated based on the statistics of the array data. Secondly, the proposed IPN-PSEUR method avoids estimating the power spectrum of the whole range of possible directions of the interference sector. Simulation results show that the performance of the proposed IPN-PSEUR beamformer is almost always close to the optimal value across a wide range of signal-to-noise ratios.

X. Sheng, D. Lu, Y. Li et al.

In this letter, inspired by the maximum inter-element spacing (IES) constraint (MISC) criterion, an enhanced MISC-based (EMISC) sparse array (SA) with high uniform degrees-of-freedom (uDOFs) and low mutual-coupling (MC) is proposed, analyzed and discussed in detail. For the EMISC SA, an IES set is first determined by the maximum IES and number of elements. Then, the EMISC SA is composed of seven uniform linear sub-arrays (ULSAs) derived from an IES set. An analysis of the uDOFs and weight function shows that, the proposed EMISC SA outperforms the IMISC SA in terms of uDOF and MC. Simulation results show a significant advantage of the EMISC SA over other existing SAs.

R. C. de Lamare

In this work, we propose a subspace-based algorithm for direction-of-arrival (DOA) estimation, referred to as two-step knowledge-aided iterative estimation of signal parameters via rotational invariance techniques (ESPRIT) method (Two-Step KAI-ESPRIT), which achieves more accurate estimates than those of prior art. The proposed Two-Step KAI-ESPRIT improves the estimation of the covariance matrix of the input data by incorporating prior knowledge of signals and by exploiting knowledge of the structure of the covariance matrix and its perturbation terms. Simulation results illustrate the improvement achieved by the proposed method.

W. Leite, R. C. de Lamare, Y. Zakharov et al.

This paper proposes design techniques for partially-calibrated sparse linear subarrays and algorithms to perform direction-of-arrival (DOA) estimation. First, we introduce array architectures that incorporate two distinct array categories, namely type-I and type-II arrays. The former breaks down a known sparse linear geometry into as many pieces as we need, and the latter employs each subarray such as it fits a preplanned sparse linear geometry. Moreover, we devise two Direction of Arrival (DOA) estimation algorithms that are suitable for partially-calibrated array scenarios within the coarray domain. The algorithms are capable of estimating a greater number of sources than the number of available physical sensors, while maintaining the hardware and computational complexity within practical limits for real-time implementation. To this end, we exploit the intersection of projections onto affine spaces by devising the Generalized Coarray Multiple Signal Classification (GCA-MUSIC) in conjunction with the estimation of a refined projection matrix related to the noise subspace, as proposed in the GCA root-MUSIC algorithm. An analysis is performed for the devised subarray configurations in terms of degrees of freedom, as well as the computation of the Cramèr-Rao Lower Bound for the utilized data model, in order to demonstrate the good performance of the proposed methods. Simulations assess the performance of the proposed design methods and algorithms against existing approaches.

W. S. Leite, R. C. de Lamare

This paper investigates the problem of direction-of-arrival (DOA) estimation using multiple partially-calibrated sparse subarrays. In particular, we present the Generalized Coarray Multiple Signal Classification (GCA-MUSIC) DOA estimation algorithm to scenarios with partially-calibrated sparse subarrays. The proposed GCA-MUSIC algorithm exploits the difference coarray for each subarray, followed by a specific pseudo-spectrum merging rule that is based on the intersection of the signal subspaces associated to each subarray. This rule assumes that there is no a priori knowledge about the cross-covariance between subarrays. In that way, only the second-order statistics of each subarray are used to estimate the directions with increased degrees of freedom, i.e., the estimation procedure preserves the coarray Multiple Signal Classification and sparse arrays properties to estimate more sources than the number of physical sensors in each subarray. Numerical simulations show that the proposed GCA-MUSIC has better performance than other similar strategies.

S. Mohammadzadeh, V. H. Nascimento, R. C. de Lamare et al.

This work presents a cost-effective technique for designing robust adaptive beamforming algorithms based on efficient covariance matrix reconstruction with iterative spatial power spectrum (CMR-ISPS). The proposed CMR-ISPS approach reconstructs the interference-plus-noise covariance (INC) matrix based on a simplified maximum entropy power spectral density function that can be used to shape the directional response of the beamformer. Firstly, we estimate the directions of arrival (DoAs) of the interfering sources with the available snapshots. We then develop an algorithm to reconstruct the INC matrix using a weighted sum of outer products of steering vectors whose coefficients can be estimated in the vicinity of the DoAs of the interferences which lie in a small angular sector. We also devise a cost-effective adaptive algorithm based on conjugate gradient techniques to update the beamforming weights and a method to obtain estimates of the signal of interest (SOI) steering vector from the spatial power spectrum. The proposed CMR-ISPS beamformer can suppress interferers close to the direction of the SOI by producing notches in the directional response of the array with sufficient depths. Simulation results are provided to confirm the validity of the proposed method and make a comparison to existing approaches

Z. Zheng, L. Lu, Y. Yu et al.

For active impulsive noise control, a filtered-x recursive least $p$-power (FxRLP) algorithm is proposed by minimizing the weighted summation of the $p$-power of the \emph{a posteriori} errors. Since the characteristic of the target noise is investigated, the FxRLP algorithm achieves good performance and robustness. To obtain a better performance, we develop a filtered-x logarithmic recursive least $p$-power (FxlogRLP) algorithm which integrates the $p$-order moment with the logarithmic-order moment. Simulation results demonstrate that the FxlogRLP algorithm is superior to the existing algorithms in terms of convergence rate and noise reduction.

W. S. Leite, R. C. de Lamare

This paper proposes an enhanced coarray transformation model (EDCTM) and a mixed greedy maximum likelihood algorithm called List-Based Maximum Likelihood Orthogonal Matching Pursuit (LBML-OMP) for direction-of-arrival estimation with non-uniform linear arrays (NLAs). The proposed EDCTM approach obtains improved estimates when Khatri-Rao product-based models are used to generate difference coarrays under the assumption of uncorrelated sources. In the proposed LBML-OMP technique, for each iteration a set of candidates is generated based on the correlation-maximization between the dictionary and the residue vector. LBML-OMP then chooses the best candidate based on a reduced-complexity asymptotic maximum likelihood decision rule. Simulations show the improved results of EDCTM over existing approaches and that LBML-OMP outperforms existing sparse recovery algorithms as well as Spatial Smoothing Multiple Signal Classification with NLAs.

T. Yu, W. Li, Y. Yu et al.

The exponential functional link network (EFLN) has been recently investigated and applied to nonlinear filtering. This brief proposes an adaptive EFLN filtering algorithm based on a novel inverse square root (ISR) cost function, called the EFLN-ISR algorithm, whose learning capability is robust under impulsive interference. The steady-state performance of EFLN-ISR is rigorously derived and then confirmed by numerical simulations. Moreover, the validity of the proposed EFLN-ISR algorithm is justified by the actually experimental results with the application to hysteretic nonlinear system identification.

A. Danaee, R. C. de Lamare, V. H. Nascimento

In this work, we present an energy-efficient distributed learning framework using low-resolution ADCs and coarsely quantized signals for Internet of Things (IoT) networks. In particular, we develop a distributed quantization-aware least-mean square (DQA-LMS) algorithm that can learn parameters in an energy-efficient fashion using signals quantized with few bits while requiring a low computational cost. We also carry out a statistical analysis of the proposed DQA-LMS algorithm that includes a stability condition. Simulations assess the DQA-LMS algorithm against existing techniques for a distributed parameter estimation task where IoT devices operate in a peer-to-peer mode and demonstrate the effectiveness of the DQA-LMS algorithm.

S. Mohammadzadeh, V. H. Nascimento, R. C. de Lamare

In this letter, we present a novel low-complexity adaptive beamforming technique using a stochastic gradient algorithm to avoid matrix inversions. The proposed method exploits algorithms based on the maximum entropy power spectrum (MEPS) to estimate the noise-plus-interference covariance matrix (MEPS-NPIC) so that the beamforming weights are updated adaptively, thus greatly reducing the computational complexity. MEPS is further used to reconstruct the desired signal covariance matrix and to improve the estimate of the desired signals's steering vector (SV). Simulations show the superiority of the proposed MEPS-NPIC approach over previously proposed beamformers.

A. Danaee, R. C. de Lamare, V. H. Nascimento

In this work, we present an energy-efficient distributed learning framework using coarsely quantized signals for Internet of Things (IoT) networks. In particular, we develop a distributed quantization-aware recursive least squares (DQA-RLS) algorithm that can learn parameters in an energy-efficient fashion using signals quantized with few bits while requiring a low computational cost. Numerical results assess the DQA-RLS algorithm against existing techniques for a distributed parameter estimation task where IoT devices operate in a peer-to-peer mode.

Y. Yu, H. He, T. Yang et al.

This work proposes diffusion normalized least mean M-estimate algorithm based on the modified Huber function, which can equip distributed networks with robust learning capability in the presence of impulsive interference. In order to exploit the system's underlying sparsity to further improve the learning performance, a sparse-aware variant is also developed by incorporating the $l_0$-norm of the estimates into the update process. We then analyze the transient, steady-state and stability behaviors of the algorithms in a unified framework. In particular, we present an analytical method that is simpler than conventional approaches to deal with the score function since it removes the requirements of integrals and Price's theorem. Simulations in various impulsive noise scenarios show that the proposed algorithms are superior to some existing diffusion algorithms and the theoretical results are verifiable.

X. Wang, Z. Yang, J. Huang et al.

Space-time adaptive processing (STAP) algorithms with coprime arrays can provide good clutter suppression potential with low cost in airborne radar systems as compared with their uniform linear arrays counterparts. However, the performance of these algorithms is limited by the training samples support in practical applications. To address this issue, a robust two-stage reduced-dimension (RD) sparsity-aware STAP algorithm is proposed in this work. In the first stage, an RD virtual snapshot is constructed using all spatial channels but only $m$ adjacent Doppler channels around the target Doppler frequency to reduce the slow-time dimension of the signal. In the second stage, an RD sparse measurement modeling is formulated based on the constructed RD virtual snapshot, where the sparsity of clutter and the prior knowledge of the clutter ridge are exploited to formulate an RD overcomplete dictionary. Moreover, an orthogonal matching pursuit (OMP)-like method is proposed to recover the clutter subspace. In order to set the stopping parameter of the OMP-like method, a robust clutter rank estimation approach is developed. Compared with recently developed sparsity-aware STAP algorithms, the size of the proposed sparse representation dictionary is much smaller, resulting in low complexity. Simulation results show that the proposed algorithm is robust to prior knowledge errors and can provide good clutter suppression performance in low sample support.

H. Ruan, R. C. de Lamare

In this work, we present a novel robust distributed beamforming (RDB) approach based on low-rank and cross-correlation techniques. The proposed RDB approach mitigates the effects of channel errors in wireless networks equipped with relays based on the exploitation of the cross-correlation between the received data from the relays at the destination and the system output and low-rank techniques. The relay nodes are equipped with an amplify-and-forward (AF) protocol and the channel errors are modeled using an additive matrix perturbation, which results in degradation of the system performance. The proposed method, denoted low-rank and cross-correlation RDB (LRCC-RDB), considers a total relay transmit power constraint in the system and the goal of maximizing the output signal-to-interference-plus-noise ratio (SINR). We carry out a performance analysis of the proposed LRCC-RDB technique along with a computational complexity study. The proposed LRCC-RDB does not require any costly online optimization procedure and simulations show an excellent performance as compared to previously reported algorithms.

Q. Jiang, S. Li, Z. Zhu et al.

This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the dictionary being used, a diagonal weighted matrix is obtained and then the sensing matrix is designed by minimizing a weighted function such that the Gram of the equivalent dictionary is as close to the Gram of dictionary as possible. An analytical solution for the corresponding sensing matrix is derived which leads to low computational complexity. We also exploit this prior information through the sparse recovery stage and propose a probability-driven orthogonal matching pursuit algorithm that improves the accuracy of the recovery. Simulations for synthetic data and application scenarios of surveillance video are carried out to compare the performance of the proposed methods with some existing algorithms. The results reveal that the proposed CS system outperforms existing CS systems.

Y. Yu, L. Lu, Z. Zheng et al.

The dichotomous coordinate descent (DCD) algorithm has been successfully used for significant reduction in the complexity of recursive least squares (RLS) algorithms. In this work, we generalize the application of the DCD algorithm to RLS adaptive filtering in impulsive noise scenarios and derive a unified update formula. By employing different robust strategies against impulsive noise, we develop novel computationally efficient DCD-based robust recursive algorithms. Furthermore, to equip the proposed algorithms with the ability to track abrupt changes in unknown systems, a simple variable forgetting factor mechanism is also developed. Simulation results for channel identification scenarios in impulsive noise demonstrate the effectiveness of the proposed algorithms.

Y. Yu, H. Zhao, R. C. de Lamare et al.

This work develops robust diffusion recursive least squares algorithms to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. The first algorithm minimizes an exponentially weighted least-squares cost function subject to a time-dependent constraint on the squared norm of the intermediate update at each node. A recursive strategy for computing the constraint is proposed using side information from the neighboring nodes to further improve the robustness. We also analyze the mean-square convergence behavior of the proposed algorithm. The second proposed algorithm is a modification of the first one based on the dichotomous coordinate descent iterations. It has a performance similar to that of the former, however its complexity is significantly lower especially when input regressors of agents have a shift structure and it is well suited to practical implementation. Simulations show the superiority of the proposed algorithms over previously reported techniques in various impulsive noise scenarios.

Y. Yu, R. C. de Lamare, Y. Zakharov

This work develops a robust diffusion recursive least squares algorithm to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. This algorithm minimizes an exponentially weighted least-squares cost function subject to a time-dependent constraint on the squared norm of the intermediate estimate update at each node. With the help of side information, the constraint is recursively updated in a diffusion strategy. Moreover, a control strategy for resetting the constraint is also proposed to retain good tracking capability when the estimated parameters suddenly change. Simulations show the superiority of the proposed algorithm over previously reported techniques in various impulsive noise scenarios.

S. Pinto, R. C. de Lamare

In this work, we present direction-of-arrival (DoA) estimation algorithms based on the Krylov subspace that effectively exploit prior knowledge of the signals that impinge on a sensor array. The proposed multi-step knowledge-aided iterative conjugate gradient (CG) (MS-KAI-CG) algorithms perform subtraction of the unwanted terms found in the estimated covariance matrix of the sensor data. Furthermore, we develop a version of MS-KAI-CG equipped with forward-backward averaging, called MS-KAI-CG-FB, which is appropriate for scenarios with correlated signals. Unlike current knowledge-aided methods, which take advantage of known DoAs to enhance the estimation of the covariance matrix of the input data, the MS-KAI-CG algorithms take advantage of the knowledge of the structure of the forward-backward smoothed covariance matrix and its disturbance terms. Simulations with both uncorrelated and correlated signals show that the MS-KAI-CG algorithms outperform existing techniques.

Y. Yu, H. Zhao, R. C. de Lamare

We propose two sparsity-aware normalized subband adaptive filter (NSAF) algorithms by using the gradient descent method to minimize a combination of the original NSAF cost function and the l1-norm penalty function on the filter coefficients. This l1-norm penalty exploits the sparsity of a system in the coefficients update formulation, thus improving the performance when identifying sparse systems. Compared with prior work, the proposed algorithms have lower computational complexity with comparable performance. We study and devise statistical models for these sparsity-aware NSAF algorithms in the mean square sense involving their transient and steady -state behaviors. This study relies on the vectorization argument and the paraunitary assumption imposed on the analysis filter banks, and thus does not restrict the input signal to being Gaussian or having another distribution. In addition, we propose to adjust adaptively the intensity parameter of the sparsity attraction term. Finally, simulation results in sparse system identification demonstrate the effectiveness of our theoretical results.

A. Flores, R. C. de Lamare

In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques, solving problems with nonlinearities elegantly. In this paper, we present data-selective adaptive kernel normalized least-mean square (KNLMS) algorithms that can increase their learning rate and reduce their computational complexity. In fact, these methods deal with kernel expansions, creating a growing structure also known as the dictionary, whose size depends on the number of observations and their innovation. The algorithms described herein use an adaptive step-size to accelerate the learning and can offer an excellent tradeoff between convergence speed and steady state, which allows them to solve nonlinear filtering and estimation problems with a large number of parameters without requiring a large computational cost. The data-selective update scheme also limits the number of operations performed and the size of the dictionary created by the kernel expansion, saving computational resources and dealing with one of the major problems of kernel adaptive algorithms. A statistical analysis is carried out along with a computational complexity analysis of the proposed algorithms. Simulations show that the proposed KNLMS algorithms outperform existing algorithms in examples of nonlinear system identification and prediction of a time series originating from a nonlinear difference equation.

M. Kaloorazi, R. C. de Lamare

Low-rank matrix approximations play a fundamental role in numerical linear algebra and signal processing applications. This paper introduces a novel rank-revealing matrix decomposition algorithm termed Compressed Randomized UTV (CoR-UTV) decomposition along with a CoR-UTV variant aided by the power method technique. CoR-UTV is primarily developed to compute an approximation to a low-rank input matrix by making use of random sampling schemes. Given a large and dense matrix of size $m\times n$ with numerical rank $k$, where $k \ll \text{min} \{m,n\}$, CoR-UTV requires a few passes over the data, and runs in $O(mnk)$ floating-point operations. Furthermore, CoR-UTV can exploit modern computational platforms and, consequently, can be optimized for maximum efficiency. CoR-UTV is simple and accurate, and outperforms reported alternative methods in terms of efficiency and accuracy. Simulations with synthetic data as well as real data in image reconstruction and robust principal component analysis applications support our claims.

S. F. B. Pinto, R. C. de Lamare

In this work, we propose a subspace-based algorithm for DOA estimation which iteratively reduces the disturbance factors of the estimated data covariance matrix and incorporates prior knowledge which is gradually obtained on line. An analysis of the MSE of the reshaped data covariance matrix is carried out along with comparisons between computational complexities of the proposed and existing algorithms. Simulations focusing on closely-spaced sources, where they are uncorrelated and correlated, illustrate the improvements achieved.

R. C. de Lamare, André Flores

Adaptive algorithms based on kernel structures have been a topic of significant research over the past few years. The main advantage is that they form a family of universal approximators, offering an elegant solution to problems with nonlinearities. Nevertheless these methods deal with kernel expansions, creating a growing structure also known as dictionary, whose size depends on the number of new inputs. In this paper we derive the set-membership kernel-based normalized least-mean square (SM-NKLMS) algorithm, which is capable of limiting the size of the dictionary created in stationary environments. We also derive as an extension the set-membership kernelized affine projection (SM-KAP) algorithm. Finally several experiments are presented to compare the proposed SM-NKLMS and SM-KAP algorithms to the existing methods.

H. Ruan, R. C. de Lamare

This work presents joint minimum mean-square error (MMSE) consensus algorithm and relay selection algorithms for distributed beamforming. We propose joint MMSE consensus relay and selection schemes with a total power constraint and local communications among the relays for a network with cooperating sensors. We also devise greedy relay selection algorithms based on the MMSE consensus approach that optimize the network performance. Simulation results show that the proposed scheme and algorithms outperform existing techniques for distributed beamforming.

S. Xu, R. C. de Lamare, H. V. Poor

This paper presents adaptive link selection algorithms for distributed estimation and considers their application to wireless sensor networks and smart grids. In particular, exhaustive search--based least--mean--squares(LMS)/recursive least squares(RLS) link selection algorithms and sparsity--inspired LMS/RLS link selection algorithms that can exploit the topology of networks with poor--quality links are considered. The proposed link selection algorithms are then analyzed in terms of their stability, steady--state and tracking performance, and computational complexity. In comparison with existing centralized or distributed estimation strategies, key features of the proposed algorithms are: 1) more accurate estimates and faster convergence speed can be obtained; and 2) the network is equipped with the ability of link selection that can circumvent link failures and improve the estimation performance. The performance of the proposed algorithms for distributed estimation is illustrated via simulations in applications of wireless sensor networks and smart grids.

S. Xu, R. C. de Lamare, H. V. Poor

This paper proposes a novel distributed reduced--rank scheme and an adaptive algorithm for distributed estimation in wireless sensor networks. The proposed distributed scheme is based on a transformation that performs dimensionality reduction at each agent of the network followed by a reduced-dimension parameter vector. A distributed reduced-rank joint iterative estimation algorithm is developed, which has the ability to achieve significantly reduced communication overhead and improved performance when compared with existing techniques. Simulation results illustrate the advantages of the proposed strategy in terms of convergence rate and mean square error performance.

A. Gully, R. C. de Lamare

This paper describes a novel technique for promoting sparsity in the modified filtered-x algorithms required for active noise control. The proposed algorithms are based on recent techniques incorporating approximations to the \ell_0-norm in the cost functions that are used to derive adaptive filtering algorithms. In particular, zero-attracting and reweighted zero-attracting filtered-x adaptive algorithms are developed and considered for active noise control problems. The results of simulations indicate that the proposed techniques improve the convergence of the existing modified algorithm in the case where the primary and secondary paths exhibit a degree of sparsity.

S. Xu, R. C. de Lamare, H. V. Poor

This paper presents new dynamic topology adaptation strategies for distributed estimation in smart grids systems. We propose a dynamic exhaustive search--based topology adaptation algorithm and a dynamic sparsity--inspired topology adaptation algorithm, which can exploit the topology of smart grids with poor--quality links and obtain performance gains. We incorporate an optimized combining rule, named Hastings rule into our proposed dynamic topology adaptation algorithms. Compared with the existing works in the literature on distributed estimation, the proposed algorithms have a better convergence rate and significantly improve the system performance. The performance of the proposed algorithms is compared with that of existing algorithms in the IEEE 14--bus system.