Problem In Array Signal Processing Research Articles

Near-Field Multiple Target Localization in Frequency Diverse Array Based on Tensor Decomposition

Target localization is a fundamental problem in array signal processing. The problem of locating near-field targets with multiple-input multiple-output (MIMO) radar has been studied extensively; however, most of the conventional matrix-based approaches suffer from limitations in terms of the representation and exploitation of the multidimensional nature of MIMO radar signals. In this paper, we addressed the problem of localizing multiple targets in the near-field region, aiming at pursuing a solution applicable for multidimensional signal that is able to achieve sufficient accuracy. A tensor-based signal model impinging on a monostatic frequency diverse array multiple-input multiple-output (FDA-MIMO) radar was formulated, and a corresponding tensor decomposition-based localization algorithm (TenDLA) that showcases the connection between the tensor-based analysis and the localization problem was developed. Additionally, a correction procedure to mitigate the estimation deviations on the range and angle was presented, yielding significant improvements in estimation accuracy. Numerical examples demonstrated the validity and effectiveness of the proposed approach, and it was shown that this approach is superior to conventional methods due to its high-resolution estimation accuracy as well as its relatively low computational costs.

An Efficient Method for Sparse Linear Array Sensor Placement to Achieve Maximum Degrees of Freedom

Compared to the uniform linear array (ULA), the sparse linear array (SLA) has many advantages such as a greater degrees of freedom (DOF), a higher resolution, and robustness against mutual coupling. The optimal placement of elements to achieve the maximum DOF in SLA has been an old problem in array signal processing. Finding the optimum placement is limited to an exhaustive computer search as yet. Therefore, some familiar SLAs (such as `nested' and `coprime' arrays) have been suggested to improve DOF although none of them necessarily can achieve the maximum DOF with a certain number of sensors. In this paper, first we have proposed a novel hole-free SLA that yields the minimum number of sensors (MSA) for the desired DOF. The optimization problem associated with such an array is a nonlinear binary optimization problem. Then, the problem is transformed into a binary linear programming (BLP) problem which could be solved exactly. Using the proposed method, a fast and efficient solution to the minimum redundancy array(MRA) is found. Finally, the simulation results show that the proposed array has a higher DOF compared to the other competitive methods for a given number of sensors, which is the maximum possible DOF. This can lead to a better target resolution and DOA estimation.

Source enumeration via RMT estimator with adaptive decision criterion based on linear shrinkage estimation of noise eigenvalues using relatively few samples

Estimating the number of signals embedded in noise is a fundamental problem in array signal processing. The classic random matrix theory (RMT) estimator based on RMT does not consider the bias term of the expectation of the eigenvalue being tested, and thus, its detection performance will be affected by this bias term, and it also suffers from noise uncertainty in its decision threshold. In order to overcome these problems, more accurate expressions for the distribution and the bias term of the expectation of the eigenvalue being tested are firstly derived by utilising the linear shrinkage (LS) technique. Then, a novel LS-RMT estimator is proposed by incorporating the bias term of the expectation of the eigenvalue being tested into the decision criterion of the RMT estimator. Moreover, both the increased under-estimation probability and the increased over-estimation probability of the RMT estimator incurred by this bias term are derived according to the sign of this bias term. Based on these results, a novel LS-RMT estimator with adaptive decision criterion (termed as ‘LS-RMT-ADC estimator’) is proposed by utilising the LS-RMT estimator, and the proposed LS-RMT-ADC estimator can adaptively select its decision threshold and determine the noise variance in the selected decision threshold. Therefore, it can overcome both the higher under-estimation probability and the higher over-estimation probability of the RMT estimator, and can also avoid the noise uncertainty in the decision threshold of the RMT estimator. Finally, simulation results are presented to show that the LS-RMT-ADC estimator outperforms the existing estimators.

Effect of varying Number of Spacing between Antenna Elements, Snapshots, SNR on AP ML, AP-SSF and ESPRIT Algorithm

The direction of arrival estimation is the main key problem in array signal processing. In this paper, the alternating projection maximum Likelihood (AP-ML), Alternating projection sub space framework (APSSF) and ESPRIT algorithm are studied. The simulation is performed in MATLAB for single and multiple sources. The effect of the varying number of spacing between antenna elements, number of snapshots and SNR are studied. The performance comparison shows that ESPRIT algorithm performs better as compared to the AP-ML and AP-SSF. Key-Words: - AP-ML, AP-SSF, Direction of Arrival, ESPRIT, Snapshots, SNR

DOA estimation based on CNN for underwater acoustic array

The direction of arrival (DOA) estimation of space signals is a basic problems in array signal processing, which is also one of the tasks in many fields such as radar arrays and sonar arrays. In array signal processing, the most commonly used array covariance matrix is a complex matrix. Since traditional neural networks can only deal with real numbers, they cannot handle real and imaginary numbers at the same time, so the input of the neural network is very limited. Based on the application of convolutional neural network (CNN) in RGB three-channel image processing, this paper proposes to use two-channel including real and imaginary covariance matrices as the input signal of the CNN in order to estimate direction of underwater acoustic signal. After modelling and simulation, compared with the traditional MUSIC algorithm, CNN algorithm has higher accuracy and shorter estimation time in small SNR environment. Therefore, the method proposed in this paper can effectively identify the incoming wave direction of the unknown signal in water after training.

Model-Aided Deep Neural Network for Source Number Detection

Source number detection is a critical problem in array signal processing. Conventional model-driven methods e.g., Akaikes information criterion (AIC) and minimum description length (MDL), suffer from severe performance degradation when the number of snapshots is small or the signal-to-noise ratio (SNR) is low. In this paper, we exploit the model-aided based deep neural network (DNN) to estimate the source number. Specifically, we first propose the eigenvalue based regression network (ERNet) and classification network (ECNet) to estimate the number of non-coherent sources, where the eigenvalues of the received signal covariance matrix and the source number are used as the input and the supervise label of the networks, respectively. Then, we extend the ERNet and ECNet for estimating the number of coherent sources, where the forward-backward spatial smoothing (FBSS) scheme is adopted to improve the performance of ERNet and ECNet. Numerical results demonstrate the outstanding performance of ERNet and ECNet over the conventional AIC and MDL methods as well as their excellent generalization capability, which also shows their great potentials for practical applications.

A Robust Direction of Arrival Estimation Method for Uniform Circular Array.

Estimating the Direction of Arrival (DOA) is a basic and crucial problem in array signal processing. The existing DOA methods fail to obtain reliable and accurate results when noise and reverberation occur in real applications. In this paper, an accurate and robust estimation method for estimating the DOA of sources signal is proposed. Incorporating the Estimating Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm with the RANdom SAmple Consensus (RANSAC) algorithm gives rise to the RAN-ESPRIT method, which removes outliers automatically in noise-corrupted environments. In this work, a uniform circular array (UCA) is converted into a virtual uniform linear array (ULA) to begin with. Then, the covariance matrix of the received signals of the virtual linear array is reconstructed, and the ESPRIT algorithm is deployed to estimate initial DOA of the source signal. Finally, the modified RANSAC method with automatically selected thresholds is used to fit the source signal to obtain accurate DOA. The proposed method can remove the unreliable DOA feature data and leads to more accuracy of DOA estimation of source signals in reverberation environments. Experimental results demonstrate that the proposed method is more robust and efficient compared to the traditional methods (i.e., ESPRIT, TLS-ESPRIT).

Linear shrinkage estimation of covariance matrices using low-complexity cross-validation

Shrinkage can effectively improve the condition number and accuracy of covariance matrix estimation, especially for low-sample-support applications with the number of training samples smaller than the dimensionality. This paper investigates parameter choice for linear shrinkage estimators. We propose data-driven, leave-one-out cross-validation (LOOCV) methods for automatically choosing the shrinkage coefficients, aiming to minimize the Frobenius norm of the estimation error. A quadratic loss is used as the prediction error for LOOCV. The resulting solutions can be found analytically or by solving optimization problems of small sizes and thus have low complexities. Our proposed methods are compared with various existing techniques. We show that the LOOCV method achieves near-oracle performance for shrinkage designs using sample covariance matrix (SCM) and several typical shrinkage targets. Furthermore, the LOOCV method provides low-complexity solutions for estimators that use general shrinkage targets, multiple targets, and/or ordinary least squares (OLS)-based covariance matrix estimation. We also show applications of our proposed techniques to several different problems in array signal processing.

Applying concepts and tools from signal processing on graphs (SPG) to problems in array signal processing

Signal processing on graphs (SPG) is an emerging area of research that extends well-established data analysis concepts and tools to support a special type of signal where data samples are defined on the vertices of a graph. Since SPG emerged in 2013, fundamental operations such as filtering, the Fourier transform, and modulation have been formally defined that uniquely consider and take advantage of the underlying complex and irregular relationship between data elements which is captured mathematically by a graph. The purpose of this study is to analyze the applicability of SPG to array signal processing. We show that signals defined on a graph, or graph signals for short, are natural models for data collected over a line array of sensors. We also apply existing SPG processing algorithms to array signal data and investigate and probe whether SPG can help increase array gain.

A Sum-of-Squares and Semidefinite Programming Approach for Maximum Likelihood DOA Estimation.

Direction of arrival (DOA) estimation using a uniform linear array (ULA) is a classical problem in array signal processing. In this paper, we focus on DOA estimation based on the maximum likelihood (ML) criterion, transform the estimation problem into a novel formulation, named as sum-of-squares (SOS), and then solve it using semidefinite programming (SDP). We first derive the SOS and SDP method for DOA estimation in the scenario of a single source and then extend it under the framework of alternating projection for multiple DOA estimation. The simulations demonstrate that the SOS- and SDP-based algorithms can provide stable and accurate DOA estimation when the number of snapshots is small and the signal-to-noise ratio (SNR) is low. Moveover, it has a higher spatial resolution compared to existing methods based on the ML criterion.

Comparing frequency-difference beamforming and delay-and-sum beamforming as an estimator of direction-of-arrival

Direction-of-arrival estimation (DOA) is an important and long-studied problem in array signal processing. Existing algorithms such as conventional delay-and-sum beamforming are limited in performance and become inadequate for a high-frequency broadband source and when the receiving linear array is sparse. Abadi, Song, and Dowling (2012), however, showed that DOAS estimation is possible in this case with an algorithm they introduced called frequency-difference beamforming. This was demonstrated empirically in their previous work using a real dataset. In addition, the resemblance between frequency-difference beamforming and delay-and-sum beamforming was briefly discussed. The purpose of this study is to analyze this relationship further and determine how well frequency-difference beamforming compares to delay-and-sum beamforming as an estimator of DOA. The approach taken in this study is to explicitly formulate the estimator equation for frequency-difference beamforming and compare it mathematically to the estimator equation of delay-and-sum beamforming. The equations are compared for the case of one DOA and two DOAs. For both cases, we show the effect of both source frequency and source bandwidth on frequency-difference beamforming. Using these results, we probe the following question: what are the conditions on the source frequency or source bandwidth for which frequency-difference beamforming will outperform delay-and-sum beamforming?

Modified MUSIC Algorithm for DOA Estimation With Nyström Approximation

Multiple signal classification (MUSIC) can be seen as one of the most popular solutions to the direction-of-arrival estimation problem in array signal processing. Traditionally, this method utilizes the whole array observations to construct the noise subspace. In this letter, based on the randomly chosen sensors outputs, we exploit the Nystrom method to approximate the noise subspace, and develop a low-complexity modified MUSIC version for far-field sources localization. Computer simulations confirm that the novel algorithm using only one-fourth sensors outputs provides almost the same estimation performance as its traditional version.

Fetal electrocardiogram estimation using polynomial eigenvalue decomposition

In this paper, we propose the application of polynomial matrix eigenvalue decomposition (PEVD) to the problem of fetal electrocardiogra (ECG) extraction from real ECG recordings obtained from abdominal leads. We model the fetal ECG extraction problem as a broadband sensor array signal processing problem in order to account for the broadband nature of the ECG noise present in the recordings. An algorithm for providing an approximate PEVD is used in order to estimate the broadband noise subspace. Suppression of the broadband noise and maternal ECG is achieved by carrying out an orthonormal projection of the recordings onto the estimated fetal subspace. The proposed scheme was evaluated with multichannel synthetic ECG signals and real ECG data from the PhysioNet Challenge database and is shown to perform favorably as compared to prior-art methods. Results indicate that our method is more robust than the prior-art ones for the task of fetal ECG estimation.

Determining the Number of Coherent/Correlated Sources Using FBSS-based Methods

Determining the number of sources from observed data, is a fundamental problem in array signal processing. In this paper, first we focus on two popular estimators based on information theoretic criteria, AIC and MDL. Then another algorith m based on eigenvalue grads, namely EGM is presented. The co mputer simu lation results prove the effective performance of the EGM for non-coherent signals but in the small differences between the incident angles of non-coherent sources, MDL and AIC have a much better detection performance than EGM . These methods can detect only non-coherent signals, and the performance of them will be sharply declined even signals are coherent and/or correlated. So, first forward/backward spatial s moothing (FBSS) method is used as a pre-processing step to solve the coherency/correlation, and then MDL, AIC and EGM algorithms are run to estimate the number of signals. Nu merical results show that FBSS-based EGM offers higher detection probability rather than FBSS-based MDL and AIC in the case of coherent sources as well as correlated ones. Also, the higher detection probability can be achieved for correlated case compared to coherent one.

Spatial Differencing Method for DOA Estimation Under the Coexistence of Both Uncorrelated and Coherent Signals

Direction-of-arrival (DOA) estimation is an important problem in array signal processing. An effective spatial differencing method is addressed, for the DOA estimation problem of a number of uncorrelated and coherent narrowband signals simultaneously impinging on the far field of a uniform linear array (ULA). In the proposed method, the uncorrelated sources are firstly estimated using conventional subspace methods, and then they are eliminated by exploiting the spatial differencing technique, that is, only coherent components remain in the spatial differencing matrix. Finally, the remaining coherent signals are estimated by utilizing the spatial differencing matrix. Compared with the previous works, the presented method can improve the DOA estimation accuracy, as well as increase the maximal number of detectable signals. The theoretical analysis and simulation results confirm the effectiveness of the method.

Joint estimation of source number and DOA using simulated annealing algorithm

The array signal processing problem has to do with two main issues: 1) the determination of source number; and 2) estimation of the directions-of-arrival (DOA) of these sources. In the classical methods, the determination of source number and the estimation of DOA parameters are executed independently rather than jointly. To jointly estimate source number and DOA, this paper proposes a simulated annealing-based algorithm. The key points of this paper are: i) the prior choices for some unknown parameters are calibrated to compute more efficiently; ii) a penalty term for the parameter number is added to the corresponding objective function Additionally to avoid overfitting; and iii) in order to move to the regions of interest quickly, some cumulants of properly chosen sensor outputs from the uniform linear array (ULA) is computed and their moduluses of Fourier transform (MFT) are mapped trickly to the uniform distribution. Finally simulation results are presented to validate the performance of the proposed method.

A Generalized Steered Response Power Method for Computationally Viable Source Localization

The process of locating an acoustic source given measurements of the sound field at multiple microphones is of significant interest as both a classical array signal processing problem, and more recently, as a solution to the problems of automatic camera steering, teleconferencing, hands-free processing, and others. Despite the proven efficacy of steered-beamformer approaches to localization in harsh conditions, their practical application to real-time settings is hindered by undesirably high computational demands. This paper presents a computationally viable implementation of the steered response power (SRP) source localization method. The conventional approach is generalized by introducing an inverse mapping that maps relative delays to sets of candidate locations. Instead of traversing the three-dimensional location space, the one-dimensional relative delay space is traversed; at each lag, all locations which are inverse mapped by that delay are updated. This means that the computation of the SRP map is no longer performed sequentially in space. Most importantly, by subsetting the space of relative delays to only those that achieve a high level of cross-correlation, the required number of algorithm updates is drastically reduced without compromising localization accuracy. The generalization is scalable in the sense that the level of subsetting is an algorithm parameter. It is shown that this generalization may be viewed as a spatial decomposition of the SRP energy map into weighted basis functions-in this context, it becomes evident that the full SRP search considers all basis functions (even the ones with very low weighting). On the other hand, it is shown that by only including a few basis functions per microphone pair, the SRP map is quite accurately represented. As a result, in a real environment, the proposed generalization achieves virtually the same anomaly rate as the full SRP search while only performing 10% the amount of algorithm updates as the full search.

Detection of the number of signals in noise with banded covariance matrices

A new approach is presented to the array signal processing problem of detecting the number of incident signals in unknown coloured noise environments with banded covariance structure. The principle of canonical correlation analysis is applied to the outputs of two spatially separated arrays. The number of signals is determined by testing the significance of the corresponding sample canonical correlation coefficients. The new method is shown to work well in unknown coloured noise situations and does not require any subjective threshold setting. The medium/high-SNR error rate may be approximately specified at a certain prescribed level, and may be traded off against the detection performance characteristic at low SNR. Simulation results are included to illustrate the performance of the proposed canonical correlation technique (CCT). It is found that the method performs well in a wide variety of coloured background noise environments. It is also demonstrated that the method is robust in the case when the noise covariance is not truly banded.

Detection and estimation using an adaptive rational function filter

Proposes a new nonlinear adaptive filter structure based on rational functions. There are several advantages to the use of this filter. First, it is a universal approximator and a good extrapolator. Second, it ran be trained by a linear adaptive algorithm, which makes it suitable for real-time adaptive signal processing. Third, it has a best approximation for a specified function. To demonstrate its utility as a tool for solving adaptive signal processing problems, the authors apply the adaptive rational function filter to the problem of estimation and detection. The estimation problem pertains to the direction of arrival (DOA) estimation problem in array signal processing. For the detection problem, the authors consider the detection of a weak radar target (a small piece of ice) in an ocean environment.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

DOA estimation method for unknown noise fields

In the paper by Rajagopal and Ramakrishna (see IEE Proc. F, Radar Signal Process., vol.138, no.5, p.495-501, 1991) a matrix decomposition method (MDM) for direction-of-arrival (DOA) estimation in an unknown noise field is presented. A solution to this array signal processing problem is derived. In this paper the authors state that the MDM used in the above paper is a variant of MUSIC (see Johnson and Degraff, 1982). They consider the example of three narrowband signals impinging on a uniform linear array.