Wideband Direction Of Arrival Estimation Research Articles

White noise reduction for wideband linear array signal processing

The performance of wideband array signal processing algorithms is dependant on the noise level in the system. In this thesis, a method is proposed for reducing the level of white noise in wideband arrays via a judiciously designed spatial transformation followed by a bank of high-pass filters. The method is initially introduced for uniform linear arrays (ULAs) and analysed in detail. The spectrum of the signal and noise after being processed by the proposed noise reduction method is analysed, and the correlation matrix of the processed noise is derived. The reduced noise level leads to a higher signal-to-noise ratio (SNR) for the system, which can have a significant effect on the performance improvement of various beamforming methods and other array signal processing applications such as direction of arrival (DOA) estimation. The performance of two well-known beamformers, the reference signal based (RSB) beamformer and the linearly constrained minimum variance (LCMV) beamformer is reviewed. Then, the theoretical effect of applying the proposed noise reduction method as a pre-processing step on the performance enhancement of RSB and LCMV beamformers is studied. The theoretical results are then confirmed by simulation. As a representative example of wideband DOA estimation application, a compressive sensing-based DOA estimation method is employed to demonstrate the improved estimation by applying the pre-processing noise reduction method, which is confirmed by simulation. Next, the idea is extended to wideband non-uniform linear arrays (NLAs). Since, NLA does not have a uniform spacing, the beam response of the row vectors of the transformation is distorted. Therefore, the transformation is re-designed using the least squares method to satisfy the band-pass requirements of the transformation. Simulation results show a satisfactory improvement in the the performance of RSB and LCMV beamformers for the NLA structure. The idea is further extended to uniform rectangular arrays (URAs) and uniform circular arrays (UCAs), as two major types of the planar arrays. Two methods are proposed for reducing the effect of white noise in wideband URAs and for each one, a different transformation is designed. The first one is based on a two-dimensional (2D) transformation and the second one is an adaptation of the method developed for the ULA case. The developed method for the UCA structure is based on a one-dimensional (1D) transformation, with modified modulation for the transformation to satisfy the required band-pass characteristics of the transformation. Same as linear array structures, the RSB and LCMV beamformers are used to demonstrate the performance enhancement of the method for planar arrays.

Wideband array self-calibration and DOA estimation under large position errors

For wideband array signals, existing self-calibration methods use a first order approximation to simplify the estimation procedure under the assumption of small sensor position errors. However, the performance will degrade severely as the position errors increase. In this paper, a novel self-calibration method based on the time-frequency distributions (TFDs) is proposed to relieve the small errors constraint. We firstly develop an approach for wideband signals to select the TFDs of each source. Then the TFDs are utilized to obtain the propagation delays, which have a simple linear relationship with the sensor positions. The direction of arrival (DOA) and positions are finally estimated by a two-step iteration without any approximation. Simulation results demonstrate that the proposed method can achieve accurate DOA and position estimation over a broad range of position errors with lower computational complexity, and outperforms existing self-calibration algorithms.

Underdetermined Wideband DOA Estimation for Off-Grid Sources with Coprime Array Using Sparse Bayesian Learning.

Sparse Bayesian learning (SBL) is applied to the coprime array for underdetermined wideband direction of arrival (DOA) estimation. Using the augmented covariance matrix, the coprime array can achieve a higher number of degrees of freedom (DOFs) to resolve more sources than the number of physical sensors. The sparse-based DOA estimation can deteriorate the detection and estimation performance because the sources may be off the search grid no matter how fine the grid is. This dictionary mismatch problem can be well resolved by the SBL using fixed point updates. The SBL can automatically choose sparsity and approximately resolve the non-convex optimizaton problem. Numerical simulations are conducted to validate the effectiveness of the underdetermined wideband DOA estimation via SBL based on coprime array. It is clear that SBL can obtain good performance in detection and estimation compared to least absolute shrinkage and selection operator (LASSO), simultaneous orthogonal matching pursuit least squares (SOMP-LS) , simultaneous orthogonal matching pursuit total least squares (SOMP-TLS) and off-grid sparse Bayesian inference (OGSBI).

Computationally Efficient Wide-Band DOA Estimation Methods Based on Sparse Bayesian Framework

For practical wide-band direction-of-arrival (DOA) estimation problems, the sparse Bayesian algorithms, implemented by expectation maximization or variational Bayesian inference techniques, generally require prohibitive computational complexity. In this paper, computationally efficient wide-band DOA estimation is considered within a sparse Bayesian framework. In particular, two computationally efficient wide-band DOA estimation methods are proposed, i.e., single and multiple observations sparse Bayesian multitask learning methods, denoted as SO-SBMTL and MO-SBMTL. The proposed methods can independently and jointly process the signals to obtain the DOA estimates, respectively, with significantly reduced computational complexity. In addition, the off-the-grid problem in wide-band DOA estimation is also considered within this framework. The remarkable feature of our proposed methods is that the off-the-grid parameter can be desirably obtained with a closed-form solution, so that numerical searching procedure is appropriately avoided and the computational complexity is substantially reduced. Experimental results have demonstrated that the proposed algorithms can achieve desirable performance with substantially reduced computational complexities. The MO-SBMTL achieves better performance than the SO-SBMTL in the scenarios of static or slow time-varying moving sources, and the off-the-grid algorithm can also efficiently estimate the true DOAs of the sources.

Wideband DOA estimation for SOBFN

This study considers the problem of wideband direction of arrival (DOA) estimation for spatial optical beam-forming network (SOBFN). Since its system configuration is different from that of the traditional microwave beam-forming networks, the authors first establish the observation model of SOBFN when multiple broadband signals are received. Two kinds of DOA estimation strategies are proposed for wideband direction finding based on the established signal model. The proposed methods decompose the wideband array output into narrowband outputs in several discrete frequency bins. Then, they take advantages of the spatial sparsity of the discrete narrowband observation models to estimate the spatial power spectrum, either coherently or non-coherently. A coarse DOA estimate is obtained via peak-searching in the reconstructed spectrum. The preliminary result is then refined by a linear interpolation procedure. Profound experiments are carried out to demonstrate and compare the performance of the two strategies. Simulation results show that the proposed approaches can achieve wideband DOA estimation of high precision and super-resolution for SOBFN. Moreover, coherent process is proved to have superior performance than the non-coherent strategy.

Wideband Direction of Arrival Estimation in the Presence of Unknown Mutual Coupling.

This paper investigates a subarray based algorithm for direction of arrival (DOA) estimation of wideband uniform linear array (ULA), under the presence of frequency-dependent mutual coupling effects. Based on the Toeplitz structure of mutual coupling matrices, the whole array is divided into the middle subarray and the auxiliary subarray. Then two-sided correlation transformation is applied to the correlation matrix of the middle subarray instead of the whole array. In this way, the mutual coupling effects can be eliminated. Finally, the multiple signal classification (MUSIC) method is utilized to derive the DOAs. For the condition when the blind angles exist, we refine DOA estimation by using a simple approach based on the frequency-dependent mutual coupling matrixes (MCMs). The proposed method can achieve high estimation accuracy without any calibration sources. It has a low computational complexity because iterative processing is not required. Simulation results validate the effectiveness and feasibility of the proposed algorithm.

Joint power distribution and direction of arrival estimation for wideband signals using sparse Bayesian learning

In this study, a novel algorithm called wideband sparse Bayesian learning (WSBL) is proposed for the power distribution and the direction of arrival (DOA) estimation of wideband signals. The received signals are firstly converted into the time–frequency domain by discrete Fourier transform, then the wideband DOA estimation problem can be constructed as a special multiple measurement vectors case of the sparse signal recovery problem. The WSBL algorithm, which exploits the source power distribution at different frequency bins is proposed for the sparse spectral estimation. It is shown that WSBL has good performance in low signal-to-noise ratio and small snapshot number scenario. Without the prior knowledge of source number and focusing matrices, WSBL can estimate the source power distribution and the DOAs of wideband signals simultaneously. In addition, WSBL can also avoid ambiguity even when the array does not meet the half-wavelength spacing condition. The sensor spacing can be larger than the half-wavelength at the lowest frequency of the wideband signals. Simulation results show the efficiency of the proposed method.

Wideband delay and Direction of Arrival Estimation using sub-Nyquist sampling

Estimating the Direction of Arrival (DOA) of the signals received by a sensor array has been at the core of the array signal processing community for decades. With the advancement of the technology, the limits on the data and data transfer are increasing day by day. Such demands of the increasing bandwidths put an immense burden on the Analog to Digital Converters (ADCs). On the other hand, in the literature most of the wideband DOA estimation algorithms depend on the narrowband signal model where the signal is first decomposed into multiple signals with narrow frequency bins, the DOA is estimated for all of them and the outputs are combined together (coherent or non-coherent) to get the final result. This process is highly computational and highly susceptible to any outliers. Compressed Sensing (CS) over the last few years has shown a great promise in overcoming these problems while preserving the structure of the signal provided it is sparse in some domain. In this paper, we propose to estimate the DOA of wideband signals using CS based reconstruction recognizing that the autocorrelation of such signals is sparse in nature. The peaks in the correlation plot represent the time delays of the corresponding signals which is directly related to their DOAs. We identify and show that the relation between the cross-correlations of the sub-Nyquist signal and the Nyquist rate signal is a block sparse CS problem. By using a block sparse CS reconstruction algorithm we are able to estimate the peak locations in the Nyquist correlation vector thereby estimating the DOAs of the wideband signals.

Underdetermined wideband DOA estimation of off-grid sources employing the difference co-array concept

A wideband off-grid model is proposed to represent dictionary mismatch under the compressive sensing framework exploiting difference co-arrays. A group sparsity based off-grid method is proposed for underdetermined wideband direction of arrival (DOA) estimation which provides improved performance over the existing group sparsity based method with a same search grid. A two-step approach is then proposed which achieves an even better performance with significantly reduced computational complexity.

An Improved Wideband Covariance Matrix Sparse Representation (W-CMSR) Method for Wideband Direction of Arrival Estimation Using Simulated Annealing

In this paper, we optimize the size of aperture and number of sensors for Wideband Covariance Matrix Sparse representation (W-CMSR) method for Wideband Direction of Arrival estimation using Simulated Annealing. The performance of W-CMSR is obtained with initial number of sensors and aperture size. Then, we find the performance of W-CMSR with optimized number of sensors and aperture size using simulated annealing. We observe that same performance of W-CMSR is obtained with reduced number of sensors and aperture size by using simulated annealing.

Novel Wideband DOA Estimation Based on Sparse Bayesian Learning With Dirichlet Process Priors

Direction of arrival (DOA) estimation methods based on joint sparsity are attractive due to their superiority of high resolution with a limited number of snapshots. However, the common assumption that signals from different directions share the spectral band is inappropriate when they occupy different bands. To flexibly deal with this situation, a novel wideband DOA estimation algorithm is proposed to simultaneously infer the band occupation and estimate high-resolution DOAs by leveraging the sparsity in the angular domain. The band occupation is exploited by exerting a Dirichlet process (DP) prior over the latent parametric space. Moreover, the proposed method is extended to deal with the off-grid problem by two schemes. One applies a linear approximation to the true dictionary and infers the hidden variables and parameters by the variational Bayesian expectation-maximization (VBEM) in an integrated manner. The other is the separated scheme where DOA is refined by a postsearching procedure based on the reconstructed results. Since the proposed schemes can automatically partition the sub-bands into clusters according to their underlying occupation, more accurate DOA estimation can be achieved by using the measurements within one cluster. Results of comprehensive simulations demonstrate that the proposed schemes outperform other reported ones.

Wideband DOA Estimation Based on Sparse Representation in 2-D Frequency Domain

In this paper, we propose a novel sparse representation (SR)-based model for wideband direction-of-arrival (DOA) estimation. Different from the classical SR-based DOA model, which only explores the sparsity of sources in spatial space, the proposed model exhibits the sparsity through the fact that any individual wideband source is characterized as a unique oblique line passing through the origin in the 2-D frequency plane of the temporal-spatial array data. To further reduce the computation complexity during the use of such sparse property, the 2-D direction information is projected into a 1-D space. Simulations show the superior performance of our approach, even in the noise corruption and less temporal samples condition.

Derivative-constrained frequency-domain wideband DOA estimation

In this paper, we present a new approach for wideband direction of arrival (DOA) estimation incorporating derivative constraints into the optimization problem. The Taylor series expansion of steering vector with respect to frequency exhibits the dependence of sensor snapshots on the derivatives of the array manifold matrix, suppression of which reduces the data to follow the narrowband data model. Two new formulations following a beamformer framework are developed based on this observation. While the first formulation estimates accurate source directions with apriori knowledge of the signal subspace dimension, the second formulation provides DOA estimates without estimating the number of sources. The coherent averaging at the reference frequency enables the two formulations to handle coherent sources. The effectiveness of the proposed formulations is illustrated with simulations.

A Novel DOA Estimation Method for Wideband Signals

For direction of arrival (DOA) estimation of wideband signals, the traditional algorithms’ estimating accuracy and complexity were mainly affected by pre-estimation of DOA. By forming an angle set which elements were arithmetic progressions in the range of possible arriving angles, the algorithm used the new angle vector to replace the preliminary estimation of arriving angles. It can avoid the impact of pre-estimation bias on performance of DOA estimation and greatly reduce the amount of computation and the consumed time for DOA estimation to favor the real-time application of wideband DOA estimation. The simulation results showed that the proposed algorithm was able to provide significant performance improvement over the conventional algorithm.

DOA estimation of wideband sources without estimating the number of sources

In this paper, we propose a new technique to estimate wideband source directions from the sensor snapshots without requiring to know the number of sources present in the scenario. This work is motivated by the fact that the existing model order estimation (number of sources) techniques for wideband source scenario are either inaccurate or computationally expensive. Direction-of-arrival (DOA) estimation is realized using a beamformer framework which imposes nulls in the spatial spectrum along the source directions. The null width along the frequency axis is widened by introducing a new data dependent term into the optimization problem, thus achieving wideband capability. Furthermore, the temporal processing of the data snapshots drastically reduces the number of snapshots required for wideband DOA estimation. The effectiveness of the proposed formulation is studied with simulated experiments.

Direction-of-Arrival Estimation of Wideband Signals via Covariance Matrix Sparse Representation

This paper focuses on direction-of-arrival (DOA) estimation of wideband signals, and a method named wideband covariance matrix sparse representation (W-CMSR) is proposed. In W-CMSR, the lower left triangular elements of the covariance matrix are aligned to form a new measurement vector, and DOA estimation is then realized by representing this vector on an over-complete dictionary under the constraint of sparsity. The a priori information of the incident signal number is not needed in W-CMSR, and no spectral decomposition or focusing is introduced. Simulation results demonstrate the satisfying performance of W-CMSR in wideband DOA estimation in various settings. Moreover, theoretical analysis and numerical examples show how many simultaneous signals can be separated by W-CMSR on typical array geometries, and that the half-wavelength spacing restriction in avoiding ambiguity can be relaxed from the highest to the lowest frequency of the incident wideband signals.

Integrative wideband DOA estimation method based on sparse representation

An integrative wideband direction of arrival (DOA) estimation method is proposed based on a novel data model using the concept of sparse representation. The new method makes full use of the frequency distribution of a received signal to generate the over-complete dictionary. The method requires no prior information of signal number. No spectral decomposition or focusing is necessary for either coherent or incoherent signals.

Improved finite samples resampling for unbiased wide-band direction of arrival estimation

This paper considers wide-band DOA estimation using the spatial resampling method for coherent averaging. In this paper a rough estimate of the resampling error distribution is obtained. Careful examination of this distribution yields an improved resampling formula suitable for, but not limited to, arrays with finite sensors. It is shown that the proposed formula yields resampling error much less than that of conventional resampling. Moreover it is shown how the resampling error can be more reduced by proper choice of the focusing frequency. Based on the this resampling formula a perfect focusing scheme is then proposed and its performance is evaluated and compared to other wide-band methods through simulations. Simulations showed quite satisfactory and robust performance of the proposed scheme. It was shown that it succeeds in situations where all considered wide-band methods fail. In addition it is bias-free and can be implemented quite efficiently. Hence it is quite suitable for reliable real-time DOA estimation in reverberant environments.

Coherent signal-subspace processing of acoustic vector sensor array for DOA estimation of wideband sources

This paper deals with the estimation of the direction of arrival (DOA) for wideband coherent sources using acoustic vector sensor array. By extending the idea of wideband focusing into acoustic vector sensor array processing, a wideband DOA estimation approach based on coherent signal-subspace processing is developed for acoustic vector sensor array. Finally, simulation results are presented, to compare the proposed method with its counterpart based on acoustic pressure sensor array, the advantages of the proposed algorithm are identified.

Wideband direction finding via shielded gradient beamspace techniques

Monopulse techniques have been used for over 50 years in the radar community to estimate the direction of arrival (DOA) of incoming echoes. In recent years, a variant of the monopulse technique has been developed, termed the shielded gradient technique, which allows DOA estimation for signals of arbitrary bandwidth. The technique maps the array-output M-vector into a frequency-invariant B-dimensional beamspace. The work presented here describes the shielded gradient beamspace model in its higher-order form, and develops wideband DOA estimation algorithms analogous to the narrow-band MUSIC, root-MUSIC, and ESPRIT algorithms. The performance of these new algorithms is studied through simulation and application to measured, in-water sonar data. They are also compared via simulation to existing wideband DOA estimation algorithms. [Work supported by the Internal Research and Development Program under Contract No. FEE-800.]