Array Manifold Vector Research Articles

Low-rank rotation matrices-based DOA estimation with a moored circular vector sensor array

Abstract Water currents affect circular vector sensor arrays (CVSAs) suspended from a moored platform, causing them to rotate underwater. This rotation alters the direction of sources within the array coordinate system over time. Traditional methods that rely on numerous snapshots often yield inaccurate results, particularly for faint sources. To improve the accuracy, we introduce a direction-finding technique for CVSAs that employs low-rank rotation matrices. The low-rank rotation matrices are constructed using the heading information of the CVSAs and the subregion array manifold vector matrices to achieve spatial focusing. When these matrices are applied to the measurement data, the resulting covariance matrix displays subspace characteristics similar to that of a stationary CVSA. Our performance analysis revealed that low-rank rotation matrices offer higher focusing gains than conventional rotation matrices. The method proposed in this study effectively improves the direction estimation performance for weak targets and extends the practical applicability of measurement techniques for rotating platforms. Both simulations and experiments confirm that our approach outperforms the modified traditional beamforming and other spatial focusing techniques in terms of resolution and precision. Notably, when the signal-to-noise ratio (SNR) is below -4 dB, the resolution for distinguishing between the two sources increases by more than 50%.

A Novel Approach for Direction of Arrival Estimation in Co-Located MIMO Radars by Exploiting Extended Array Manifold Vectors.

Multiple-input multiple-output (MIMO) radars enable better estimation accuracy with improved resolution in contrast to traditional radar systems; thus, this field has attracted attention in recent years from researchers, funding agencies, and practitioners. The objective of this work is to estimate the direction of arrival of targets for co-located MIMO radars by proposing a novel approach called flower pollination. This approach is simple in concept, easy to implement and has the capability of solving complex optimization problems. The received data from the far field located targets are initially passed through the matched filter to enhance the signal-to-noise ratio, and then the fitness function is optimized by incorporating the concept of virtual or extended array manifold vectors of the system. The proposed approach outperforms other algorithms mentioned in the literature by utilizing statistical tools for fitness, root mean square error, cumulative distribution function, histograms, and box plots.

A Covariance Matrix Reconstruction Approach for Single Snapshot Direction of Arrival Estimation.

Achieving accurate single snapshot direction of arrival (DOA) information significantly improves communication performance. This paper investigates an accurate and high-resolution DOA estimation technique by enabling single snapshot data collection and enhancing DOA estimation results compared to multiple snapshot methods. This is carried out by manipulating the incoming signal covariance matrix while suppressing undesired additive white Gaussian noise (AWGN) by actively updating and estimating the antenna array manifold vector. We demonstrated the estimation performance in simulation that our proposed technique supersedes the estimation performance of existing state-of-the-art techniques in various signal-to-noise ratio (SNR) scenarios and single snapshot sampling environments. Our proposed covariance-based single snapshot (CbSS) technique yields the lowest root-mean-squared error (RMSE) against the true DOA compared to root-MUSIC and the partial relaxation (PR) approach for multiple snapshots and a single signal source environment. In addition, our proposed technique presents the lowest DOA estimation performance degradation in a multiple uncorrelated and coherent signal source environment by up to 25.5% with nearly negligible bias. Lastly, our proposed CbSS technique presents the best DOA estimation results for a single snapshot and single-source scenario with an RMSE of against the true DOA compared to root-MUSIC and the PR approach with nearly negligible bias as well. A potential application for CbSS would be in a scenario where accurate DOA estimation with a small antenna array form factor is a limitation, such as in the intelligent transportation system industry and wireless communication.

Microphone Array Beamforming With High Flexible Interference Attenuation and Noise Reduction

This paper studies the problem of microphone array beamforming to enhance a speech signal of interest in adverse acoustic environments, where interference and additive background noise coexist. The problem is formulated as one of convex optimization whose solution under a specified level of interference attenuation leads to an interference controlled maximum noise reduction (ICMR) beamformer, which can be expressed as a linear combination of two MVDR beamformers: one attempts to extract the desired source signal while the other attempts to extract the interference. The combination coefficients are functions of the array manifold vectors, noise coherence matrix, and the specified interference attenuation factor. By tuning the interference attenuation factor, the ICMR beamformer can be implemented to achieve aggressive interference attenuation or even eliminate interference completely; but this may lead to less additive noise suppression or even noise amplification. To control the maximum sacrifice in gain (SG) of the signal-to-noise ratio (SNR) that is acceptable for additive reduction, a variant of ICMR is derived, which is named as the ICMR-SG beamformer. Simulations are performed and the results show that the ICMR beamformer is able to control the amount of interference attenuation. In comparison, ICMR-SG controls the maximum SG of SNR while achieving the optimal possible level of interference attenuation.

Single-Channel Spatial Spectrum Estimation Direction Finding by the Time-Modulated Linear Array

In this letter, a novel direction-finding method with spatial spectrum estimation is proposed and verified, based on the time-modulated linear array (TMLA) and a single radio-frequency channel. Its principle is as follows. The TMLA receives and periodically modulates the incident signal. After the power combiner, the modulated signal is down-converted to the intermediate frequency and sampled in the single-channel receiver. In the digital domain, the array manifold vector can be calculated from the Fourier coefficients and the harmonic characteristic matrix related to modulation sequences, and thus, the autocorrelation matrix can be estimated. Afterward, the multiple signal classification algorithm is applied to estimate the incident angle, and the spatial smoothing method is exploited to deal with the direction finding of coherent sources. The proposed method has a simple structure and low computational complexity. Numeric simulations and corresponding experiments have been conducted to verify its effectiveness.

High-resolution and low-sidelobe forward-look sonar imaging using deconvolution

For the two-dimensional forward-look sonar imaging, the conventional beamformer (CBF) and the matched filter (MF) are often used due to the simplicity and robustness. However, the angular and range resolutions are limited and the sidelobes (SLs) are high. In this paper, we propose a deconvolution method to improve the resolutions and reduce the SLs. The proposed method uses a two-step Richardson-Lucy (R-L) algorithm to deconvolve the raw sonar image produced by CBF and MF, which is actually a post-beamformer processing method. In the first step the R-L algorithm is applied to the angular dimension, where the CBF beampattern is used as the point spread function (PSF); in the second step the R-L algorithm is applied to the range dimension where the auto-correlation function (ACF) of the transmitted linear frequency modulation (LFM) pulse is taken as the PSF. Furthermore, the non-ideal conditions including the low signal-to-noise ratio, the array manifold vector error and the echo distortion error are considered. Via numerical simulations and real data analysis, we show that the proposed method can improve the angular and range resolutions and reduce SLs significantly, while maintains a good robustness against these non-ideal conditions.

Parameter Estimation for Two-Dimensional Incoherently Distributed Source with Double Cross Arrays.

A direction of arrival (DOA) estimator for two-dimensional (2D) incoherently distributed (ID) sources is presented under proposed double cross arrays, satisfying both the small interval of parallel linear arrays and the aperture equalization in the elevation and azimuth dimensions. First, by virtue of a first-order Taylor expansion for array manifold vectors of parallel linear arrays, the received signal of arrays can be reconstructed by the products of generalized manifold matrices and extended signal vectors. Then, the rotating invariant relations concerning the nominal elevation and azimuth are derived. According to the rotating invariant relationships, the rotating operators are obtained through the subspace of the covariance matrix of the received vectors. Last, the angle matching approach and angular spreads are explored based on the Capon principle. The proposed method for estimating the DOA of 2D ID sources does not require a spectral search and prior knowledge of the angular power density function. The proposed DOA estimation has a significant advantage in terms of computational cost. Investigating the influence of experimental conditions and angular spreads on estimation, numerical simulations are carried out to validate the effectiveness of the proposed method. The experimental results show that the algorithm proposed in this paper has advantages in terms of estimation accuracy, with a similar number of sensors and the same experimental conditions when compared with existing methods, and that it shows a robustness in cases of model mismatch.

Synthesis of Multibeam Sparse Circular-Arc Antenna Arrays Employing Refined Extended Alternating Convex Optimization

A refined extended alternating convex optimization (REACO) method is presented to synthesize multibeam sparse circular-arc antenna arrays with minimum element spacing control by considering real antenna array structure characteristics. This method consists of the initial step and a few refining steps. At the initial step, an initial array with dense elements distributed on a circular-arc is considered, and its array manifold vector is described by rotating a simulated isolated element pattern (IEP) without considering element mutual coupling. The collective excitation coefficient vector (CECV) and its energy bound are introduced for each element, and consequently, the common element positions for generating desired multibeam patterns can be found by minimizing the number of active CECVs under multiple constraints. This minimization problem is further formulated as performing a sequence of alternating convex optimization (ACO) in which the CECV and an auxiliary weighting vector are alternately chosen as the optimization variables so that the minimum element spacing constraint can be easily dealt with. Once the initial optimization step is finished, a few refining steps are performed in which the element positions and excitations are successively updated in each step by renewing the array manifold vector through rotating the simulated nearby active element patterns (AEPs) of the antenna array obtained at the previous step. In such a way, the mutual coupling can be incorporated into the multibeam sparse array synthesis. An example of synthesizing a sparse circular-arc conformal array with 23 beams covering the space from −63.25° to 63.25° is conducted to validate the effectiveness and advantage of the proposed method.

Robust Synthesis Algorithm for Directional Modulation Signal with Array Manifold Vectors Uncertainty

Directional modulation (DM) has become a new research hotspot of physical layer security (PLS) communication at the transmitter side. In this paper, we propose a robust synthesis algorithm for DM signal under the condition of the array manifold vectors perturbation. This algorithm optimizes the constraints of sidelobe level and Euclidean distance of constellation points by considering the worst case performance of array manifold vectors. Furthermore, we also design an active constellation extension (ACE) method to relax the equality constraint of desired modulation symbols into a robust inequality constraint at the desired direction. These constraints can be reformulated in a convex form with l2 and l∞ regularization, which are computationally tractable. Simulation results show better performance of the proposed robust algorithm compared with the benchmark synthesis algorithms in the presence of array manifold vectors uncertainty.

On Estimation of Time-Varying Variances of Source and Noise for Sensor Array Processing

Estimation of time-varying variances of signals for beamforming in sensor arrays is a challenging problem. Based on the assumption that the array manifold vector and the noise pseudo-coherence matrix are known a priori or are well estimated, we present in this paper two estimators for estimating the time-varying variances of the source signal of interest and the noise. These two estimators are then extended to deal with the following situations: 1) there are multiple candidates of the noise pseudo-coherence matrix or the noise pseudo-coherence matrix is a linear combination of some base pseudo-coherence matrices, and 2) the estimation variance is large and smoothing is needed. Simulations for speech enhancement applications are performed and the results show that the proposed estimators can well track the time-varying variances of both the speech and noise signals. It is also demonstrated that the optimal beamformer using the variance parameters estimated with the presented estimators outperforms the widely used traditional optimal beamformers in terms of improvement in both the signal-to-noise ratio (SNR) and the log-spectral distortion (LSD).

Combined root‐MUSIC algorithms for multi‐carrier MIMO radar with sparse uniform linear arrays

In this study, sparse uniform linear arrays are used to improve the direction-of-arrival (DOA) estimation accuracy for the multiple-input multiple-output radar. With a suitable choice of multi-carrier frequencies, the DOA estimation ambiguity problem caused by spatial under-sampling can be resolved. Two kinds of search-free DOA estimation algorithms based on root-multiple signal classification (MUSIC) are proposed. The first algorithm directly applies the root-MUSIC to each carrier frequency separately for the true DOAs as well as their spurious DOAs, then, a novel DOA replicas matching algorithm is proposed to obtain the true DOAs from the ambiguous ones. The second algorithm utilises the manifold separation technique (MST) to align the noise subspaces of all multi-carrier frequencies. Using the MST, the separable representation of the array manifold vector of each carrier frequency is obtained, then the root-MUSIC polynomials of all multi-carrier frequencies are combined to construct a new polynomial, the true DOAs can be obtained directly by applying polynomial rooting without any matching processing. The two proposed algorithms are both practical, computationally efficient and robust. Numerical simulations verify the effectiveness of the proposed algorithms in terms of root-mean-squared error.

Investigation of Low-Sidelobe Beampattern Controlling Methods for Acoustic Transmitting Array of Underwater Vehicles

Abstract In underwater unmanned vehicles, complex acoustic transducer arrays are always used to transmitting sound waves to detect and position underwater targets. Two methods of obtaining low-sidelobe transmitting beampatterns for acoustic transmitting arrays of underwater vehicles are investigated. The first method is the boundary element model optimization method which used the boundary element theory together with the optimization method to calculate the driving voltage weighting vector of the array. The second method is the measured receiving array manifold vector optimization method which used the measured receiving array manifold vectors and optimization method to calculate the weighting vector. Both methods can take into account the baffle effect and mutual interactions among elements of complex acoustic arrays. Computer simulation together with experiments are carried out for typical complex arrays. The results agree well and show that the two methods are both able to obtain a lower sidelobe transmitting beampattern than the conventional beamforming method, and the source level for each transmitting beam is maximized in constraint of the maximum driving voltage of array elements being constant. The effect of the second method performs even better than that of the first method, which is more suitable for practical application. The methods are very useful for the improvement of detecting and positioning capability of underwater unmanned vehicles.

Capacity improvement analysis of 3D-beamforming in small cell systems

We analyze three dimensional (3D) beamforming characteristics and applications in wireless small cell communication based on physical structure of array antenna, addressing on the 3D beampattern property of planar rectangular array antenna beamforming. Firstly, array manifold vector is formulated based on rectangular array antenna, and formulas are derived pertaining to antenna beampattern parameters in detail. Secondly, the effect of array antenna configuration on 3D beamforming is analyzed. Thirdly, 3D beamforming is extended and applied to massive MIMO small cell wireless communication scenario by analyzing capacity gain of single small cell over that of two dimensional (2D) beamforming. Numerical results are presented to show properties of the 3D beamforming.

Knowledge‐aided STAP with sparse‐recovery by exploiting spatio‐temporal sparsity

In this paper, novel knowledge-aided space-time adaptive processing (KA-STAP) algorithms using sparse representation/recovery (SR) techniques by exploiting the spatio-temporal sparsity are proposed to suppress the clutter for airborne pulsed Doppler radar. The proposed algorithms are not simple combinations of KA and SR techniques. Unlike the existing sparsity-based STAP algorithms, they reduce the dimension of the sparse signal by using prior knowledge resulting in a lower computational complexity. Different from the KA parametric covariance estimation (KAPE) scheme, they estimate the covariance matrix using SR techniques that avoids complex selections of the Doppler shift and the covariance matrix taper. The details of the selection of potential clutter array manifold vectors according to prior knowledge are discussed and compared with the KAPE scheme. Moreover, the implementation issues and the computational complexity analysis for the proposed algorithms are also considered. Simulation results show that our proposed algorithms obtain a better performance and a lower complexity compared with the sparsity-based STAP algorithms and outperform the KAPE scheme in presence of errors in prior knowledge.

A Superresolution Wide Null Beamformer for Undersampled Signal Reconstruction in SIMO SAR

With single-input single-output (SISO) SAR systems, employing a single transmitter and receiver beam, there exists a high resolution, wide swath contradiction. However, by using multiple receiver beams and employing array processing techniques, this contradiction can be overcome, allowing greater flexibility and a wider range of application requirements to be met. In this paper the use of single-input multiple-output (SIMO) SAR systems for overcoming this contradiction is of interest, and a novel beamformer is proposed for processing in the cross-range direction. In order to fully describe the system, the array manifold vector is utilized, which is a key concept in the design of the beamformer. In particular, this beamformer is a superresolution beamformer capable of forming wide nulls using subspace based approaches and allows the suppression of ambiguities in multiple sets of received undersampled SAR data in the cross-range direction and reconstruction of the Doppler spectrum to form a single unambiguous set of SAR data. Compared to the existing reconstruction algorithm, only a single weighting vector is required for a block of ambiguous Doppler frequencies compared to a weight vector required for each ambiguous Doppler frequency. The capabilities of the proposed beamformer are shown to give an improved performance in ambiguity suppression via computer simulation studies in a representative maritime environment.

Estimating DOA and polarization with spatially spread loop and dipole pair array

The nonuniform L-shaped spatially spread loop and dipole (SSLD) array whose inter-element spacing is greater than half a wavelength is studied. A joint parameter estimation algorithm of direction of arrival (DOA), frequency and polarization is presented for plane-wave signals. The direct sampling and the corresponding delayed sampling data are used to construct the data correlation matrix. On the basis of the subspace theory and the least square method, the frequency and the steering vector of the whole array are obtained. According to the relationship of the array manifold vector between electric dipoles and magnetic loops, the polarization parameters are given. The unambiguous phase estimates are acquired by applying virtual baseline array transformation to the spatial steering vectors, and they are used as coarse references to disambiguate the cyclic phase ambiguities in phase differences between two adjacent array elements on the array, then the high accuracy DOA estimates are obtained. Closed-form solutions for each parameter are obtained. This method has advantages of lower calculation complexity and no parameter matching. The experiment results verify the effectiveness and feasibility of the presented algorithm.

A JOINT PARAMETER ESTIMATION METHOD WITH CONICAL CONFORMAL CLD PAIR ARRAY

A novel direction of arrival (DOA) and polarization estimation method with sparse conical conformal array consisting of concentred loop and dipole (CLD) pairs along the z-axis direction is proposed in this paper. In the algorithm, the DOA and polarization information of incident signals are decoupled through transformation to array steering vectors. According to the array manifold vector relationship between electric dipoles and magnetic loops, the signal polarization parameters are given. The phase differences between reference element and elements on upper circular ring are acquired from the steering vectors of upper circular ring, it can be used to give rough but unambiguous estimates of DOA. The phase differences are also used as coarse references to disambiguate the cyclic phase ambiguities in phase differences between two array elements on lower circular ring. Without spectral peak searching and parameter matching, this method has the advantage of small amount of calculation. Finally, simulation results verify the effectiveness of the algorithm.

Effect of Antenna Layout on the Capacity of Massive MIMO

This paper addresses the problem of the effect of different antenna layouts on the capacity of massive multiple-input multiple-output (MIMO) system capacity. Based on the narrow-band, flat fading channel model, the effect of scattering environment and antenna layout are considered by incorporating the power azimuth spectrum (PAS) and the array manifold vector. Under the same antenna aperture, six antenna layouts are investigated among which the UCA yields the best capacity while ULA yields the lowest capacity. The more symmetric the antenna geometry is, the better capacity performance it has.

Research on a New Array-Manifold of Single Vector Hydrophone

For the purpose of improving the signal processing of single vector hydrophone, this paper combined two velocity signals as two complex data, so as to change array-manifold of single vector hydrophone. Taking two-dimension single vector hydrophone as an example, this paper compared the capability of signal processing of new array-manifold single vector hydrophone with old one from conventional beam-forming(CBF) ,minimum variance distortionless response (MVDR) and multiple signal classification (MUSIC). As for CBF, the analysis indicates, the capability of spatial filtering of new array-manifold could improve 0.51db and the HPBW of new array-manifold will be smaller than old array-manifold. When the noise power is 0, the HPBW of new array-manifold will be narrower than old array-manifold 19.26°. As for MVDR, the capability of signal processing of new array-manifold is the same as old array-manifold. In MUSIC algorithm, the value measuring angle resolution shows the superiority of the new array-manifold- angle resolution. Simulation and measured data proved the better performance of the method presented by this paper.

An Enumerative NonLinear Programming approach to direction finding with a general spatially spread electromagnetic vector sensor array

In this paper, the geometry of a general spatially spread electromagnetic vector sensor (SSEMVS) array is firstly presented. This array has a special cross product structure of the array manifold vector. The g parameters are then defined to uniquely characterize the cross product. With g parameters, the identifiability analysis of the cross product vector based direction finding algorithms of the general SSEMVS array is carried out. The analysis shows that the array has to be carefully designed to avoid ambiguity directions. Finally, a cross-product based Enumerative NonLinear Programming (ENLP) algorithm for the direction of arrival (DOA) estimation with the general SSEMVS array is proposed. The algorithm finds the optimum estimation of DOA in least square sense. Extensive simulations show that the proposed algorithm outperforms existing algorithms, and can approach the CRB effectively.