Uniform Rectangular Array Research Articles

A PARAFAC-based algorithm for multidimensional parameter estimation in polarimetric bistatic MIMO radar

In this article, we investigate the problem of applying the parallel factor quadrilinear decomposition technique to multidimensional target parameter estimation in a polarimetric bistatic multiple-input multiple-output (MIMO) radar system with a uniform rectangular array at the transmitter and a cross-dipole-based uniform rectangular array at the receiver. The signal model is developed, and a novel algorithm is proposed exploiting the quadrilinear alternating least squares to jointly estimate the two-dimensional direction of departure (2D-DOD), two-dimensional direction of arrival (2D-DOA), polarization parameters and Doppler frequency. Multidimensional parameters can be automatically paired by this algorithm to avoid the performance degradation resulting from wrong pairing. The developed algorithm requires neither multidimensional spectral peak searching nor covariance matrix estimation and several eigen-value decompositions that may bring error accumulation. Furthermore, multiple targets having close 2D-DODs and close 2D-DOAs or even the same 2D-DOD or 2D-DOA are distinguishable by means of polarization diversity. The algorithm improves the performance of multi-target identification and three-dimensional localization. Numerical simulations demonstrate the effectiveness of the proposed algorithm.

Direction Finding Using Higher Order Statistics Without Redundancy

In the last decade, 2q -MUSIC, an extension of MUSIC algorithm to an arbitrary even order 2q, has been proposed to process direction-finding problems. Despite of its better performance compared with MUSIC, it suffers from the high computational complexity, thus limiting its practical application. This letter proposes a method called Non-Redundant-2q-MUSIC using 2qth order statistics for uniform linear arrays and uniform rectangular arrays. The proposed method lowers the computational complexity effectively by removing the redundancy of the virtual array and the 2q th-order cumulant matrix. And root-MUSIC can be applied to avoid calculating the pseudo-spectrum. It is illustrated in both theoretical proof and computer simulations that the proposed method performs properly and effectively.

2-D Unitary ESPRIT-Like Direction-of-Arrival (DOA) Estimation for Coherent Signals with a Uniform Rectangular Array

A unitary transformation-based algorithm is proposed for two-dimensional (2-D) direction-of-arrival (DOA) estimation of coherent signals. The problem is solved by reorganizing the covariance matrix into a block Hankel one for decorrelation first and then reconstructing a new matrix to facilitate the unitary transformation. By multiplying unitary matrices, eigenvalue decomposition and singular value decomposition are both transformed into real-valued, so that the computational complexity can be reduced significantly. In addition, a fast and computationally attractive realization of the 2-D unitary transformation is given by making a Kronecker product of the 1-D matrices. Compared with the existing 2-D algorithms, our scheme is more efficient in computation and less restrictive on the array geometry. The processing of the received data matrix before unitary transformation combines the estimation of signal parameters via rotational invariance techniques (ESPRIT)-Like method and the forward-backward averaging, which can decorrelate the impinging signals more thoroughly. Simulation results and computational order analysis are presented to verify the validity and effectiveness of the proposed algorithm.

Limited Feedback Precoding for Massive MIMO

The large-scale array antenna system with numerous low-power antennas deployed at the base station, also known as massive multiple-input multiple-output (MIMO), can provide a plethora of advantages over the classical array antenna system. Precoding is important to exploit massive MIMO performance, and codebook design is crucial due to the limited feedback channel. In this paper, we propose a new avenue of codebook design based on a Kronecker-type approximation of the array correlation structure for the uniform rectangular antenna array, which is preferable for the antenna deployment of massive MIMO. Although the feedback overhead is quite limited, the codebook design can provide an effective solution to support multiple users in different scenarios. Simulation results demonstrate that our proposed codebook outperforms the previously known codebooks remarkably.

Forward/backward spatial reconstruction method for directions of arrival estimation of uncorrelated and coherent signals

An effective method to classify the directions of arrival (DOA) estimation of narrow-band signals in a coherent environment is proposed. The basic idea is to rearrange the correlation matrix. By combining the forward reconstructed correlation matrix with its conjugated backward form together, it is always possible to estimate any ⌊2(M+1)/3⌋ one-dimensional DOAs using an M-element uniform linear array (ULA) and any ⌊2(3−2√2)MN⌋ two-dimensional DOAs using an M×N-element uniform rectangular array. Other arrays that contain centrosymmetric sub-arrays can also be applied with our method. Simulation results demonstrate that the proposed method could both enlarge the effective aperture and reduce the computational complexity.

Joint 2-D DOA Estimation and Phase Calibration for Uniform Rectangular Arrays

A precise model of the array response is required to maintain the performance of direction-of-arrival (DOA) estimation. When modeling errors are present or the sensor environment is time-varying, autocalibration becomes necessary. In this paper, the problem of phase autocalibration for uniform rectangular array (URA) geometries is considered. For the case with a single source, a simple and robust least-squares algorithm for joint 2-D DOA estimation and phase calibration is presented. When performing phase autocalibration with a URA, the phase and DOA parameters cannot be identified together without ambiguity. This problem is discussed and a suitable remedy is suggested. An approximate Cramér-Rao bound and analytical expressions for the mean squared error performance of the proposed estimator are presented. The proposed algorithm for phase autocalibration is extended for the case with multiple sources. The results are evaluated using a representative body of simulations.

Joint 4-D Angle and Doppler Shift Estimation via Tensor Decomposition for MIMO Array

A joint 4-dimensional (4-D) angle and Doppler shift estimation method is proposed for bistatic multiple-input multiple-output (MIMO) uniform rectangular array (URA). The key idea behind the proposed approach is to use tensor decomposition to estimate the target parameter matrices, and use Vandermonde structure enforcing strategy to regress the parameters. This algorithm can effectively estimate all the parameters simultaneously, and requires neither parameter pairing nor multi-dimensional nonlinear peak searching.

Two-dimensional direction of arrival estimation by exploiting the symmetric configuration of uniform rectangular array

In this study, a new two-dimensional direction of arrival (2D DOA) estimation method is proposed for a uniform rectangular array (URA). The impinging signals are a mixture of uncorrelated and coherent signals. The method consists of two steps. The DOAs of uncorrelated signals are first estimated by a modified 2D estimation of signal parameters via rotational invariance techniques (ESPRIT). Then the contributions of uncorrelated signals and noises are eliminated after performing a subtraction operation on the elements of the covariance matrix and only those of coherent signals remain. Based on these subtracted elements, a decorrelating matrix with a larger size is constructed to estimate the DOAs of coherent signals. These two-step processes can be carried out in parallel because there is no inherent relationship between them. The proposed method has high estimation precision, needs no 2D angle searching and is suitable for the array no matter whether the number of sensors is odd or even. Simulation results demonstrate the effectiveness and performance of the proposed method.

Eigenstructure-based ambiguity resolution algorithm for distributed subarray antennas VHF radar

Distributed subarray antennas (DSAs) have been proposed to enhance angular resolution and the accuracy of direction of arrival (DOA) estimation. This results in the well-known grating lobes in the array beampattern or ambiguities in DOA estimation. Presented is a slanting DSA composed of two widely-separated uniform rectangular arrays. By exploiting the translational invariance and the aperture coupling in the DSA configuration, a novel ambiguity resolution algorithm is proposed. It can provide closed-form, low-variance and automatically paired 2D direction cosine estimates. Simulation results are presented to verify the efficacy of the ambiguity resolution algorithm.

Fast Signal Recovery in the Presence of Mutual Coupling Based on New 2-D Direct Data Domain Approach

The performance of adaptive algorithms, including direct data domain least square, can be significantly degraded in the presence of mutual coupling among array elements. In this paper, a new adaptive algorithm was proposed for the fast recovery of the signal with one snapshot of receiving signals in the presence of mutual coupling, based on the two-dimensional direct data domain least squares (2-D D3LS) for uniform rectangular array (URA). In this method, inverse mutual coupling matrix was not computed. Thus, the computation was reduced and the signal recovery was very fast. Taking mutual coupling into account, a method was derived for estimation of the coupling coefficient which can accurately estimate the coupling coefficient without any auxiliary sensors. Numerical simulations show that recovery of the desired signal is accurate in the presence of mutual coupling.

Estimation of 2-D DOA using non-circular music method for Uniform Circular and Rectangular Arrays

This paper extends the Non-Circular MUltiple SIgnal Classification (MUSIC) (NC-MUSIC) method for the common array geometries including Uniform Circular Arrays (UCAs) and Uniform Rectangular Arrays (URAs), which enables the algorithm to estimate 2-D Direction Of Arrival (DOA). A comparison between UCAs and URAs of NC-MUSIC is made in this paper. The simulations show that the NC-MUSIC method doubles the maximum estimation number of standard MUSIC. Using non-circular signals, the performance of URAs is improved remarkably while the improvement of UCAs is not so significantly. Moreover, the influence of arrays structures on the NC-MUSIC method is discussed.

An ESPRIT-Based Algorithm for 2D-DOA Estimation

In this paper, we propose an Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT) based algorithm for estimating the two-dimensional-direction-of-arrivals (2D-DOA) of signals impinging on a uniform rectangular array (URA). The basic idea of the proposed algorithm is to successively apply two rounds of one-dimensional ESPRIT (1D-ESPRIT) algorithm for 2D-DOA estimation. The first round 1D-ESPRIT is applied on columns of the URA whereas the other round 1D-ESPRIT is on the rows of the URA. In between, a grouping technique is developed to produces signal groups each containing signals with distinguishable spatial signatures. The grouping technique is performed by using the subspace projection method where the needed spatial information is provided by the first round 1D-ESPRIT algorithm. Computer simulations show that, in addition to having significantly reduced computational complexity, the proposed algorithm possesses better estimation accuracy as compared to the conventional 2D-ESPRIT algorithm.

A Low Complexity 1D-Based Successive GSC Structure for 2D Adaptive Beamformer Implementation

In this study, we propose a one dimensional (1D) based successive generalized sidelobe canceller (GSC) structure for the implementation of 2D adaptive beamformers using a uniform rectangular antenna array (URA). The proposed approach takes advantage of the URA feature that the 2D spatial signature of the receive signal can be decomposed into an outer product of two 1D spatial signatures. The 1D spatial signatures lie in the column and the row spaces of the receive signal matrix, respectively. It follows that the interferers can be successively eliminated by two rounds of 1D-based GSC structure. As compared to the conventional 2D-GSC structure, computer simulations show that in addition to having significantly low computational complexity, the proposed adaptive approach possesses higher convergence rate.

ESPRIT-Like Two-Dimensional DOA Estimation for Coherent Signals

A second-order statistics-based algorithm is proposed for two-dimensional (2D) direction-of-arrival (DOA) estimation of coherent signals. The problem is solved by arranging the elements of the correlation matrix of the signal received from a uniform rectangular array to a block Hankel matrix. In noiseless cases, it is shown that the rank of the block Hankel matrix equals the number of the DOAs and is independent of the coherency of the incoming waves. Therefore, the signal subspace of the block Hankel matrix can be estimated properly and spans the same column space as the array response matrix. Two matrix pencil pairs containing the DOA parameters are extracted from the signal subspace. This matrix pencil-based estimation problem is then resolved using our previously proposed pairing-free 2D parameter estimation algorithm. Simulation results show that the proposed algorithm outperforms the spatial smoothing method in terms of mean square error (MSE).

Computationally efficient 2D beamspace matrix pencil method for direction of arrival estimation

In this paper, we propose a new 2-dimensional beamspace matrix pencil (2D BMP) method for direction of arrival (DOA) estimation of plane wave signals using a uniform rectangular array (URA). Based on some a priori information about DOA, the proposed method transforms the complex signal subspace in 2D matrix pencil (2D MP) method [Y. Hua, Estimating two-dimensional frequencies by matrix enhancement and matrix pencil, IEEE Trans. Signal Process. 40 (9) (1992) 2267-2280] into a real and reduced dimensional beamspace using the discrete Fourier transform (DFT) matrix transformation. Consequently, the computational complexity is reduced (several times) in comparison with 2D MP method. Computer simulations are provided to show that 2D BMP method gives comparable performance in terms of average mean square error of the estimated DOA with lesser floating point operations as compared to the existing (MP) methods.

Optimized microphone deployment for near-field acoustic holography: To be, or not to be random, that is the question

Arrays with sparse and random sensor deployment are known to be capable of delivering high quality far-field images without grating lobes. This raises the question of whether or not this idea can be applied to near-field imaging as well. To answer this question that has not yet been widely investigated in previous research, numerical simulations are undertaken in this paper to optimize the microphone deployment for both far-field and near-field arrays with the latter being the main focus. In the simulation, a recently introduced near-field equivalent source imaging (NESI) technique is employed for the near-field imaging. Global optimization techniques including the simulated annealing (SA) algorithm and the intra-block Monte Carlo (IBMC) algorithm are exploited to find the optimal microphone position efficiently. The combined use of the SA and the IBMC algorithms enables efficient search for satisfactory deployment with excellent beam pattern and relatively uniform distribution of microphones. In the near-field optimization, a special kind of beam pattern and cost function definition is used for the multiple-input-multiple-output (MIMO) imaging problem. As indicated by the simulation results, random deployment of microphones is necessary to avoid grating lobes in far-field imaging. In the near-field simulation, all results suggest that the optimal near-field array is the uniform rectangular array (URA) and the random deployment presents no particular benefit in near-field imaging.

Signaling Strategies for the Hybrid MIMO Phased-Array Radar

The hybrid MIMO phased array radar (HMPAR) is a notional concept for a multisensor radar architecture that combines elements of traditional phased-array radar with the emerging technology of multiple-input multiple output (MIMO) radar. A HMPAR comprises a large number, MP, of T/R elements, organized into M subarrays of P elements each. Within each subarray, passive element-level phase shifting is used to steer transmit and receive beams in some desired fashion. Each of the M subarrays are in turn driven by independently amplified phase-coded signals which could be quasi-orthogonal, phase-coherent, or partially correlated. Such a radar system could be used in an airborne platform for concurrent search, detect, and track missions. This paper considers various signaling strategies which could be employed in the notional HMPAR architecture to achieve various objectives quantified by transmit beampatterns and space-time ambiguity functions. First, we propose a method to generate multiple correlated signals for uniform linear and rectangular arrays that achieve arbitrary rectangular transmit beampatterns in one and two dimensions, while maintaining desirable temporal properties. Examples of the range of transmit beampatterns possible with this technique are illustrated for an array of MP=900 elements, arranged using different values of M and P. Then the space-time, or MIMO, ambiguity function that is appropriate for the HMPAR radar system is derived. Examples of ambiguity functions for our signals using a one-dimensional HMPAR architecture are given, demonstrating that one can achieve phased-array-like resolution on receive, for arbitrary transmit beampatterns.

Adaptive beamforming for array imaging of plate structures using lamb waves

Lamb waves are considered a promising tool for the monitoring of plate structures. Large areas of plate structures can be monitored using active arrays employing beamforming techniques. Dispersion and multiple propagating modes are issues that need to be addressed when working with Lamb waves. Previous work has mainly focused on standard delay-and-sum (DAS) beamforming while reducing the effects of multiple modes through frequency selectivity and transducer design. This paper presents a minimum variance distortionless response (MVDR) approach for Lamb waves using a uniform rectangular array (URA) and a single transmitter. Theoretically calculated dispersion curves are used to compensate for dispersion. The combination of the MVDR approach and the two-dimensional array improves the suppression of interfering Lamb modes. The proposed approach is evaluated on simulated and experimental data and compared with the standard DAS beamformer. It is shown that the MVDR algorithm performs better in terms of higher resolution and better side lobe and mode suppression capabilities. Known issues of the MVDR approach, such as signal cancellation in highly correlated environments and poor robustness, are addressed using methods that have proven effective for the purpose in other fields of active imaging.

Estimation of two-dimensional direction-of-arrival for uncorrelated and coherent signals with low complexity

In this study, a low complexity two-dimensional direction-of-arrival (2-D DOA) estimation method is proposed with uniform rectangular array (URA) when uncorrelated and coherent signals coexist. By using a new method of modified estimation of signal parameters via rotation invariance techniques (ESPRIT), the DOAs of uncorrelated signals are first estimated. Afterwards, the contributions of uncorrelated signals are eliminated, and then a new Toeplitz matrix without the information of uncorrelated signals is constructed. Using the product of the Toeplitz matrix and its conjugate transpose matrix, the remaining coherent signals can be resolved. With the two-step processing, the proposed method can resolve more signals with low computational complexity. Simulation results demonstrate the effectiveness and efficiency of the proposed method. The Cramer–Rao bound (CRB) for this signal scenario is also derived.

Polarization Difference Smoothing for Direction Finding of Coherent Signals

The subspace-based two-dimensional direction finding with an array of electromagnetic vector sensors for multiple coherent signals amid unknown noise fields is investigated. The noise can be spatially nonuniform and/or correlated. A novel preprocessing method, called polarization difference smoothing (PDS), is proposed. With PDS the unknown noise is removed by using the difference of pairs of electromagnetic component's data correlation matrices, and the coherent signals are decorrelated by summing these difference correlation matrices. Unlike most other existing preprocessing techniques, such as spatial smoothing and forward-backward averaging, PDS processing does not decrease the array aperture and is applicable to arbitrary array geometry. As an example a uniform rectangular array is considered, and a computationally-efficient propagator-based algorithm (PDS-propagator) is derived. Monte Carlo simulations demonstrate that, with an appropriately chosen PDS matrix, the PDS-based eigenstructure algorithms can offer better performance than the polarization smoothing-based (PS) counterparts. Incidently in the presence of external interference noise, the PDS-based algorithms can underperform the PS-based algorithms.