2D Unitary ESPRIT Research Articles

2D-Unitary ESPRIT Based Multi-Target Joint Range and Velocity Estimation Algorithm for FMCW Radar

Millimeter-wave FMCW radar has been widely used in joint range-velocity estimation of multiple targets. However, most existing algorithms are unable to estimate the range-velocity information with high accuracy simultaneously and fail to discriminate the targets with either closely spaced ranges or closely spaced velocities in the 2D range-Doppler spectrum. In order to deal with these problems, this paper proposes a 2D-Unitary ESPRIT-based joint range and velocity estimation algorithm of multiple targets for FMCW radar. Firstly, The 1D-IF signal is constructed into a 2D virtual array signal, the virtual array signals are preprocessed by a 2D-spatial smoothing technique to generate a new matrix signal. Then, according to the 2D-Unitary ESPRIT algorithm, the 2D real-valued information of the target parameters is obtained from this matrix signal, and then a new complex-value matrix is constructed. Finally, the eigenvalue decomposition of this new complex-value matrix is performed, and the range-velocity estimates of multiple targets are, respectively, calculated from the real and imaginary parts of the eigenvalues, and paired automatically. The simulation results illustrate that the proposed algorithm not only provides highly accurate range-velocity estimates but also has high-resolution performance and achieves automatic pairing of the range-velocity estimates in multi-target scenarios, thus effectively improving the multi-target joint range and velocity estimation performance of FMCW radar.

Novel Rank Enhancing Algorithm for 2D Sparse Arrays with Contiguous Coarrays

Sparse array is an irregular array with a high degree of freedom in its difference coarray domain. Nested array and coprime array are two important one dimensional sparse arrays. For fixed number of sensors, nested array has a high degree of freedom, resolution and accuracy than coprime array. 1D nested arrays do not provide 2D scanning. 2D nested array which is an extension of 1D nested array provides both 2D scanning as well as high degree of freedom, however direction of arrival (DoA) estimation techniques used for 2D nested array such as 2D unitary ESPRIT and 2D spatial smoothing MUSIC has high computational complexity. This paper shows that spatial smoothing is not necessary to apply 2D MUSIC in the difference coarray domain of 2D nested array. A new Hermitian Toeplitz matrix is constructed instead of spatial smoothing. 2D MUSIC on this Hermitian Toeplitz matrix can resolve the DoA of sources with less computations.

Joint DOA and channel estimation with data detection based on 2D unitary ESPRIT in massive MIMO systems

We propose a novel method for joint two-dimensional (2D) direction-of-arrival (DOA) and channel estimation with data detection for uniform rectangular arrays (URAs) for the massive multiple-input multiple-output (MIMO) systems. The conventional DOA estimation algorithms usually assume that the channel impulse responses are known exactly. However, the large number of antennas in a massive MIMO system can lead to a challenge in estimating accurate corresponding channel impulse responses. In contrast, a joint DOA and channel estimation scheme is proposed, which first estimates the channel impulse responses for the links between the transmitters and antenna elements using training sequences. After that, the DOAs of the waves are estimated based on a unitary ESPRIT algorithm using previous channel impulse response estimates instead of accurate channel impulse responses and then, the enhanced channel impulse response estimates can be obtained. The proposed estimator enjoys closed-form expressions, and thus it bypasses the search and pairing processes. In addition, a low-complexity approach toward data detection is presented by reducing the dimension of the inversion matrix in massive MIMO systems. Different cases for the proposed method are analyzed by changing the number of antennas. Experimental results demonstrate the validity of the proposed method.

Three‐dimensional super resolution ISAR imaging based on 2D unitary ESPRIT scattering centre extraction technique

Two-dimensional inverse synthetic aperture radar (2D ISAR) system can produce 2D electromagnetic images of a target, while failed to provide the 3D information. In this study, a novel method for 3D super resolution ISAR imaging is proposed via employing 2D U-estimation of signal parameters via rotational invariance technique (U-ESPRIT) and slice principle. First, the 3D scattered field data tensor is converted into a set of 2D matrix by stacking slices of the 3D data along one specific dimension. Then, 2D U-ESPRIT is applied to extract isolated scatterers from each slice. Combined with least-square method, complex scattering amplitudes are also estimated. Finally, 3D reconstructed scattering centres model with specific locations and complex scattering amplitudes is obtained, which can characterise the target to a great extent. The reverse process, reconstruction of the 3D ISAR image, can be readily done in real time by means of the extracted scattering centres. Experimental results are presented to demonstrate the effectiveness of the proposed algorithm.

2D Unitary ESPRIT Based Super-Resolution Channel Estimation for Millimeter-Wave Massive MIMO With Hybrid Precoding

Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) with hybrid precoding is a promising technique for the future 5G wireless communications. Due to a large number of antennas but a much smaller number of radio frequency (RF) chains, estimating the high-dimensional mmWave massive MIMO channel will bring the large pilot overhead. To overcome this challenge, this paper proposes a super-resolution channel estimation scheme based on two-dimensional (2D) u- nitary ESPRIT algorithm. By exploiting the angular sparsity of mmWave channels, the continuously distributed angle of arrivals/departures (AoAs/AoDs) can be jointly estimated with high accuracy. Specifically, by designing the uplink training signals at both base station (BS) and mobile station (MS), we first use low pilot overhead to estimate a low-dimensional effective channel, which has the same shift-invariance of array response as the high-dimensional mmWave MIMO channel to be estimated. From the low-dimensional effective channel, the super- resolution estimates of AoAs and AoDs can be jointly obtained by exploiting the 2D unitary ESPRIT channel estimation algorithm. Furthermore, the associated path gains can be acquired based on the least squares (LS) criterion. Finally, we can reconstruct the high-dimensional mmWave MIMO channel according to the obtained AoAs, AoDs, and path gains. Simulation results have confirmed that the proposed scheme is superior to conventional schemes with a much lower pilot overhead.

Super‐resolution ISAR imaging via 2D unitary ESPRIT

A novel method employing two-dimensional (2D) unitary ESPRIT and a spatial smoothing technique is proposed for super-resolution ISAR imaging. The spatial smoothing technique is employed to resolve the contradiction that 2D unitary ESPRIT requests multiple snapshots; however, in radar imaging applications only one snapshot of the radar data are available. Experimental results are presented to verify the high resolution and feasibility of the proposed imaging algorithm in ISAR imaging.

DOA estimation using recursive 2D unitary ESPRIT

AbstractIn mobile communications, it is important to have a knowledge of the multipath wave propagation environment. It is a very effective means of analysis for this purpose to estimate the signal parameters (such as the direction of arrival) of the individual arriving waves. ESPRIT is considered an interesting parameter estimation method. It is an algorithm in which eigenvalue expansion is iteratively applied to the correlation matrix of the input data, and the parameters are estimated. The method works effectively when the number of array elements is small, but a long time is required to arrive at the estimate when the number of elements is increased. Consequently, this paper extends recursive ESPRIT based on QR decomposition, in which recursive calculation is performed, to 2D estimation. Furthermore, in order to improve computation efficiency and to make estimation pairing easy, recursive 2D unitary ESPRIT is proposed. The complex representation is used as the simplest method of pairing for the estimated signal parameters. Spatial averaging is also introduced. Computer simulations of direction angle and azimuth angle estimation for arriving waves with high correlation are performed. The features of the proposed method are thereby demonstrated from the viewpoints of accuracy of estimation, computation time, and tracking performance. Important results are obtained, which will provide a path to future development. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 86(9): 67–77, 2003; Published online in Wiley InterScience (www.interscience.wiley. com). DOI 10.1002/ecja.10036

DOA estimation and pairing method in 2D‐ESPRIT using triangular antenna array

AbstractThis paper discusses the method for direction‐of‐arrival estimation by an application of 2D‐ESPRIT to a triangular planar array with an equilateral triangular lattice arrangement often used as a phased array for direction finding. It is difficult to apply the 2D‐Unitary ESPRIT to the triangular array due to its element arrangement. Instead, the 2D‐ESPRIT based on the standard ESPRIT is used. As the paring method for a multidimensional ESPRIT, the complex pairing (CP) method, simultaneous Schur decomposition (SSD), and mean eigenvalue decomposition (MEVD) have been proposed. In the case of 2D‐Unitary ESPRIT, the simple CP method can be used for an extremely accurate estimation. Since CP cannot be used for the standard ESPRIT, SSD with a high computational load and MEVD requiring introduction of a reliability test need to be used. In this paper, as a pairing method of the signal parameters, a complex mean eigenvalue expansion method is proposed that does not require a reliability test and has a low computational cost. Through computer simulation, the azimuth angle and the elevation angle of multiple waves are estimated simultaneously so that the method's effectiveness is verified. A radiation pattern synthesis for separate reception of multiple waves is attempted with multiple beam forming weights obtained in the process of 2D‐ESPRIT. The effectiveness of the synthesis method is confirmed. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 86(6): 59–68, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.10016