Ambiguous Angle Research Articles

An Improved Unfolded Coprime Linear Array Design for DOA Estimation with No Phase Ambiguity

In this paper, the direction of arrival (DOA) estimation problem for the unfolded coprime linear array (UCLA) is researched. Existing common stacking subarray-based methods for the coprime array are invalid in the case of its subarrays, which have the same steering vectors of source angles. To solve the phase ambiguity problem, we reconstruct an improved unfolded coprime linear array (IUCLA) by rearranging the reference element of the prototype UCLA. Specifically, we design the multiple coprime inter pairs by introducing the third coprime integer, which can be pairwise with the other two integers. Then, the phase ambiguity problem can be solved via the multiple coprime property. Furthermore, we employ a spectral peak searching method that can exploit the whole aperture and full DOFs of the IUCLA to detect targets and achieve angle estimation. Meanwhile, the proposed method avoids extra processing in eliminating ambiguous angles, and reduces the computational complexity. Finally, the Cramer–Rao bound (CRB) and numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed method.

High-accuracy 2D DOA estimation with three parallel sparse nested array

To improve the performance for two-dimensional (2D) direction of arrival (DOA) estimation in the presence of limited antennas in practice, we propose a novel three parallel sparse nested array with extended aperture and reduced mutual coupling. The proposed array consists of three subarrays where locations of antennas have closed-form expressions, to efficiently achieve increased degrees of freedom in difference coarray domain. The unit inter-antenna spacings and the displacements among subarrays are all expanded by D1, D2 or D3 fold for aperture extension and mutual coupling reduction in physical array domain. By exploiting the configuration, the two methods, i.e., BOMP-based and CMT-BCS-based methods, are further explored for high-precision but ambiguous angle estimation, and then the coprime-ness between the displacements is utilized to solve the angle ambiguities. Simulation results demonstrate the superiority of the proposed array and methods for 2D DOA estimation over the existing technologies.

Synthetic sparse nested array with extended aperture and reduced mutual coupling for DOA estimation

To obtain a larger aperture for improving direction of arrival (DOA) estimation performance, we present a synthetic sparse nested array consisting of three subarrays with dual-polarization antennas, and then propose a cascade method composing of three steps for super-resolution angle estimation with range of 180 degree. There is a systematic procedure to determine the number and positions of antennas in each single-polarization subarray used for the synthetic sparse nested array, in order to efficiently reduce mutual coupling and obtain increased degrees of freedom and aperture for difference coarray with limited physical antennas. By exploiting the configuration and fully utilizing the aperture of the proposed array, two sparse uniform linear arrays are achieved in difference coarray domain, for giving coarse estimation and fine but ambiguous estimation in the first and second steps, respectively. Then an automatic pair matching based on pseudo ambiguous angles is provided to obtain unique DOA estimation in the third step. Theoretical analysis and simulation results are given to demonstrate the superiority of the proposed array and method for high-accuracy DOA estimation in the presence of mutual coupling.

A Propagator Method for Bistatic Coprime EMVS-MIMO Radar

In this paper, a novel two-dimensional (2D) direction-of-departure (DOD) and 2D direction-of-arrival (DOA) estimate algorithm is proposed for bistatic multiple-input multiple-output (MIMO) radar system equipped with coprime electromagnetic vector sensors (EMVS) arrays. Firstly, we construct the propagator to obtain the signal subspace. Then, the ambiguous angles are estimated by using rotation invariant technique. Based on the characteristic of coprime array, the unambiguous angles estimation is achieved. Finally, all azimuth angles estimation is followed via vector cross product. Compared to the existing uniform linear array, coprime MIMO radar is occupying large array aperture, and the proposed algorithm does not need to obtain signal subspace by eigendecomposition. In contrast to the state-of-the-art algorithms, the proposed algorithm shows better estimation performance and simpler computation performance. The proposed algorithm’s effectiveness is proved by simulation results.

Efficient tensor decomposition method for noncircular source in colocated coprime MIMO radar**Project supported by the National Natural Science Foundation of China (Grant Nos. 61701507, 61890542, and 61890540).

An effective method via tensor decomposition is proposed to deal with the joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation of noncircular sources in colocated coprime MIMO radar. By decomposing the transmitter and receiver into two sparse subarrays, noncircular property of source can be used to construct new extended received signal model for two sparse subarrays. The new received model can double the virtual array aperture due to the elliptic covariance of imping sources is nonzero. To further exploit the multidimensional structure of the noncircular received model, we stack the subarray output and its conjugation according to mode-1 unfolding and mode-2 unfolding of a third-order tensor, respectively. Thus, the corresponding extended tensor model consisted of noncircular information for DOA and DOD can be obtained. Then, the higher-order singular value decomposition technique is utilized to estimate the accurate signal subspace and angular parameter can be automatically paired via the rotational invariance relationship. Specifically, the ambiguous angle can be eliminated and the true targets can be achieved with the aid of the coprime property. Furthermore, a closed-form expression for the deterministic CRB under the NC sources scenario is also derived. Simulation results verify the superiority of the proposed estimator.

Sparse nested linear array for direction of arrival estimation

In this paper, we provide an approach to perform direction of arrival (DOA) estimation with the hole-free part of difference coarray, including the physical sparse uniform linear array (ULA) itself. The sparse two-level nested linear array (NLA), whose inter-element spacings are all enlarged by the identical rate compared with the conventional two-level NLA, is selected as the example to present our work due to the typicalness, under-determinedness and the relatively obvious mutual coupling effect. The difference coarray of the sparse two-level NLA is a sparse ULA and the existing methods can not be exploited for it. We derive the sparse uniform linear array discrete Fourier transform (SULA-DFT) algorithm based on the original DFT method to extend its application from only conventional ULA to sparse ULA to solve this problem. With the SULA-DFT, reliable estimation for positive angle within a limited range under a constraint condition between angle and sparsity of array is able to be obtained directly without any ambiguous angle. Compared with the conventional two-level NLA and many other state of the art configurations, the sparse two-level NLA is able to get least mutual coupling effect and largest array aperture and the SULA-DFT often obtain better estimation accuracy with the sparse two-level NLA. On the whole, sparse two-level NLA with more sparsity gets better estimation accuracy. The numerical simulations verify the superiority of the SULA-DFT with the sparse two-level NLA.

Wideband two dimensional interferometric direction finding algorithm using base-triangles and a proposed minimum planar array

In wideband interferometric direction finding ambiguity is inevitable due to practical antenna array dimensions. A new algorithm for wideband interferometer direction finding is developed to resolve the ambiguity problem with minimum number of antennas. The method is based on direction finding by three antennas arranged at the three vertices of a triangle named the base-triangle. A two dimensional matrix of ambiguous angles is generated. The ambiguity problem is resolved by an auxiliary base-triangle formed by a fourth antenna in the arrangement. The common angle between the two ambiguous directions derived from the two base-triangles, is the desired angle. As such a four antenna array is optimized with the proposed algorithm to minimize the direction finding error through the 6–18 GHz frequency band for different signal to noise ratios and in the presence of channel phase tracking error. The array performance is evaluated through Monte-Carlo simulations for a coverage of ±45° azimuth and ±45° elevation and a polynomial expression is fitted to the evaluated Root Mean Square errors. Finally, a comparison is made between the proposed method and various correlative interferometer methods. The method has an accuracy better or equal to the cosine function correlative interferometer with much less computation time.

Partial Angular Sparse Representation Based DOA Estimation Using Sparse Separate Nested Acoustic Vector Sensor Array.

In this paper, the issue of direction of arrival (DOA) estimation is discussed, and a partial angular sparse representation (SR)-based method using a sparse separate nested acoustic vector sensor (SSN-AVS) array is developed. Traditional AVS array is improved by separating the pressure sensor array and velocity sensor array into two different sparse array geometries with nested relationship. This improved array geometry can achieve large degrees of freedom (DOF) after the extended vectorization of the cross-covariance matrix, and only partial SR of the angle is required by exploiting the cyclic phase ambiguity caused by the large inter-element spacing of the virtual array. Joint sparse recovery is developed to amend the grid offset and unitary transformation is utilized to transform the complex atoms into real-valued ones. After sparse recovery, the sparse vector can simultaneously provide high-resolution but ambiguous angle estimation and unambiguous reference angle estimation embedded in the AVS array, and they are combined to obtain unique and high-resolution DOA estimation. Compared to other state-of-the-art DOA estimation methods using the AVS array, the proposed algorithm can provide better DOA estimation performance while requiring lower complexity. Multiple simulation results verify the effectiveness of the approach.

Refinement of the theory of formation of rainbow with incorporation of the refined unambiguous angles of incidence, reflection, and refraction

This paper is concerned with one of the most common atmospheric optical phenomenon − the rainbow. In order to get rid of the ambiguity present in the traditional theory of formation of rainbow which is based on the traditional ambiguous angles of incidence, reflection, and refraction, a novel unambiguous theory of formation of rainbow which makes use of the refined unambiguous angles of incidence, reflection, and refraction has been offered. As a result, the present contribution will enhance and sophisticate the relevant optical physics literature there by enriching the same as well.

Target Tracking Using SePDAF under Ambiguous Angles for Distributed Array Radar.

Distributed array radar can improve radar detection capability and measurement accuracy. However, it will suffer cyclic ambiguity in its angle estimates according to the spatial Nyquist sampling theorem since the large sparse array is undersampling. Consequently, the state estimation accuracy and track validity probability degrades when the ambiguous angles are directly used for target tracking. This paper proposes a second probability data association filter (SePDAF)-based tracking method for distributed array radar. Firstly, the target motion model and radar measurement model is built. Secondly, the fusion result of each radar’s estimation is employed to the extended Kalman filter (EKF) to finish the first filtering. Thirdly, taking this result as prior knowledge, and associating with the array-processed ambiguous angles, the SePDAF is applied to accomplish the second filtering, and then achieving a high accuracy and stable trajectory with relatively low computational complexity. Moreover, the azimuth filtering accuracy will be promoted dramatically and the position filtering accuracy will also improve. Finally, simulations illustrate the effectiveness of the proposed method.

Sparse Array Angle Estimation Using Reduced-Dimension ESPRIT-MUSIC in MIMO Radar

Sparse linear arrays provide better performance than the filled linear arrays in terms of angle estimation and resolution with reduced size and low cost. However, they are subject to manifold ambiguity. In this paper, both the transmit array and receive array are sparse linear arrays in the bistatic MIMO radar. Firstly, we present an ESPRIT-MUSIC method in which ESPRIT algorithm is used to obtain ambiguous angle estimates. The disambiguation algorithm uses MUSIC-based procedure to identify the true direction cosine estimate from a set of ambiguous candidate estimates. The paired transmit angle and receive angle can be estimated and the manifold ambiguity can be solved. However, the proposed algorithm has high computational complexity due to the requirement of two-dimension search. Further, the Reduced-Dimension ESPRIT-MUSIC (RD-ESPRIT-MUSIC) is proposed to reduce the complexity of the algorithm. And the RD-ESPRIT-MUSIC only demands one-dimension search. Simulation results demonstrate the effectiveness of the method.