A Sparse-Array Design Method Using Q Uniform Linear Arrays for Direction-of-Arrival Estimation.

Nowadays, sparse arrays have been a hotspot for research in the direction of arrival (DOA). In order to achieve a big value for degrees of freedom (DOFs) using spatial smoothing methods, researchers try to use multiple uniform linear arrays (ULAs) to construct sparse arrays. But, with the number of subarrays increasing, the complexity also increases. Hence, in this paper, a design method, named as the cross-coarray consecutive-connected (4C) criterion, and the sparse array using Q ULAs (SA-UQ) are proposed. We first analyze the virtual sensor distribution of SA-U2 and extend the conclusions to SA-UQ, which is the 4C criterion. Then, we give an algorithm to solve the displacement between subarrays under the given Q ULAs. At last, we consider a special case, SA-U3. Through the analysis of DOFs, SA-UQ can find underdetermined signals. Moreover, SA-U3 can obtain DOFs close to other sparse arrays using three ULAs. The simulation experiments prove the performance of SA-UQ.

A Mixed-Field Circular and Non-Circular Source Localization Algorithm Based on Exact Spatial Propagation Geometry.

In passive localization techniques, as the scale of the array of the sensors used increases, the source distribution may be a coexistence of near-field (NF) and far-field (FF) sources. Most of the existing algorithms dedicated to the localization of mixed-field sources are based on a simplified model, which has model errors and cannot make good use of non-circular properties when non-circular signals are present in the sources. In this paper, we present a mixed-field circular and non-circular source localization algorithm based on exact spatial propagation geometry. First, we make an initial estimate of the source parameters using exact spatial geometry relations. The MUSIC algorithm is then used in combination with the non-circular properties of the signal to achieve an accurate estimate. The algorithm does not lose performance due to model mismatch and is able to make good use of the non-circular properties of the sources to improve the estimation accuracy. The simulation results show that the proposed algorithm can effectively distinguish between sources and that the algorithm performs satisfactorily.

An L-Shaped Three-Level and Single Common Element Sparse Sensor Array for 2-D DOA Estimation.

The degree of freedom (DOF) is an important performance metric for evaluating the design of a sparse array structure. Designing novel sparse arrays with higher degrees of freedom, while ensuring that the array structure can be mathematically represented, is a crucial research direction in the field of direction of arrival (DOA) estimation. In this paper, we propose a novel L-shaped sparse sensor array by adjusting the physical placement of the sensors in the sparse array. The proposed L-shaped sparse array consists of two sets of three-level and single-element sparse arrays (TSESAs), which estimate the azimuth and elevation angles, respectively, through one-dimensional (1-D) spatial spectrum search. Each TSESA is composed of a uniform linear subarray and two sparse subarrays, with one single common element in the two sparse subarrays. Compared to existing L-shaped sparse arrays, the proposed array achieves higher degrees of freedom, up to 4Q1Q2+8Q1-5, when estimating DOA using the received signal covariance. To facilitate the correct matching of azimuth and elevation angles, the cross-covariance between the two TSESA arrays is utilized for estimation. By comparing and analyzing performance parameters with commonly used L-shaped and other sparse arrays, it is found that the proposed L-shaped TSESA has higher degrees of freedom and array aperture, leading to improved two-dimensional (2-D) DOA estimation results. Finally, simulation experiments validate the excellent performance of the L-shaped TSESA in 2-D DOA estimation.

Null Broadening Robust Adaptive Beamforming Algorithm Based on Power Estimation.

In order to solve the problem of severely decreased performance under the situation of rapid moving sources and unstable array platforms, a null broadening robust adaptive beamforming algorithm based on power estimation is proposed in this paper. First of all, we estimate the interference signal power according to the characteristic subspace theory. Then, the correspondence between the signal power and steering vector (SV) is obtained based on the orthogonal property, and the interference covariance matrix (ICM) is reconstructed. Finally, with the aim of setting virtual interference sources, null broadening can be carried out. The proposed algorithm results in a deeper null, lower side lobes and higher tolerance of the desired signal steering vector mismatch under the condition of low complexity. The simulation results show that the algorithm also has stronger robustness.

Joint Estimation for Time Delay and Direction of Arrival in Reconfigurable Intelligent Surface with OFDM.

Recently, the joint estimation for time delay (TD) and direction of arrival (DOA) has suffered from the high complexity of processing multi-dimensional signal models and the ineffectiveness of correlated/coherent signals. In order to improve this situation, a joint estimation method using orthogonal frequency division multiplexing (OFDM) and a uniform planar array composed of reconfigurable intelligent surface (RIS) is proposed. First, the time-domain coding function of the RIS is combined with the multi-carrier characteristic of the OFDM signal to construct the coded channel frequency response in tensor form. Then, the coded channel frequency response covariance matrix is decomposed by CANDECOMP/PARAFAC (CPD) to separate the signal subspaces of TD and DOA. Finally, we perform a one-dimensional (1D) spectral search for TD values and a two-dimensional (2D) spectral search for DOA values. Compared to previous efforts, this algorithm not only enhances the adaptability of coherent signals, but also greatly decreases the complexity. Simulation results indicate the robustness and effectiveness for the proposed algorithm in independent, coherent, and mixed multipath environments and low signal-to-noise ratio (SNR) conditions.

A Fast ML-Based Single-Step Localization Method Using EM Algorithm Based on Time Delay and Doppler Shift for a Far-Field Scenario.

This study discusses the localization problem based on time delay and Doppler shift for a far-field scenario. The conventional location methods employ two steps that first extract intermediate parameters from the received signals and then determine the source position from the measured parameters. As opposed to the traditional two-step methods, the direct position determination (DPD) methods accomplish the localization in a single step without computing intermediate parameters. However, the DPD cost function often remains non-convex, thereby it will cost a high amount of computational resources to find the estimated position through traversal search. Weiss proposed a DPD estimator to mitigate the computational complexity via eigenvalue decomposition. Unfortunately, when the computational resources are rather limited, Weiss's method fails to satisfy the timeliness. To solve this problem, this paper develops a DPD estimator using expectation maximization (EM) algorithm based on time delay and Doppler shift. The proposed method starts from choosing the transmitter-receiver range vector as the hidden variable. Then, the cost function is separated and simplified via the hidden variable, accomplishing the transformation from the high dimensional nonlinear search problem into a few one dimensional search subproblems. Finally, the expressions of EM repetition are obtained through Laplace approximation. In addition, we derive the Cramér⁻Rao bound to evaluate the best localization performance in this paper. Simulation results confirm that, on the basis of guaranteeing high accuracy, the proposed algorithm makes a good compromise in localization performance and computational complexity.

Two-Dimensional Direction-of-Arrival Fast Estimation of Multiple Signals with Matrix Completion Theory in Coprime Planar Array.

In estimating the two-dimensional (2D) direction-of-arrival (DOA) using a coprime planar array, the main issues are the high complexity of spectral peak search and the limited degree of freedom imposed by the number of sensors. In this paper, we present an algorithm based on the matrix completion theory in coprime planar array that reduces the computational complexity and obtains a high degree of freedom. The algorithm first analyzes the covariance matrix of received signals to estimate the covariance matrix of a virtual uniform rectangular array, which has the same aperture as the coprime planar array. Matrix completion theory is then applied to estimate the missing elements of the virtual array covariance matrix. Finally, a closed-form DOA solution is obtained using the unitary estimation signal parameters via rotational invariance techniques (Unitary-ESPRIT). Simulation results show that the proposed algorithm has a high degree of freedom, enabling the estimation of more signal DOAs than the number of sensors. The proposed algorithm has reduced computational complexity because the spectral peak search is replaced by Unitary-ESPRIT, but attains similarly high levels accuracy to those of the 2D multiple signal classification algorithm.

Direct Position Determination of Multiple Non-Circular Sources with a Moving Coprime Array.

Direct position determination (DPD) is currently a hot topic in wireless localization research as it is more accurate than traditional two-step positioning. However, current DPD algorithms are all based on uniform arrays, which have an insufficient degree of freedom and limited estimation accuracy. To improve the DPD accuracy, this paper introduces a coprime array to the position model of multiple non-circular sources with a moving array. To maximize the advantages of this coprime array, we reconstruct the covariance matrix by vectorization, apply a spatial smoothing technique, and converge the subspace data from each measuring position to establish the cost function. Finally, we obtain the position coordinates of the multiple non-circular sources. The complexity of the proposed method is computed and compared with that of other methods, and the Cramer⁻Rao lower bound of DPD for multiple sources with a moving coprime array, is derived. Theoretical analysis and simulation results show that the proposed algorithm is not only applicable to circular sources, but can also improve the positioning accuracy of non-circular sources. Compared with existing two-step positioning algorithms and DPD algorithms based on uniform linear arrays, the proposed technique offers a significant improvement in positioning accuracy with a slight increase in complexity.

Two-Dimensional DOA Estimation for Coherently Distributed Sources with Symmetric Properties in Crossed Arrays.

In this paper, a novel algorithm is proposed for the two-dimensional (2D) central direction-of-arrival (DOA) estimation of coherently distributed (CD) sources. Specifically, we focus on a centro-symmetric crossed array consisting of two uniform linear arrays (ULAs). Unlike the conventional low-complexity methods using the one-order Taylor series approximation to obtain the approximate rotational invariance relation, we first prove the symmetric property of angular signal distributed weight vectors of the CD source for an arbitrary centrosymmetric array, and then use this property to establish two generalized rotational invariance relations inside the array manifolds in the two ULAs. Making use of such relations, the central elevation and azimuth DOAs are obtained by employing a polynomial-root-based search-free approach, respectively. Finally, simple parameter matching is accomplished by searching for the minimums of the cost function of the estimated 2D angular parameters. When compared with the existing low-complexity methods, the proposed algorithm can greatly improve estimation accuracy without significant increment in computation complexity. Moreover, it performs independently of the deterministic angular distributed function. Simulation results are presented to illustrate the performance of the proposed algorithm.