Low Complexity Direction Of Arrival Estimation Research Articles

A Low-Complexity DOA Estimation Algorithm for Distributed Source Localization

As a key aspect of radio monitoring and positioning, direction of arrival (DOA) techniques have been widely used in wireless communications, radar detection, and radio astronomy. DOA estimation can be used to locate a source in space and provide technical support for signal enhancement. However, in complex electromagnetic environments, distributed source models have high complexity; thus, the existing DOA estimation algorithms for distributed sources cannot adapt to application scenarios that require high real-time performance. This letter derives a low-complexity distributed source model and proposes a novel DOA estimation algorithm based on the minimum variance distortionless response criterion. The experimental results demonstrate that the proposed algorithm is superior to some other algorithms in terms of parameter estimation accuracy and source resolution for distributed sources.

A low-complexity two-dimensional DOA estimation algorithm based on an L-shaped sensor array

In this paper, a derivative-based MUSIC (multiple signal classification) algorithm for a mixture of circular and noncircular signals (DB-MUSIC-M) is proposed for two-dimensional (2D) direction of arrival (DOA) estimation employing an L-shaped uniform array. The DB-MUSIC-M transforms the 2D DOA estimation problem into a single one-dimensional (1D) estimation by finding the derivative of the objective function of the 2D improved MUSIC (I-MUSIC) algorithm, which greatly reduces its computational complexity. As it utilizes both the pseudo covariance matrix and the covariance matrix of the array data, the maximum number of signals that can be estimated is much higher than the total number of sensors. As a special case, the derivative-based MUSIC (DB-MUSIC) for circular signals is also proposed. There is no need for angle pairing for the proposed algorithms and they can handle the angle ambiguity problem effectively. As shown by simulation results, the proposed DB-MUSIC-M algorithm outperforms existing algorithms, with significantly reduced complexity compared to a direct 2D search method. Moreover, the proposed approach can be applied to some other array structures such as the uniform planar array.

Low-Complexity One-Bit DOA Estimation for Massive ULA with a Single Snapshot

Existing one-bit direction of arrival (DOA) estimate methods based on sparse recovery or subspace have issues when used for massive uniform linear arrays (MULAs), such as high computing cost, estimation accuracy depending on grid size, or high snapshot-number requirements. This paper considers the low-complexity one-bit DOA estimation problems for MULA with a single snapshot. Theoretical study and simulation results demonstrate that discrete Fourier transform (DFT) can be applied to MULA for reliable initial DOA estimation even when the received data are quantized by one-bit methods. A precise estimate is then obtained by searching within a tiny area. The resulting method is called one-bit DFT. This method is straightforward and simple to implement. High-precision DOA estimates of MULA can be obtained with a single snapshot, and the computational complexity is significantly less than that of existing one-bit DOA estimation methods. Moreover, the suggested method is easily extensible to multiple snapshot scenarios, and increasing the number of snapshots can further improve estimation precision. Simulation results show the effectiveness of the one-bit DFT method.

Low-Complexity 2D DOA Estimation and Self-Calibration for Uniform Rectangle Array with Gain-Phase Error

Most subspace-based algorithms need exact array manifold for direction of arrival (DOA) estimation, while, in practical applications, the gain-phases of different array elements are usually inconsistent, degrading their estimation performance. In this paper, a novel low-complexity 2D DOA and gain-phase error estimation algorithm is proposed by adding auxiliary array elements in a uniform rectangular array (URA). Firstly, the URA is modeled as the Kronecker product of two uniform linear arrays (ULAs) to decouple the 2D DOA estimation. Then, several well-calibrated auxiliary array elements are added in the two ULAs, based on which the rotation invariant factor of the URA destroyed by the gain-phase error is reconstructed by solving constrained optimization problems. Lastly, ESPRIT is used to estimate the 2-D DOA and the gain-phase error coefficients. The closed-form expressions of the estimation CRBs are also derived, providing insight into the impact of gain-phase error on DOA estimation. Simulation results are used to validate the effectiveness of the proposed algorithm and the correctness of the theoretical analysis.

Low Complexity DOA Estimation for Massive UCA with Single Snapshot

In this paper, a low complexity direction of arrival (DOA) estimation method for massive uniform circular array (UCA) with single snapshot is proposed. Firstly, the coarse DOAs are estimated by finding the peaks from the circular convolution between a fixed coefficient vector and the received data vector. Thereafter, in order to refine coarse DOA estimates, we reconstruct the direction matrix based on the coarse DOA estimations and take the first order Taylor expansion with DOA estimation offsets into account. Finally, the refined estimations are obtained by compensating the offsets, which are obtained via least squares (LS) without any complex searches. In addition, the refinement can be iteratively implemented to enhance the estimation results. Compared to the offset search method, the proposed method achieves a better estimation performance while requiring lower complexity. Numerical simulations are presented to demonstrate the effectiveness of the proposed method.

High-Resolution and Low-Complexity Direction of Arrival Estimation for Hybrid Array of Subarrays

In this paper, the problem of direction-of-arrival (DoA) estimation for a hybrid array of subarrays is considered in millimeter-wave communication systems. Unlike much prior work using the outputs from the analog subarrays with symbol-wise processing, the proposed framework jointly exploits multiple outputs in time domain for high-resolution DoA estimation. With block-wise processing, the proposed method designs an optimal hybrid combiner maximizing beamforming gain, while reducing a receiver complexity based on fast Fourier transform filtering for each blocked signal. The performance of the proposed method is analyzed, including estimation performance with a limited training signal, training overhead, and computational complexity. An extension of the proposed method to a uniform planar array case is also discussed. Numerical results show the effectiveness of the proposed algorithm.

Low-complexity neural network based DOA estimation for wideband signals in massive MIMO systems

Massive multiple-input multiple-output (MIMO) has become one of the most promising technologies for wireless communication systems, in which the direction-of-arrival (DOA) plays an important role in interference cancellation and transmission reliability. However, the challenge of conventional wideband DOA estimation algorithms is that their high computational complexity brings great difficulties for their effective application in massive MIMO systems. In this paper, we propose a wideband low-complexity DOA estimation algorithm based on a principal component analysis (PCA) neural network for massive MIMO systems. First, a new criterion for constructing a focusing matrix is proposed to avoid complex angle pre-estimation. To further reduce the complexity of the eigenvalue decomposition (EVD), we propose a signal subspace estimation algorithm based on PCA, which uses only a limited amount of self-organizing learning to estimate the weights of the network and the signal subspace and does not require prior sample training. Moreover, to increase the estimation accuracy, we use the Akaike information criterion (AIC) to divide signal and noise subspaces accurately. The theoretical analysis and simulation results show that the computational complexity of the proposed algorithm is effectively reduced, and the angles of wideband sources can be accurately estimated in massive MIMO systems.

A Low-Complexity 2D-DOA Estimation Algorithm with Massive URA

Conventional Direction of Arrival (DOA) estimation algorithms, such as Multiple Signal Classification (MUSIC), Root-MUSIC, and Estimating Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithms, are difficult to apply to large-scale antenna arrays. Because these algorithms not only require a lot of snapshots of the received data, but also the hardware equipment cannot meet the algorithm complexity requirements. This paper presents a low-complexity DOA estimation algorithm for large-scale Uniform Rectangle Array (URA). We first obtain coarse initial DOA estimates via the two-dimensional fast Fourier transform and then search for the accurate estimates within a very small region. The proposed algorithm only needs one snapshot of the received data to obtain the estimation accuracy of the traditional algorithm. The algorithm also has good robustness, and it can estimate DOA accurately even under extremely low signal-to-noise ratio and many sources. Theoretical results and numerical simulations are provided to assess the superiority of the proposed algorithm.

Low-Complexity DOA Estimation Based on Constraint Solution Space

The Weighted Subspace Fitting (WSF) algorithm is one of the universal algorithms in Direction-Of-Arrival (DOA) estimation, which is of high accuracy. However, it involves the multi-dimensional nonlinear optimization problem, and the computational complexity is usually high. In this paper, we propose a low-complexity DOA estimation algorithm based on constraint solution space. Firstly, we use ESPRIT algorithm to limit the solution space around the best solution and reduce the computational range. Then, we find the best solution in a smaller solution space constraint by Cramr-Rao Bound (CRB), and seek repeatedly until reaching the global optimal solution of WSF algorithm by using the space of the best solution. By limiting the searching process in smaller solution space, this strategy controls the direction of convergence and reduces computational complexity. The experimental results show that this algorithm needs less iterations when the same DOA accuracy is required, and the computational complexity is apparently reduced.

Low‐complexity DOA estimation method for a co‐prime linear array

The problem of direction-of-arrival (DOA) estimation for a co-prime linear array is researched. A low-complexity DOA estimation method is proposed. The co-prime array is decomposed into two sparse uniform linear sub-arrays whose inter-element spacing meets the co-prime condition. Then the received signals of the two sub-arrays are processed for statistical signal processing. Although the DOA estimation based on the under-sampled signal will produce phase ambiguity, the sparse array element spacing that satisfies the co-prime condition makes the phase ambiguity have certain periodic rules. Finally, the unique solution corresponding to the true DOA can be obtained in the phase ambiguities of the two sub-arrays through the application of the co-prime nature. Simulation results validate the effectiveness of the proposed method.

CFAR Block-Sparse Bayesian Learning Algorithm for the Off-grid DOA Estimation with Coprime Array

Constant false-alarm rate Block-sparse Bayesian learning (CFAR-BSBL) algorithm is proposed to reduce the computational complexity and improve Direction of arrival (DOA) estimation accuracy of offgrid signals with coprime array. Firstly, a signal model with normalized noise is built to avoid the learning procedure of noise parameter. Secondly, a block sparse Bayesian framework is built with the introduction of a temporary correlation matrix in order to use t he temporal structure of incident signals. Then the algorithm uses CFAR detection to detect the grids close to the real DOA and relieve the dependence on the number of signals. Finally, an off-grid process based on the closest grids is adopted to deal with the off-grid problem. The proposed CFAR-BSBL algorithm can obtain high accuracy and low complexity DOA estimation of off-grid signals with coprime array.

Accurate DOA Estimation for Large-Scale Uniform Circular Array Using a Single Snapshot

A large-scale antenna array is an enabling technique for millimeter-wave communications. Uniform circular arrays (UCAs) have the spatial invariance property, ensuring the same beamforming performance in the whole angular region. However, the direction-of-arrival (DOA) estimation in UCAs is challenging since the array response of a UCA does not conform to a Vandermonde structure as that of a uniform linear array. This letter proposes an accurate and low-complexity DOA estimation approach by exploiting the good correlation property of the array response of the UCA. The DOA estimates are first obtained from a circular convolution between a single snapshot and the designed coefficient vector. Then, by searching for the best initial phase of the coefficient vector, the DOA estimates can be refined to a configurable accuracy. The simulation results demonstrate that the proposed approach outperforms the state of the art by orders of magnitude in estimation accuracy.

Low-Complexity and High-Resolution DOA Estimation for Hybrid Analog and Digital Massive MIMO Receive Array

A large-scale fully digital receive antenna array can provide very high-resolution direction of arrival (DOA) estimation, but resulting in a significantly high RF-chain circuit cost. Thus, a hybrid analog and digital (HAD) structure is preferred. Two phase alignment (PA) methods, HAD PA (HADPA) and hybrid digital and analog PA (HDAPA), are proposed to estimate DOA based on the parametric method. Compared to analog PA (APA), they can significantly reduce the complexity in the PA phases. Subsequently, a fast root multiple signal classification HDAPA (root-MUSIC-HDAPA) method is proposed specially for this hybrid structure to implement an approximately analytical solution. Due to the HAD structure, there exists the effect of direction-finding ambiguity. A smart strategy of maximizing the average receive power is adopted to delete those spurious solutions and preserve the true optimal solution by linear searching over a set of limited finite candidate directions. This results in a significant reduction in computational complexity. Eventually, the Cramer–Rao lower bound (CRLB) of finding emitter direction using the HAD structure is derived. Simulation results show that our proposed methods, root-MUSIC-HDAPA and HDAPA, can achieve the hybrid CRLB with their complexities being significantly lower than those of pure linear searching-based methods, such as APA.

Low-complexity ESPRIT-based DOA estimation for MIMO radar with L-shaped array

ABSTRACTAiming at the problem of two-dimensional (2D) angles estimation for monostatic multiple-input–multiple-output radar with L-shaped array, a novel reduced-dimensional (RD) direction of arrival estimation (DOA) method based on estimation of signal parameters by rotational invariance techniques (ESPRIT) algorithm is proposed. First, through the RD matrix design and RD transformation, the higher dimensional received data can be transformed into a lower dimensional signal space. Then the signal space can be achieved via the eigen-value decomposition. Last, conjoint with the ESPRIT algorithm, 2D spatial angle parameters with automatic pairing can be jointly estimated. The proposed method can remove data redundancy of high dimensional received data at the greatest degree and enhance sensors efficiency without costing the aperture of array, with a result of better performance than 2D-ESPRIT algorithm. Moreover, compared with the multiple signal classification (MUSIC)-like algorithms, the proposed method has the better overall performance and is more available for a lower computation complexity and higher instantaneity of application. Simulation results verify that the correctness of theoretical analysis and the effectiveness of proposed algorithm.

Two-dimensional direction-of-arrival estimation of coherently distributed noncircular signals via symmetric shift invariance

In practical applications such as mobile communication, radar and sonar, the effect of angular spread on the source energy can no longer be ignored due to multipath phenomena. Therefore, a spatially distributed source model is more realistic than the point source mode in these complex cases. A lot of direction-of-arrival (DOA) estimation methods for distributed sources have been published. Whereas researches concentrated on the complex circular signal case, the noncircular property of signal can be employed to further improve the estimation performance, which has received extensive attention recently. To date, several low-complexity DOA estimation algorithms for two-dimensional (2D) coherently distributed (CD) noncircular sources have been proposed. However, all these algorithms need obtain the approximate shift invariance relationship between the sub-arrays by applying the one-order Taylor series approximation to the generalized steering vectors, which may introduce additional errors and affect the estimation accuracy. In this paper, a novel 2D DOA estimation algorithm based on the symmetric shift invariance relationship is proposed using the centro-symmetric three-dimensional (3D) linear arrays. Firstly, the extended array model is established by exploiting the noncircularity of the signal. Then, it is proved that the deterministic angular distribution function vector of the CD source has a symmetrical property for arbitrary centro-symmetric array, based on which the symmetric shift invariance relationships of extended generalized steering vectors are established in the three sub-arrays of 3D linear arrays. On the premise of such relationships, the center azimuth and elevation DOAs are obtained by the polynomial rooting method without spectral peak searching. Finally, the cost function implementing the parameter matching is constructed by the symmetric shift invariance relationship of the generalized steering vector of the whole array. Theoretical analysis and simulation experiment show that compared with the existing low-complexity algorithms, the proposed algorithm avoids the additional errors introduced by the Taylor series approximation, which allows it to achieve higher estimation accuracy with the small complexity cost. Moreover, the proposed algorithm can achieve omnidirectional angle estimation in the three-dimensional space.

Low-Complexity DOA Estimation Based on Compressed MUSIC and Its Performance Analysis

This paper presents a new computationally efficient method for direction-of-arrival (DOA) estimation with arbitrary arrays. The total angular field-of-view is first divided into several small sectors and the original noise subspace exploited by the multiple signal classification (MUSIC) algorithm is mapped from one sector to the other sectors by a Hadarmard product transformation. This transformation gives a new noise-like subspace cluster (NLSC), whose intersection is found to be simultaneously orthogonal to the steering vectors associated with the true DOAs and several virtual DOAs. Based on such a multiple orthogonality, a novel compressed MUSIC (C-MUSIC) spatial spectrum at hand is derived. Unlike MUSIC with tremendous spectral search, C-MUSIC involves a limited search over only one sector, and hence it is computationally very attractive. To obtain the intersection of NLSC for more than two sectors, a low-complexity method is also proposed in the present work, which shows advantages over the existing alternative projection method (APM) and singular value decomposition (SVD) techniques. Furthermore, the mean square errors (MSEs) of the proposed estimator is derived. Simulation results illustrate that C-MUSIC trades-off MSEs by complexity and resolution as compared to the standard MUSIC efficiently.

Low-complexity ESPRIT-based DOA estimation for colocated MIMO radar using reduced-dimension transformation

Direction of arrival (DOA) estimation for colocated multiple-input multiple-output (MIMO) radar is considered. An estimation of signal parameters via rotational invariance techniques (ESPRIT)-based DOA estimation for the MIMO radar using reduced-dimension transformation is proposed to reduce the complexity. The proposed algorithm has very close angle estimation performance to conventional ESPRIT; also it has slightly better performance than conventional ESPRIT for low SNR. Simulation results verify the usefulness of the proposed algorithm.