Improvement of DOA estimation accuracy by using sub-arrays

This paper mainly introduces a novel estimation method for direction of arrival (DOA) estimation. Recently, direction-of-arrival (DOA) estimation has been widely employed in wireless communication networks, electromagnetic (EM) environment management, and radar tracking. However, traditional DOA estimation algorithms and systems are based on multiple digital receivers with expensive hardware. To overcome this challenge, we propose a novel DOA estimation method based on a space-time coding method and an easy-configurable antenna array. With this programmable L-shape antenna array and space-time coding method, a two-dimensional DOA estimation is realized.

The data model for direction of arrival (DOA) estimation is revisited and studied with more attention to the practical implementation of the antenna arrays and verified through measurement results. A complete data model for a single-channel direction finding system that includes, for the first time, the effects of the switching mechanism among antennas is presented. In order to combat coupling among antenna elements and the radio frequency switch nonidealities, a comprehensive model is developed, which includes more accurate noise modeling. The effect of the phase center (PC) in DOA estimation is then discussed and an improved data model is presented, which includes the antenna’s PC movement. The Cramer–Rao bound for circular arrays including the newly introduced parameter for the PC is derived. The new model shows significant improvement in the estimation accuracy.

Recently, popular machine learning algorithms have successfully been applied to the direction of arrival (DOA) estimation. An implementation of determination of DOA estimation is presented based on deep neural networks (DNNs) to reduce the computational complexity of traditional superresolution DOA estimation methods. The classical DOA estimation algorithms have limitations due to unforeseen effects, such as array perturbations. Instead of computing an inverse mapping based on the incomplete forward mapping that relates the signal directions to the array outputs, the DOA problem is approached as a mapping, which can be approximated using a suitable DNN trained with input output pairs. The neural network architecture is based on a multilayer perception and a group of parallel DNNs to perform detection and DOA estimation, respectively. Simulation results are performed to investigate the effect of network parameters on estimation accuracy so that they can be roughly determined in the case of one signal scenario. Based on a set of simulations and experimental measurements, the performance of the optimum network is also assessed and compared to that of the classical DOA estimation methods for multiple signals. It has been shown that the proposed method can not only achieve reasonably high DOA estimation accuracy, but also dramatically reduce the computational complexity and the memory space.

DOA (Direction of Arrival) estimation is a major problem in array signal processing applications. Recently, compressive sensing algorithms, including convex relaxation algorithms and greedy algorithms, have been recognized as a kind of novel DOA estimation algorithm. However, the success of these algorithms is limited by the RIP (Restricted Isometry Property) condition or the mutual coherence of measurement matrix. In the DOA estimation problem, the columns of measurement matrix are steering vectors corresponding to different DOAs. Thus, it violates the mutual coherence condition. The situation gets worse when there are two sources from two adjacent DOAs. In this paper, an algorithm based on OMP (Orthogonal Matching Pursuit), called ILS-OMP (Iterative Local Searching-Orthogonal Matching Pursuit), is proposed to improve DOA resolution by Iterative Local Searching. Firstly, the conventional OMP algorithm is used to obtain initial estimated DOAs. Then, in each iteration, a local searching process for every estimated DOA is utilized to find a new DOA in a given DOA set to further decrease the residual. Additionally, the estimated DOAs are updated by substituting the initial DOA with the new one. The simulation results demonstrate the advantages of the proposed algorithm.

Direction of arrival (DOA) estimation performance severely degrades for the reasons that the perturbation from their assumed nominal complex gain values in practical sensor system. In this paper, to mitigate the effects of the uncertainty perturbation, a two-step method for joint DOAs and sensor errors estimation is proposed. In the first step, convex optimization and l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm penalties are used to conduct a second-order cone framework to estimate DOAs roughly under the assumption that all sensor gains are identity. Second, we calibrate the perturbed gains with the DOAs estimated by the first step. The iterative process of the DOAs and gains estimation is taken until convergence. Furthermore, a refinement procedure is addressed to alleviate the effects of the grid limitations to spatial locations. In the present method, no auxiliary calibrated sensors or co-operation signal source is required. And the two-step method can handle both uncorrelated signals and coherent signals, it is also a high resolution method and robust in the condition of low signal-to-noise ratio (SNR). Several aspects are taken into consideration, and numerical experimental results are given to show the advantages of the new method for the DOA estimation.

Collaborative Direction of Arrival estimation by using Alternating Direction Method of Multipliers in distributed sensor array networks employing Sparse Bayesian Learning framework

An algorithm to improve direction of arrival (DOA) estimation accuracy with an extended sensor array in the presence of multiple coherent signal sources is proposed. The algorithm uses virtual element theory to extend the sensor array, estimates virtual element information via linear prediction and expands the array aperture in practical sense; the sparsity of the target orientation in angle space is exploited to establish an over-complete dictionary and a reception model for the array signal in sparse space; the received array data is preprocessed using singular value decomposition (SVD) method and target DOA estimation is realized by calculating the best atoms. The algorithm improves DOA estimation accuracy by extended array and uses SVD to control computational complexity effectively, which ensures the accuracy and efficiency. Computer simulation shows that the proposed algorithm is able to accurately estimate the DOA for both single-target and closely spaced multi-target cases in low signal-to-noise ratio environments, and also has excellent DOA estimation performance in the presence of multiple coherent signal sources.

This letter investigates the impact of the antenna element directivity on compressed sensing (CS)-based direction of arrival (DOA) estimation employing the uniform circular array (UCA) antenna. In the CS-based approach, the reconstruction accuracy of sparse signals is determined by a sensing matrix, which depends on the array antenna configuration in the DOA estimation. In our study, we analyze the cross-correlation between column vectors of the sensing matrix and clarify the estimation accuracy for various antenna element radiation patterns.

Precision of direction of arrival (DOA) estimation using novel three dimensional array geometries

Uniform linear array (ULA) geometry does not perform well for direction of arrival (DOA) estimation at directions close to the array endfires. Shirvani and Akbari solved this problem by displacing two elements from both ends of the ULA to the top and/or bottom of the array axis. Shirvani-Akbari array (SAA) presents a considerable improvement in the DOA estimation of narrowband sources arriving at endfire directions in terms of DOA estimation accuracy and angular resolution. In this paper, all new proposed SAA configurations are modelled and also examined, numerically. In this paper, two well-known DOA estimation algorithms, multiple signal classification (MUSIC) and minimum variance distortionless response (MVDR), are used to evaluate the effectiveness of proposed arrays using total root mean square error (RMSE) criterion. In addition, two new scenarios are proposed which divide angular search to two parts, directions close to array endfires as well as middle angles. For middle angles, which belong to (−70∘≤𝜃≤70∘), ULA is considered, and for endfire angles, the angles which belong to (−90∘≤𝜃≤−70∘) and (70∘≤𝜃≤90∘), SAA is considered. Simulation results of new proposed scenarios for DOA estimation of narrowband signals show the better performance with lower computational load.

For direction of arrival (DoA) estimation, the data-driven deep-learning method has an advantage over the model-based methods since it is more robust against model imperfections. Conventionally, networks are based singly on regression or classification and may lead to unstable training and limited resolution. Alternatively, this paper proposes a two-branch neural network (TB-Net) that combines classification and regression in parallel. The grid-based classification branch is optimized by binary cross-entropy (BCE) loss and provides a mask that indicates the existence of the DoAs at predefined grids. The regression branch refines the DoA estimates by predicting the deviations from the grids. At the output layer, the outputs of the two branches are combined to obtain final DoA estimates. To achieve a lightweight model, only convolutional layers are used in the proposed TB-Net. The simulation results demonstrated that compared with the model-based and existing deep-learning methods, the proposed method can achieve higher DoA estimation accuracy in the presence of model imperfections and only has a size of 1.8 MB.

ABSTRACTGenetic algorithm (GA)-based direction of arrival (DOA) estimation is proposed using fourth-order cumulants (FOC) and ESPRIT principle which results in Multiple Invariance Cumulant ESPRIT algorithm. In the existing FOC ESPRIT formulations, only one invariance is utilised to estimate DOAs. The unused multiple invariances (MIs) must be exploited simultaneously in order to improve the estimation accuracy. In this paper, a fitness function based on a carefully designed cumulant matrix is developed which incorporates MIs present in the sensor array. Better DOA estimation can be achieved by minimising this fitness function. Moreover, the effectiveness of Newton’s method as well as GA for this optimisation problem has been illustrated. Simulation results show that the proposed algorithm provides improved estimation accuracy compared to existing algorithms, especially in the case of low SNR, less number of snapshots, closely spaced sources and high signal and noise correlation. Moreover, it is observed that the optimisation using Newton’s method is more likely to converge to false local optima resulting in erroneous results. However, GA-based optimisation has been found attractive due to its global optimisation capability.

We report the performance analysis of Phase and Amplitude Gradient (PAGE) method for Direction of Arrival (DoA) estimation using underwater Acoustic Vector Sensor (AVS). We consider an AVS which consists of two pairs of hydrophones placed along the horizontal plan in a cross pattern. We have also compared the DoA estimation accuracy of PAGE with pressure gradient method. The analysis has been done in the presence of underwater ambient noise at sea-state 3 and signal to noise ratio (SNR) from −30 dB to 20 dB. The underwater ambient noise is assumed to be additive colored Gaussian noise in nature. Study has been done by varying inter-sensor spacing ( $d$ ) varying from $\lambda/2$ to $\lambda/12$ . Performance has been computed in terms of Root Mean Square Angular Error (RMSAE).

This paper proposes a method to enhance direction of arrival (DoA) estimation accuracy and resolve range ambiguity in interleaved subcarrier-based multiple-input multiple-output (MIMO) single carrier-frequency division multiple access (SC-FDMA) systems for radar applications. Using the virtual array in the MIMO configuration, a large effective aperture can be synthesized using a relatively small number of transmitting and receiving antenna elements, enabling high angular resolution. To realize this virtual array, orthogonality among multiple transmitters must be ensured. For instance, the interleaved subcarrier allocation scheme enables signals from multiple transmitting antenna elements to be orthogonal. However, this allocation introduces range-dependent phase shifts between transmitting antenna elements, which degrade DoA estimation accuracy, and reduces the maximum unambiguous detection range. To mitigate these problems, we propose a method to compensate for the phase shift in each virtual array, along with a range ambiguity resolution method based on phase linearity analysis. The proposed methods are validated through simulations. With the proposed method, the average DoA estimation error is reduced from 5.63° to 0.2°. Furthermore, the proposed method successfully resolves range ambiguity, reducing the estimation error to 0 m for a target at 1500 m, which lies beyond the system’s maximum unambiguous range of 384 m. The results confirm that the proposed approach improves DoA estimation accuracy and resolves range ambiguity in interleaved MIMO SC-FDMA systems.

In order to solve the problem that the channel gain-phase mismatch would deteriorate the performance of direction of arrival (DOA) estimation in actual direction finding (DF) system, a novel efficient gain-phase calibration algorithm based on the self-checking signal is proposed in this paper. By injecting a self-checking signal into the actual DF system, the whole calibration process could divide into the off-line pre-calibration and the auto-calibration part. Thus, it could realize the real-time auto-calibration efficiently during the DOA estimation process. Moreover, in order to verify the effectiveness of the proposed method, a practical DF signal processor based on the FPGA and DSP is implemented in this paper, and the experiments are carried out in the anechoic chamber. The experiment result shows that the proposed method could calibrate the gain-phase mismatch in real-time and have higher DOA estimation accuracy.