Direction of Arrival Estimation by Convex Optimization Methods With Unknown Sensor Gain and Phase

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.

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.

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

FOMP algorithm for Direction of Arrival estimation

We propose a Taylor expansion multiple signal classification (TE MUSIC) method for joint direction of departure (DOD) and direction of arrival (DOA) estimation in a bistatic multiple-input multiple-output (MIMO) array. First, using a Taylor expansion of the steering vector, a two-dimensional (2D) search in the conventional MUSIC method for MIMO arrays is reduced to a two-step one-dimensional (ID) search in the proposed TE MUSIC method. Second, DOAs of the targets can be achieved via Lagrange multiplier by a ID search. Finally, substituting the DOA estimates into the 2D MUSIC spectrum function, DODs of the targets are obtained by another ID search. Thus, the DOD and DOA estimates can be automatically paired. The performance of the proposed method is better than that of the MIMO ESPRIT method, and is similar to that of the 2D MUSIC method. Furthermore, due to the ID search, the TE MUSIC method avoids the high computational complexity of the 2D MUSIC method. Simulation results are presented to show the effectiveness of the proposed method.

Based on the extended noise subspace, the case of weak signal direction of arrival (DOA) estimation in presence of strong jamming is studied, and a novel approach is given in this paper. Under the condition knowing the number of strong interferences, first, the method forms the extended noise subspace, then, uses the conventional multiple signal classification (MUSIC) algorithm to constrain the strong interferences effectively and estimates weak signals' DOA information accurately based on the extended noise subspace. The method does not require the angle information of strong interferences and it has the same computation burden as conventional MUSIC. Theoretic analysis and computer simulation demonstrate the method is effective and feasible.

A new direction of arrival (DOA) estimation method is proposed for coherent GPS signals, which applies to the GPS receiver with rich multipath, strong interference and low SNR. In this method, the interference is first suppressed by projecting the received signal onto the interference orthogonal subspace. Afterwards, the noise is eliminated by the spatial difference matrix. Then, the coherent GPS signals are decorrelated by the reconstructed Toeplitz matrix, and the DOA estimation is improved by a new constructed matrix. The proposed method can obtain more accurate DOA estimation for coherent GPS signals with strong interference and low SNR in the GPS receiver. Simulation results demonstrate the effectiveness and efficiency of the proposed method.

The sparse signal recovery-based direction of arrival (DOA) estimation has received a great deal of attention over the past decade. From the sparse representation point of view, $$\ell _0$$ -norm is the best choice to evaluate the sparsity of a vector. However, solving an $$\ell _0$$ -norm minimization problem is non-deterministic polynomial hard (NP-hard). Thus, The common idea for many sparse DOA estimation methods is to use the $$\ell _1$$ -norm as the sparsity metric. However, its sparse solution may not coincide with the solution resulting from the $$\ell _0$$ -norm thus deteriorating the DOA estimation performance. In this paper, we propose a new sparse method based on $$\ell _p$$ ( $$0<p<1$$ ) regularization for DOA estimation to achieve a sparser solution than $$\ell _1$$ regularization. In particular, we use the Taylor expansion to convert the $$\ell _p$$ -norm minimization problem to a weighted $$\ell _1$$ -norm problem. Then, a two-step iterative method is employed to achieve the DOA estimate. The $$\ell _p$$ ( $$0<p<1$$ ) regularization is able to improve the angle resolution, leading to an improved performance in low SNR and correlated signal scenarios. Numerical results show that our proposed method has better estimation performance than many other methods do.

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.

A novel direction of arrival (DOA) estimation method is proposed when uncorrelated and coherent wideband linear frequency modulated (LFM) signals coexist in multipath environment. By using the concentration property of signals, the wideband LFM signals are first transformed into fractional Fourier (FRF) domain to construct the array model, in which the time-variant steering vector is changed into time-invariant one. Afterwards, the DOAs of uncorrelated wideband LFM signals are estimated by the total least square estimation of signal parameters via rotation invariance technique (TLS-ESPRIT). Then, a spatial difference matrix is constructed to eliminate uncorrelated wideband LFM signals, and the coherent wideband LFM signals are resolved by performing a forward spatial smoothing technique. The proposed method can resolve more accute DOAs of uncorrelated and coherent wideband LFM signals in multipath environment with no a priori knowledge of the initial frequency and chirp rate of wideband LFM signals simultaneously. Simulation results demonstrate the effectiveness of the proposed method.

The direction of arrival (DOA) estimation is a key issue in array signal processing, and there are many well-known methods, e.g., Capon, MUSIC, Root-MUSIC and some other DOA estimation algorithms in the literature. Nevertheless, the effective DOA estimation for closely spaced multiple sources with large power differences is still a difficult problem due to the deteriorated resolution for the low power sources. In this paper, a novel DOA estimation method called Capon-MUSIC algorithm is proposed, which has a much higher resolution for closely spaced multiple sources with obvious power differences. Finally, some numerical experiments are provided to demonstrate the effectiveness of the proposed method.

High resolution method for direction of arrival (DOA) estimation using array antenna is studied actively [1]. In almost previous studies, it is assumed that antenna elements have the same directional patterns. However, it is very difficult to make many antenna elements they have just the same directional patterns. Furthermore, the directional patterns are distorted due to mutual coupling between the elements [2]. The estimation accuracy is decayed if the directional patterns are distorted intensively. In this paper, sub-array techniques are proposed to recover the estimation accuracy. An array is divided into plural sub-arrays and DOAs are estimated using respective sub-array. The estimated directions are averaged to obtain a final result. Two types of sub-array techniques, "Partitioned Arrays" and "Shifted Arrays" are examined and the performances of respective types are compared.

In this paper we propose for comparative analysis of wideband direction of arrival (DOA) estimation methods with nested array. Previously developed methods, Incoherent method, Coherent signal subspace processing (CSSM) and Weighted average of signal subspace (WAVES) could not perform satisfactory DOA estimation due to the single dimensionality and associated with lesser degree of freedom. In nested array, DOA estimation is done on the same source that is Gaussian source with additive white Gaussian noise (AWGN). While, nested array performed DOA estimation by decomposing uniform linear array (ULA) into multidimensional array, by which algorithm gets improved performance compare to the conventional methods. In nested array, power spectrum is measured by using multiple signal classification (MUSIC) and performance index is evaluated using Monte Carlo simulation.

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.