Real-Valued MUSIC for Efficient Direction of Arrival Estimation With Arbitrary Arrays: Mirror Suppression and Resolution Improvement

Performance of direction of arrival (DOA) estimation is one of the most important issues in array signal processing. Subspace-based algorithms provide a good compromise between the estimation accuracy and computational complexity. However, these methods are exposed to performance breakdown at low SNR scenarios. A major reason for such performance breakdown is the subspace swap phenomenon (intersubspace leakage). In this article, we elaborate on a novel modified signal subspace model through exploiting a supervised index for the estimation of DOA. With the developed model we refine the signal subspace so as to enhance the performance of the DOA estimation. In the proposed scheme, we define a fuzzy similarity matrix for the eigenvalues of the array output correlation matrix to capture the distribution of the eigenvalues. Then, we build up a transformation matrix between the fuzzy similarity matrix and the eigenspace of the correlation matrix, and construct a nonlinear transformation function to adjust the fuzzy similarity matrix. Subsequently, we define a supervised evaluation index named signal subspace reconstruction error for DOA estimation and construct a cost function of the signal subspace to develop a supervised model for the signal subspace. The signal subspace can be modified through adjusting the parameter in the nonlinear transformation function and optimizing the abovementioned cost function. Finally, the performance of DOA estimation can be enhanced with the modified signal subspace. The main characteristic of the proposed model is circularly applied feedback of the estimated DOA for refining the estimated subspace. It is a closed loop and supervised method not reported before. This article opens a specific way for improving the performance of the DOA estimation in array signal processing by a supervised index. However, the proposed method is still unsatisfying in some scopes of signal-to-noise ratio. We believe that exploiting a validity index for DOA estimation in array signal processing is still a general and interesting problem.

High-Accuracy DOA Estimation Algorithm at Low SNR Through Exploiting a Supervised Index

It is well-known that the multiple signal classification (MUSIC) algorithm is computationally time-consuming because it requires a complex-valued full-dimension eigenvalue decomposition (EVD) and a complex-valued spectral searching. In this paper, we exploit the virtual signal model of forward/backward average of array covariance matrix (FBACM) to show that its real part (R-FBACM) is a real symmetric matrix. Based on that, we prove that by evaluating two half-dimension EVD after an orthogonally similar transformation performed on the estimated R-FBACM, we are able to reconstruct the original eigenspace whereas the maximum number of estimated sources is reduced as compared to the upper limit $\mathit{M}-\text{1}$ for original MUSIC. Numerical results show that the proposed method provides satisfactory estimation accuracy and improved resolution with reduced complexity.

Half-Dimension Subspace Decomposition for Fast Direction Finding With Arbitrary Linear Arrays

In this paper, we study the two-dimensional direction of arrival (2D-DOA) estimation problem in a switching uniform circular array (SUCA), which means performing 2D-DOA estimation with a reduction in the number of radio frequency (RF) chains. We propose a covariance matrix completion algorithm for 2D-DOA estimation in a SUCA. The proposed algorithm estimates the complete covariance matrix of a fully sampled UCA (FUCA) from the sample covariance matrix of the SUCA through a neural network. Afterwards, the MUSIC algorithm is performed for 2D-DOA estimation with the completed covariance matrix. We conduct Monte Carlo simulations to evaluate the performance of the proposed algorithm in various scenarios; the performance of 2D-DOA estimation in the SUCA gradually approaches that in the FUCA as the SNR or the number of snapshots increases, which means that the advantages of a FUCA can be preserved with fewer RF chains. In addition, the proposed algorithm is able to implement underdetermined 2D-DOA estimation. 

/pdf/2d-doa-estimation-in-switching-uca-using-deep-learning-based-6v1ug7d1.pdf

2D-DOA Estimation in Switching UCA Using Deep Learning-Based Covariance Matrix Completion

The multiple signal classification (MUSIC) algorithm based on the orthogonality between the signal subspace and noise subspace is one of the most frequently used methods in the estimation of direction of arrival (DOA), and its performance of DOA estimation mainly depends on the accuracy of the noise subspace. In the most existing researches, the noise subspace is formed by (defined as) the eigenvectors corresponding to all small eigenvalues of the array output covariance matrix. However, we found that the estimation of DOA through the noise subspace in the traditional formation is not optimal in almost all cases, and using a partial noise subspace can always obtain optimal estimation results. In other words, the subspace spanned by the eigenvectors corresponding to a part of the small eigenvalues is more representative of the noise subspace. We demonstrate this conclusion through a number of experiments. Thus, it seems that which and how many eigenvectors should be selected to form the partial noise subspace would be an interesting issue. In addition, this research poses a much general problem: how to select eigenvectors to determine an optimal noise subspace? 

How to Determine an Optimal Noise Subspace?

In this article, an augmented subspace-based algorithm for detecting the direction of arrival (DOA) of signals is presented. In the developed scheme, a uniform circular antenna array with a full range of lateral capacity is first transformed into a uniform linear antenna array in which the steering matrix has a Vandermonde form. This kind of structure can be exploited to formulate computationally efficient search-free estimation methods. In the process of virtual transformation, a novel DOA unit matrix of an assumed sector where the signals to be detected are located is built and optimized to find response matrices of the real and virtual antenna arrays to signals from the sector. By utilizing singular value decomposition (SVD) of the response matrix of the real antenna array to possible signals from the sector, a stable virtual transformation matrix between the real and virtual antenna arrays is obtained. Meanwhile, the aperture of the original array is also expanded during this process. Then, a virtual cyclic optimization algorithm is introduced to thoroughly mine information from the correlation matrices of the virtual antenna array receiving data and to optimize the signal subspace. Subsequently, the DOA can be efficiently determined through the reconstruction of the steering matrix. In the experimental part of the study, root-mean-square errors and probability of success are used to evaluate the performance of the algorithms. In particular, simulation results demonstrate that the proposed methods provide significant accuracy improvements, especially for low signal-to-noise ratio thresholds.

Fast Direction of Arrival Estimation for Uniform Circular Arrays With a Virtual Signal Subspace

From granulation-degranulation mechanisms to fuzzy rule-based models: Augmentation of granular-based models with a double fuzzy clustering

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Fast Direction of Arrival Estimation for Uniform Circular Arrays With a Virtual Signal Subspace

From granulation-degranulation mechanisms to fuzzy rule-based models: Augmentation of granular-based models with a double fuzzy clustering