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This paper presents a new fast direction of arrival (DOA) estimation technique, using both the projection spectrum and the eigenspectrum. First, the rough DOA range is selected using the projection spectrum; then, a linear matrix equation is used to acquire a noise pseudo-eigenvector. Finally, the fine DOA estimation is obtained from an eigenspectrum approach based on the noise pseudo-eigenvector. Without the need to form the covariance matrix from a block of the array data and without a prior knowledge of the number of incoming signals, reduced complexity is achieved, in contrast to conventional subspace-based algorithms. Simulation results show that the proposed algorithm has a good resolution performance and deals well with both uncorrelated and correlated signals. Since the new approach can reduce computational complexity while maintaining better or similar resolution capability, it may provide wider application prospects in real-time DOA estimation when contrasted to other comparable methods.

The direction of arrival (DOA) has been applied in many fields, including speech, radio, telecommunication, and medical signal processing. In the past few decades, a large number of accurate high-resolution DOA estimation techniques have been proposed. One popular approach is the subspace-based method, used in the well-known MUltiple Signal Classification (MUSIC) algorithm [

A direct data domain least squares (D^{3}LS) approach [^{3}LS approach, methods [

In this paper, an effective method is proposed for developing a fast DOA estimation algorithm when uncorrelated and correlated signals are present in highly nonstationary environments. The proposed method consists of two approaches. First, we use a suboptimal projection spectrum approach to select the rough DOA ranges of the incoming signals. This is done forming small spectrum peaks, generated by removing the signal from a given direction, instead of solving a more exact projection operator, as in Kim’s and Wen's methods. The whole process reduces algorithm computational cost. Secondly, the solution of a linear-matrix equation, formed by a forward-backward data matrix, is applied as a noise pseudo-eigenvector, which performs a function similar to a noise eigenvector. Then, a fine DOA estimation can be obtained from an eigenspectrum. This approach allows us to reduce computational cost and obtain a good algorithm resolution. In contrast to Kim’s and Wen's algorithms, the proposed algorithm has better or similar capability of resolution but offers lower computational complexity. Moreover, the proposed algorithm deals well with both uncorrelated and correlated signals and processes only a signal data snapshot without the use of the covariance matrix. Therefore, it may provide wider application prospects in real-time DOA estimation.

This paper is organized as follows. In Section

In the section, we prepare mathematical models and representations of signals. In what follows, the operators

Our objective is to estimate the DOA from

In this section, the proposed DOA estimation is derived, determining the rough and fine DOA estimation algorithms, presented in Sections

In Kim’s and Wen’s methods, the rough incidence angle ranges are estimated by using the bearing response, requiring the use of nonlinear-generalized-eigenvalue or SVD algorithm in the different look directions. However, such processing may bring high computation complexity against real-time requirement. In the subsection, we present a simple novel DOA estimation algorithm, called the orthogonal projection technique, to estimate the rough DOA ranges from incoming signals using a single snapshot for achieving fast tracking varying signals under highly nonstationary environments. Let us define an orthogonal projection matrix as

Then, (

Then, (

In the conventional subspace-based methods, the covariance matrix is decomposed into its constituent eigenvectors and eigenvalues. Recalling that the eigenvectors of the noise eigenvalues are orthogonal to the signal subspace spanned by the eigenvectors of the signal eigenvalues, then MUSIC algorithm uses the orthogonality of these subspaces efficiently to get a high-resolution DOA estimation. However, such processing is time-consuming against real-time applications and may lose performance for correlated signals. This subsection presents a procedure of finding a noise pseudo-eigenvector based on the solution of a linear-matrix equation, formed by a forward-backward data matrix, for real-time requirement and for the purpose of working well in correlated signals.

By using the orthogonal projection method, we state that if

Combining (

Obtain the rough DOA ranges of the incoming signals and a steering vector

Use the steering vector

Obtain the fine DOA estimation of the incoming signals by searching for local peak values in the eigenspectrum

Use the steering vector

Fine-tune the DOA estimation of the incoming signals in step (3) by searching for local peak values of the eigenspectrum

The computational cost of solving a nonlinear generalized eigenvalue algorithm is about

To compare the performance of the described DOA finding method, MUSIC, ESPRIT, Wen’s, and Kim’s method, in terms of the probability of resolution, the methods were investigated in the narrowband farfield DOA estimations with computer experiments. The probability of resolution is defined as follows. Two signals with DOA

In each experiment, it was assumed that the powers of all the incoming sources were equal. The noise at each array sensor was assumed to be additive white Gaussian noise process with zero mean. We also assumed a uniform linear array with half-wavelength element spacing. We examined the conventional MUSIC and ESPRIT algorithm when the number of snapshots was 100, whereas the proposed algorithm, Kim’s, and Wen’s methods only used a single snapshot. A total of 300 independent test runs were done to get each simulated point, and the DOA scanning was performed over [0°,90°] with a step size of

In the first experiment, three signals with the same SNR of 20 dB were impinging on the array of 23 sensors. Figures

DOA estimation using the proposed algorithm and MUSIC for three uncorrelated signals from [2.3°,9.7°,17.8°] under the SNR of 20 dB and the number of sensors

DOA estimation using the proposed algorithm and MUSIC for two coherent signals from [2.3°,9.7°] and one uncorrelated signal from [17.8°] under the SNR of 20 dB and the number of sensors

In the second experiment, we considered three uncorrelated signals from [2.3°,9.7°,17.8°], impinging on the array of 23 sensors. Figure

Comparison of results of the probability of resolution from ESPRIT, the proposed algorithm, Kim’s, and Wen’s methods, with for three uncorrelated signals from [2.3°,9.7°,17.8°] having different SNR, where the number of sensors

In the third experiment, three uncorrelated signals from [2.3°,2.3° +

Comparison of results from ESPRIT, the proposed algorithm, Kim’s, and Wen’s methods, for the probability of resolution versus the angle spacing of the incoming signals for three uncorrelated signals from [2.3°,9.7°,17.8°] having the SNR of 20 dB, where the number of sensors

In the fourth experiment, we considered three uncorrelated signals from [2.3°,9.7°,17.8°], impinging on the array with SNR of 20 dB. Figure

Comparison of results of results of the probability of resolution from ESPRIT, the proposed algorithm, Kim’s, and Wen’s methods, with three uncorrelated signals from [2.3°,9.7°,17.8°] having the different number of sensors, where the SNR of 20 dB.

As expected, from Figure

A new fast direction of arrival estimation technique is presented based on both a simple projection spectrum and the eigenspectrum. The advantages of this method over MUSIC, ESPRIT, Kim’s, and Wen’s methods are as follows: (1) it has a lower computation loads; (2) it allows arbitrary signal statistics, for example, nonstationary and coherent; (3) it is capable of tracking high varying signals. Computer simulations have shown that the proposed algorithm handles the coherent or uncorrelated signals well, whereas MUSIC does not, as well as better resolution as compared with Kim’s method, or similar resolution to Wen's method. Since this new approach improves performance by reducing computational complexity while maintaining sufficient resolution in highly nonstationary environments, it will have a wider range of prospective applications in real-time DOA estimation than other comparable methods.