Electromagnetic vector sensor (EVS) array has drawn extensive attention in the past decades, since it offers two-dimensional direction-of-arrival (2D-DOA) estimation and additional polarization information of the incoming source. Most of the existing works concerning EVS array are focused on parameter estimation with special array architecture, e.g., uniform manifold and sparse arrays. In this paper, we consider a more general scenario that EVS array is distributed in an arbitrary geometry, and a novel estimator is proposed. Firstly, the covariance tensor model is established, which can make full use of the multidimensional structure of the array measurement. Then, the higher-order singular value decomposition (HOSVD) is adopted to obtain a more accurate signal subspace. Thereafter, a novel rotation invariant relation is exploited to construct a normalized Poynting vector, and the vector cross-product technique is utilized to estimate the 2D-DOA. Based on the previous obtained 2D-DOA, the polarization parameter can be easily achieved via the least squares method. The proposed method is suitable for EVS array with arbitrary geometry, and it is insensitive to the spatially colored noise. Therefore, it is more flexible than the state-of-the-art algorithms. Finally, numerical simulations are carried out to verify the effectiveness of the proposed estimator.
Direction-of-arrival (DOA) estimation using sensor array is one of the most popular methods for source localization, and it has struck a series of technical elevations in wireless communications [
Many attempts have been done with respect to 2D-DOA estimation using EVS array, and various estimators have been proposed. The most popular method is the vector cross product [
In this paper, we generalize the issue of source localization using the EVS array. We consider that the EVSs are displaced in arbitrary geometry. Moreover, spatially colored noise appears in the array. An improved higher-order singular value decomposition (HOSVD) estimator is proposed. Firstly, the temporal cross-correlation scheme is utilized to eliminate the spatially colored noise. Thereafter, the crosscovariance measurement is arranged into a fourth-order tensor. The HOSVD is adopted to obtain an enhanced signal subspace. Then, a normalized Poynting vector is constructed, and 2D-DOAs are obtained via the shift invariance property of the previously constructed Poynting vector. Finally, the polarization parameters are achieved via the least squares technique. Our algorithm is insensitive to the sensors’ position and spatially colored noise. Numerical examples are given to show the superiority of the proposed algorithm.
Throughout the paper, lowercase letters represent vectors and uppercase letters denote matrices, respectively;
Let us first introduce some preliminaries concerning tensors. Interested readers are recommend to refer to [
Let
The mode-
The following principles are important for mode-
The HOSVD of an
A single EVS consists of six-component electromagnetic antennas. For an incoming source that impinges on an isolated EVS, the electromagnetic response of the EVS is given by [
An important characteristic is that
In this paper, we consider an
Illustration of the EVS array with arbitrary geometry.
Suppose the source signals are uncorrelated and
Obviously, the noise is eliminated in
Actually,
The HOSVD of
Inserting
By Hermitian unfolding
Combined with the result of (
Since
Since the virtual response matrix
Let
Inserting (
Equivalently,
According to the first line of (
In fact,
Then, we have
Since
Accordingly, we can get
Denote the estimates of
Obviously, the estimated 2D-DOA are automatically paired.
It is easy to find
So the
According to (
Then,
Therefore,
Obviously,
Also, the polarization parameters are paired automatically.
Now, we have accomplished the estimation algorithm for distributed EVS array. To help the reader better understand the proposed algorithm, we summarize its algorithmic steps in Table
Algorithmic steps of the proposed algorithm.
Step No. | Operation |
---|---|
Step 1 | Estimate the noiseless covariance matrix |
Step 2 | Rearrange the covariance measurement into a fourth-order tensor |
Step 3 | Construct |
Step 4 | Perform eigendecomposition on |
Step 5 | Calculate |
Step 6 | To get |
Step 7 | Estimate |
Step 8 | Estimate |
Next, we summarize the main complexity (number of complex multiplication that is required) of typical algorithms. The main complexity of ESPRIT in [
Comparison of the complexity.
Method | Complexity |
---|---|
ESPRIT | |
PARAFAC | |
Proposed |
The identifiability of the proposed approach is equal to the maximum
Numerical simulations are carried out to show the superiority of the proposed algorithm. In the following simulations, we assumed an EVS array with
Scatter results of the proposed algorithm. In such simulation, we consider
The root mean square error (RMSE) performance versus SNR. Herein, RMSE for a parameter
The RMSE performance versus
The RMSE performance versus colored parameter
Scatter results of the proposed algorithm: (a) 2D-DOA estimation, (b) polarization parameter estimation.
Average RMSE performance comparison versus SNR with Gaussian white noise: (a) average RMSE on 2D-DOA estimation; (b) average RMSE on polarization parameter estimation.
Average RMSE performance comparison versus SNR with colored noise: (a) average RMSE on 2D-DOA estimation; (b) average RMSE on polarization parameter estimation.
Average RMSE performance comparison versus
Average RMSE performance comparison versus
In this paper, a novel HOSVD algorithm is proposed for distributed EVS array, the core of which is to estimate 2D-DOA by the vector cross product of the normalized Poynting vector, which is achieved from cross-correlation tensor signal subspace. The proposed algorithm is better than the state-of-the-art algorithms since it is insensitive to the spatially colored noise and sensor position. Numerical simulation results verify the effectiveness of the proposed algorithm. It should have a bright future in radar, sonar, and wireless communication as well as Internet of Things.
There is no available data for this paper.
The authors declare no conflict of interest.
This work was supported by the Humanities and Social Sciences projects of the Ministry of Education under grant 20YJAZH132 and Natural Science Foundation project of CQCST under grant cstc2018jcyjAX0398.