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Source localization using sensor array in the near-field is a two-dimensional nonlinear parameter estimation problem which requires jointly estimating the two parameters: direction-of-arrival and range. In this paper, a new source localization method based on sparse signal reconstruction is proposed in the near-field. We first utilize

Source localization using sensor array is one of the most important topics in array signal processing society. A great number of source localization methods were proposed in the past few decades. However, most of these methods focused on source localization in far-field case, in which the signal can be regarded as planar wave and only direction-of-arrival (DOA) estimation is required. When the range between the sources and the array is not sufficiently large compared with the aperture of the array (i.e., in the near-field case), the wavefront of the signal at the array is characterized by both azimuth and range. Thus, the performance of the DOA estimation methods for far-field case degrades significantly in the near-field.

In recent years, a majority of methods have been proposed to deal with the source localization problem in the near-filed, such as maximum likelihood methods [

In this paper, a novel SSR-based source localization method is proposed in the near-field. Firstly, just like the method in [

The paper is organized as follows. Section

Consider this case in which

A near-field source impinges onto a ULA with

Let

By making use of the Fresnel approximation [

Given the knowledge of the observed signals

For convenience we make the following assumptions:

The source signals are uncorrelated to each other and independent of the noise.

The noises are spatially uncorrelated Gaussian white noise.

The intersensor spacing of the array

Under the above assumptions, the spatial correlation between the

Then, the one-dimensional estimation problem can be cast into a sparse signal recovery problem as follows. Define a set

Under the assumptions (A1) and (A2) in Section

Define

In order to fit the data

Now, the problem in (

In this section, the approach of L1-SVD [

In this section, some numerical experiments are given to show the effectiveness and efficiency of the proposed method. We make a comparison in terms of RMSE and resolution ability between the proposed method and the method in [

Firstly, we present an experiment to compare the proposed method with the method in [

Angular spatial spectra for the two methods.

Range spatial spectra for the two methods.

According to Figures

Subsequently, we investigate RMSE of DOA and range estimation versus SNR. To make a fair comparison, the two near-field sources are moved to

RMSE of DOA estimation versus SNR.

RMSE of range estimation versus SNR.

In the second experiment, we evaluate RMSE of DOA and range estimation as a function of the number of snapshots. The parameters are kept the same as before except SNR = 10 dB; the RMSE of DOA and range estimation with respect to the number of snapshots are illustrated in Figures

RMSE of DOA estimation with respect to the number of snapshots.

RMSE of range estimation with respect to the number of snapshots.

In this subsection, the angular resolution ability regarding SNR is investigated. Two sources are defined to be resolved in a run if both

Angular resolution ability as a function of SNR.

Now, we assess the angular resolution ability for the above two methods as a function of the number of snapshots. The parameters used in this experiment are kept the same as the previous one except SNR = 10 dB. Figure

Angular resolution ability as a function of the number of snapshots.

According to the results from the above simulation experiments, it can be concluded that the proposed method shows a better performance compared to the method in [

In this paper, a novel near-field source localization approach is proposed for a uniform linear array. Firstly, just like the method in [

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported in part by Chongqing Research Program of Basic Research and Frontier Technology of China under Grant nos. cstc2015jcyjA40055 and cstc2016jcyjA0515 and in part by Chongqing Municipal Education Commission of China under Grant nos. KJ1500917 and KJ1600936.