International Journal of Antennas and Propagation

Volume 2016, Article ID 7515028, 11 pages

http://dx.doi.org/10.1155/2016/7515028

## An OPMA for Robust Mutual Coupling Coefficients Estimation of URA with Single Snapshot in MIMO HF Sky-Wave Radar

School of Electronics and Information Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Nangang District, Harbin 150001, China

Received 17 March 2016; Accepted 22 June 2016

Academic Editor: Herve Aubert

Copyright © 2016 Yuguan Hou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Due to the fluctuation of the signal-to-noise ratio (SNR) and the single snapshot case in the MIMO HF sky-wave radar system, the accuracy of the online estimation of the mutual coupling coefficients matrix of the uniform rectangle array (URA) might be degraded by the classical approach, especially in the case of low SNR. In this paper, an Online Particle Mean-Shift Approach (OPMA) is proposed, which is to get a relatively more effective estimation of the mutual coupling coefficients matrix with the low SNR. Firstly, the spatial smoothing technique combined with the MUSIC algorithm of URA is introduced for the DOA estimation of the multiple targets in the case of single snapshot which are taken as coherent sources. Then, based on the idea of the particle filter, the online particles with a moderate computational complexity are used to generate some different estimation results. Finally, the mean-shift algorithm is applied to get a more robust estimate of the equivalent mutual coupling coefficients matrix. The simulation results demonstrate the validity of the proposed approach in terms of the success probability, the statistics of bias, and the variance. The proposed approach is more robust and more accurate than the other two approaches.

#### 1. Introduction

Multiple-input and multiple-output (MIMO) radar systems, characterized by multiple antenna elements at the transmitter and the receiver, have demonstrated the great potential for increased ability of the target detection [1–7]. One important application of MIMO radar system is the HF radar [2–5], including the HF sky-wave radar and the HF ground-wave radar. However, one important challenge in MIMO systems is that the mutual coupling becomes particularly significant as the antenna element spacing is decreased. In many practical problems, the direction of arrival (DOA) is the significant information, while at the same time many classical DOA estimation algorithms suffer from sensitivity to mutual coupling, such as MUSIC algorithm [8]. Hence, the DOA estimation for the multiple narrowband signals has been a classical problem in the array signal processing. High-resolution array-processing algorithms for source localization are known to be sensitive to errors in the model for the sensor-array spatial response. In particular, unknown gain, phase, and mutual coupling as well as errors in the sensor positions can seriously degrade the performances of array-processing algorithms. With few exceptions, high-resolution source localization algorithms require an exact characterization of array, including knowledge of the sensor positions, sensor gain/phase response, mutual coupling, and receiver equipment effects. All such information is inevitably subject to errors [9]. The presence of mutual coupling distorts the phase vectors of radiation sources and the eigenstructure of the covariance matrix [10]. In [11], the effects of the mutual coupling on the direction finding accuracy of a linear array with dipole elements were studied. It was found that a known coupling did not affect the estimation performance much. In the case of an unknown mutual coupling, the performance of most high-resolution direction finding algorithms could be degraded. Therefore, a relatively precise coupling coefficient could well establish the high-resolution DOA.

In recent years, a great effort has been seen in the algorithms of the calibration and the coupling coefficients estimation [12–25]. The paper [12] described a calibration algorithm that estimated the calibration matrix consisting of the unknown gain, phase, and mutual coupling coefficients as well as the sensor positions by using a set of calibration sources in known locations, which was based on a maximum likelihood approach. However, this method requires a set of calibration sources at known locations. Two methods to compensate the unknown mutual coupling were proposed in [13], while, just the same as [12], calibration sources were required in both of them. Unlike previous array calibration methods, literature [14] proposed an algorithm that was able to calibrate the array parameters without the prior knowledge of the array manifold. Literature [15] presented a new array calibration procedure for over-the-horizon (OTH) radar, using disparate sources. The method in [16] used the signals impinging on the array to carry out both the DOA estimation and the array calibration simultaneously. In order to express the coupling coefficients, the array coupling matrix was investigated in [17, 18]. Literature [17] proposed a robust subspace-based DOA estimation algorithm in the presence of mutual coupling for ULA, which was based on the banded symmetric Toeplitz matrix model. An accurate estimate of mutual coupling matrix could be achieved simultaneously for array calibration. The method of moments (MoM) was used in [18] to evaluate the mutual coupling between the elements of a given array. The MoM admittance matrix was then used to eliminate the effects of mutual coupling. Reducing the effect of mutual coupling is also an important method for high-resolution DOA estimation [19–21]. The mutual coupling effect of a compact uniform circular array (UCA) is shown in [19] in order not to affect the favorable characteristics of the FFT-based preprocessing technique but only results in a modulation of the signal component at the receiver with a diagonal matrix. In [20], the author divided the antenna into two or more identical subarrays and discussed what kind of errors mutual coupling introduced to the accuracy of the ESPRIT algorithm. In [21], the author estimated the angles when mutual coupling was significant with dummy elements. It has been shown in the pioneering work in [22] that, by applying a group of auxiliary array elements, the MUSIC algorithm can be adopted directly for DOA estimation for ULA at first. Once preliminary DOAs are estimated, the coupling coefficients can be estimated. Then, given the estimated coupling information, the full antenna array with an enlarged array output vector can be processed to refine the DOA estimation. In [23], the 2D DOA estimation in the presence of mutual coupling was presented by setting the sensors on the boundary of the URA as auxiliary sensors. In [24, 25], the modeling and estimation of mutual coupling in a uniform linear array of dipoles were discussed and a method of the mutual coupling compensation using subspace fitting was presented.

However, in MIMO HF sky-wave radar, the application of DOA estimation is often in the domain of the two-dimensional range-Doppler spectra, the peak of which is taken as the single snapshot for the receive array signal processing. The classical approaches mentioned above might be degraded in the case of the single snapshot and the low SNR. In this paper, an online particle mean-shift approach (OPMA) for the robust antenna mutual coupling coefficients estimation with the single snapshot is proposed. The goal is to find an optimal or a suboptimal estimation for the mutual coupling coefficients matrix in the case of the single snapshot. Due to the fact that the estimation of the unknown mutual coupling coefficients is related to the additive noise, the estimated mutual coupling coefficients matrix is modeled as a posteriori probability density function. Moreover, a tracking process based on the idea of particle filter and the mean-shift algorithm is applied to search the most rapid increase of the probability density function.

This paper is organized as follows. In Section 2, the problem and the system model are briefly formulated. The spatial smoothing technique of the uniform rectangle array is introduced. Moreover, the equivalent equation of the mutual coupling coefficients matrix is derived. An OPMA is utilized in Section 3 to further improve the precision of the mutual coupling coefficients matrix estimation. Simulation results for different scenarios are shown in Section 4 and conclusions will follow in Section 5.

#### 2. Problem Formulation and System Model

Consider a collocated MIMO HF sky-wave radar system with the assumption of the narrowband waveform [2]. The transmit antenna is a uniform linear array. The receive antenna is a uniform rectangle array (URA) which is shown in Figure 1.