DOA Estimation Performance Analysis and Verification of Dual Crossed-Loop/Monopole Antenna Array
The compact high-frequency surface wave radar using a crossed-loop/monopole (CLM) antenna as the receiving sensor has been widely used in ocean remote sensing and target monitoring. However, the direction of arrival (DOA) estimation accuracy of a single CLM antenna is the dominant factor that restricts the target monitoring performance of the compact HF radar. Besides, the single CLM antenna can estimate two signals simultaneously at most, but its effectiveness is challenged by the pattern distortion and the existence of coherent sources, which limits the application range of the compact HF radar. In this study, a compact array combining two CLM antennas is proposed to improve the DOA estimation accuracy and solve the multisource DOA estimation problem. The estimation error and multisource DOA estimation performance of a dual CLM antenna array are analyzed by formula derivation and simulation. Furthermore, the field experiment results are given to demonstrate the performance improvement of the dual CLM antenna array.
By using the vertical polarization electromagnetic wave that travels along the curvature of ocean surface with low loss, the high-frequency surface wave radar (HFSWR) can be used for real-time ocean remote sensing over the horizon range, including not only the measurement of ocean surface dynamic parameters [1, 2] but also the detection and tracking of targets [3, 4]. According to the antenna type, the HF radar can be divided into two types: the phased array system  and the CLM antenna system [6, 7]. The CLM antenna consists of three elements, including an omnidirectional monopole and two cross-placed loops, which are named as loop B and loop A . The development of the CLM antenna enables the HF radar to be used at some scenarios without requiring a large antenna field, which also reduces the installation and maintenance costs.
However, the compact HF radar with the single CLM antenna has some defects in practical application. Firstly, the excessive DOA estimation error caused by antenna pattern distortion in practice significantly reduces the performance of sea-state remote sensing  and hard target tracking . The CLM antenna can achieve DOA estimation by using the multisignal classification (MUSIC) algorithm [11, 12] for direction finding, but since the MUSIC algorithm requires antenna pattern information, the unavoidable distortion of antenna pattern can easily cause DOA estimation errors . Although many methods of calibration and pattern measurement have been proposed [14–16], the DOA estimation accuracy still limits the performance of hard target detection and tracking. Furthermore, a machine learning algorithm  has been proposed recently and has achieved good performance, but the algorithm relies on a large amount of data for training. Moreover, a CL processing method  applied to the CLM antenna has also been proposed to avoid the complexity of measuring antenna pattern, but the improvement of the algorithm is limited. Secondly, a single CLM antenna with three elements is challenged in the case of multisource DOA estimation. Although a single CLM antenna can theoretically distinguish two signal sources, the multisource estimation problem is still difficult to solve due to the antenna pattern distortion and the existence of coherent sources. For an HF radar with the range resolution of kilometers, a range-Doppler (RD) unit containing two or more signals from ocean echoes or vessel targets is a possible event, especially when the application environment has a 360-degree look angle, such as floating platforms and offshore drilling platforms. This case will lead to the problem of coherent signal estimation, but the decoherence algorithm applied to the single CLM antenna has not been explored yet.
An effective way is using a dual CLM antenna array as the receiving sensor to solve the aforementioned problems while retaining the advantage of its small size. In this study, the DOA estimation performance of the dual CLM antenna array is investigated. The estimation error of the dual CLM antenna array based on the MUSIC algorithm is theoretically derived. Then, simulations are conducted to analyze the multisource DOA estimation performance. The estimation results of field experimental data are given to prove that the DOA estimation accuracy of the dual CLM antenna array is higher than that of the single CLM antenna, which is consistent with the theoretical formula. Moreover, a multisource case of vessel targets in the shore-based HF radar data is studied, the result also confirms that it is effective to estimate the DOAs of multisource with dual CLM antenna array.
This article is organized as follows. Section 2 analyzes the estimation error and multisource DOA estimation performance of the dual CLM antenna array by theoretical derivation and simulation. Section 3 gives the experimental results. Section 4 contains a brief conclusion.
2. Analysis of DOA Estimation Performance
2.1. MUSIC Algorithm and Estimation Error
In the case of single signal source, the signal model can be written aswhere is the received data vector of size , m is the number of array elements, is the echo signal, is the steering vector of array, and is the white noise. The covariance matrix of received data can be decomposed into signal part and noise part, which can be expressed aswhere , is the variance of noise, and and represent conjugate and conjugate transpose operation, respectively. Eigen decomposition of can be written aswhere represents signal subspace formed by eigenvectors corresponding to large eigenvalues and represents the noise subspace formed by eigenvectors corresponding to small eigenvalues. Ideally, the steering vector of signal subspace is orthogonal to the noise subspace, viz., . DOA estimation based on the MUSIC algorithm is achieved by finding the that minimizes , which can be expressed as
The steering vector of a CLM antenna with the normal direction of 0° can be written as
The dual CLM antenna array is a combination of uniform linear array (ULA) and CLM antenna, as shown in Figure 1. Therefore, when the normal directions of CLM antennas and the array are both 0°, its steering vector can be expressed aswhere is the phase shift, is the spacing of adjacent elements, and is the wavelength.
Stoica and Nehorai  have proved that the estimation error of the MUSIC algorithm obeys the Gaussian distribution whose mean is zero, and its variance can be written aswhere N is the number of snapshots and is the signal-to-noise ratio of samples. can be written aswhere is the derivative of to θ, viz., .
For an idealized CLM antenna, the MUSIC error variance has been deduced by  and can be expressed as
Similarly, the MUSIC error variance of the dual CLM antenna array can be expressed as
Comparing (9) and (10), is always less than with the same N and values. Figure 2 shows the theoretical MUSIC error of different antenna types when , the incident angle equals 0° and the spacing of adjacent array elements is set as half of the wavelength. From this figure, it is seen that the MUSIC performance of the dual CLM antenna array is superior to that of the single CLM antenna and close to that of the three-elements ULA. But the differences between the antennas decrease with the increase of SNR.
2.2. Analysis of Two-Sources DOA Estimation Performance
According to , there are only phase delay and amplitude weighting between the coherent signals, i.e., the frequencies of two coherent signals are the same. Conversely, the two signals are incoherent signals when they have different frequencies. For two coherent signals coming from and , we can rewrite (1) aswhere , in which is the complex scalar describing the gain and phase relationship between the two coherent signals, and . Notice that is singular and the rank of is 1 when the signals are coherent. Obviously, the rank of also drops to 1, i.e., the dimension of the signal subspace is less than the number of signal sources, so the accurate DOA estimation cannot be achieved. To solve this problem, decorrelate processing is needed to restore the nonsingularity of . The forward spatial smoothing algorithm  is a typical decorrelate algorithm. The principle of the algorithm is to divide the receiving antenna array into several subarrays, then use the covariance matrices of data received by subarrays to obtain the modified nonsingular covariance matrix. The robustness of this algorithm comes at the expense of a reduced effective aperture. Besides, the algorithm requires that the number of subarrays must be greater than or equal to the number of signal sources, and the size of each subarray must be greater than the number of signal sources. Obviously, the algorithm cannot be applied to the single CLM antenna since it does not meet the latter requirement. For the dual CLM antenna array using the algorithm, two CLM antennas can be regarded as two subarrays, then the modified covariance matrix can be expressed aswhere and are the received data of antenna-1 and antenna-2, respectively. The covariance matrix is substituted into (3) and (4) to achieve the DOA estimation of coherent signals.
To analyze the multisource DOA estimation performance of the dual CLM antenna array under the incoherent and coherent conditions, Monte Carlo simulations are carried out in this section. The simulation parameters are as follows: the number of snapshots is 30, and the snapshots are statistically independent, the number of independent trial times is 500, and the spacing of adjacent elements is half of the wavelength.
Figure 3 shows the MUSIC spectrum of the dual CLM antenna array at different SNRs in the incoherent and coherent cases. It is seen that the spectral peak in the incoherent case is sharper than that in the coherent case when the SNRs of signals are equal. With the decrease of the SNR, the peak outlines of both cases are gradually smoothed. When the SNR is equal to 15 dB, the spectral peaks can hardly be distinguished in the coherent case, while the two spectral peaks can still be clearly discernible in the incoherent case. The results show that the spatial smoothing algorithm can achieve the DOA estimation of coherent signals, but the estimation performance in the coherent case is worse than that in the incoherent case.
In our simulations, we define two signals coming from and , and the corresponding DOA estimation results are and . The power of two signals is equivalent. Here, the trial is considered as a successful estimation if and . Figure 4(a) shows the probability of successful estimation under different SNRs at the incident angles of 0° and 40°. As can be seen from the figure, a higher SNR (approximately 15 dB) is required for the coherent case to achieve the same estimation performance as in the incoherent condition.
In Figure 4(b), we set and change the value of to show the DOA estimation performance at different angular separations when SNR = 20 dB. It can be observed that the estimation performance in the incoherent case is superior to that of the coherent case when the incident angles of two signals are close. On the other hand, when the SNR is set as 20 dB, the two signals with an angular deviation greater than 25° can be accurately estimated in the incoherent case, but the angular deviation is required to be greater than 65° in the coherent case. On the other hand, these simulation results also provide the theoretical basis for the actual estimation ability of the compact HF radar under different conditions.
3. Field Experiment and Results
In order to validate the experimental performance of the dual CLM antenna array, a field experiment was carried out at Longhai (, ) in Fujian, China. The compact radar system used in the field experiment is OSMAR-SD  developed by the Radar and Signal Processing Laboratory, Wuhan University. The radar works at 13.05 MHz with a bandwidth of 60 kHz which theoretically produced a 2.5 km range resolution. The receiving antenna system is a dual CLM antenna array with a spacing of 14 m between the two CLM antennas. In addition, an Automatic Identification System (AIS) receiver is installed at the radar site to receive the information broadcast by vessels equipped with an AIS transmitter. The AIS information provides characteristics of vessels including Maritime Mobile Service Identify (MMSI), location, velocity, and so on.
3.1. Comparison of DOA Estimation Accuracy
The constant false-alarm-rate (CFAR) algorithm  is used here to detect the targets in the RD spectrum, and the data received by the two CLM antennas are processed separately. The location, velocity, and heading of the vessel reported by the AIS are converted to range, radial velocity, and azimuth under the radar coordinate. Then, the intersection of detection results of the two CLM antennas is matched with the AIS-reported vessels by using an empirical strategy of a two-dimensional threshold, that is, if the distance between the detected target and the AIS-reported vessels is within a range bin and the velocity difference is less than two Doppler bins, the target pairs are recognized to be matched. The matched targets are used for DOA estimation and the corresponding vessel azimuths calculated from AIS information are used as ground truth information. It should be noted that a sliding window method  is used to form snapshots for the MUSIC algorithm since OSMAR-SD is a coherent Doppler radar.
Figure 5 shows the DOA estimation results, where the horizontal axis represents the azimuth information reported by the AIS, the vertical axis represents the radar estimated results and the black line represents the ideal estimation. The number of data point is 7559. Apparently, the results of the dual antenna array are more concentrated around the black line, which means that the estimations of the dual antenna array are closer to the real values. The comparison of correlation coefficients and root-mean-square errors (RMSEs) between the estimated results and AIS-reported results shown in Table 1 also proves that the dual CLM antenna array has higher estimation accuracy.
Figure 6 shows the error distribution of DOA estimation results. It is obvious that the error distribution curve of the dual CLM antenna array is narrower and more concentrated on zero. The proportions of samples whose absolute error is less than 5° are also shown in the figure. The proportions responsible for two CLM antennas are 0.802 and 0.557, respectively, and the proportion of the dual CLM antenna array is 0.906. The increase of the proportion also indicates the performance improvement of the dual CLM antenna array.
Figure 7 shows the estimation errors of the single antenna and the dual antenna array associated with SNRs, where the dotted lines represent the theoretical values, and the solid lines represent the error values obtained by statistically calculating the estimation results of experimental data. The experimental results of the single antenna and the dual antenna array are both obtained by employing the MUSIC algorithm with the measured pattern. It is seen that the processing results of experimental data are similar to the theoretical curves, and the trends of curves are consistent. This figure also verifies that the estimation performance of the dual CLM antenna array is better, especially when the SNR is relatively low. However, the results of experimental data show higher error values than the theoretical curves. The cause of this difference may be pattern distortion and the measurement error of antenna pattern. The pattern distortion may cause the experimental estimation error to deviate from the results obtained from (9) and (10), and the measurement error between measured pattern and actual pattern may also cause this difference.
3.2. Results of Two-Sources DOA Estimation
Figure 8 shows a coherent case of multisource in experimental data. In Figure 8(a), there is an RD unit containing two vessel targets according to the AIS reports. The azimuths of the two vessels are 65° and 177°, respectively. The MMSI and static information (size and ship type) of vessels are also shown in the figure. It is seen from Figure 8(b) that a strong peak appears at the Doppler frequency point reported by the AIS, which is the echo signal of vessel targets.
Figure 9 shows the normalized MUSIC spectrum of multisource DOA estimation, where the result of the dual antenna array is obtained by applying the forward spatial smoothing algorithm, and the results of antenna-1 and antenna-2 are obtained by the traditional MUSIC algorithm. It can be observed that only one dominant peak responding to the azimuth of the second vessel target is shown in the spectrum of two CLM antennas, and the peak in the spectrum of antenna-1 deviates significantly from the actual azimuth value. However, the MUSIC spectrum of the dual CLM antenna array shows two peaks at 66° and 177°, which is consistent with the actual azimuth of targets. This estimation results indicate the defect of the single CLM antenna that it cannot achieve the multisource estimation. It also verifies the feasibility of using the dual CLM antenna array to estimate the DOAs of multisource. On the other hand, based on the simulation results in the previous section, it can be reasonably inferred that the dual CLM antenna array will have better performance under the incoherent case in practical applications. However, since only shore-based radar data are available for analysis now, the experimental performance varying with the SNR and angular separation is expected to be discussed after obtaining more abundant data, such as platform-mounted radar data.
In this article, we propose to use the dual CLM antenna array as the receiving sensor of the HF radar to improve the DOA estimation accuracy and solve the multisource DOA estimation problem. The DOA estimation accuracy and multisource estimation performance of the dual CLM antenna array are studied by formula derivation and simulations. The estimation results of thousands of detected samples prove that the dual CLM antenna array has higher estimation accuracy than the single CLM antenna. The estimation error of experimental data is also consistent with the theoretical curve. A multisource case in shore-based radar data is investigated, and the result verifies that the dual CLM antenna array can achieve multisource DOA estimation while the single CLM antenna fails. This improvement extends the application range of the compact HF radar and makes it possible to install the radar in the environment such as the floating platform.
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China (Grant nos. 61671331, 41706200, and 61661009), the National Key R&D Program of China (Grant no. 2017YFC0405703), the Fundamental Research Funds for the Central Universities (Grant no. 2042018kf1009), and the Natural Science Foundation of Jiangsu Province (Grant no. SBK2019040262).
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