1. Introduction
Up to now shore-based HF surface wave radars, which operate in the band from 3–30 MHz, have been extensively used for ocean surface current [
1], wave [
2], and wind measurement [
3], as well as ship detection [
4,
5,
6]. The capability of obtaining ocean parameters with a relatively high temporal resolution and a fairly extensive coverage makes HF radars suitable for oceanography research [
7], hazard forecasting [
8], coastal engineering [
9], and maritime security [
10,
11]. Many types of HF radars are in operation worldwide [
12,
13,
14]. Estimating the range and bearing from the backscattering patch to the receiving antennas is a necessary step for a HF radar to map ocean surface currents [
15]. The distance from the backscattering patch to the radar is quite easy to estimate, whereas the estimation of target bearing is much more complicated. Direction-finding and beam-forming methods have been commonly adopted to estimate the direction-of-arrival (DOA) of the sea echo for HF radars [
16]. For example, direction-finding techniques, such as multiple signal classification (MUSIC) algorithm, have been used by the Seasonde HF radar and the multi-frequency HF (MHF) radar to determine DOAs of sea surface current echoes. Kirincich et al. recently compared the performance of different direction-finding methods for HF radar current measurements [
17]. In contrast, the WavE RAdar (WERA), which takes advantage of a long receiving array, adopts the beam-forming method to steer in the desired direction. However, in practical situations, both of the approaches are negatively affected by array uncertainties [
18]. Without array calibration, the beam-forming method may result in an incorrect beam with a broadened beamwidth, and the direction-finding approach would yield a spurious direction with a poor angular resolution [
19,
20,
21].
Unlike the use of array amplitude pattern in direction-finding HF radars [
22], the performance of a phased-array HF radar significantly depends on the accuracy of the phase differences (or time delay) among receiving elements [
23]. Cost-effective and real-time array calibration methods for phased-array HF radars have received significant attention in the past several years. For example, Fabrizio et al. developed an adaptive algorithm that estimates the receiver frequency response corrections for HF radar arrays [
24]. Later, a maximum-likelihood (ML)-based phase error calibration method in which sea echoes are regarded as disparate sources was developed for the Ocean State Monitor and Analysis Radar (OSMAR) [
25]. Afterwards, Fernandez et al. developed a phase error calibration method treating ship echoes as disparate sources [
26]. Subsequently, Flores-Vidal et al. employed a number of unknown ship echoes to solve the phase errors from a cost function [
27]. Recently, Chen et al. developed an approach that is based on the MUSIC algorithm (so-called MU method) for calibrating phase errors while using single-DOA sea echoes [
28], and this method was compared with the ML-based method based on current measurements [
18]. Almost all of the aforementioned methods only consider the phase uncertainty for each receiving element as a constant value that does not vary with direction. However, phase distortion in the receiving elements [
29,
30], which has a negative impact on the radar performance, is neglected in the aforementioned methods. This phase distortion problem was recently found in a small-aperture HF radar based on a circular array [
31].
In order to address the phase distortion problem, the conventional array signal model is modified by adding a direction-based phase error matrix, and a new array phase manifold calibration method using measured phase responses of incoming ship echoes is proposed to compensate the array phase distortions. An assessment on the proposed array calibration method is made based on the DOA estimations and current measurements that are obtained from the datasets collected by a multi-frequency HF (MHF) radar, especially in the phase distortion case. The paper is organized, as follows:
Section 2 contains the array signal model and a modified array signal model. The array phase manifold calibration method and DOA estimation method are also presented in this section. A description of the MHF radar and an example of array phase manifold measurement are given in
Section 3. The assessment on the proposed calibration method based on DOA estimations and current measurements is provided in
Section 4. The results are discussed in
Section 5.
Section 6 consists of a conclusion.
5. Discussion
HF radar current measurement and target detection performance is associated with DOA estimation capability, which strongly depends on the accuracy of array manifold. Both the proposed calibration technique (APM method) and traditional phase error calibration method (MU method) show significant improvements on HF radar DOA estimation and current measurement comparing with the no calibration strategy. In the case that phase distortion is significant, the RMSDs have been reduced while using the APM method as compared with the MU method.
For current comparison, the ADCP was deployed at the cell, which is
from the radar boresight. At this bearing the phase distortions of the radar at these three operating frequencies are not significant (see
Table 3). At the bearing of
, the steering vector for the MU method
and the steering vector for the APM method
are approximately the same. As a consequence, the DOA performances at the bearing of
using the APM method and the phase error method are nearly the same. This is why the APM method slightly, but not significantly, improves the current measurement performance compared with the MU method for these datasets.
Another interesting work is that the APM method has been applied to four-element HF radar datasets. As reported in
Table 5, the current measurements that were obtained from the four-element HF radar datasets using the APM method are as good as those obtained from eight-element MHF radar datasets using the MU method. This is extremely useful for compact HF radars, since they are more convenient than large array radar to deploy.
6. Conclusions
The receiving array signal model for a phased-array HF radar has been investigated and modified. Phase distortions have been observed in the MHF radar receiving elements. The APM method based on measuring array manifold HF radar ship echoes as well as AIS data has been proposed. The performance of the APM method has been compared with the no calibration strategy and the phase error calibration method.The DOA estimations and current measurements using the MUSIC algorithm show a reasonable improvement after taking the phase distortion into consideration and using the APM method.
Array calibration is critical for HF surface wave radar applications, and it can significantly improve azimuth estimation performance as well as current measurements. The phase error calibration, which has been studied in the past few decades, is not sufficient for the MHF radar in the phase distortion situation. The APM method provides a feasible way to measure the array manifold and calibrate the array distortion. This method will be validated in other radar sites in the future.