In high-frequency (HF) hybrid sky-surface wave radar, the first-order sea clutter broadening is severe under the action of ionospheric phase disturbance and bistatic angles. In this paper, a cascaded method is described to suppress the spread sea clutter. Firstly, the radar configuration and sea clutter broadening model are introduced based on the newly developed integrated HF sky-surface wave experimental system. In the cascaded processing method, a new ionospheric decontamination method based on general parameterized time-frequency (GPTF) analysis is proposed to estimate or correct the ionospheric phase distortion with large amplitude. Then, the forward-backward linear prediction (FBLP) algorithm is used to suppress the spread sea clutter caused by bistatic angle. Simulation results show that such ionospheric decontamination method based on GPTF is helpful for the large-amplitude ionospheric contamination when the target masking effect happens even after ionospheric phase decontamination. Finally, the proposed method is examined by the measured data. Experimental results indicate that the proposed method can well suppress the broadening sea clutter for HF hybrid sky-surface wave radars.
Ship detection is an important mission of the HF over-the-horizon radar. Based on the propagation mode associated with sky-wave transmitting and surface wave receiving, HF hybrid sky-surface wave radar not only maintains the superiority of HF sky-wave radar which has a long detection range and wide coverage, the advantage of HF surface wave radar which has a stable propagation channel but also keeps a good invisibility and anti-interference ability [
Based on the hybrid operating mode of sky-wave transmitting and ground-wave receiving, HF hybrid sky-surface wave radar is expected to improve detection probability for ships by overcoming defects of existing sky-wave and ground-wave OTH radar and making complementary advantages of both. Ionosphere is a dispersive, hierarchical, and nonstationary medium. Unfortunately, the ionospheric disturbance often causes the sea clutter spectrum and target to spread in the frequency domain, rendering extended coherent integration pointless. On the other hand, HF hybrid sky-surface wave radar is actually a bistatic radar system. The receiving beam width is wide for the array aperture of our radar experimental system. Thus, the sea clutter spectrum will show different broadening characteristics in the different resolution cells. What is worse, ionospheric phase disturbance further contributes to the sea clutter spectrum broadening. Thus, the broadening of the first-order sea clutter spectrum is very severe under the influence of ionosphere and bistatic angles. In the process of cascade processing of broadened sea clutter in this paper, ionospheric phase decontamination was first processed. At this time, decontaminated broadening sea clutter is only caused by bistatic angles. Therefore, the broadening sea clutter suppression was processed after decontamination.
For the ionospheric phase path disturbance, the method of extracting the contamination function is often used for compensation. The current ionospheric phase disturbance suppression method extracts the frequency modulation function by estimating the instantaneous frequency variation of the broadened echo spectrum, thereby obtaining the ionospheric phase disturbance correction function, and then correcting the echo signal by using the obtained correction function. It can sharpen the broadened echo spectrum and improve the target detection performance of the radar. For ionospheric contamination with small amplitude, the maximum entropy spectrum estimation method, the phase gradient algorithm (PGA) method [
In 1997, Melyanovski [
The content of this paper is organized as follows. Firstly, the radar configuration and sea clutter broadening model are described based on the newly developed integrated HF sky-surface wave experimental system. Secondly, a cascaded processing method for ionospheric decontamination and sea clutter suppression is presented. In this method, the time-frequency analysis method based on GPTF is proposed to correct the ionospheric phase contamination with large amplitude. Then, the FBLP algorithm is used to suppress the broadening bistatic sea clutter caused by bistatic angle, which is based on the prior knowledge of distribution characteristics and the multidimensional feature of first-order sea clutter [
Based on the propagation mode associated with sky and surface wave, the HF hybrid sky-surface wave radar not only maintains the superiority of HF sky-wave radar which has a long detection range and wide coverage, the advantage of HF surface radar which has a stable propagation channel but also keeps a good invisibility and anti-interference ability. The system layout of the HF hybrid sky-surface wave radar is shown in Figure
Geometry and layout diagram of HF sky-surface wave radar.
Thus, the total Bragg frequency expression for HF hybrid sky-surface wave radar can be written as follows [
Therefore, the maximum covering range of the first-order sea clutter Bragg frequency can be obtained by the following formula [
For a sea clutter scattering cell at a certain range and beam direction in HF hybrid sky-surface wave radar, the broadening sea clutter model can be written as follows [
Ionospheric disturbances have the characteristics of change rapidly over time. Compared with the nonparametric time-frequency analysis method, the parameterized time-frequency analysis method selects the appropriate kernel describing the nonstationary signal by introducing the model of the prior signal information. When the kernel form is consistent with the analyzed signal, the time-frequency resolution can be effectively improved. The typical methods have adaptive chirp wavelet decomposition, atomic decomposition, and polynomial Fourier transform, etc., but such methods mainly use polynomial kernels, which are not suitable for analyzing strong time-varying nonstationary signals that change faster with time.
The method of short-time Fourier transform (STFT) is to window the signal based on the Fourier transform. The default window signal is approximately stationary. It can simultaneously describe the signal in the time domain and the frequency domain, thus reflecting the variation of the signal spectrum over time. Since the fixed-length window function cannot capture the change of the signal frequency in time, the time-frequency representation of the STFT is poorly concentrated, and the time-frequency characteristics of the signals cannot be accurately described. The generalized parameterized time-frequency analysis method uses the frequency rotation operator to rotate the time-frequency characteristics of the nonstationary signal by introducing the frequency rotation and translation operator, so that the signal tends to be stable, and then, the STFT is used for the rotated signal, and finally, the frequency is utilized. The translation operator shifts the signal time-frequency characteristics to the true ridge position. Since the signal analyzed by STFT is an approximate stationary signal, the generalized parameterized time-frequency analysis can effectively improve the time-frequency resolution, and there is no cross-term interference.
Assuming that the instantaneous frequency of the signal is an arbitrary function
According to formula (
At this time, the instantaneous frequency
According to the introduction of the principle of GPTF in Section
Time-frequency approximation principle.
It can be seen from Figure Step1:determining the transform kernel form according to the signal priori form. Step 2: the number of iterations Step4: performing parameterized time-frequency analysis Step 4: detecting the peak ridge line Step 5: according to the ridge line form, select a suitable fitting method, and fit the ridge line and estimate transformation kernel parameter Step 6: the number of iterations is increased by one, and the transformation kernel parameter is updated Step7: calculating a termination condition Step 8: setting the termination condition parameter Step 9: comparing the size of Λ and Step 10: outputting a transformation kernel parameter to obtain a time-frequency curve.
According to the above steps of transforming the kernel parameter estimation, the flowchart of the design is shown in Figure
The flowchart of transform kernel parameter estimation.
Based on the above analysis process and steps, the derivation process of ionospheric decontamination based on GPTF is as follows: Step 1: assume that the signal after the ionospheric contamination is expressed as follows [ where Step 2: derive the signal and obtain the Doppler curve form, which can be expressed as follows:
Since the cosine Doppler curve of the signal has periodicity, the ridge line is fitted using the Fourier series for the curve. The Doppler instantaneous frequency form is known. Since the Doppler curve is known to be a cosine form by prior knowledge, the transform kernel of the applied harmonics is as follows:
There is a certain relationship between the cosine series coefficient of the curve and its Fourier transform coefficient. Consider the Fourier transform to find the coefficients of the cosine series of each order. The discrete form of the Doppler curve parameter estimation method is derived as follows.
Radar sampling interval
After equation (
According to the characteristics of the orthogonal trigonometric function set, formula (
The transformation kernel parameter can be obtained as follows:
If the dominant factor of sea clutter broadening is the bistatic angle, or the sea clutter disturbed by the ionospheric phase path has been dedisturbed, then the suppression of bistatic sea clutter is required. At present, there are few studies on the problem of HF radar bistatic sea clutter suppression. The bistatic sea clutter shows different characteristics from monostatic sea clutter, and it makes the traditional Bragg line theoretical prediction or monostatic sea clutter characteristic suppression methods fail. At present, there are two main ideas for the bistatic sea clutter suppression method [
Based on this, this paper uses the FBLP algorithm to suppress the sea clutter. The FBLP algorithm of this paper was previously a conference paper by authors, which was published in [
When the CLEAN or root cancellation algorithms are used to suppress sea clutter for traditional SVD, it is necessary to detect sea clutter firstly in order to suppress sea clutter. However, due to the influence of wind direction or ocean current in the actual marine environment, the characteristics of the sea clutter spectrum are complex, which makes the identification and extraction of the first-order sea clutter difficult, resulting in insufficient sea clutter suppression and the formation of false targets and tracks.
Figure
The range-Doppler spectrum and asymmetry of the measured sea clutter in HF sky-surface wave radar. (a) Range-Doppler spectrum of actual sea clutter. (b) The asymmetry of actual sea clutter spectrum.
For a bistatic HF radar with the hybrid operating mode of sky-wave transmitting and ground-wave receiving, it is assumed that there are
The parameters of each sea clutter signal are estimated below based on a linear prediction method. When the signal-to-noise ratio (SNR) is sufficiently high, the sea clutter signal can be written as the sum of the first
Besides, so as to track the time-varying behavior of the sea clutter, the coefficients of the prediction error filter must be estimated over short data segments so that the filter coefficients could be updated adaptively. And the prediction equation matrix, which is defined in [
Simply, we denote as
And the weight coefficient matrix
As the linear equations above are overdetermined, the total least square method is used to solve this problem [
That is to say, the order of prediction error filter should exceed the estimated signal number. Afterwards, we define frequency estimation matrix as follows:
It is easy to observe that each row in
The signal frequency could be estimated from the roots of (
Simply, we denote as
Through the previous analysis, in order to better achieve the purpose of suppressing sea clutter based on the FBLP algorithm, we use the first-order sea clutter obtained in the theoretical Bragg band of the range-Doppler spectrum, combined with the multidimensional features of the measured first-order sea clutter to better identify and suppress sea clutter. First, the range of the sea clutter Bragg band is determined in advance on the range-Doppler spectrum, and then, the FBLP algorithm is used to extract and estimate the parameters of the sea clutter signal. Based on the previous processing, we use the SNR threshold method defined below to determine the number of first-order sea clutter signals of interest. Specially, we suppose
The SNR of each signal is given by
According to the local dominant characteristics of sea clutter, the SNR of each signal component can be compared with the threshold to screen out the suspected sea clutter signal. Then, according to the frequency domain symmetry property of the sea clutter, combined with the frequency estimation matrix
The processing diagram of bistatic sea clutter suppression based on FBLP algorithm is shown in Figure
The processing diagram of bistatic sea clutter suppression based on the FBLP algorithm.
Simulation parameter setting is as follows: the signal type is a linear frequency modulated (LFM) signal, pulse repetition period is PRT = 40 ms, pulse accumulation time is
Sea clutter suppression with ionospheric phase disturbance based on GPTF and FBLP. (a) Contaminated sea clutter and decontaminated sea clutter spectrum by S2-method, STFT, and GPTF. (b) Estimated phase contamination by PGA, STFT, and GPTF. (c) Decontaminated sea clutter spectrum by GPTF. (d) The broadening sea clutter suppression based on the FBLP algorithm.
Figure
The performance of ionosphere decontamination based on GPTF is verified by the measured data of HF sky-wave radar. The measured data have been processed by the traditional range-Doppler-azimuth processing. The echo accumulation time is 40 ms. The results of ionospheric decontamination based on GPTF at range gate = 60 and azimuth angle DBF = 3° and at range gate = 100 and azimuth angle DBF = 5° are shown in Figures
Decontamination results based on the GPTF method using the HF sky-wave radar. Decontamination result by the GPTF method (a) at range gate = 60 and azimuth angle DBF = 3° and (b) at range gate = 100 and azimuth angle DBF = 5°.
In order to justify the effectiveness of the cascade suppression processing method based on GPTF and FBLP proposed in this paper, the following uses the measured data of HF sky-surface wave radar to verify. The measured data were acquired using the newly developed “high-frequency sky-surface wave radar experimental platform.” The measured data have been processed by the traditional range-Doppler-azimuth processing. The echo accumulation time is 50 s. The suppressed sea clutter spectrum by GPTF and FBLP algorithm at range gate = 35 and azimuth angle DBF = 10° is shown in Figures
The broadening sea clutter suppression based on GPTF and FBLP algorithm. (a) Decontamination result by GPTF method. (b) Sea clutter suppression by FBLP.
As shown in Figures
Ship detection is an important mission of the HF hybrid sky-surface wave radar. The sea clutter spectrum is influenced by composite factors such as the bistatic angle and ionospheric phase disturbance. Thus, an ionospheric decontamination and sea clutter suppression method for HF hybrid sky-surface wave radars based on GPTF analysis is proposed. In this method, the time-frequency analysis method based on GPTF is proposed to correct the ionospheric phase contamination with large amplitude. Compared with the traditional nonparametric time-frequency analysis method, the phase contamination function extracted by this GPTF method has higher accuracy. At this time, the FBLP algorithm is used to suppress the sharped sea clutter spectrum. Finally, the proposed method is examined by measured data. Experimental results indicate that the proposed method can well suppress the broadening sea clutter for HF hybrid sky-surface wave radar. Although some positive results have been obtained, it must be pointed that there is still a need for more studies and improvements.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
The authors would like to express their sincere thanks to the National Natural Science Foundation Project (grant no. 61701309), the Shanghai Natural Science Fund (grant nos. 17ZR1428800 and 20ZR1455000), the Shanghai Sailing Program (grant no. 17YF1418500) and members of the Shanghai Radio Equipment Research Institute for technical support.