- Open Access
Ionospheric decontamination for skywave OTH radar based on complex energy detector
© Wei et al.; licensee Springer. 2012
Received: 21 March 2012
Accepted: 18 October 2012
Published: 26 November 2012
For over-the-horizon (OTH) radar, the ocean clutter is very strong. And this becomes a big challenge for the target detection. The clutter suppression is a very important procedure for the OTH radar. For the skywave OTH radar, the radar signal will propagate through the ionosphere. This will cause a contamination due to its unstable movement. Then the Bragg frequencies will be smeared and clutter spectrum will spread wider rather than a single line spectra. This smear will cause the target more difficult to be detected and even buried in clutter. Compensation is necessary to cancel the ionospheric effect. This article proposes the clutter decontamination algorithm based on the complex energy detector (CED). The energy detector (ED) is originally proposed to demodulate the real AM–FM signals. The ED is expanded to complex domain. After the expansion, there is no mutual coupling between the amplitude and frequency component for an AM–FM signal. The phase of the Bragg clutter return contaminated by the ionosphere is modeled by a frequency-modulated signal, while its magnitude is amplitude modulated. The CED algorithm is applied to track the instantaneous frequency of the contaminated return signal, which is then used for compensation. Simulation results are presented. The simulation results show that, comparing with the Hankel rank reduction algorithm, the proposed algorithm has better performance under the situation of large frequency fluctuation.
where g is the acceleration due to gravity, and f c is the radar frequency, c is the speed of light.
The ocean clutter signal is very strong and can conceal the target if it is moving slowly, target detection would fail. For a skywave radar case, this problem is even more serious as the clutter signal may be contaminated by the ionosphere path or wind over the ocean surface. The ionosphere is typically multi-layered and there are generally multiple ionospheric propagation paths to and from targets and clutter sources. Radar performance can degrade when one of the ionospheric propagation paths is so distorted as to reduce the spectral isolation between scatter of the transmitted waveform . This contamination or distortion can cause the first-order Bragg lines shift near the theoretical frequency in Equation (1). This smearing can lead the clutter spectrum spans more widely in frequency domain and masks the targets. The performance of OTHR strongly depends on the radar frequency and it is time varying. Although the frequency management systems can adaptively select a proper frequency for the OTH radar, it can only partially eliminate the ionospheric effect, and thus it is not possible to totally avoid the smearing [3–5]. So, the clutter contamination is still an important factor to be considered. To detect the targets under the contaminated clutter environment, the clutter should be corrected first. The instantaneous frequency (IF) of the contaminated clutter will vary from pulse-to-pulse, and thus broadening the clutter spectrum. This can be corrected if the IF is compensated to be a fixed value.
In general, the ionosphere instability is modeled by a multiplicative noise . This causes the Bragg frequency shifts around the theoretical value. The key idea of the compensation scheme is to find the IF of the Bragg line. Several algorithms have been proposed. Bourdlillon et al.  used maximum entropy spectral analysis algorithm to compensate the clutter. In this algorithm, one coherent processing interval (CPI) is divided into several short segments, during a short segment the Bragg frequency is regarded as stable. Within each segment, the frequency is estimated by high-resolution spectral analysis algorithm. This method performs well in slow perturbations, but if the frequency is not stable in the short duration or fast moving, its performance can be degraded. Parent and Bourdlillon  presented a simple energy-weighted phase differential estimator to track the IF of the contamination. This estimator requires a more complex transmission waveform and is not suitable to conventional FMCW radar systems. Khan  proposed an algorithm to suppress the clutter based on AR model. It got a good result to make the target clearly shown after clutter removed. The contamination was not considered. Howland and Cooper  used the Wigner–Ville distribution (WVD) to estimate the IF. WVD method is a two-dimensional computation. Moreover, due to limited data samples are used on both sides, the estimation on two edges is very coarse. As the compensation performance is determined by the accuracy of the frequency estimation, so the estimated frequency on both sides often should be discarded in order not to degrade its performance.
Poon et al.  proposed to suppress the clutter based on Hankel rank reduction (HRR) method. Lu et al.  proposed an improvement to HRR algorithm. In their study, they proposed to compensate the clutter using the IF shift and thus achieved a better performance in suppressing the clutter. The HRR can be used to estimate the IF of superimposed sinusoidal signals, but its performance decreases dramatically when the IF changes fast. Peleg and Friedlander  modeled the phase perturbation using a polynomial phase with constant magnitude. Then the higher-order phases are peeled-off order by order. Lu et al.  used this algorithm to compensate the skywave clutter. The problem for this algorithm is that there is no basic rule on how to determine the order for the polynomial phase. The order plays a key role in the performance of this algorithm.
In this article, a novel decontamination algorithm based on the complex energy detector (CED) is proposed. The energy detector (ED) was originally proposed for demodulating the AM–FM-modulated signals . Bovik et al.  proposed to improve its performance by analytic wavelet transform (see, e.g., ). In this article, the detector is expanded for complex signals. I/Q orthogonal process is often used in radar environment. With this expansion, there will be no mutual coupling between the magnitude and frequency component for one signal. As in this application, only the frequency component is of concern.
The output of the CED operator is the square of the IF of one signal, IF can be derived directly via this detector by calculating its square root. Comparing with some other decontamination methods, CED is easy to implement. The algorithm is based on the complex AM–FM signal model, the impact of the magnitude is also considered. It can track larger frequency fluctuation than the HRR algorithm thus in this situation, it has better performance in compensating the contamination.
In this article, we consider the single-mode propagation model, which means that the Bragg components and the moving target in the same range cell are contaminated by the same function. This article is organized as follows. Section 2 introduces the ED and the CED method, and the principle on calculating the IF shift is explained. In Section 3, the clutter correction algorithm will be presented. Section 4 will give some simulation results to show its performance. And Section 5 concludes this article.
2. ED and CED
In the above equation, and are the first- and second-order derivatives of signal s r , respectively. It has been shown that if the real signal is AM–FM modulated, then the magnitude and frequency component can be derived by ψ(s r ) and . It is obviously that there is a coupling between the magnitude and frequency component. As in our application, only the frequency component is of concern. Moreover, in radar application environment, the signal is often processed by I/Q decomposition and in complex domain (see, for example ).
where a is the instantaneous magnitude of the complex signal x, ψ(a) the CED of the signal magnitude which can be computed by Equation (5).
For the reason of simplicity, time index t is omitted. From Equation (7), it is found that, by applying the CED to the AM–FM signal, the first-order derivate of the phase signal can be derived directly. From Equation (3), is the sum of 2πf b and linear scalar of the f(t). So, f(t) can be recovered using Equation (7). Once f(t) is demodulated, it can be used to compensate the phase shift caused by the ionosphere. This is the idea of the CED. It should be noted that after a squaring root operation of Equation (7), the actual IF of the Bragg component is derived. Theoretically, the frequency shift caused by the ionosphere can be obtained by subtracting the Bragg frequency 2πf b . But, considering the ocean current velocity, as it will cause a frequency shift to the first-order peak proportional to its velocity , 2πf b is replaced by the average value of the actual IF.
Equation (17) holds under the assumption of high CNR, while in Equation (18), the statistical property of the additive noise is used. The σ n 2 is the variance of the real or equivalently the imaginary part of the additive complex noise.
3. The decontamination algorithm based on CED
For the data of one cell in a CPI, perform FFT, and transform it into frequency domain.
Search the strongest peak at the range of [−5f b , 5f b ], where f b is the theoretical Bragg frequency.
Filter out the strongest Bragg peak, or equivalently, mask other frequency bin. This Bragg peak will be used for estimating the IF.
Transform the filtered data into time domain via IFFT.
Perform CED to the Bragg component.
Compute the square root of the CED, and extract the frequency modulation component.
Apply a low pass filter to the result of step 6 to reduce the ripple due to differentiation.
Compensate the clutter using Equation (23), get the “clean” version of the clutter.
In step (3), a rectangular window in frequency domain is used to extract strongest Bragg component. The bandwidth of this filter is an important factor to be considered. The basic rule for choosing this parameter is to retain most of the contamination component while reject other unwanted ones. On the one hand, if it is too wide, then part of the second-order spectrum and more noise will be included. This will impact the performance of the CED algorithm. On the other hand, if it is too narrow, the contamination of one Bragg component may not be fully covered. Howland and Cooper  suggested the bandwidth to be 0.5 Hz as a typical value.
In the following section, some simulation results will be presented to show the performance of the CED algorithm. The result of CED algorithm will be compared with formerly proposed HRR algorithm.
4. Simulation results
k 1/k 2
f m 1
Figures 4 and 5 show the result when fm 1 = 0.1, B = 0.6. In which, Figure 4 shows the contaminated data, Figure 5 shows the decontaminated return signal by using the CED algorithm. In the figure, we can also see that, after the compensation, both of the Bragg peaks and target are much sharper. The target can be discriminated, while in the contaminated data of Figure 4, the target is buried.
By analyzing the simulation results, we conclude that the CED algorithm-based compensation can work and outperform HRR algorithm in large frequency perturbations. As in this situation the HRR algorithm will fail to track the IF change thus it degrades the compensation performance.
In this article, a novel skywave OTH radar ocean clutter decontamination algorithm based on the CED is proposed. The ED was originally designed to demodulate the AM–FM-modulated signals. In this article, it is expanded to complex domain. With this expansion, the frequency shift of the clutter can be derived directly by computing the root square of CED for one complex signal. The clutter is then corrected by using the IF shift estimated by the CED algorithm. The procedure of algorithm is presented clearly. Simulation results are also presented. Simulation results suggest that the CED algorithm can be used to compensate the clutter frequency fluctuation due to ionosphere instability or movement. Its result is better than HRR algorithm in large perturbations. It is also easy to implement with proper computational complexity.
This study was supported by the National Science Foundation of China under Grant 61032010, and by the NSAF under Grant 11076006. The authors would like to thank the anonymous reviewers for their constructive comments and suggestions helped in improving the quality and presentation of this article.
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