Deep Learning Aided Time–Frequency Analysis Filter Framework for Suppressing Ionosphere Clutter

Abstract

In a heterogeneous environment, the ionosphere is dynamically changing in the Earth’s middle latitude, and backscatter from fast-moving irregularities in the plasma can cause ionosphere clutter to extend. Suppressing varying ionosphere clutter and exploring obscured targets are challenging tasks for high frequency surface wave radar (HFSWR). For responding to these challenges, this research presents a multi-channel deep learning time–frequency feature filter framework (DL-TFF). Firstly, we observed the behavior of the ionosphere clutter for a long period of time before selecting the representative ionosphere clutter. Secondly, different transform techniques are applied to provide a time–frequency representation of the non-stationary echo signals, and representation results of different echo components are collected as a training set for feature learning. Thirdly, we design a multi-channel time–frequency feature learning network (MTF), which is responsible for mining discriminative time–frequency information between targets and different types of ionosphere clutter. Experimental results on real HFSWR data sets have demonstrated that DL-TFF can remove varying ionosphere clutter and simultaneously reveal covered targets. Moreover, its suppression effectiveness is more ideal than the previous classical method.

1. Introduction

The ionosphere is the region of the Earth’s atmosphere in which gases are ionized by radiation [1]. Ionospheric irregularities have a considerable effect on the radio waves that propagate through them [2]. The unwanted echo component from the ionosphere is called ionosphere clutter. When a high-frequency over-the-horizon radar system (HF-OTHR) is employed for such missions as remote sensing of the sea surface or surveillance applications, the signal contamination is usually caused by ionospheric irregularities and heterogeneous sea clutter. For this reason, many targets are covered by clutter with a wide distribution. HF-OTHR system can be divided into different systems according to the propagation path of radio waves, including high frequency surface wave radar (HFSWR), skywave over-the-horizon radar (skywave OTHR) and high-frequency hybrid sky–surface wave radar (HFHSSWR). As for radar systems, detecting targets of interest emerging into nonhomogeneous clutter is the biggest impediment [3,4]. As a consequence, there is a need to develop ionosphere clutter suppression methods.

The ionosphere clutter has non-stationarity, and the target signal is relatively stable as time goes by. Many suppressed approaches have been developed based on this valuable differentiation point. Time–frequency analysis as a type of representative signal analysis technique can provide an image of the frequency information of a signal as a function of time. More specifically, time–frequency analysis techniques are measurement and graphical representation methods of how the frequency feature of a signal changes over time. Current time–frequency analysis methods can be divided into linear methods and non-linear methods. Particularly, linear frequency analysis has been developed into diverse techniques in many applications. In inverse synthetic aperture radar (ISAR), Qian et al. recently presented a new super-resolution ISAR imaging method using improved U-net structure and short-time Fourier transform (STFT) [5]. In order to obtain the ideal detection performance in a heterogeneous environment, Jing et al. recently added a contrastive learning module into a multi-task autoencoder and captured time–frequency characteristics between clutter and target for binary detection [6]. Zhang et al. proposed an efficient Z-transform-based finite-difference time-domain (Z-FDTD) and applied it to electromagnetic scatterings in the 3D biaxial anisotropy [7].

As for HF-OTHR systems, using the time–frequency analysis method to remove the ionospheric phase contamination has attracted much attention. As the typical time–frequency analysis methods, both STFT and Wigner–Ville distribution (WVD) have their own strengths and weaknesses. Hence, a high time–frequency cohesive and low cross method was proposed for combining the advantage of STFT and WVD [8]. Furthermore, the joint transformation method is also suitable for the combination of STFT and other improved WVD methods [9]. As for skywave OTHR, Li et al. firstly proposed an ionospheric phase contamination correction method based on an improved S-transform method and phase gradient algorithm (PGA) [10]. The S-transform is a time–frequency analysis technique proposed by Stockwell, Mansinha and Lowe [11]. It can provide frequency-dependent resolution and maintain a direct relationship with the Fourier spectrum [12].

HFHSSWR mainly suffers from the reflection from F-layers of the ionosphere [13]. Hence, Zhou et al. paid attention to the echoes of direct waves that only had phase distortions without experiencing sea attenuation [14]. They applied a modified S-transform because it can provide high resolution in both time and frequency by optimizing induced parameters while dealing with the dilemma of either better time localization or better frequency localization [14]. S²-method as an improved method of the S-method has many advantages. It can give the representation of a multicomponent signal such that the distribution of each component is Wigner distribution [12]. Furthermore, S²-method can avoid producing cross terms no matter how long the window function is. For correcting the ionospheric phase contamination and suppressing the broad sea clutter, the time–frequency analysis method based S²-method was proposed in [15]. However, with the S²-method as a nonparametric method, the elimination performance of cross-term interference is not very good. It roughly describes the resolution expression and the time–frequency characteristics of the signals. Hence, an ionosphere decontamination method based on general parameterized time–frequency (GPTF) analysis was also proposed to estimate the ionospheric phase distortion with large amplitude [16].

All the above methods are designed for suppressing ionospheric phase contamination. In order to suppress the ionosphere clutter in HFSWR, Su et al. presented a ridgelet analysis method for the time–frequency image of radar signal [17]. Ridgelet analysis is usually applied for image or 2D signal processing based on multi-resolution analysis (MRA). The continuous ridgelet transform can provide a sparse representation of both smooth functions and perfectly straight edges [18]. This proposed method combines the ridgelet transform and wavelet image processing to preserve the target submerged in clutter and effectively mitigate the clutter.

Most suppression methods based on time–frequency analysis are applied for mitigating ionospheric phase contamination in over-the-horizon radar (OTHR) systems. Furthermore capturing the time–frequency feature of the ionosphere clutter and targets contributes to removing the various ionosphere clutter. A deep learning network is a promising choice. Therefore, in this paper, we propose a novel approach based on the neoteric time–frequency analysis technique and deep learning network to remove ionosphere clutter with different amplitude or different extended regions. We firstly separate the various components of received echoes by using improved time–frequency transform techniques. Then, the representation results of each type of component are collected as a training set for the proposed feature learning network (MTF). Finally, the proposed network can reveal the submerged targets and filter out ionosphere clutter in different layers. To the best of our knowledge, this is the first study to explore time–frequency features by cooperating multi-channel deep neural networks (DNN) for suppressing ionosphere clutter in HFSWR systems.

The remainder of this article is organized as follows. Section 2 introduces the neoteric time–frequency analysis technique for accurately representing the time–frequency feature of different types of clutter and targets. Section 2 also specifically introduces each step of the proposed framework. Section 3 first proved the feasibility of FSST (Fourier synchrosqueezing transform) in multicomponent separation. Then, exploring the optimal parameters of FSST and shows the experiment results and the suppression effect of the proposed methodology. Section 4 thoroughly compares the suppression performance between the proposed methodology and other classical approaches. This section also analyzes the detection performance by analytical mean. Section 5 presents the main conclusions, emphasizing the suppression effect and detection ability of the proposed approach.

2. Materials and Method

2.1. Multicomponent Echoes Signal Decomposition with Synchrosqueezing

Linear time–frequency and time-scale analysis are standard tools for investigating non-stationary signals or deterministic signals with varying frequencies. However, the traditional time–frequency transforms, such as STFT and continuous wavelet transform (CWT) are restricted by the Heisenberg uncertainty principle, which means the high resolution on both time and frequency domains cannot be achieved simultaneously [19]. Accordingly, the traditional linear time–frequency analysis methods may generate a “blurred” time–frequency representation and cannot characterize the time–frequency features of non-stationary signals [20]. Synchrosqueezing transform (SST) is a time–frequency (TF) analysis technique, it was designed to decompose signals into constituent components with time-varying oscillatory characteristics [21]. This method aims to sharpen a TS representation while remaining invertible [22,23]. SST has been successfully used in medical electrocardiography (ECG) [24] for analyzing non-stationary signals. SST was introduced in the context of CWT [21]. Then, STFT-based SST (FSST) was introduced by Oberlin et al., giving sufficient theoretical considerations [22].

In this section, we propose a novel methodology using FSST to extract the non-stationary components of the received echo signals. This technique is applied to the real HFSWR data.

We define echo signals as $\chi (t)$, generally, $\chi (t)$ is an additive mixture of many types of clutter $c(t)$, external interference $i(t)$, noise $n\left(t\right)$ and potentially a target signal $s(t)$:

$$\chi (t)=c(t)+i(t)+n(t)+s(t)$$

(1)

For a particular range bin, the ionosphere clutter model [25] can be expressed as

$$\xi (t)=\mu \epsilon (t)\exp (j2\pi \psi (t))$$

(2)

where $\mu$ is the root mean square amplitude, $\epsilon (t)$ represents time-varying clutter amplitude, $\psi (t)$ is the time-varying ionospheric Doppler frequency. A target signal can be expressed as

$$s_m(t)={\alpha }_m\exp (j2\pi f_{m}t+{\phi }_m)$$

(3)

where ${\alpha }_m$ is the amplitude of the mth target signal and its value equals $\sqrt{SCR}$ (signal-to-clutter ratio) at t point, ${\phi }_m$ is the random phase and $f_m$ is the frequency of the mth target. The received target signal echoes $s(t)$ is represented by a superposition of target components at t moment, which can be expressed as follows:

$$s(t)={\displaystyle \sum _{m=1}^M{s}_m}(t)+n(t)$$

(4)

where m represents the number of received target signals at a range-Doppler cell, $m=1,2,\dots ,M-1,M$. $n\left(t\right)$ is Gaussian white noise at this moment. In this article, we focus on a common problem that the varying ionosphere covers targets. The interference and other types of clutter are ignored in the following study. Hence, the received signal model can be defined as $\chi (t)=s(t)+\xi (t)+n(t)$ in the following research.

We denote by $\widehat{\chi }$ the Fourier transform of function $\chi$ with the following normalization:

$$\widehat{\chi }(v)={\displaystyle \underset{ℝ}{\int }\chi (x)e^{-2i\pi vx}}dx$$

(5)

The STFT is a local version of the Fourier transform obtained by means of a sliding window g:

$$V_f(\eta ,t)={\displaystyle \underset{ℝ}{\int }(s}(\tau )+\xi (\tau )+n(\tau ))g\left(\tau -t\right)e^{-j[2\pi \eta (\tau -t)]}d\tau$$

(6)

The representation of ${|\mathrm{V}}_f(\eta ,t){|}^2$ in the TF plane is called the spectrogram of signal f. We now want to study the STFT of a multicomponent radar echoes signal of the form:

$$\chi (t)=s(t)+\xi (t)+n(t)$$

(7)

Assuming that it has slow variations on the instantaneous amplitudes and frequencies, we can write the following approximation in the vicinity of a fixed time $t_0$, which amounts to approximate $f$ by a sum of pure waves:

$$\begin{array}{ll}\chi (t)\approx & {\displaystyle \sum _{k=1}^K{\alpha }_m}\left(t_0\right)e^{-2j\pi \left[{\phi }_m\left(t_0\right)+{\phi }_m^{\prime }\left(t_0\right)\left(t-t_0\right)\right]}\\ & +\mu \epsilon \left(t_0\right)\exp \left[j2\pi \psi \left(t_0\right)+{\psi }^{\prime }\left(t_0\right)\left(t-t_0\right)\right]+n\left(t_0\right)\end{array}$$

(8)

The corresponding approximation for the STFT

$$V_f(\eta ,t)\approx {\displaystyle \sum _{k=1}^K{s}_k(t)\widehat{g}}(\eta -\phi {\prime }_k(t))+\xi (t)\widehat{g}(\eta -{\psi }_{\prime }(t))+n(t)\widehat{g}(\eta )$$

(9)

The representation of this multicomponent signal by $V_f\left(\eta , t\right)$ in the TF plane shows that the peaks are concentrated around two so-called ridges, defined by $\eta =\phi {\prime }_k(t)$,$\eta =\psi {\prime }_k(t)$. If frequencies $\phi {\prime }_k(t)$ and $\psi {\prime }_k(t)$ can be separated for different k, each component has a distinct domain in the TF plane. Moreover, SST as a decomposition method can separate and demodulate the different components of signals. Beginning with STFT, the FSST moves the coefficients $V_f\left(\eta , t\right)$ according to the map $\left(\eta ,t\right)\to \left({\widehat{\omega }}_f\left(\eta ,t\right),t\right)$ [21], ${\widehat{\omega }}_f$ is the local instantaneous frequency defined by

$${\widehat{\omega }}_f(\eta ,t)=\frac{1}{2\pi }{\partial }_t\arg V_f(\eta ,t)=\mathcal{R}e\left(\frac{1}{2i\pi }\frac{{\partial }_t{V}_f(\eta ,t)}{V_f(\eta ,t)}\right)$$

(10)

The operator defined in (10) is an approximation for the instantaneous frequency of the received signal at time t, filtered at frequency η. Then, the FSST coefficients are given by:

$$T_f(\omega ,t)=\frac{1}{g(0)}{\displaystyle {\int }_{ℝ}{V}_f}(\eta ,t)\delta \left(\omega -{\widehat{\omega }}_f(\eta ,t)\right)d\eta$$

(11)

where $\delta$ denotes the Dirac distribution FSST, we will use the Hanning window g and assume the signals met the preconditions. The FSST sharpens the information relative to components in the TF plane around the ridges associated with $\phi {\prime }_k(t)$ and $\psi {\prime }_k(t)$. Each component $s_k$ can be recovered by integrating $T_f(\omega ,t)$ around a small frequency band around the curve of $\phi {\prime }_k(t)$ and $\psi {\prime }_k(t)$ associated with the kth component [20].

$$s_k(t)={\displaystyle {\int }_{|f-\phi {\prime }_k(t)|<d}{T}_s^g(f,t)df}$$

(12)

2.2. Proposed Deep Learning Aided Time–Frequency Analysis Filter Framework

The evident benefit of time–frequency transforms is displayed in Figure 1a, the separability of the clutter and target means the clutter elimination methods based on time–frequency maps are reasonable and promising. From the perspective of graphics characteristics, the energy of the target is usually concentrated on a certain frequency, the clutter is usually chaotic. However, it is not straightforward to utilize time–frequency transforms to achieve target detection in HFSWR systems. As the clutter and target may not be discrete, they may overlap and interweave as shown in Figure 1b, we can observe that the coupling appears in the two frequencies. In this case, the performance of the previous ridgelet analysis method [17] is limited, consequently, developing an alternative approach is the main purpose of this study.

In this research, we propose a filter framework (DL-TFF) for suppressing the ionosphere clutter in HFSWR systems. Figure 2 shows the scheme of the proposed framework, which consists of four steps. The first step is radar signal processing. Then, we apply FSST to provide a concentrated time–frequency representation of the received echoes for identifying non-stationary signal components. Next, the time–frequency representation results are as input data of a multi-channel time–frequency feature learning network (MTF). This network accurately captures the difference between clutter and target in time and frequency domains. Hence, our proposed methodology can eliminate the clutter component and find out obscured targets. More precisely, we will introduce the proposed framework according to the following four steps: signal preprocessing, time–frequency representation of the received echoes, echoes components feature learning and model output.

2.2.1. Signal Preprocessing

In the traditional signal preprocessing, the raw radar returns are filtered, amplificated, demodulated, pulse compression performed and beamformed. After the above-mentioned steps, the global threshold normalization is proposed for avoiding the noise seriously damaging the detection results. We search for the maximum value of a batch of time domain experimental data, which contains all the range bins. We donate the maximum value of batch data as $Ma{x}_{vu}$, and $Ma{x}_{vu}$ is normalized. Consequently, the remaining data in this batch is mapped into [0, 1].

2.2.2. Time–Frequency Representation of the Received Echoes

After the signal preprocessing, we apply the FSST to achieve the time–frequency analysis of received echoes, because FSST can accurately estimate the variation of signal frequency with time. We select the time domain data with a given range cell as input data to perform FSST.

In the FSST, the (6), (9) and (10) are applied to each batch of data for generating the multiple univariate multicomponent TF planes with high resolution in both time and frequency. The used FSST is established assuming g as a Hanning window, which has a smaller order characteristic and makes the signal decrease more sloping, thereby making the impulse responses faster for amplitude up and down [26,27,28]. The output data size of the FSST is $320\times 320$ and then we select $320\times 5$ data as the input data of the designed learning network.

2.2.3. Feature Learning of Different Types of Echo Components

The basic idea of feature learning is to mine the discriminative information of both clutter and target in time–frequency map. The structure diagram of the designed MTF learning network consists of five inception modules. We firstly select ionosphere clutter echo data, target echo data and noise data as training sets, and these samples are manually labeled. As for the target echo, the amplitude value on the output spectrum is unchanged and the size of the selected data set is $320\times 5$.

Obviously, the training data set is not sufficient for distinguishing the targets from clutter, hence, a data augmentation approach is adopted in this study. We propose two different schemes by considering the difference in data distribution in heterogeneous scenes. Specifically, aiming at augmenting the target data, we generate the new targets by randomly moving the known targets, the new targets can be placed in arbitrary range-Doppler cells. The range-Doppler cells of removed targets will not have a target sample. Aiming at augmenting the compounded data, we immerse the simulated targets into the real ionosphere clutter, some simulated targets are placed at the edge of the clutter contamination region, and some simulated targets are totally sunk into the clutter contamination region.

Considering the moving target echoes and rapidly changing clutter scenes, we apply five inception modules and they are stacked on top of each other. The design philosophy of the inception architecture is based on exploring how an optimal local sparse structure in a convolutional vision network can be approximated and covered by using available dense components [29]. An inception module consists of four branches, which are convolved with different filters, and finally spliced the learning feature together. Intuitively, convolution with multiple scales can simultaneously extract the features of different scales. Moreover, using the principle of sparse matrix decomposition into dense matrix calculation to speed up convergence [29]. Since the combination of features with strong correlation can accelerate the convergence of the DNN network.

During the collection of original echo data, we find the ionosphere clutter has different distribution characteristics in the range-Doppler (RD) spectrum. Hence, the convolution kernels are designed in different sizes, $19\times 1$, $11\times 3$, $3\times 3$, $1\times 1$, which are propitious to capture the ionosphere clutter characteristics from the time–frequency representation results. The output correlation statistics of these inception modules are bound to vary, such as the features of higher abstraction are captured by higher layers. For decreasing the computational resources, some inception modules are restricted to filter sizes $1\times 1$, which can achieve dimension reductions and projections. Observing from Figure 2, the $1\times 1$ convolution is used before the other types of convolutions. Moreover, the utilization of $1\times 1$ also can rectify linear activation. When more convolution is superimposed on the sensing field with the same size, richer features can be extracted.

In addition, the designed convolution kernel with a bigger size has fewer filters for decreasing the computational expense, as shown in Figure 2, the number of $11\times 3$ filters and $19\times 1$ filters is 32, the number of smaller $3\times 3$ filters is 64. Furthermore, the max-pooling layers with stride 2 in inception modules are used to halve the resolution of the grid. Finally, besides using two max-pooling layers, a dropout layer is added to increase the robustness of the model and a full connection layer maps the learned “distributed feature representation” into the sample label space. The objective of training a designed network is to minimize the contrastive loss, as shown in the following:

$${\mathcal{l}}_{\mathrm{loss}}=\frac{1}{2}{{\displaystyle \sum _{p=1}^{HWC}\left(t_p-y_p\right)}}^2$$

(13)

The loss function of the regression layer is half-mean-squared-error. Where H, W, and C represent the height, width and the number of output channels, respectively, and p indexes into each element of t and y linearly.

3. Results

3.1. Data Sets

The DL-TFF framework is trained and tested by using a real data set. These data are collected from an HFSWR system, located in Weihai, China. The main parameters information of the HFSWR system is shown in

Table 1. The related parameters of the applied HFSWR system.

Properties	Specification
Frequency bandwidth	60 kHz
Carrier frequency	4.7 MHz
Coherent integration time	144 s
Waveform	FMICW
Range resolution	1.5 km
Doppler frequency resolution	6.5 mHz
Transmit power	8 kW
Antenna system	Uniform linear monopole array

.

In order to visually observe the behavior of the ionosphere clutter, Figure 3 shows the range-time-intensity (RTI) plots for the HFSWR returns over approximately a 24 h interval with a specific operating frequency. Many types of ionosphere clutter can be observed during this long period, including specular reflection from the E-layer, multiple bounces by the E-layer, spread F-region ionosphere clutter and specular reflection from the F-layer. We can also find that the spread F-region ionosphere clutter with strong echoes energy is the main clutter at night. This kind of ionosphere clutter must cover many targets. In the daytime, there is little E-layer specular reflection clutter with relatively weak energy.

In this study, we select the two representative types of ionosphere clutter as analyzed objects, they are specular reflections from the E-layer and spread F-region ionosphere clutter.

3.2. The Parameter Analysis of Time–Frequency Representation

In this design process, the STFT uses the Hanning window and we analyze the FSST results with different sizes of Hanning window. The range of window sizes can be observed in Figure 4. We can find that the window size has a considerable effect on the representation results. When the window size is too small, the FSST cannot improve the definition around each ridge, the ridges of each component are interwoven. When the window size is too large, the ridges of different components are adjoining. We cannot distinguish the target components and clutter components, thereby failing to select the characteristic information. We find an optimal range [160, 200] of window size len after comparing the performance of FSST with different window sizes. In this article, we set the window size is 160 for a series of experiments.

3.3. Time–Frequency Representation of Radar Received Echoes

In the process of time–frequency representation of the received echoes, we successively perform the STFT and FSST to explore the differences between the targets and ionosphere clutter through experiments. We select the different types of clutter, including the specular E-layer reflection clutter, multiple bounces from the E-layer, spread E-layer ionosphere clutter and spread F-layer ionosphere clutter.

3.3.1. The Time–Frequency Analysis of Targets Echoes

The radar returns of complex objects (ships, aircrafts, ionosphere and sea surface) in the optical region depend on the frequency and the angle of illumination. The target signal detection in a nonhomogeneous environment is an important and fundamental problem for developing radars [30]. Therefore, the time–frequency analysis of target echoes is especially important. We first select the real target echoes as analysis objects, STFT is first calculated with (6). Figure 5a shows the amplitude of STFT of the real target echoes, using the Hanning window with $len=160$. Next, FSST is calculated by using (10), we can observe that the ridges of real targets are distinctly sharpened, showing as straight lines in the time–frequency plane. The representation information of targets concentrates on a few frequencies. To explore the FSST further, we simulate two targets that are next to each other in the RD spectrum. Although these two simulated targets are performed STFT, they still fuse together and cannot be separated. After performing the FSST, as shown in Figure 5b, each simulated target occupies a distinct domain of the TF plane, which fully proves selecting FSST is a promising idea.

3.3.2. The Time–Frequency Analysis of Ionosphere Clutter

Figure 6 shows the amplitude of FSST of the received radar echoes, using the Hanning window with $len=160$. We select the specular E-layer reflection data in a fixed range cell, the range cell is 64.5 km. This echoes data received in August 2021. It can be observed that STFT concentrates the information around the ridges that correspond to the time-varying frequency. The representation of information of the clutter is dispersed in a little wide region. Next, FSST is calculated by using (10). Figure 6b shows that FSST improves the definition of each ridge, which offers a more accurate identification of the components in the time–frequency plane. The time–frequency representation of each component has ideal resolution, which contributes to extracting the characteristics information for the following MTF learning network.

As the specular E-layer reflection and multiple bounces from the E-layer clutter usually occupy a few range cells and a large number of Doppler cells, which are suitable for frequency separation. For exploring the robustness of the FSST, we select the spread clutter in both the E-layer and the F-layer. The spread clutter from the E-layer is selected from Figure 7a, the fixed range cell is 120 km. The data of spread clutter from the F-layer is selected at the range of 249 km. From Figure 7, we can observe that the representation of spread clutter in the time–frequency plane is evenly concentrated around many ridges. These ridges occupy the most area of the TF plane and no entirely straight ridges are available. FSST has an obvious advantage when separating the frequencies.

The echoes energy of both the banded ionosphere clutter and spread ionosphere clutter is relatively uniformly distributed over the contaminated area. In Figure 8, we should note that the uneven ionosphere clutter looks like some scattered targets in the RD spectrum, such as the ionosphere clutter in the yellow circle. The uneven ionosphere clutter may be viewed as some targets after performing the STFT. When using the FSST, each ridge can be accurately identified in the time–frequency plane, the information relative to uneven clutter components in the TF plane around the ridge is markedly different from the targets.

According to the long-term observations, some range cells are usually contaminated, which may cover vessels and aircraft. After performing the FSST, the size of the training set is $320\times 320$, we choose five frequency points on a time–frequency representation results map, thereby the size of input training data is $320\times 5$ and the training set contains 3072 batches of training data. As each target always occupies 320 time units, ranging from 1 to 3 frequency units. The network uses a $320\times 5$ window to perform a slide-window calculation on a whole picture, which can significantly decrease the amount of time and the calculation cost. The test set contains 500 batches of training data. For the convenience of analysis, the simulated target signal is added to the clutter as mixed samples.

3.4. Model Training Details

In the training process, a total of 3072 samples are collected from four batches of received echoes data, the time range is about ten minutes. The training set and the test set are independent, which effectively adjusts the specific structures of the designed network. The related parameters of the overall structural properties of designed networks are listed in

Table 2. Network hierarchy and related parameters of the DL-TFF framework.

Blocks	Layer	Filter Size	Stride	Padding	Output Size
Input	Input				320 × 5 × 128
	Conv 5 × 5	5 × 5 × 32	1, 1	Same
	ReLU1
	Conv 3 × 3	3 × 3 × 128	1, 1	Same
	ReLU2
	crossChannelNorm
Inception 1	Inception				320 × 5 × 160
	depthConcatenation		2, 1	Same
	maxpool 3 × 3
Inception 2	Inception				80 × 5 × 160
	depthConcatenation		2, 1	Same
	maxpool 3 × 3
Inception 3	Inception				80 × 5 × 160
	depthConcatenation		2, 1	Same
	maxpool 3 × 3
Inception 4	Inception				40 × 5 × 160
	depthConcatenation		2, 1	Same
	maxpool 3 × 3
Inception5	Inception				20 × 5 × 160
	depthConcatenation		2, 1	Same
	maxpool 3 × 3
	Conv 3 × 3	3 × 3 × 32	1, 1	Same	2 × 1 × 32
	ReLu
	Maxpool 5 × 5
Output	Dropout 40%				1
	Full
	connected (1)
	Regression

. Furthermore, the specific parameters of the designed inception module are listed in

Table 3. Related parameters of designed inception module.

Channel	Layer	Filter Size	Stride	Padding	Output Size
Channel 1	Conv 1 × 1	1 × 1 × 32	1, 1	Same	320 × 5 × 32
	ReLU
Channel 2	Conv 1 × 1	1 × 1 × 64	1, 1	Same	320 × 5 × 64
	ReLu
	Conv 3 × 3	3 × 3 × 64	1, 1	Same
	ReLu
Channel 3	Conv 1 × 1	1 × 1 × 16	1, 1	Same	320 × 5 × 32
	ReLu
	Conv 11 × 3	11 × 3 × 32	1, 1	Same
	ReLu
Channel 4	Conv 1 × 1	1 × 1 × 16	1, 1	Same	320 × 5 × 32
	ReLu
	Conv 19 × 1	19 × 1 × 32	1, 1	Same
	ReLu

. In addition, the max epoch is set as 500, the batch size is set as 200 and the learning rate is set as 10⁻⁴.

3.5. The Global Region Suppression Results of Ionosphere Clutter by Using Proposed Framework

In this section, we present the analysis of two different ionosphere clutter, they are specular reflection ionosphere clutter and spread ionosphere clutter. First, the proposed methodology is used for the specular reflection ionosphere clutter collected from HFSWR. Second, the proposed methodology is used for the spread ionosphere clutter. For both cases, the performance of the proposed methodology is compared with the previous method proposed by Su et al.

3.5.1. The Suppression Results of Specular Reflection Ionosphere Clutter

In the specular reflection ionosphere clutter experiment, as shown in Figure 9, we select a batch of received echoes data with specular reflection contamination. In order to assess the effects of the proposed methodology, we add some simulated targets into real ionosphere clutter contaminated regions with a random distribution. The SNR of found targets is 20 dB, 15 dB and 10 dB from far and near. From Figure 9c, the covered targets can be identified after using the proposed methodology and we mark them in yellow circles. Moreover, we also find that the sea clutter and ground clutter are slightly suppressed. This phenomenon can be attributed to the fact that the sea clutter and ground clutter are relatively stable in time-scale (TS) planes, but the motion of ocean waves and the multipath effect lead to the broadening of sea clutter and ground clutter. When the frequencies $\phi {\prime }_k(t)$ and $\psi {\prime }_k(t)$ are not separated enough when k varies, each mode does not occupy a distinct domain, failing to be thoroughly separated. Therefore, the suppression effect of sea clutter and ground clutter by using the proposed methodology is not obvious. The proposed methodology is aimed at the ionosphere clutter with obvious time-varying characteristics, so the suppression effect of ionosphere clutter is ideal.

However, the performance of the method proposed by Su et al. is not satisfactory. The ionosphere clutter is not thoroughly eliminated, but the covered targets can be ferreted out. The interesting phenomenon from Figure 9b is that all kinds of clutter are broadened after suppression. The reason for these unexpected results is that ridgelet analysis can raise the sidelobe of the signal.

3.5.2. The Suppression Results of Spread Ionosphere Clutter

In the spread ionosphere clutter experiment, as shown in Figure 10, we select a batch of received echoes data with a large contamination area. To verify the validity of the proposed method, we add many simulated targets into real ionosphere clutter contaminated regions with a random distribution. From Figure 10c, it is evident that targets emerge after suppressing the clutter, and we mark these exposed targets in yellow circles. From 120 km to 285 km and −0.80 Hz to 0.91 Hz, the obscured targets with different echo energies are found, and the contaminated regions are clean. The results of the global region experiment demonstrate that our proposed methodology provides significant help in discriminating a target signal from clutter. Figure 10b displays the suppression results of the compared method. The spread ionosphere clutter cannot be suppressed, but the energy of some areas is weakened, accordingly, the covered targets can be found. Undoubtedly, the number of exposed targets using compared method is less than that using the proposed methodology.

4. Discussion

4.1. The Suppression Results Comparison of Local Stable Ionosphere Clutter

For analyzing the effectiveness of the proposed method, we design a local region experiment. We also select related clutter suppression methods proposed by Su et al., as compared methods. In the local region experiment, we select a range cell as the local test region and the range of this region is 180 km. Figure 11 shows two kinds of time–frequency maps of a batch of echoes under the same background. In the yellow circles of Figure 11, we can observe that the STFT time–frequency representation map of clutter may look like a target. After performing SST, we reasonably conclude that FSST has higher frequency separation ability compared with STFT. However, some stable frequency points may be viewed as potential targets, which need to be verified by using powerful learning tools. The designed multi-channel learning network is utilized to extract the feature of time–frequency representation and learn the difference and similar characteristics for identifying them. The final results of the proposed methodology are also shown in Figure 11, the compared method cannot ideally suppress the clutter, which means that this method mistakenly regards the stable clutter as the target. DL-TFF framework has the ability to suppress clutter, but it also detects some false targets, such as the clutter with 0.466 Hz. The distribution of clutter is not always rapidly changing, which is the main reason for the degradation of previous method performance.

4.2. The Suppression Results Comparsion of Local Region Ionosphere Clutter

Moreover, we compare the performance of the proposed methodology and compared the method termed “Ridgelet”. The suppression results of the DL-TFF framework and Ridgelet analysis method at a specific range bin have been given in Figure 12. When the Doppler frequency is about −0.18 Hz, “Ridgelet” cannot find out the obscured targets, proposed DL-TFF framework can reveal this covered target. Moreover, the compared method always decreases the magnitude of real targets when suppressing the ionosphere clutter. Our proposed DL-TFF framework almost perfectly preserves the magnitude of real targets, sometimes may increase the magnitude of real targets, thereby the SCR of found targets is also increased. Obviously, the proposed method has a more thorough suppression effect and makes more obscured targets emerge.

4.3. Analysis of Detection Properties

We add a simulated target into 100 batches of ionosphere clutter data with a certain range cell for evaluating the detection probability of the proposed methodology. The detection performances of different methods are given by Monte Carlo simulations of 100 trials. The detection problem can be formulated as a classical binary hypothesis test model, this model can be described as:

$$\left\{\begin{array}{l}{H}_0:y=C_{\mathrm{CUT}}+N,y_k=C_k,k\in \Phi \hfill \\ H_1:y=s+C_{\mathrm{CUT}}+N,y_k=C_k,k\in \Phi \hfill \end{array}\right.$$

(14)

where $C_{\mathrm{CUT}}$ is the real ionosphere clutter at a certain range cell, s represents the target, f_d is the normalized target Doppler frequency and $f_d=-0.3 \mathrm{Hz}$. $k=1,2,\dots ,K$ for each range cell k, K is the total number of training samples.

The detection is made by the well-known OS-CFAR (ordered-statistic constant false-alarm rate) detector [31]. The given false alarm probability $P_{fa}={10}^{-2}$. The performance analysis is given by detection probability $P_d$ against the SCR. As shown in Figure 13, the detection probability under the situation of different clutter environment is displayed. We can observe that the proposed methodology is superior to the compared method, we express the compared method as “Ridgelet” in Figure 13. We can find that the proposed methodology always has better results in the varying ionosphere clutter. The surprising phenomenon is that the “Ridgelet” even has worse detection results compared with the original RD spectrum. This phenomenon can be attributed that the “Ridgelet” only distinguishes the ionosphere clutter and targets, it cannot effectively find targets submerged in clutter. The proposed methodology can expectedly expose the covered targets under the case of low SCR.

5. Conclusions

In this article, we proposed a cooperative ionosphere clutter filter framework, which consists of a type of neoteric time–frequency transform and a multi-channel feature learning network. This proposed framework firstly captures the distinction of both variation trend and magnitude scale in the time–frequency representation map of different echo components. Then, the proposed framework learns both the unapparent distinctions and occasional similarities of the different types of echo components. The proposed framework and compared method have been applied to real HFSWR data. As predicted, the proposed framework felicitously eliminates the different types of ionosphere clutter and finds out the targets coupling with clutter, which overcomes the shortcoming of the compared method. Moreover, the proposed methodology can effectively reduce the clutter power by more than 30 dB according to Figure 12, at the same time, it also can improve the detection probability of a target signal with a low SNR (0 to 10 dB) according to Figure 13. Generally, the proposed framework has more ideal suppression effects and enhances the detection ability of obscured targets. In future work, we will use the proposed methodology to suppress the ionosphere clutter in the skywave OTHR system. Moreover, we also plan to enlarge the feature information dimensionality of the learning network, the spatial information will be simultaneously explored by designing novel learning networks.