# Weak Target Detection within the Nonhomogeneous Ionospheric Clutter Background of HFSWR Based on STAP

Authors: Xin Zhang; Qiang Yang; Weibo Deng
Journal: International Journal of Antennas and Propagation
 (2013)

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## Abstract

High Frequency Surface Wave Radar (HFSWR) can perform the functions of ocean environment monitoring, target detection, and target tracking over the horizon. However, its system's performance is always limited by the severe ionospheric clutter environment, especially by the nonhomogeneous component. The nonhomogeneous ionospheric clutter generally can cover a few Doppler shift units and a few angle units. Consequently, weak targets masked by the nonhomogeneous ionospheric clutter are difficult to be detected. In this paper, a novel algorithm based on angle-Doppler joint eigenvector which considers the angle-Doppler map of radar echoes is adopted to analyze the characteristics of the nonhomogeneous ionospheric clutter. Given the measured data set, we first investigate the correlation between the signal of interest (SOI) and the nonhomogeneous ionospheric clutter and then the correlation between the nonhomogeneous ionospheric clutters in different two ranges. Finally, a new strategy of training data selection is proposed to improve the joint domain localised (JDL) algorithm. Simulation results show that the improved-JDL algorithm is effective and the performance of weak target detection within nonhomogeneous ionospheric clutter is improved.


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## Body

## 1. Introduction

HFSWR exploits the surface wave mode of vertical polarization electromagnetic wave propagating over the sea water to detect ships and aircrafts at distances beyond the line of sight. It has drawn much attention in recent years for its notable features of large scale, long distance, and all-day adaptability. In general, the factors which affect the performance of HFSWR are the sea clutter, ionospheric clutter, radio interference, and noise, among which, the key factor that determines targets detection performance is the ionospheric clutter [1]. The situation herein is very complex, since the motion states of the ionosphere are distinct at different temporal and spatial locations. Until now, a widely accepted model for the ionospheric clutter in HFSWR is still not found. It follows that how to suppress the ionospheric clutter and how to improve the weak target detection performance in HFSWR systems are hot topics worth further investigation.In HFSWR systems, long coherent integration time is necessary for better detection performance and higher Doppler resolution. During this process, the state of the ionosphere is changing rapidly and irregularly, which leads to an obvious problem that the ionospheric clutter can cover a few Doppler shift units after the coherent integration. Therefore, it is difficult for the frequency domain adaptive matched filtering algorithm to detect the weak targets buried in the ionospheric clutter. On the other hand, both the beam-broadening effect resulting from the smaller array aperture compared to the wavelength, and the regional characteristic of ionosphere can lead to the fact that ionospheric clutter always covers a broad angular region. Consequently, the ionospheric clutter is difficult to be suppressed either in the Doppler domain or in the angle domain.Space-time adaptive processing (STAP) is proposed by Brennan and Reed in the 1970s and has become one of the major research directions around the world [2]. It has been mainly exploited to suppress homogeneous and nonhomogeneous clutters in airborne radar systems in the Doppler-angle domain [3–6]. It also has been applied in many other specific applications, both in military and civil fields, such as spaceborne radar, communication, sonar, navigation, and microphone array [7, 8]. In HFSWR systems, STAP has been adopted to counter the sea clutter in shipborne radar systems [9] and suppress the ionospheric clutter in shore-based radar systems.Groups led by Fabrizio and Adve have begun to investigate the problem of ionospheric clutter suppression based on STAP and obtained a bulk of measured data [10–13]. In [13], Ravan et al. developed a new model to predict the radio wave propagation in ionosphere plasma density irregularities, and it turns out that their model fits the data gathered in Canada well. Ravan and Saleh et al. also analyzed a group of STAP algorithms such as joint domain localized, direct data domain, hybrid, PAMF, and further a new proposed fast algorithm FFA [13, 14]. Joint domain localized (JDL) is a classical statistical STAP algorithm broadly used in airborne radar [15]. It features preferable low computational cost and high performance in homogeneous clutter suppression. Especially for the clutter with independent and identical distribution, JDL is highly effective. But in HFSWR, the ionospheric clutter is nonhomogeneous. It is always difficult to obtain enough training data for JDL. Direct data domain (D3), hybrid, and PAMF are classical STAP algorithms for nonhomogeneous clutter in airborne radar systems. These algorithms suffer from high computational cost and poor real-time performance in HFSWR due to the long coherent integration time (CIT) and large space-time dimension. FFA is also a low computational cost algorithm, but how to divide the space-time region is still under investigation.In this paper, we first analyze the correlation between the SOI and the nonhomogeneous ionospheric clutter; and then, the correlation between the nonhomogeneous ionospheric clutters at two different ranges has been analyzed. On this basis, we propose a new strategy to select the training data set. By means of the reasonable training data selection, the nonhomogeneous ionospheric clutter can be suppressed more effectively. Meanwhile, weak targets in the direction of ionospheric can also be detected.In Section2, we first analyze the correlation including the correlation between the SOI and the nonhomogeneous ionospheric clutter and the one between the nonhomogeneous ionospheric clutters at two different ranges. In Section 3, we proposed an improved-JDL algorithm according to the analysis results given in Section 2. Finally, the superiority of the improved-JDL algorithm is demonstrated via simulation based on practically measured data.


## 2. Characteristic Analysis of Nonhomogeneous Ionospheric Clutter

In HFSWR, the electromagnetic waves travel not only mainly over the sea surface but also partly into the sky due to nonidealities of the receiver antenna array. Under certain conditions, the electromagnetic waves emitted into the sky can be reflected by the ionosphere and then received by the nonideal receiver antenna array. This is how the ionospheric clutter emerges. The ionospheric clutter is very intricate as a result of the nonhomogeneous layered structure and the rapidly changing state of the ionosphere. For these reasons, ionospheric clutter suppression is a critical difficulty in HFSWR. The study of ionospheric clutter suppression depends heavily on the understanding of the characteristics of ionospheric clutter.Firstly, we analyze the characteristics of the ionospheric clutter. The measured data is obtained through the HFSWR system in Weihai, China on May 12, 2012, and then processed by matched filters in range, Doppler, and digital beam-forming in turn. A range-Doppler map in one beam is shown in Figure1, and an angle-Doppler map in one range bin is shown in Figure 2.Figure 1
Range-Doppler Map.Angle-Doppler Map.
(a)
200 km
(b)
350 kmIn STAP, the data is processed on the basis of the angle-Doppler map. In this case, characteristics of the nonhomogeneous ionospheric clutter should be analyzed based on the angle-Doppler map.In Figure2, the nonhomogeneous ionospheric clutter covers a large region of the angle-Doppler map. It does not make any sense to analyze such a broad region. So we divide the whole angle-Doppler region into small scales, and the characteristic analysis of the nonhomogeneous ionospheric clutter should also be in the light of the small local angle-Doppler region. We call this small local region the Angle-Doppler Local Region (ADLR). The analysis in Section 2 is solely concentrated on the concept of ADLR.In Section2.1, we have to decide what the appropriate size of ADLR is in order to make sure that the clutter in the ADLR is simple.We supposeXl is an ADLR sequence for l=0,1,2,… of independent range samples as discussed in the literature [2]. But the sample in one range bin may relate with some samples in other independent range bins.In Section2.2, we propose the correlation analyzing method based on the angle-doppler joint eigenvector (ADJE) of ADLR.Based on the correlation analyzing method in Section2.2 and the size of ADLR decided in Section 2.1, we analyze the SOI correlation in the noise environment (in Section 2.3) and in the ionospheric clutter environment (in Section 2.4).In the last Section2.5, we analyze the ionospheric clutter correlation between ADLRs in different range bins.


### 2.1. Size of the ADLR

In this part, we try to make an appropriate decision of the size of ADLR in order to make sure that the clutter in this ADLR is as simple as possible. If the data in the ADLR are with high correlation both in beam-domain and frequency-domain, we can consider the clutter in the ADLR simple.The correlation coefficient of the data with two different beams can be calculated by (1); The correlation coefficient of the data with two different Doppler shifts can be calculated by (2):
(1)ρk,j=(1/Nr)∑rXk(r,fd0)Xj*(r,fd0)(1/Nr)∑r|Xk(r,fd0)|2(1/Nr)∑r|Xj*(r,fd0)|2,(2)ρfd1,fd2=(1/Nr)∑rXfd1(r,φ0)Xfd2*(r,φ0)(1/Nr)∑r|Xfd1(r,φ0)|2(1/Nr)∑r|Xfd2*(r,φ0)|2,
where r indicates the index of range bins, Nr is the number of range bins which are used to calculate the correlation coefficient, Xk and Xj are the training data with direction k and j with Doppler shift fd0,(·)* is the complex conjugate operator, and Xfd1 and Xfd2 are the training data with Doppler shift fd1 and fd2 with direction φ0.We analyze the angle correlation with different angle intervals as given by (1). The results are shown in Figure 3.Correlation coefficients with different beam intervals.
(a)
Range = 200 km
(b)
Range = 200 km,fd0 = −1.2 HzFigure3(a). The ionospheric clutter exists within the Doppler shifts between −2 Hz and 0.12 Hz. The correlation coefficient at beam interval 5° is greater than the ones when the beam intervals are 10° and 15°.Figure3(b). The correlation coefficient decreases as the beam interval increases. We can deduce from these two figures that the ionospheric clutters have similar characteristics when the beam interval is narrower than 5°.We also analyze the Doppler frequency correlation with different Doppler shift intervals as given by (2). The results are shown in Figure 4.Correlation coefficients with different Doppler shift intervals.
(a)
Range = 200 km
(b)
Range = 200 km,φ0 = −10°Figure4(a). The ionospheric clutter exists within all the angles ranging from −30° to 30°. The correlation coefficient achieves its maximum when the Doppler shift interval is 34 mHz. The ones when the Doppler shift intervals are 68 mHz and 102 mHz are almost the same and both less than the one with 34 mHz.Figure4(b). The correlation coefficient decreases as the Doppler shift interval increases. From these two figures, we can also deduce that the ionospheric clutters have similar characteristics when the Doppler shift interval is less than 34 mHz.In order to maintain the characteristics of ADLR, correlation coefficients within the ADLR data must be high enough. It follows that the size of ADLR cannot be too large. Synthetically, it is preferable to choose the ±5°, ±34 mHz interval around the cell under test. This is in agreement with the radar theory that correlation coefficient increases as the beam interval and Doppler shift interval decrease.


### 2.2. Correlation Analysis Method Based on ADJE

In the case of HFSWR, the data in an ADLR cannot be absolutely simple. An ADLR often consists of multiple echo components such as noise, clutter, interference, and targets. The characteristics of ADLRs with different echo components are different. In this part, we mainly analyze the correlation between ADLRs with different echo components.We first calculate the self-correlation matrix of the data in one ADLR and then obtain the ADJEs through the decomposition of the covariance matrix. In this case, the characteristic of the ADLR is represented by the vector sum of the ADJEs. The following correlation analysis is based on the ADJEs representation.Firstly, we choose the ADLR which covers ±5° (3 beams) and ±34 mHz (3 Doppler shifts) in one range bin and a9×1 vector Xr can be written by Kronecker product. So the self-correlation matrix is 9×9, and we can get 9 ADJEs by eigen decompostion. A certain number of ADJEs which make greater contribution to represent the characteristics of the ADLR are selected to calculate the correlation coefficient.The correlation analysis method based on ADJE is as follows.(i)
Calculate the self-correlation matrixRx of the data Xr in the ADLR with rth range bin by Rx=XrHXr.(ii)
Eigen-decomposeRx to obtain 9 eigenvalues λ1,λ2,…,λ9 and 9 ADJEs ξ1,ξ2,…,ξ9, then the normalized ADJEs by ξ-i=ξi/|ξi|,i=1,…,9.(iii)
Determine the contribution of the normalized ADJEsλi(ξ-i,Xr), i=1,2,…,9;(iv)
Choose the normalized ADJEς which makes the greatest contribution for Xr. And ς can represent the characteristic of  Xr. In the case of HFSWR, especially for the Es layer ionospheric clutter, there may be more than one kind of clutter component that exists in an ADLR. Hence, for uncorrelated clutters, there may be two or more dominant normalized ADJEs, and the vector sum of the ADJEs is introduced to represent the characteristics of this ADLR.(v)
Repeat the above procedure; we can obtainK normalized ADJEs ςi, i=1,2,…,K in K different range bins.(vi)
Calculate the correlation coefficients utilizing theK normalized ADJEs ςi, i=1,2,…,K from step (v) by
(3)ρij=ςiHςj,i,j=1,2,…,K.


### 2.3. SOI Correlation in the Noise Environment

The following analysis is based on the assumption that the noise in HFSWR is Gaussian. We consider two ADLRs: one is with SOI only, and in the other one there exist both SOI and noise, and the signal-to-noise ratio (SNR) is changing.Gracheva and Cerutti-Maori have analyzed the channel correlation of sea data and have mentioned the relationship between channel correlation and the clutter to noise ratio (CNR) [16]. CNR is defined as
(4)CNR=(1/Nr)∑r∥Xc(rc)∥2σn2.We consider the ADLR in a single range bin(Nr=1). The CNR in this ADLR can be defined as
(5)CNRADLR=∥Xc(rc)∥2σn2.The SNR is defined as(6)SNR=∥Xt(rt)∥2σn2.We can replace the CNRADLR in the literature [16] with the SNR as
(7)ρ=11+1/SNR.We analyze the correlation between two ADLRs (ADLR1 and ADLR2) by utilizing the algorithm introduced in Section 2.2. The relationship between correlation coefficient and the SNR is obtained via 10000 Monte-Carlo trials.Under the condition that there are only SOI in ADLR1 and only Gaussian noise in ADLR2, the correlation between ADLR1 and ADLR2 is shown as the red dotted line in Figure 5. The correlation coefficient is kept at a low level. This result is consistent with the radar theory that the SOI is uncorrelated with the noise.Figure 5
The relationship between correlation and SNR.In this case, there are both SOI and noise in ADLR2, and the SNR is variant. The simulation result by (7) is shown as the green dotted line with marker “*” in Figure 5. The correlation coefficient is very close to 1 when the SNR is greater than 20 dB and very close to zero when the SNR is less than −20 dB. When SNR∈[-20,20] dB, the correlation coefficient increases as the SNR increases.We make a similar analysis with the measured data in ADLR2. The result is shown as a blue solid line in Figure 5. Compared to the simulation results, the correlation coefficient decreases faster as the SNR decreases and the correlation coefficient is greater than zero when the SNR is less than 0 dB. The reason for this error is that the characteristics of SOI and noise could be both reflected in ADLR2 when the SNR is small.In light of the error present in the above analysis, we modify the equation as follows.We mark the ADLR1 which only contains SOI1 as SD1 and the Doppler-angle data as Zt; we also mark the ADLR2 which contains SOI2 and Gaussian noise as SD2 and the Doppler-angle data as Zsn, and the power of the noise is σ2. We calculate the normalized ADJEs of ADLR1 and ADLR2 utilizing Zt and  Zsn for ξt and ξsn, respectively. So ξsn can be written as
(8)ξsn≈λtξt′+σ2ξnλt2+σ4,
where λt is the eigenvalue of SOI2, ξt′ is the eigenvector of SOI2, and ξn is the eigenvector of noise.So the correlation coefficient can be written as(9)ρ=ξtHξsn≈ξtH·λtξt′+σ2ξnλt2+σ4=λtλt2+σ4·11+1/SNR+σ2λt2+σ4·ρsn,
where ξtHξt′=1/(1+1/SNR), ρsn is a statistical value related to the SOI and distribution of the noise, ρsn=ξtHξn.When SOI2 is dominant in SD2, ξsn≈ξt′, the correlation coefficient is ρ=ξtHξt′=1/(1+1/SNR).When noise is dominant in SD2, ξsn≈ξn, correlation coefficient is ρ=ξtHξn=ρsn.The simulation result based on (9) are shown as a black dot-dash line in Figure 6 fits the measured data much better than the simulation result given by (7) does.Figure 6
The relationship between correlation and SNR.


### 2.4. SOI Correlation in the Ionospheric Clutter Environment

We mark the ADLR1 which only contains SOI1 as SD1 and the Doppler-angle data as Zt(rt); we also mark the ADLR3 which contains SOI2 and the ionospheric clutter as SD3 and the Doppler-angle data as Zc(rc), and rt and rc are the range bins of SD1 and SD3. The SCR of SOI2 and the ionospheric clutter are written as
(10)SCR=∥Zt(rt)∥2(1/Nr)∑r∥Zc(rc)∥2.We analyze the SOI correlation in the ionospheric clutter background as in Section2.3. We can get the following:
(11)ρ={11+1/SCR,forSCR>HSCR,ρsc,forSCR<LSCR,λtλt2+λc2·11+1/SCR+λcλt2+λc2·ρsc,others,
where ρsc is the correlation coefficient between SOI and the ionospheric clutter, λt and λc are the eigenvalues of SOI2 and the ionospheric clutter in ADLR3, and LSCR and HSCR are the upper limit and lower limit of SCR, respectively, and they are related to the characteristics of the ionospheric clutter.The correlation of SOI in the ionospheric clutter environment utilizing the measured data at the range of 180 km and 185 km is shown in Figure7.The relationship between correlation and SCR.
(a)
Range = 180.00 km
(b)
Range = 185.00 kmIf there is only ionospheric clutter in ADLR3, the correlation coefficients between ADLR1 and ADLR2 are shown as a red-dotted line. It is related to the characteristic of ionospheric clutter and has different values at different ranges. The result of correlation analysis utilizing measured data is shown as a blue solid line. And the result calculated by (11) fits the measured data well.It can be seen from (11) and Figure 7 that the relationship between correlation and SCR can be divided into three parts:(a)
the correlation coefficient keeps  a low value when the SCR is small, and it mainly depends on the characteristics of the ionospheric clutter;(b)
when the SCR is large enough, the correlation coefficient is close to 1;(c)
when the SCR is an intermediate value, the correlation coefficient is related not only to the SCR but also to the characteristics of SOI and ionospheric clutter.


### 2.5. Range Correlation of Nonhomogeneous Ionospheric Clutter

The motion of ionosphere is complex with the major factor of nonuniform plasma. Due to this complex motion, the ionospheric clutter in HFSWR is nonhomogeneous.We calculate the correlation coefficients of ADLRs in different ranges within 150 km to 430 km referred to 225 km at the Doppler shift −1.2 Hz utilizing the algorithm mentioned in Section2.2. The result is shown in Figure 8. The correlation of nonhomogeneous ionospheric clutter decreased as the range interval increased. But there may be a few high correlated range data due to the nonhomogeneous characteristics of the ionospheric clutter.Figure 8
Range correlation of ionospheric clutter at −1.2 Hz.


## 2.1. Size of the ADLR

In this part, we try to make an appropriate decision of the size of ADLR in order to make sure that the clutter in this ADLR is as simple as possible. If the data in the ADLR are with high correlation both in beam-domain and frequency-domain, we can consider the clutter in the ADLR simple.The correlation coefficient of the data with two different beams can be calculated by (1); The correlation coefficient of the data with two different Doppler shifts can be calculated by (2):
(1)ρk,j=(1/Nr)∑rXk(r,fd0)Xj*(r,fd0)(1/Nr)∑r|Xk(r,fd0)|2(1/Nr)∑r|Xj*(r,fd0)|2,(2)ρfd1,fd2=(1/Nr)∑rXfd1(r,φ0)Xfd2*(r,φ0)(1/Nr)∑r|Xfd1(r,φ0)|2(1/Nr)∑r|Xfd2*(r,φ0)|2,
where r indicates the index of range bins, Nr is the number of range bins which are used to calculate the correlation coefficient, Xk and Xj are the training data with direction k and j with Doppler shift fd0,(·)* is the complex conjugate operator, and Xfd1 and Xfd2 are the training data with Doppler shift fd1 and fd2 with direction φ0.We analyze the angle correlation with different angle intervals as given by (1). The results are shown in Figure 3.Correlation coefficients with different beam intervals.
(a)
Range = 200 km
(b)
Range = 200 km,fd0 = −1.2 HzFigure3(a). The ionospheric clutter exists within the Doppler shifts between −2 Hz and 0.12 Hz. The correlation coefficient at beam interval 5° is greater than the ones when the beam intervals are 10° and 15°.Figure3(b). The correlation coefficient decreases as the beam interval increases. We can deduce from these two figures that the ionospheric clutters have similar characteristics when the beam interval is narrower than 5°.We also analyze the Doppler frequency correlation with different Doppler shift intervals as given by (2). The results are shown in Figure 4.Correlation coefficients with different Doppler shift intervals.
(a)
Range = 200 km
(b)
Range = 200 km,φ0 = −10°Figure4(a). The ionospheric clutter exists within all the angles ranging from −30° to 30°. The correlation coefficient achieves its maximum when the Doppler shift interval is 34 mHz. The ones when the Doppler shift intervals are 68 mHz and 102 mHz are almost the same and both less than the one with 34 mHz.Figure4(b). The correlation coefficient decreases as the Doppler shift interval increases. From these two figures, we can also deduce that the ionospheric clutters have similar characteristics when the Doppler shift interval is less than 34 mHz.In order to maintain the characteristics of ADLR, correlation coefficients within the ADLR data must be high enough. It follows that the size of ADLR cannot be too large. Synthetically, it is preferable to choose the ±5°, ±34 mHz interval around the cell under test. This is in agreement with the radar theory that correlation coefficient increases as the beam interval and Doppler shift interval decrease.


## 2.2. Correlation Analysis Method Based on ADJE

In the case of HFSWR, the data in an ADLR cannot be absolutely simple. An ADLR often consists of multiple echo components such as noise, clutter, interference, and targets. The characteristics of ADLRs with different echo components are different. In this part, we mainly analyze the correlation between ADLRs with different echo components.We first calculate the self-correlation matrix of the data in one ADLR and then obtain the ADJEs through the decomposition of the covariance matrix. In this case, the characteristic of the ADLR is represented by the vector sum of the ADJEs. The following correlation analysis is based on the ADJEs representation.Firstly, we choose the ADLR which covers ±5° (3 beams) and ±34 mHz (3 Doppler shifts) in one range bin and a9×1 vector Xr can be written by Kronecker product. So the self-correlation matrix is 9×9, and we can get 9 ADJEs by eigen decompostion. A certain number of ADJEs which make greater contribution to represent the characteristics of the ADLR are selected to calculate the correlation coefficient.The correlation analysis method based on ADJE is as follows.(i)
Calculate the self-correlation matrixRx of the data Xr in the ADLR with rth range bin by Rx=XrHXr.(ii)
Eigen-decomposeRx to obtain 9 eigenvalues λ1,λ2,…,λ9 and 9 ADJEs ξ1,ξ2,…,ξ9, then the normalized ADJEs by ξ-i=ξi/|ξi|,i=1,…,9.(iii)
Determine the contribution of the normalized ADJEsλi(ξ-i,Xr), i=1,2,…,9;(iv)
Choose the normalized ADJEς which makes the greatest contribution for Xr. And ς can represent the characteristic of  Xr. In the case of HFSWR, especially for the Es layer ionospheric clutter, there may be more than one kind of clutter component that exists in an ADLR. Hence, for uncorrelated clutters, there may be two or more dominant normalized ADJEs, and the vector sum of the ADJEs is introduced to represent the characteristics of this ADLR.(v)
Repeat the above procedure; we can obtainK normalized ADJEs ςi, i=1,2,…,K in K different range bins.(vi)
Calculate the correlation coefficients utilizing theK normalized ADJEs ςi, i=1,2,…,K from step (v) by
(3)ρij=ςiHςj,i,j=1,2,…,K.


## 2.3. SOI Correlation in the Noise Environment

The following analysis is based on the assumption that the noise in HFSWR is Gaussian. We consider two ADLRs: one is with SOI only, and in the other one there exist both SOI and noise, and the signal-to-noise ratio (SNR) is changing.Gracheva and Cerutti-Maori have analyzed the channel correlation of sea data and have mentioned the relationship between channel correlation and the clutter to noise ratio (CNR) [16]. CNR is defined as
(4)CNR=(1/Nr)∑r∥Xc(rc)∥2σn2.We consider the ADLR in a single range bin(Nr=1). The CNR in this ADLR can be defined as
(5)CNRADLR=∥Xc(rc)∥2σn2.The SNR is defined as(6)SNR=∥Xt(rt)∥2σn2.We can replace the CNRADLR in the literature [16] with the SNR as
(7)ρ=11+1/SNR.We analyze the correlation between two ADLRs (ADLR1 and ADLR2) by utilizing the algorithm introduced in Section 2.2. The relationship between correlation coefficient and the SNR is obtained via 10000 Monte-Carlo trials.Under the condition that there are only SOI in ADLR1 and only Gaussian noise in ADLR2, the correlation between ADLR1 and ADLR2 is shown as the red dotted line in Figure 5. The correlation coefficient is kept at a low level. This result is consistent with the radar theory that the SOI is uncorrelated with the noise.Figure 5
The relationship between correlation and SNR.In this case, there are both SOI and noise in ADLR2, and the SNR is variant. The simulation result by (7) is shown as the green dotted line with marker “*” in Figure 5. The correlation coefficient is very close to 1 when the SNR is greater than 20 dB and very close to zero when the SNR is less than −20 dB. When SNR∈[-20,20] dB, the correlation coefficient increases as the SNR increases.We make a similar analysis with the measured data in ADLR2. The result is shown as a blue solid line in Figure 5. Compared to the simulation results, the correlation coefficient decreases faster as the SNR decreases and the correlation coefficient is greater than zero when the SNR is less than 0 dB. The reason for this error is that the characteristics of SOI and noise could be both reflected in ADLR2 when the SNR is small.In light of the error present in the above analysis, we modify the equation as follows.We mark the ADLR1 which only contains SOI1 as SD1 and the Doppler-angle data as Zt; we also mark the ADLR2 which contains SOI2 and Gaussian noise as SD2 and the Doppler-angle data as Zsn, and the power of the noise is σ2. We calculate the normalized ADJEs of ADLR1 and ADLR2 utilizing Zt and  Zsn for ξt and ξsn, respectively. So ξsn can be written as
(8)ξsn≈λtξt′+σ2ξnλt2+σ4,
where λt is the eigenvalue of SOI2, ξt′ is the eigenvector of SOI2, and ξn is the eigenvector of noise.So the correlation coefficient can be written as(9)ρ=ξtHξsn≈ξtH·λtξt′+σ2ξnλt2+σ4=λtλt2+σ4·11+1/SNR+σ2λt2+σ4·ρsn,
where ξtHξt′=1/(1+1/SNR), ρsn is a statistical value related to the SOI and distribution of the noise, ρsn=ξtHξn.When SOI2 is dominant in SD2, ξsn≈ξt′, the correlation coefficient is ρ=ξtHξt′=1/(1+1/SNR).When noise is dominant in SD2, ξsn≈ξn, correlation coefficient is ρ=ξtHξn=ρsn.The simulation result based on (9) are shown as a black dot-dash line in Figure 6 fits the measured data much better than the simulation result given by (7) does.Figure 6
The relationship between correlation and SNR.


## 2.4. SOI Correlation in the Ionospheric Clutter Environment

We mark the ADLR1 which only contains SOI1 as SD1 and the Doppler-angle data as Zt(rt); we also mark the ADLR3 which contains SOI2 and the ionospheric clutter as SD3 and the Doppler-angle data as Zc(rc), and rt and rc are the range bins of SD1 and SD3. The SCR of SOI2 and the ionospheric clutter are written as
(10)SCR=∥Zt(rt)∥2(1/Nr)∑r∥Zc(rc)∥2.We analyze the SOI correlation in the ionospheric clutter background as in Section2.3. We can get the following:
(11)ρ={11+1/SCR,forSCR>HSCR,ρsc,forSCR<LSCR,λtλt2+λc2·11+1/SCR+λcλt2+λc2·ρsc,others,
where ρsc is the correlation coefficient between SOI and the ionospheric clutter, λt and λc are the eigenvalues of SOI2 and the ionospheric clutter in ADLR3, and LSCR and HSCR are the upper limit and lower limit of SCR, respectively, and they are related to the characteristics of the ionospheric clutter.The correlation of SOI in the ionospheric clutter environment utilizing the measured data at the range of 180 km and 185 km is shown in Figure7.The relationship between correlation and SCR.
(a)
Range = 180.00 km
(b)
Range = 185.00 kmIf there is only ionospheric clutter in ADLR3, the correlation coefficients between ADLR1 and ADLR2 are shown as a red-dotted line. It is related to the characteristic of ionospheric clutter and has different values at different ranges. The result of correlation analysis utilizing measured data is shown as a blue solid line. And the result calculated by (11) fits the measured data well.It can be seen from (11) and Figure 7 that the relationship between correlation and SCR can be divided into three parts:(a)
the correlation coefficient keeps  a low value when the SCR is small, and it mainly depends on the characteristics of the ionospheric clutter;(b)
when the SCR is large enough, the correlation coefficient is close to 1;(c)
when the SCR is an intermediate value, the correlation coefficient is related not only to the SCR but also to the characteristics of SOI and ionospheric clutter.


## 2.5. Range Correlation of Nonhomogeneous Ionospheric Clutter

The motion of ionosphere is complex with the major factor of nonuniform plasma. Due to this complex motion, the ionospheric clutter in HFSWR is nonhomogeneous.We calculate the correlation coefficients of ADLRs in different ranges within 150 km to 430 km referred to 225 km at the Doppler shift −1.2 Hz utilizing the algorithm mentioned in Section2.2. The result is shown in Figure 8. The correlation of nonhomogeneous ionospheric clutter decreased as the range interval increased. But there may be a few high correlated range data due to the nonhomogeneous characteristics of the ionospheric clutter.Figure 8
Range correlation of ionospheric clutter at −1.2 Hz.


## 3. Strategy of Choosing the Training Data Based on Correlation

The full STAP algorithm is ideal and requires the training data to meet two conditions. One is that the clutter must be independent, and identically distributed. The other is that the number of the training data must be twice greater than the degrees of freedom of the clutter [17].In HFSWR, the first condition is difficult to meet due to the complex echoes. The long coherent integrated time (CIT) leads to the large degrees of freedom. So it requires considerable training data which are difficult to be attained in the practical system. Compared with the fully STAP, the partial STAP algorithm has the advantage of less computation. So the partial STAP has become the researchers priority.The JDL algorithm is one of the partial STAP algorithms. It can reduce the degrees of freedom by using a transformation matrixT. Therefore, it can solve the problem of the limited training data and it also can reduce the computation.The result of Section2.5 showed that the range of correlation of the nonhomogeneous ionospheric clutter rise, and fall irregularly. In order to suppress the nonhomogeneous ionospheric clutter effectively utilizing the JDL, we should ensure that the training data are highly related with the clutter cell under test.


### 3.1.  Strategy Based on the Correlation

In this part, we choose the appropriate samples as the training data to obtain the covariance matrix more accurately based on the correlation analysis above.The receiver antenna array of HFSWR is described as theN elements uniform linear array (ULA). d is the interelement spacing, a coherent integrated time contains M pulses, T is the pulse repetition time, and fs is the system sampling rate. For a given range bin, the data sampled by the N elements form an N-dimensional vector, and the data received by one element in a CIT form an M-dimensional vector. So that an NM×1 dimensional vector of the space-time snapshots in lth range bin is formed as defined by
(12)Xl=[x1x2⋯xM]T,
where xi=[xi,1xi,2⋯xi,N]T,i=1,2,…,M.We define the space-time steering vector as(13)v(ϕt,ft)=b(ft)⊗a(ϕt),
where a(ϕt) is a space steering vector as defined by (14) and b(ft) is a time steering vector as defined by (15):
(14)a(ϕt)=[1ZsZs2⋯ZsN-1]T,(15)b(ft)=[1ZtZt2⋯ZtM-1]T,
where Zs=ej2π(d/λ)sinϕt and Zt=ej2π(ft/fR).JDL algorithm can transform the independent range samples to the LPR by using the transformation matrixT to reduce the degrees of freedom. Thus, T is the key of the JDL algorithm. Wang has discussed how to choose the LPR in the literature [18]: the clutter can be suppressed more effectively as the LPR larger, at the same time the heavily computational cost is a big problem. With all things considered in the case of HFSWR, the LPR we are concerned about contains three angle units and three Doppler shift units (ηa=3,ηd=3), which is the same size as the ADLR we mentioned in Section 2. So that the transformation matrix T can be written as
(16)T=[b(f-1)b(f0)b(f1)]⊗[a(ϕ-1)a(ϕ0)a(ϕ1)].Thus the new range samples and the new space-time steering vector in JDL can be written as(17)X~l=TH·Xl,v~=TH·v.Then, we analyze the correlation of the range samples utilizing algorithm in Section2. We choose the K training data which is highly correlated with the cell under test (CUT) by setting a threshold. Finally, we calculate the covariance matrix R^ utilizing the K chosen training data as defined by
(18)R^=1K∑0K-1ZkZkH.We assume that CUT is thetth range bin. Xt is the sample in CUT. Therefore, training data Zk should be highly correlated with the sample Xt. And Zk are chosen from Xl,l=1,2,…,t-p,t+p,… where p is the number of protected range bins which are used to keep the training data to be independent of  Xt. That is because the target in HFSWR often spreads a few range bins, and the range samples in these range bins are nonindependent.When we get the covariance matrixR^, the optimal weights can be expressed as
(19)Wopt=R^-1v~.The implementation of the improved-JDL can be shown as in the following steps and Figure9.(i)
Determine the size of LPR and the transformation matrixT as shown in (16).(ii)
Calculate the ADJEs of CUT and the range samples near the CUT as mentioned in steps (i)~(v) in  Section 2.2.(iii)
Calculate the correlation coefficients between the CUT and the nearby range samples as (3).(iv)
Compare the correlation coefficients with the thresholdc0. If it is greater than c0, these range samples can be treated as training data; otherwise it will be discarded.(v)
Calculate the covariance matrix of the ionospheric clutter utilizing the chosen training data as (18).Figure 9
Implementation of improved-JDL.


### 3.2. Threshold Chosen

The key point of the improved-JDL is the thresholdc0. Due to different c0, the chosen training data can be absolutely different. This can result in different covariance matrix and space-time weights. Curve of the improvement factor (IF) and the threshold is shown in Figure 10. The IF is no longer improved as the threshold raised when the threshold is greater than 0.4. Thus, we can choose the threshold that is greater than 0.4 for single target situation.Figure 10
The relationship between the IF and correlation coefficient threshold.In the case of HFSWR, the targets often travel with batch. In this condition, the interference between targets must be concerned. Figure11 shows the correlation between the range sample 1 with only strong target and the range sample 2 with weak target and the ionospheric clutter. The SCR in Figure 11 is the weak target to ionospheric clutter ratio in range sample 2.Figure 11
Correlation between the strong target and the weak target within ionospheric clutter.When theSCR<0dB, the correlation coefficients between the strong target and the weak target are mostly less than 0.8. When the SCR<-10dB, the correlation coefficients are mostly less than 0.7. As the threshold increased, the number of chosen training data may decrease and the covariance matrix may be calculated inexactly because there are not enough training data.With both of the correlation and the number of training data considered, the threshold should be little greater than 0.7. Thus it cannot only keep the training meeting highly correlated but also avoid the interferences of the strong targets.


## 3.1.  Strategy Based on the Correlation

In this part, we choose the appropriate samples as the training data to obtain the covariance matrix more accurately based on the correlation analysis above.The receiver antenna array of HFSWR is described as theN elements uniform linear array (ULA). d is the interelement spacing, a coherent integrated time contains M pulses, T is the pulse repetition time, and fs is the system sampling rate. For a given range bin, the data sampled by the N elements form an N-dimensional vector, and the data received by one element in a CIT form an M-dimensional vector. So that an NM×1 dimensional vector of the space-time snapshots in lth range bin is formed as defined by
(12)Xl=[x1x2⋯xM]T,
where xi=[xi,1xi,2⋯xi,N]T,i=1,2,…,M.We define the space-time steering vector as(13)v(ϕt,ft)=b(ft)⊗a(ϕt),
where a(ϕt) is a space steering vector as defined by (14) and b(ft) is a time steering vector as defined by (15):
(14)a(ϕt)=[1ZsZs2⋯ZsN-1]T,(15)b(ft)=[1ZtZt2⋯ZtM-1]T,
where Zs=ej2π(d/λ)sinϕt and Zt=ej2π(ft/fR).JDL algorithm can transform the independent range samples to the LPR by using the transformation matrixT to reduce the degrees of freedom. Thus, T is the key of the JDL algorithm. Wang has discussed how to choose the LPR in the literature [18]: the clutter can be suppressed more effectively as the LPR larger, at the same time the heavily computational cost is a big problem. With all things considered in the case of HFSWR, the LPR we are concerned about contains three angle units and three Doppler shift units (ηa=3,ηd=3), which is the same size as the ADLR we mentioned in Section 2. So that the transformation matrix T can be written as
(16)T=[b(f-1)b(f0)b(f1)]⊗[a(ϕ-1)a(ϕ0)a(ϕ1)].Thus the new range samples and the new space-time steering vector in JDL can be written as(17)X~l=TH·Xl,v~=TH·v.Then, we analyze the correlation of the range samples utilizing algorithm in Section2. We choose the K training data which is highly correlated with the cell under test (CUT) by setting a threshold. Finally, we calculate the covariance matrix R^ utilizing the K chosen training data as defined by
(18)R^=1K∑0K-1ZkZkH.We assume that CUT is thetth range bin. Xt is the sample in CUT. Therefore, training data Zk should be highly correlated with the sample Xt. And Zk are chosen from Xl,l=1,2,…,t-p,t+p,… where p is the number of protected range bins which are used to keep the training data to be independent of  Xt. That is because the target in HFSWR often spreads a few range bins, and the range samples in these range bins are nonindependent.When we get the covariance matrixR^, the optimal weights can be expressed as
(19)Wopt=R^-1v~.The implementation of the improved-JDL can be shown as in the following steps and Figure9.(i)
Determine the size of LPR and the transformation matrixT as shown in (16).(ii)
Calculate the ADJEs of CUT and the range samples near the CUT as mentioned in steps (i)~(v) in  Section 2.2.(iii)
Calculate the correlation coefficients between the CUT and the nearby range samples as (3).(iv)
Compare the correlation coefficients with the thresholdc0. If it is greater than c0, these range samples can be treated as training data; otherwise it will be discarded.(v)
Calculate the covariance matrix of the ionospheric clutter utilizing the chosen training data as (18).Figure 9
Implementation of improved-JDL.


## 3.2. Threshold Chosen

The key point of the improved-JDL is the thresholdc0. Due to different c0, the chosen training data can be absolutely different. This can result in different covariance matrix and space-time weights. Curve of the improvement factor (IF) and the threshold is shown in Figure 10. The IF is no longer improved as the threshold raised when the threshold is greater than 0.4. Thus, we can choose the threshold that is greater than 0.4 for single target situation.Figure 10
The relationship between the IF and correlation coefficient threshold.In the case of HFSWR, the targets often travel with batch. In this condition, the interference between targets must be concerned. Figure11 shows the correlation between the range sample 1 with only strong target and the range sample 2 with weak target and the ionospheric clutter. The SCR in Figure 11 is the weak target to ionospheric clutter ratio in range sample 2.Figure 11
Correlation between the strong target and the weak target within ionospheric clutter.When theSCR<0dB, the correlation coefficients between the strong target and the weak target are mostly less than 0.8. When the SCR<-10dB, the correlation coefficients are mostly less than 0.7. As the threshold increased, the number of chosen training data may decrease and the covariance matrix may be calculated inexactly because there are not enough training data.With both of the correlation and the number of training data considered, the threshold should be little greater than 0.7. Thus it cannot only keep the training meeting highly correlated but also avoid the interferences of the strong targets.


## 4. Results of Measured Data

We inject one target in the measured data represented in Figure1 for the single target situation and two targets for the multitargets situation. The parameters of the targets are shown in Tables 1 and 2.Table 1
Single target situation.
Range (km)
Doppler shift (Hz)
Angle (°)
SCR (dB)
200.25
−1.2
0
5Table 2
Mutitargets situation.
Range (km)
Doppler shift (Hz)
Angle (°)
SCR (dB)
200.25
−1.2
0
0
211.25
−1.2
0
10For the single target situation, the injected target can be detected when the threshold is over 0.6 as shown in Figure12. Compared with the results of the three thresholds, the IF is almost the same. That is in agreement with the conclusion in Section 3.2. However, there are four fake targets at 159.75 km, 231.75 km, 265.5 km, and 319.5 km when the threshold is 0.8. And two fake targets exist when the threshold is 0.7. When the threshold decreases to 0.6, there is no fake target any more. That is because when we process the data in these ranges with threshold 0.7 or 0.8, the training data we have obtained is too few to suppress the ionospheric clutter when the threshold is higher. In this case, the energy of the ionospheric clutter stays at a high level and it is easy to be treated as a “fake target.” But the number of the training data increased as the threshold decreased. Thus, there is no fake target when the threshold is lower.Figure 12
The results by using the improved-JDL for single target situation.So for the single target situation, the threshold is set mainly considering the fake targets.For the multitargets’ situation, the results are shown in Figure13. Focusing on the two-injected targets at range of 200.25 km and 211.25 km, they can both be detected when the threshold is 0.7 or 0.8. And the IF of target 1 is almost the same. But when the threshold is 0.6, the energy of target 1 is weakened. That is because is when the threshold down to 0.6, target 2 is treated as training data. Thus, the covariance matrix of the ionospheric clutter contains the characteristics of target, and so target 1 is weakened.Figure 13
The results by using the improved-JDL for multitarget situation.Similar to the single target situation, there may be fake targets when the thresholds are high and the number of fake targets decreased as the threshold increased. In the actual situation, the multitargets situation is common. So the analysis of this part can make great sense.Considering both the IF and fake targets problem, the threshold should be set within 0.6 and 0.7 when the improved-JDL algorithm is utilized in HFSWR.We also consider the range-spread targets in HFSWR as shown in Table3; we can suppress the ionospheric clutter and detect the two targets as shown in Figure 14 utilizing the improved-JDL method with correlation threshold c0=0.6 and the number of protected range bins p=2.Table 3
Range-spread targets situation.
Range (km)
Doppler shift (Hz)
Angle (°)
SCR (dB)
186.75–191.25
−1.2
0
0
227.25–231.75
−1.2
0
10Figure 14
The results by using the improved-JDL for multitarget situation (range-spread targets).


## 5. Conclusion

To counter the nonhomogeneous ionospheric clutter background of HFSWR, this paper proposes a feature analytical algorithm based on the Angle-Doppler Joint Eigenvector to analyze the range correlation of the nonhomogeneous ionospheric clutter. It turns out that the range correlation coefficient is irregular in its variation. In light of this prior knowledge, a further step is taken to deal with the weak target detection problem in HFSWR by analyzing the correlation between targets’ signals and the ionospheric clutter and the negative effect imposed by strong targets on weak targets detection.To sum up, this paper proposes a correlation based training data chosen strategy for the JDL algorithm, and discusses the corresponding decision threshold selection in detail. Consequently, decision thresholds should be set up according to the practical situation of the nonhomogeneous ionospheric clutter and values between 0.6 and 0.7 are preferable. This improved-JDL algorithm is validated by measured data which shows that the weak target detection performance can be notably improved in the background of nonhomogeneous ionospheric clutter.



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*Source: 382516-2013-10-08.xml*