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.

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 [

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 [

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 [

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 Section

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 Figure

Range-Doppler Map.

Angle-Doppler Map.

200 km

350 km

In 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 Figure

In Section

We suppose

In Section

Based on the correlation analyzing method in Section

In the last Section

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 (

We analyze the angle correlation with different angle intervals as given by (

Correlation coefficients with different beam intervals.

Range = 200 km

Range = 200 km,

We also analyze the Doppler frequency correlation with different Doppler shift intervals as given by (

Correlation coefficients with different Doppler shift intervals.

Range = 200 km

Range = 200 km,

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.

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 a

The correlation analysis method based on ADJE is as follows.

Calculate the self-correlation matrix

Eigen-decompose

Determine the contribution of the normalized ADJEs

Choose the normalized ADJE

Repeat the above procedure; we can obtain

Calculate the correlation coefficients utilizing the

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) [

We consider the ADLR in a single range bin

The SNR is defined as

We can replace the CNR_{ADLR} in the literature [

We analyze the correlation between two ADLRs (ADLR_{1} and ADLR_{2}) by utilizing the algorithm introduced in Section

Under the condition that there are only SOI in ADLR_{1} and only Gaussian noise in ADLR_{2}, the correlation between ADLR_{1} and ADLR_{2} is shown as the red dotted line in Figure

The relationship between correlation and SNR.

In this case, there are both SOI and noise in ADLR_{2}, and the SNR is variant. The simulation result by (

We make a similar analysis with the measured data in ADLR_{2}. The result is shown as a blue solid line in Figure _{2} when the SNR is small.

In light of the error present in the above analysis, we modify the equation as follows.

We mark the ADLR_{1} which only contains SOI_{1} as SD_{1} and the Doppler-angle data as _{2} which contains SOI_{2} and Gaussian noise as SD_{2} and the Doppler-angle data as _{1} and ADLR_{2} utilizing _{2}, _{2}, and

So the correlation coefficient can be written as

When SOI_{2} is dominant in SD_{2},

When noise is dominant in SD_{2},

The simulation result based on (

The relationship between correlation and SNR.

We mark the ADLR_{1} which only contains SOI_{1} as SD_{1} and the Doppler-angle data as _{3} which contains SOI_{2} and the ionospheric clutter as SD_{3} and the Doppler-angle data as _{1} and SD_{3}. The SCR of SOI_{2} and the ionospheric clutter are written as

We analyze the SOI correlation in the ionospheric clutter background as in Section _{2} and the ionospheric clutter in ADLR_{3}, and

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 Figure

The relationship between correlation and SCR.

Range = 180.00 km

Range = 185.00 km

If there is only ionospheric clutter in ADLR_{3}, the correlation coefficients between ADLR_{1} and ADLR_{2} 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 (

It can be seen from (

the correlation coefficient keeps a low value when the SCR is small, and it mainly depends on the characteristics of the ionospheric clutter;

when the SCR is large enough, the correlation coefficient is close to 1;

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.

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 Section

Range correlation of ionospheric clutter at −1.2 Hz.

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 [

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 matrix

The result of Section

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 the

We define the space-time steering vector as

JDL algorithm can transform the independent range samples to the LPR by using the transformation matrix

Thus the new range samples and the new space-time steering vector in JDL can be written as

Then, we analyze the correlation of the range samples utilizing algorithm in Section

We assume that CUT is the

When we get the covariance matrix

The implementation of the improved-JDL can be shown as in the following steps and Figure

Determine the size of LPR and the transformation matrix

Calculate the ADJEs of CUT and the range samples near the CUT as mentioned in steps (i)

Calculate the correlation coefficients between the CUT and the nearby range samples as (

Compare the correlation coefficients with the threshold

Calculate the covariance matrix of the ionospheric clutter utilizing the chosen training data as (

Implementation of improved-JDL.

The key point of the improved-JDL is the threshold

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. Figure

Correlation between the strong target and the weak target within ionospheric clutter.

When the

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.

We inject one target in the measured data represented in Figure

Single target situation.

Range (km) | Doppler shift (Hz) | Angle (°) | SCR (dB) |
---|---|---|---|

200.25 | −1.2 | 0 | 5 |

Mutitargets situation.

Range (km) | Doppler shift (Hz) | Angle (°) | SCR (dB) |
---|---|---|---|

200.25 | −1.2 | 0 | 0 |

211.25 | −1.2 | 0 | 10 |

For the single target situation, the injected target can be detected when the threshold is over 0.6 as shown in Figure

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 Figure

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 Table

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 | 10 |

The results by using the improved-JDL for multitarget situation (range-spread targets).

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.

The authors express gratitude to the Institute of Electronic and Information Technology, which provided the HFSWR data, and to those who helped during the writing of this paper. This work was supported in part by the National Science Fund Committee (NSFC) under Grant 61032011.