The penetrating depth analysis of Lunar Penetrating Radar onboard Chang’e3 rover
1 Introduction
The Chang’e3 satellite was successfully launched from the Xichang satellite launching center on 2013 December 2 and landed in northern Mare Imbrium after 12 days. With successful separation of lander and rover, the Yutu lunar rover started its observation mission. Lunar Penetrating Radar (LPR), as one of the important scientific payloads on the Yutu lunar rover, obtained a large amount of scientific data.
LPR is a kind of nanosecond radar operating in the time domain, with separate transmitting and receiving antennae. The ultrabroadband nanosecond pulse generated by the transmitting antenna of LPR propagates into lunar regolith and crustal rock. If the pulse encounters an uneven layer or the interface of different media, it will be reflected and scattered back to the radar. Through data processing, analysis and inversion, the thickness and distribution of lunar regolith as well as the geological structure of the lunar subsurface along the rover’s path can be obtained. In the LPR system, two detection channels are designed. Channel 1 has a center frequency of 60 MHz with a band of 40–80 MHz, while Channel 2 has a center frequency of 500 MHz with a band of 250–750 MHz. With a depth resolution of meterscale, Channel 1 aims to detect the structure of the shallow lunar crust. Also, with a depth resolution of less than 30 centimeters, Channel 2 is used to detect the thickness and structure of lunar regolith (Fang et al. 2014 ).
The LPR detection on the Moon can be divided into three stages. The first stage was during the first Moon day after the rover landed, on which the rover moved from navigation point N0101 to N0108. Some useful parameters, such as the system gain, time window and attenuation settings, were tested and eventually confirmed to ensure the LPR worked optimally for detection. The second stage was during the second Moon day, on which the rover moved from point N0201 to N0209. Lots of detection data were obtained in this stage. In the third stage, which corresponded to the third Moon day and later time, some detection data were obtained in the permanent point (N0209) under different settings, such as radar highvoltageoff, radar highvoltageon and different attenuation values.
A number of investigators have done scientific researches using the LPR data and initial results were reported (Su et al. 2014 , Zhang et al. 2014 , Dai et al. 2014 ). However, no research about the penetrating depth of LPR has been carried out in these studies. The penetrating depth is very important. On one hand, it can be used to determine whether the target is within the effective detection range. On the other hand, it may help to distinguish useful echoes from noise, which will eventually contribute to noise suppression and layer recognition (Davis & Annan 1989 ). Moreover, complex and heterogeneous lunar media (Heiken et al. 1991 ) will complicate reflected echoes, so it is particularly important to find the boundary between reflected echoes and noise.
As an electromagnetic signal propagates in a medium, it will attenuate. Actually, there will be a reflected signal if any different impedance exists in different media, and the reflected signal will be received by the receiving antenna, so the penetrating depth is theoretically infinite. However, existing noise and the restriction of minimum detection power in the LPR system make the penetrating depth finite. In other words, when the reflected signal is less than the minimum detection power or submerged in noise, it is very difficult to detect. Although a signal submerged in noise can be detected with some methods (Tugnait 1993 , Gelchinsky & Shtivelman 1983 , Coppens 1985 ), mostly certain conditions are required. In this study, the penetrating depth means the boundary between the last useful reflected echoes and noise.
In this paper, two methods based on a radar transmission equation are introduced in Section
2 The Methods Based on Radar Equation
In this section, two methods based on the radar equation are introduced to calculate the penetrating depth. First, the method with system calibration parameters is described and the penetrating depths of two channels (60 MHz and 500 MHz) are estimated. Then, using highvoltageoff data, the minimum detection power is modified and new penetrating depths of the two channels are obtained correspondingly.
2.1 Estimation of Penetrating Depth with System Calibration Parameters
According to the system calibration parameters (system gain and minimum detection power) and the radar equation, this method may estimate the penetrating depth in theory. As shown in Figure
Using the traditional radar equation (Ulaby et al. 2015 ), we can get
The traditional radar equation can also be written in the form of system gain, which is shown as follows
The penetrating attenuation between two media under vertical incidence can be evaluated using the following equations
The system gain and the minimum detection power of Channel 1 are 152 dB and –124 dB, while they are 133.3 dB and –118 dB respectively for Channel 2, according to the calibration report (Zhang et al.
2014
). In order to use the above radar equation, there are also two parts we need to figure out. The first part is the lunar subsurface structure: with the assumption of a two layer structure (lunar regolith and crustal rock), for Channel 1 data, we only consider the attenuation of rock and the reflection coefficient between the rock and lunar regolith, while the attenuation of regolith and reflection coefficient between the lunar regolith and rock are considered for Channel 2 data. The second part is the dielectric property of the media, which contains the relative dielectric of lunar regolith, the relative dielectric of lunar crustal rock and the loss tangent of this area. Statistics and analysis of samples from Apollo 15–17 (Heiken et al.
1991
) and inversion data from KAGUYA (Ono et al.
2009
) suggest that the relative dielectric of lunar regolith is from 2.3 to 3.5, while the relative dielectric of lunar crustal rock is from 6.6 to 8.8. The Chang’e3 landing site is a young lava flow in the northeastern part of Mare Imbrium where the extremely rich FeO and (FeO + TiO_{2}) content has reached
Figure
2.2 Estimation of Penetrating Depth Using HighVoltageOff Data
Considering that the noise of LPR data may be greater than the minimum detection power, if we still use the minimum detection power as the threshold of penetrating depth, it will be inaccurate. So in this section, highvoltageoff data from navigation point N0209 are used to calculate the noise floor. At the navigation point N0209, the highvoltage of the LPR transmitter was closed, which means that the LPR only received background noise. In the absence of strong interference introduced by the transmitting signal, the data are more accurate for identifying noise. After comparison of the noise floor with minimum detection power, the minimum detection power is replaced by the noise value. With the new minimum detection power and radar transmission equation in Section
The data acquired from 2014–02–15 T23:19:14 to 2014–02–15 T23:24:57 are chosen for estimation of penetrating depth. During this period, the LPR was working with the same settings as in the second stage. One trace of data from Channel 1 and Channel 2 is shown in Figures




The mean and the standard deviation of the noise floor associated with Channel 1 are 0 and 2.1, respectively. Taking three times the standard deviation and referring to the gain control method (Fang et al.
2014
), the power of noise is –117.1 dB, which is greater than the minimum detection power in Channel 1 (–124 dB). Replacing the minimum detection power with –117.1 dB, Figure
The mean and the standard deviation of the noise floor for Channel 2 are 0 and 0.7, respectively. Taking three times the standard deviation, the power of noise is –115.8 dB, which is greater than the minimum detection power for Channel 2 (–118 dB). Based on the method in Section
3 Correlation Coefficient Method
In Section
3.1 The Principle
The difference in correlation coefficients between reflected echoes and noise in the LPR data profile is used to estimate the penetrating depth of radar waves. The experiments demonstrate that reflected echoes of adjacent traces have a high correlation, namely high resemblance, but noises have random correlation.
Figure
Figure
Let X be the original radar data matrix with a size of
Step 1. Select the sliding window
Step 2. Calculate the mean of the selected sliding window of trace j and
Step 3. Calculate the correlation coefficient based on two adjacent trace data;
Step 4. Repeat steps 1 to 3 from i= 1 to
Step 5. Extract depth curve. First, obtain the cumulationdivision matrix D. m is cumulation length, typically 200 is selected.
Step 6. Compensate the correlation error. The final penetrating curve should subtract half the correlation interval.
Actually, in the correlation coefficient matrix C, the boundary between high correlation and random correlation is already clearly shown. The final curve is retrieved in
3.2 Simulation and Verification
In this section, a simulation is built to verify the validity of CCM.
Figure
Based on CCM, firstly we obtained the correlation coefficient matrix shown in Figure
4 Data Processing Based on Lunar data
The CCM was applied to process Chang’e3 radar data. Data taken by Channel 1 from N0106 to N0207 are chosen, while data from N0105 to N0208 are selected for Channel 2. While operating at these navigation points, the radar worked with the same instrument parameters, thus we can splice these data together.
Based on the CCM (the sliding window n of 60 MHz data is 13 points and
Figure
5 Analysis and Discussion
The depths estimated by three methods are listed in Table
Notes: In Channel 1, ε _{ r } is 6.6 and in Channel 2, ε _{ r } is 2.3. 

The first method is based on the system calibration parameters and radar equation, which is a theoretical calculation method. Because some a priori assumptions, such as radio scattering sectional area, attenuation in the loss medium and dielectric constant, need to be assumed, the accuracy of assumptions will directly influence the final calculation results. Moreover, there must be some differences between the ground calibration environment and the insitu detection environment, so unavoidable deviation exists in the results. In addition, the intensity of signal in the whole time delay of real data is larger than minimum detection power, thus it is not accurate when we use the minimum detection power as the threshold.
In the second method, we calculate the noise with the highvoltageoff data and replace the minimum detection power with the noise value, which is greater than what is used in the first method. However, using the radar equation inherently makes some assumptions, which will eventually influence the results.
In the third method, the radar equation and the ground calibration parameter are not involved and we estimate the depth only with the measured radar data. This method is based on the different correlation coefficient between the reflected echoes and noise to obtain the distancevarying penetrating depth along the profile of the rover. Actually, as the rover moves along the lunar surface, the depth should not be constant. Therefore, the CCM method is more consistent with the real situation than the traditional methods.
Different display ranges, namely dynamic range, are used to show the weak signal and eventually to verify the validity of CCM results. If the original display range is
A comparison of the Channel 1 radar profile displayed in different ranges (−10 to 10, −1 to 1, −0.5 to 0.5, −0.2 to 0.2) with the associated depth curve is shown in Figure
Figure
6 Conclusions
In this study, we analyze the penetrating depth of LPR with three methods, among which the first two methods utilize the radar equation and they are more inclined to be applied in theoretical calculations. The CCM, based on the different correlation between reflected echoes and noise to acquire the penetrating depth, is the main work of this study, which is first introduced and used for LPR data. Without a priori assumptions about the structure and dielectric properties of the Moon, CCM estimates the distribution of depth only using measured data. Through analysis of the results of three methods, CCM is verified to be an effective and practical method to estimate penetrating depth. The results indicate that the ultimate penetrating depth of Channel 1 (N0106 to N0207) ranges from 136.9 m to 165.5 m with a dielectric constant of 6.6, and the penetrating depth of Channel 2 (N0105 to N0208) ranges from 13.0 m to 17.5 m with a dielectric constant of 2.3.
However, it should be noted that the depth estimated by CCM is the boundary between reflected echoes and noise, but it does not mean that there is a real reflected layer at this depth. Especially for the Channel 1 data, the interference is strong enough to hide the subsurface reflected signal, so maybe the real penetrating depth is much shallower. Moreover, whether there are other useful echoes hiding in the noise and whether they can be extracted from the noise are controversial and need further study.
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