Dual-Frequency Signal Enhancement Method of Moving Target Echoes for GNSS-S Radar

Abstract

The GNSS-S radar utilizes the signals of a global navigation satellite system (GNSS) to carry out target detection. Due to the very low power of GNSS signals, long-term accumulation is needed to improve the gain of the echo signals. However, when it is used for moving object detection, the random movement of the target will cause residual Doppler frequency after the echoes are correlated and compressed through the direct signal. The residual Doppler frequency will cause two problems: on the one hand, the signal coherence will deteriorate, affecting the coherent accumulation gain; on the other hand, the amplitude of the signal after compression will decrease due to the sensitivity of GNSS signals to Doppler frequency. Therefore, how to increase the signal amplitude and eliminate the phase fluctuation caused by the Doppler frequency shift in the GNSS echoes of moving targets is an important issue for GNSS-S radar to detect moving targets. This paper proposes a dual-frequency GNSS echo enhancement method that uses the dual-frequency signals transmitted by the GNSS satellites to enhance and regularize the target echo. First, the phase relationship model of the GNSS dual-frequency echo is constructed, and the phase difference is made to the compressed dual-frequency echo signal to obtain the differential phase without fluctuation; then, the amplitudes of the dual-frequency echo signals are added together; and finally, a new signal with enhanced amplitude and consistent phase is constructed by using the dual-frequency additive amplitude and differential phase, and the long-term coherent accumulation of the signal is carried out, which can improve the processing gain of the weak echo signal of the moving target. The simulation and field experiments show that this method makes full use of the energy of the GNSS dual-frequency signal and eliminates the phase fluctuation in the echo signal of the moving target so that the compressed signal energy remains consistent in the slow-time dimension. After long-term coherent accumulation, the echo SNR was greatly improved, which enabled the detection of two high-speed cars by GNSS-S radar in the experiment.

1. Introduction

Currently, there are multiple global navigation satellite systems, such as BDS, GPS, GALILEO, and GLONASS, with more than 120 satellites in orbit [1,2]. They continuously transmit navigation signals to Earth, which forms a layer of multifrequency and widespread electromagnetic waves in near-Earth space. Using the scattering characteristics of these GNSS electromagnetic waves on the ground, the detection of ground targets can be realized, which is GNSS-S radar. It can be applied to target recognition, wind and sea wave measurement, vegetation inversion, etc. [3]. Since GNSS-S radar does not need to transmit signals, it has the advantages of low power consumption, self-concealment, antistealth, etc. [4]. It can realize global detection and has broad application prospects.

However, the GNSS signal structure is mainly designed for navigation, positioning, and timing [5]. When used for target detection, it faces many problems, such as extremely low signal power and poor resistance to Doppler frequency shift [6,7,8]. In recent years, many scientific and technological workers have conducted extensive theoretical research and experimental verification work around the key technical challenges of GNSS-based target detection. The concept of GNSS-based radar detection was proposed in reference [9]. A maritime target detection test was carried out in references [10,11], which verified the feasibility of using GNSS signals for target detection. In reference [12], the system link budget using GNSS signals for detection was analyzed, and it was pointed out that when limited by the signal power of GNSS, the realization of target detection requires long-term integration. In reference [13], a signal processing architecture for GNSS-based radar was proposed that utilizes correlation operations between direct signals and reflected signals to improve the processing gain of reflected signals. In references [14,15], the method of multiframe accumulation is used to accumulate GNSS echo signals for a long time, achieving the detection of maritime target echo signals. In references [16,17,18], a GNSS-based detection test for ground-level buildings was carried out. Since the target is still, long-term coherent integration is used to obtain the echo signal of the target. In references [19,20], experiments were conducted using GNSS signals to detect ships, achieving long-term energy accumulation by correcting the distance migration of target motion. Due to the slow motion of the target, the impact of target motion Doppler on echo compression gain was very small. In reference [21], a mixed mode of coherent integration and noncoherent integration is proposed, and noncoherent integration is used to solve the influence of the Doppler frequency shift of moving targets on signal coherence. Since noncoherent integration produces a square loss [22], the gain improvement is very limited. In references [23,24,25], Radon Fourier transform and fractional Fourier transform are used to estimate the Doppler frequency shift of the moving target echo, and the estimated motion parameters are used to compensate the echo phase to achieve long-term coherent accumulation. However, it is mainly applied to the phase compensation of the chirp signal of the traditional radar without considering the amplitude loss when the GNSS signal is demodulated and compressed.

In our previous works, a novel demodulation and compression method for GNSS echo was proposed to solve the problem of weak signal detection, which is shown in reference [26]. In this paper, a dual-frequency GNSS-S signal echo processing method is proposed to solve the problems of energy loss and phase fluctuation caused by the residual Doppler frequency after demodulation and compression of the GNSS-S echo signal of a moving target. First, the phase relationship model of the GNSS dual-frequency echo signal is constructed, and the phase difference is made to the compressed dual-frequency echo signal to obtain the differential phase without fluctuation; then, the amplitudes of the dual-frequency echo signals are added together; and finally, a new signal with enhanced amplitude and consistent phase is constructed by using the dual-frequency additive amplitude and differential phase, and the long-term coherent accumulation of the signal is carried out, which can improve the processing gain of the weak echo signal of the moving target.

The following parts of this paper are structured as follows: Section 2 introduces the GNSS-S dual-frequency differential processing method; Section 3 presents the simulation and the experiment results; Section 4 discusses the results; and finally, a conclusion is given in Section 5.

2. Methodology

2.1. Composition of the GNSS-S Radar System

The schematic diagram of the GNSS-S radar system proposed in this paper is shown in Figure 1. It mainly includes four parts: the antenna module, the RF module, the sampling module, and the processing module. The antenna module includes the direct receiving antenna and the scattering receiving antenna, which are both dual-frequency antennas and can simultaneously receive B1 and B3 signals of BDS. The RF module implements the amplifying, filtering, and downconversation of the RF signals and divides the dual-frequency signals into four channels. The sampling module carries out the AD sampling of the four signals. Finally, the GNSS-S detection algorithms are carried out in the processing module.

The physical diagram of the GNSS-S radar system is shown in Figure 2, and the main technical parameters are shown in

Table 1. Main parameters of the system.

Parameter	Value
Gain of the direct receiving antenna	3 dBi
Gain of the scattering receiving antenna	15 dBi
Working Frequency	1561.098 MHz and 1268.52 MHz
Working Bandwidth	4.092 MHz and 20.46 MHz
Beam angle of the scattering receiving antenna	±13°
Sampling rate	200 MSPS
Number of channels	4
Storage capacity	1 TB

. The direct receiving antenna, which is an omnidirectional receiving antenna that points towards the zenith, receives direct signals from GNSS satellites [27]. The scattering receiving antenna, which is a high-gain directional receiving antenna that points towards the detected target, receives the scattering echo of the target [28]. Both the direct and scattering signals are input to the processing host to realize the simultaneous sampling of the four signals and execute the processing algorithm.

2.2. Geometry Configuration

The geometric structure of the GNSS-S radar system is shown in Figure 3, which includes two antennas and is a bistatic radar configuration [29]. The direct antenna receives the direct signal of the GNSS satellite, and the scattering antenna receives the GNSS signal scattered by the target. The detection of the target is realized by the distance difference between the direct signal and the scattering signal. The distance from the GNSS satellite to the GNSS-S receiver is D, the distance from the GNSS satellite to the target is $d_1$, and the distance from the target to the GNSS-S receiver is $d_2$. The bistatic angle between the target, satellite, and receiver is α. The bistatic distance between the GNSS-S receiver and the target is the propagation path difference $\Delta R$ between the direct signal and the scattering signal, which is given by Equation (1).

$$\Delta R=d_1+d_2^{}-D$$

(1)

According to the path difference $\Delta R$, the time difference $\Delta t$ between the scattering signal and the direct signal can be calculated, as shown in Formula (2), where c is the propagation speed of the electromagnetic wave, which is 299,792,458 m/s.

$$\Delta t=\frac{\Delta R}{c}=\frac{d_1+d_2^{}-D}{c}$$

(2)

2.3. Signal Model

The GNSS signal structure is Code Division Multiple Access (CDMA), which is composed of navigation messages, pseudorandom noise (PRN) code, and signal carriers [30]. The signal expression is shown as Equation (3).

$$s_d(t)=A_1·D(t)·C\left(t\right)·\cos (2\pi f_{c}t+\varphi )$$

(3)

where $s_d(t)$ denotes the direct GNSS signal, and $A_1$ denotes the signal amplitude. $D(t)$ and $C\left(t\right)$ represent navigation messages and PRN codes, respectively, with a value range of ±1. $f_c^{}$ and $\varphi$ are carrier frequency and initial phase, respectively.

According to the geometric configuration of the GNSS-S system given in Figure 3, the scattering signal model is expressed as Equation (4).

$$s_{\mathrm{s}}(t)=A_2·D(t-\Delta t)·C(t-\Delta t)·\cos \left[2\pi (f_c^{}+f_d)·(t-\Delta t)+\varphi \right]$$

(4)

where $s_{\mathrm{s}}(t)$ denotes the scattering signal, $f_d$ is the Doppler frequency shift caused by the target motion, and $\Delta t$ is the time difference in Equation (2).

Firstly, the scattering signal is quadrature demodulated to remove the carrier frequency $f_c^{}$, and the phase $\varphi$ can be adjusted to 0 by a phase-lock loop. The demodulated signal can be obtained as shown in Equation (5). Due to the motion of the target, the demodulated signal has a residual Doppler shift $f_d^{}$.

$$s_s^{\prime }(t)=A_2^{\prime }·D(t-\Delta t)·C(t-\Delta t)·\exp \left\{-j·2\pi ·f_d·(t_{}-\Delta t)\right\}$$

(5)

Then, a PRN code correlation operation is performed on the demodulated signal $s_s^{\prime }(t)$ to realize signal compression and obtain spread spectrum gain. Then, the modulated navigation messages are removed by the direct navigation message information. The compressed signal is shown in Equation (6).

$$s_c(t)=A_3·X(t-\Delta t)·dec(f_d)·\exp \left\{-j·2\pi ·f_d·(t_{}-\Delta t)\right\}$$

(6)

where $s_c(t)$ denotes the compressed echo signal, $X(·)$ denotes the autocorrelation function (ACF) of the PRN code, and $dec(·)$ denotes the attenuation function of the ACF, which is caused by the target motion Doppler $f_d$.

The image of the ACF of the PRN code is a sharp triangle. The peak of the ACF function under different $f_d^{}$ is shown in Figure 4. When the Doppler frequency shift is above 200 Hz, the correlation value will be significantly attenuated.

What is more severe is that the GNSS signal power is inherently very weak. Taking the BDS signal as an example, the signal power reaching the ground is −130 dBm, while the noise power is −101 dBm (bandwidth is 20 MHz). When there is a residual Doppler frequency after carrier demodulation, the compressed signal energy will be attenuated. In reality, the GNSS signal is submerged under the noise, and the demodulated and compressed GNSS signal value is shown in Figure 5. It can be seen that when the frequency shift reaches 300 Hz, the signal energy attenuates to the noise level, and the signal cannot be detected.

In order to facilitate further coherent accumulation of the compressed signal, the compressed signal is intercepted in blocks according to the code period and arranged vertically, which is converted into a “τ-tm” two-dimensional signal, as shown in Equation (7). The specific process is described in reference [26]. The converted time $t$ can be expressed as $t=t_m+\tau$, where $t_m$ is the number of integer cycles, called slow time, and τ is the time in a cycle, called fast time. Generally, the fast time τ and slow time $t_m$ are selected based on the signal characteristics of GNSS. The fast time τ has a length of one PRN code cycle (such as 1 ms for both BDS B1I and B3I), and the slow time $t_m$ is the number of code cycles. The ACF function after signal compression is also a periodic function, that is $X(t_m+\tau )=X\left(\tau \right)$.

$$s_c(\tau ,t_m)=A_3·X(\tau -\Delta t)·dec(f_d)·\exp \left\{-j·2\pi ·f_d·(t_m+\tau -\Delta t)\right\}$$

(7)

2.4. Dual-Frequency Processing Methods

Because the GNSS signal is extremely weak, it is still not enough to detect the echo signal of the target after the quadrature demodulation and code autocorrelation of the scattering signal. In order to improve the SNR of the echo signal, it is necessary to further accumulate the signal over a long time, which requires long-term coherent accumulation of the signal along the slow time $t_m$. However, it can be seen from Equation (7) that the amplitude of the compressed signal is attenuated due to the residual Doppler frequency $f_d$, and the signal phase fluctuates along the slow time $t_m$, which limits the effect of coherent accumulation. This paper proposes a dual-frequency differential processing method that uses GNSS dual-frequency echoes for signal enhancement. The processing flow is shown in Figure 6.

Firstly, the GNSS signals at F1 and F2 frequencies are demodulated and compressed to obtain carrier frequencies $f_{c1}$ and $f_{c2}$, as well as 2D data blocks. The amplitudes and phases of the compressed two frequencies signals are denoted as $(A_1,{\phi }_1)$ and $(A_2,{\phi }_2)$, respectively. Secondly, calculate the phase correction factor k according to the phase relationship model of the $f_{c1}$ and $f_{c2}$ echo signals and perform phase difference on the dual-frequency signals to obtain the differential phase $\Delta \phi$. Thirdly, accumulate the amplitude of the dual-frequency signal to obtain the additive amplitude, which is denoted as AA, and combine it with the dual-frequency differential phase $\Delta \phi$ to form a new dual-frequency differential signal $\Delta s$, whose amplitude and phase are $(AA,\Delta \phi )$. Finally, coherent accumulation is performed on the dual-frequency differential signal $\Delta s$ to further improve the SNR of echo signals, and a continuous target motion track diagram can be obtained.

Generally, the GNSS system simultaneously transmits multiple signals at different frequencies. Taking BDS as an example, it simultaneously transmits signals at three frequencies: B1, B2, and B3. The signals of any two frequencies can be used as signal illumination sources for radar detection, and the signal propagation paths and frequency relationship are shown in Figure 7. The carrier frequency of the navigation satellite signal is $f_c$, which can be removed after quadrature demodulation with the help of a direct signal. The main residual frequency of the 2D data block after demodulation and compression is the Doppler shift $f_d$ caused by the target motion, which is related to the target velocity and carrier frequency.

Considering that the height from the satellite to the ground is much greater than the distance between the target and receiver and that the Doppler caused by satellite motion has been resolved by the direct signals, when the radial velocity between target and receiver is v, the bistatic angle is $\alpha$, and the wavelengths of the dual-frequency carrier signals are ${\lambda }_1$ and ${\lambda }_2$, respectively; the resulting Doppler $f_{d1}$ and $f_{d2}$ can be expressed as Equations (8) and (9).

$$f_{d1}=\frac{v}{{\lambda }_1}(1+\cos \alpha )$$

(8)

$$f_{d2}=\frac{v}{{\lambda }_2}(1+\cos \alpha )$$

(9)

Substituting the above equations into Equation (7), the echo signal model can be obtained, as shown in Formulas (10) and (11). It can be seen that the phase of the echo signal is related to the moving speed v of the target and the wavelength ${\lambda }_{}$ of the carrier wave. When performing coherent accumulation directly, the effect of long-term accumulation will be affected due to the change in the signal phase.

$$\begin{array}{l}{s}_{\mathrm{c}1}(\tau ,t_m)=A_3·X(\tau -\Delta t)·dec(\frac{v·(1+\cos \alpha )}{{\lambda }_1})·\\ \exp \left\{-j·2\pi ·\frac{v·(1+\cos \alpha )}{{\lambda }_1}·(t_m+\tau -\Delta t)\right\}\end{array}$$

(10)

$$\begin{array}{l}{s}_{\mathrm{c}2}(\tau ,t_m)=A_3^{\prime }·X^{\prime }(\tau -\Delta t)·dec(\frac{v·(1+\cos \alpha )}{{\lambda }_2})·\\ \exp \left\{-j·2\pi ·\frac{v·(1+\cos \alpha )}{{\lambda }_2}·(t_m+\tau -\Delta t)\right\}\end{array}$$

(11)

Since the signals of the two frequencies $f_{c1}$ and $f_{c2}$ are transmitted by the same satellite, the bistatic angle $\alpha$ is same, and the phase difference in the echoes of the two frequency signals is mainly caused by the difference in wavelength. The phase scaling factor $k$ is defined as shown in Equation (12).

$$k=\frac{{\lambda }_2}{{\lambda }_1}=\frac{f_{c1}}{f_{c2}}$$

(12)

The amplitudes of the two frequency echo signals in Equations (10) and (11) are added to obtain the joint amplitude $AA$, as shown in Equation (13). The phase of the echo signal at frequency $f_{c2}$ is multiplied by the scaling factor $k$ and subtracted from the signal at frequency $f_{c1}$ to obtain a differential phase $\Delta \phi$, as shown in Equation (14). After subtraction, the fluctuation of the single-frequency signal over time t is canceled out. The differential phase $\Delta \phi$ is close to zero, with only small amplitude random noise ${\phi }_{noise}$.

$$AA=A_3·X(\tau -\Delta t)·dec(\frac{v·(1+\cos \alpha )}{{\lambda }_1})+A_3^{\prime }·X^{\prime }(\tau -\Delta t)·dec(\frac{v·(1+\cos \alpha )}{{\lambda }_2})$$

(13)

$$\begin{array}{l}\Delta \phi =\left\{2\pi ·\frac{v·(1+\cos \alpha )}{{\lambda }_1}·(t_m+\tau -\Delta t)\right\}-k·\left\{2\pi ·\frac{v·(1+\cos \alpha )}{{\lambda }_2}·(t_m+\tau -\Delta t)\right\}\\ ={\phi }_{noise}\end{array}$$

(14)

Then, a new signal $\Delta s(\tau ,t_m)$ is composed of joint amplitude $AA$ and differential phase $\Delta \phi$, as shown in Equation (15). It fully utilizes the amplitude of dual-frequency signals and eliminates the fluctuation of the signal phase over time, allowing for long-term coherent accumulation to improve signal SNR.

$$\Delta s(\tau ,t_m)=AA·\exp \{-j·{\phi }_{noise}\}$$

(15)

3. Simulation and Experimental Results

In this section, firstly, the processing effect of the dual-frequency echo of a point target was simulated using the B1 and B3 signals of the BDS satellite. Then, detection experiments were carried out to verify the effectiveness of the GNSS-S dual-frequency echo signal processing method for high-speed weak target echo signal processing.

3.1. Simulation

In order to deeply observe the detailed effect of this method, a simulation is performed in this section. Firstly, the phase changes in dual-frequency echo signals caused by moving targets were analyzed. Then, the effect of using the dual-frequency differential method to eliminate phase fluctuations was simulated. Finally, the effect of the coherent accumulation of dual-frequency differential signals is presented. During the simulation, the original signal is generated according to the real signal format of the GNSS satellite, and Gaussian white noise is added as background interference. The simulation uses signals of BDS B1 and B3 frequency, and the sampling frequency fs is 200 MHz. The detailed parameters are shown in

Table 2. Parameters of the Simulation.

Parameter	Value
Signal type	BDS B1, B3
Carrier frequency	B1:1561.098 MHz; B3:1268.52 MHz
PRN code period	1 ms
SNR	−20 dB
Initial speed of the target	16 m/s
Acceleration of the target	10 m/s2

.

After the target echo signal is demodulated and correlation compressed, the data are vertically arranged according to PRN code period, and then the target trajectory of the B1 echo signal and B3 echo signal is obtained, as shown in Figure 8. In order to intuitively analyze the signal phase fluctuation, a higher echo SNR is adopted in the simulation; so, the signal trace can be seen after the signal demodulation in Figure 8.

Figure 8a is the target echo trajectory of the B1 signal, and Figure 8b is the target echo trajectory of the B3 signal. Because the bandwidth of the B3 signal is larger than the bandwidth of the B1 signal, the track line in the figure is thinner than that of B1; that is, it has a higher range resolution.

Then, the SNR of the B1 and B3 echo signals in Figure 8 is calculated to form the SNR curve shown in Figure 9. Due to the acceleration, the velocity of the target is increasing, and the residual Doppler shift of the echo is also increasing, which makes the SNR of the compressed echo decrease. Since the frequency of the B1 signal (1561.098 MHz) is larger than that of the B3 signal (1268.52 MHz), the same target motion speed will cause a greater Doppler shift. So, the decline amplitude of the SNR curve of B1 (blue curve) in Figure 9 is greater than that of the B3 signal (orange curve).

Due to the fact that the B1 and B3 signals are simultaneously transmitted by the same satellite, the amplitudes of the two correlated compressed single-frequency signals in Figure 8 can be directly added to obtain the trajectory of amplitude enhancement, as shown in Figure 10. Comparing the color bars on the right side of Figure 8 and Figure 10, it can be observed that after combining the signal amplitudes of the two frequencies, the signal energy increases by one time, from 10,000 to 20,000.

Due to the low power of the real GNSS signal, further coherent accumulation is required after amplitude accumulation to detect the signal. Then, in order to analyze the relationship between the signal phase changes in B1 and B3, the signal cells from the original data in Figure 8 were selected, as shown in Figure 11a,b. It can be seen that due to the existence of target movement, the signal phase (the blue lines) is constantly changing between ±180° (the red lines) with slow time $t_m$. It can be seen that due to the influence of signal phase changes between each piece of data, long-term coherent accumulation cannot be performed.

After unwrapping the signal phase, the continuously changing phase diagram is shown in Figure 12a. Since the carrier frequencies of the BDS B1 and B3 signals are different, the Doppler slopes and the initial phase of the two frequency echoes are different. In order to realize the phase difference correction of the dual-frequency signal, it is very necessary to correct the slope and initial phase of the two frequency echo signals to be consistent. For the correction of the signal phase slope, the correction coefficient $k$ is calculated according to Equation (12). Then, the phase of the B3 signal is multiplied by the correction coefficient $k$ for correction. The corrected signal phases of the two frequencies are shown in Figure 12b, and it can be seen that the slopes of the two signals have become consistent.

Then, the corrected phases of the B1 and B3 signals are differentiated, and then the initial phase deviation is subtracted to obtain echo signals with consistent phases. The phase of the corrected differential signal is shown in Figure 13, and the variation range of the signal phase (the blue lines) is basically maintained within the range of ±45° (the red lines), which ensures the coherence of the signal phase.

After the target echo signals are demodulated and correlation compressed, the signals are in the form of complex numbers. Before phase correction, residual Doppler will cause an irregular rotation of the signal phase in the slow-time dimension, as shown in Figure 14a. Because the GNSS echo signal is very weak, it is necessary to perform coherent accumulation on the signal to enhance SNR. As shown in Figure 14b, in order to achieve gain improvement after signal accumulation, it is necessary to adjust the phase difference in the adjacent signals to within 120°. From Figure 13, it can be seen that the phase difference between adjacent signals is less than 90°, which ensures an increase in amplitude after signal addition.

The phase-corrected signal is coherently accumulated for 200 ms along the slow time $t_m$, and the trajectory of the target echo signal is obtained as shown in Figure 15. The SNR of the signal in Figure 15 is calculated to form the curve shown in Figure 16. Compared with Figure 9, the SNR of the signal is greatly improved, and it no longer attenuates with increasing velocity.

3.2. Experiments

In order to further prove the effectiveness of the proposed method, a field test was carried out in Beijing Environmental Science and Technology Park using the experiment equipment shown in Figure 2. The experimental site is shown in Figure 17. The B1 and B3 frequency signals of the BDS satellite are selected as the illumination source.

Figure 18 shows the experimental scene, with the detection equipment installed on the roadside to detect cars passing by at high speeds. During the experiment, the detected target 1 was a small car with a speed of approximately 45 km/h. The detected target 2 is an SUV vehicle with a speed of approximately 35 km/h. The two cars are traveling in the same direction, from south to north.

Figure 19 shows the distribution of the BDS satellites received at the experimental site. In the figure, the receiver is located at the center, and two cars pass from south to north. In order to achieve target detection, satellites that form a backscattering geometric relationship are selected from visible satellites as the illumination source. Four typical satellites that constitute backscatter are selected as the illumination sources for detection. The information on the four satellites is shown in

Table 3. Position information on the selected four satellites.

Satellite ID	Elevation/°	Azimuth/°	Bistatic Angle α/°
1	35	140	51
3	44	189	45
6	62	234	74
38	49	169	50

.

Figure 20 shows the original 2D data after the signal is compressed. In the figure, the horizontal axis R represents the bistatic distance, and the vertical axis tm represents slow time. Since the navigation satellite signal scattered by the car is extremely weak, the target information cannot be directly observed without accumulation in the slow-time dimension.

In order to compare the accumulation effects of single-frequency and dual-frequency processing methods, the signal accumulation images obtained by the two methods are listed below. Firstly, the single-frequency signal is used for coherent accumulation processing to obtain the target echo signal trajectory in the “time–distance” domain. Figure 21 shows images of echo traces of B1 frequency signals of four satellites: No. 1, No. 3, No. 6, and No. 38, and Figure 22 shows images of echo traces of B3 frequency signals of these four satellites. The images show that the accumulation effect of single-frequency signals is limited, which is due to the effect of the target velocity in the single-frequency echo. The maximum coherent accumulation time is 6 ms, and the signal becomes weaker when the accumulation time is further increased. After accumulation, only the echo trajectories of satellite No.38 are faintly visible, while the echo trajectories of satellites No.1, No.3, and No.6 are almost invisible.

For the satellite echo signals in Figure 21 and Figure 22, the SNR curve of the signal is obtained by counting the SNR row by row, as shown in Figure 23. Figure 23a is the SNR of the echo of the B1 signals, and Figure 23b is the SNR of the echo of the B3 signals. It can be seen that except for the No. 38 satellite, which has a higher SNR (the highest value is about 5 dB), the SNR of other satellites is very low.

Then, the scattering signals of B1 and B3 frequencies of BDS satellites No. 1, No. 3, No. 6, and No. 38 are, respectively, processed by the dual-frequency method proposed in this paper, and then the coherent accumulation is carried out for 500 ms to obtain the “time–distance” domain accumulation results, as shown in Figure 24. In the figure, the vertical axis is the slow time $t_m$, and the horizontal axis is the bistatic distance R. The two cars move from south to north, and the distance between them and the GNSS-S receiver changes from close to distant. Therefore, two echo signal trajectories are obtained in Figure 24, which correspond to the echo signals of the two cars, respectively. As the distance increases, the echo signal power gradually becomes weaker. In addition, the echo trajectories obtained by the four BDS satellites in Figure 24 are different, which is due to the difference in bistatic RCS characteristics of the vehicles under different illumination angles of the GNSS satellite.

For the satellite echo signals in Figure 24, the SNR curve of the signal is obtained by calculating the SNR row by row, as shown in Figure 25. It can be seen that the SNR of the satellite echo has been greatly improved (the highest SNR reaches 28 dB).

As can be seen from Figure 24, the target echo trajectories achieved from different satellites are different, which is due to the different bistatic RCS characteristics of the targets in different directions. Finally, the echo trajectories of the four satellites are incoherently accumulated after geometry calibration to obtain a more continuous target echo trajectory with enhanced energy, as shown in Figure 26. Because the echo signal energy of different satellites is different, it is necessary to normalize the respective signal energies first and then perform the joint accumulation of multisatellite signals.

In Figure 26, the horizontal axis represents the bistatic distance of the moving target. As the distance increases, the signal strength gradually weakens, and when the distance exceeds 75 m, the signal disappears. Therefore, it can be inferred that the maximum detectable bistatic distance of the car targets is approximately 75 m. According to the geometric relationship shown in Figure 3, the detectable ground distance for the car targets is approximately 59 m.

4. Discussion

In the present research, this article proposes a dual-frequency processing method to address the problem of weak GNSS echo signals and residual Doppler effects on signal accumulation gain when using GNSS-S radar for moving target detection. This method utilizes signals of two frequencies naturally transmitted by GNSS satellites to achieve an increase in echo gain from two aspects: on the one hand, the amplitude of the echo signals at two frequencies is added to make up for the amplitude attenuation of the single-frequency signal caused by residual Doppler after correlation compression; on the other hand, the phase fluctuation of the echo signal caused by the residual Doppler is eliminated through the phase difference in the dual-frequency signal, and the gain of coherent accumulation of the echo signal is improved.

The GNSS signal itself is very weak (the power reaching the ground is only about −130 dBm), and when used for target detection, the scattered echo power of the target further attenuates. To achieve the detection of target echoes, it is necessary to accumulate the signals for a long time to improve the SNR of the echoes. When used for detecting moving targets, the movement of the target brings additional Doppler frequency, which makes it very difficult to perform long-term coherent accumulation. In existing research, some scholars have combined coherent integration with incoherent integration to further improve SNR. However, due to the square loss of incoherent integration, the improvement effect of SNR is limited. Other scholars have carried out research on time–frequency analysis methods such as fractional Fourier transform and Radon Fourier transform to analyze the frequency characteristics of the echoes. After identifying the Doppler frequency in the echo, they can suppress the fluctuation of the echo phase by compensation to extend the coherent integration time. However, when the target motion is a high-order motion, the time–frequency analysis operation will be very complex and the amount of calculation will be large.

However, as the GNSS signal is a PRN-encoded signal, it is sensitive to Doppler frequency shifts. The residual Doppler caused by target motion will cause attenuation of signal amplitude when performing correlation compression on the echo signal, which cannot be compensated by later coherent accumulation. Fortunately, the GNSS satellite system naturally transmits signals at multiple frequencies, and these signals have natural similarities. They are all sent by the same satellite and have the same propagation path. Therefore, if the signals of these multiple frequencies can be fully utilized during target detection, the energy of the echo signal will be significantly increased to make up for the shortcomings of weak signal power.

In addition, the multiple frequency signals transmitted by GNSS satellites are of the same source and frequency. Using the dual-frequency difference method proposed in this paper, the phase fluctuation caused by target motion can be effectively eliminated, which will improve the coherence of the echo signals, and a longer coherent accumulation time can be used to improve the SNR of the echo signals. This is very helpful for improving the detection ability of weak GNSS echo signals. Moreover, the algorithm is simple and can avoid complex mathematical operations, which will facilitate the realization of real-time processing.

However, the processing method in this paper only considers signals with two frequencies, while the GNSS satellite system usually transmits signals at multiple frequencies, for example, BDS transmits signals at three frequencies at the same time. If three or more frequency signals can be further considered in the processing process, the gain of the target echo can be increased again.

5. Conclusions

GNSS-S radar uses GNSS signals as the illumination source, which has significant advantages and broad application prospects. However, due to the fact that GNSS signals are mainly used for positioning and timing and are not specifically designed for target detection, their signal power is extremely weak, and their processing gain is easily affected by Doppler frequency shift. When used for detecting moving targets, it is necessary to eliminate the influence of residual Doppler frequency in order to effectively improve signal gain. This paper makes full use of the two-frequency signals transmitted by the GNSS satellite and proposes a dual-frequency GNSS-S echo signal processing method. By analyzing the relationship between the amplitude and phase of two-frequency echo signals, a new ideal differential signal is constructed by combining the additive amplitude and differential phase of the dual-frequency signal. The amplitude of the signal is enhanced, and the phase is consistent, which can be used for long-term coherent accumulation to improve the echo SNR. The effectiveness of this method is verified by simulation and field experiments. It can significantly improve the processing gain of coherent accumulation and successfully realize the detection of high-speed moving cars by GNSS-S radar.