5G Radiation Source Location Based on Passive Virtual Aperture Technology by Single-Satellite

Abstract

With the development of 5th-Generation Mobile Communication (5G) technology and the deployment of low-Earth orbit satellites, using satellites to locate 5G radiation sources is of great significance in commerce and the military as an important task of integrated sensing and communication. Recently, passive virtual aperture technology has been introduced into passive location to improve accuracy, but the existing method, using matched filters to search the Doppler information to realize the location, has the disadvantages of high complexity and poor range resolution. In this paper, an improved 5G radiation source location based on a virtual aperture is proposed, which uses the improved Golden Section search-fractional Fourier algorithm (GSS-FRFT) to improve the existing passive virtual aperture location methods. First, the received signals are coherently accumulated to convert the time gain into spatial gain, and the subcarrier phase information is extracted by Fast Fourier Transform based on the 5G signal characteristics to obtain the azimuth signal. Then, an improved high-order GSS-FRFT algorithm is proposed to analyze the Doppler information, and signal focusing and satellite ephemeris data are used to estimate the effective velocity and solve the radiation source location. The simulation results show that the proposed method can improve the location accuracy compared with other single-satellite location methods and has high resolution, high accuracy and low complexity compared with the existing passive virtual aperture location method.

1. Introduction

With the rapid advancement of 5th-Generation Mobile Communication Technology (5G) network construction and the forward-looking deployment of 6th-Generation Mobile Communication Technology (6G), the realization of integrated sensing and communication has become a current research hotspot and future development trend. In addition, various countries and companies are vigorously deploying low-orbit communication satellites. Against this background, it is of great significance to use low-orbit communication satellites to detect and locate radiation sources such as communication base stations or terminals. On the one hand, location results can be used by communication satellites to provide more accurate user services, and, on the other hand, directional shielding or interference can be realized by detecting non-cooperative users.

Source location technology has been greatly developed in the past decades, and uses intercepted signals to realize the real-time and all-weather detection of radiation sources, with the advantages of long detection distance, low power consumption and strong anti-interference ability [1,2]. Typical passive location methods include direction of arrival (DOA), Doppler shift localization, time difference of arrival (TDOA), frequency difference of arrival (FDOA) and the joint location method [3]. For DOA systems, antenna arrays or phase interferometers are usually used for direction finding [4], which is a typical single-satellite location method. The principle of the method determines that a complex antenna array is need for high precision, so the location accuracy is relatively poor, limited by the moving platform [5]. The problem for the systems using phase interferometers is that a long baseline is needed for higher location precision, but this causes phase ambiguity, which needs complex antenna structures to solve. For systems using antenna arrays, DOA algorithms include a conventional beamformer (CBF), multiple signal classification (MUSIC) and a maximum likelihood estimator (MLE) [6]. In addition, with the development of deep learning, the DOA algorithm based on neural networks has been applied to reduce the computational complexity and improve the precision [7]. However, the algorithm’s improvement has a limit on the estimation performance improvement, and the traditional methods based on scalar sensors all require complex antenna structures to improve performance. Therefore, in recent years, the electromagnetic vector sensor (EMVS) array has been used to perform two-dimensional azimuth estimation, which further improves the DOA accuracy [8,9].

Doppler systems use multiple measurements of Doppler information to complete the source location, which is also a typical single-satellite location method. Compared with the DOA method, the principle is simple, but long-time observation is need and the measurement accuracy of the instantaneous Doppler information is limited [10,11]. TDOA and FDOA methods rely on the multi-satellite platform, using the time difference or frequency difference between different satellites to achieve location; these have high location accuracy but require time synchronization strictly due between the satellites, resulting in high system complexity and cost [12,13]. Multi-satellite systems also use methods that combine a variety of location methods, such as the combination of TDOA, FDOA and differential Doppler rate (DDR) [14], or the combination of time of arrival (TOA) and TDOA [15].

Orthogonal frequency-division multiplexing (OFDM) is an efficient multi-carrier transmission technology, with the advantages of flexibility, large bandwidth and good orthogonal characteristics, and it is the signal form of 5G communication. In addition to the above general passive location methods, there are passive location methods for OFDM signals, such as the MLE location algorithm, least squares estimator (LSE) location algorithm, and spectrum location method based on maximum likelihood estimation and OFDM signal multi-carrier technology [16]. In addition, for communication radiation sources, there is a single-satellite location method, Multi-RTT, which uses the round-trip time difference of the received communication signals to obtain the distance between the satellite and the radiation source at different positions of the satellite. The principle of the method is simple, but the location accuracy is limited and the observation time is long [17].

Recently, researchers introduced the synthetic aperture into passive location to improve the location accuracy, which can solve the contradiction between the location accuracy and the system complexity of the existing passive location algorithms [18]. Li et al. proposed an improved method applied to the spaceborne platform, and analyzed the performance of the algorithm [19,20]. Zhang et al. proposed a passive location method based on a virtual aperture for 5G sources [21]. However, the algorithm uses matched filters to search the Doppler information, which have limited accuracy and large computation. And the azimuth resolution is high but the range resolution is poor.

On this basis, the paper proposes a virtual aperture passive location method based on Golden Section search-fractional Fourier transform (GSS-FRFT). GSS-FRFT is improved by using the maximum value of high-order origin moment as the search target, which can improve the resolution. In addition, due to the influence of satellite orbit curvature and Earth curvature, an iterative algorithm for effective velocity estimation is used. The paper also theoretically analyzes the resolutions and algorithm complexity.

The paper is organized as follows. The signal model of passive location based on the virtual aperture for 5G signals and the principle of the proposed method are introduced in Section 2. Section 3 presents the theoretical analysis of resolutions and algorithm complexity. Section 4 gives the simulation results. Finally, the conclusions are drawn in Section 5.

2. The Signal Model and Principle of the Proposed Method

2.1. The Signal Model

The model of the passive virtual aperture location method is shown in Figure 1. The flight path over the radiation source is regarded as a straight line. In the location plane, the flight path direction is the azimuth direction and the direction perpendicular to the flight path is the range direction. However, because of the influence of the satellite orbit curvature and Earth curvature, the actual satellite velocity cannot satisfy the straight-line distance model, as Figure 1 shows. Therefore, the effective velocity, $v_r$, is introduced as the satellite velocity to reconcile the contradiction between the actual velocity and the straight-line distance model. The satellite can receive the signal emitted by the radiation source from A to B. The slant distance from the satellite to the radiation source during the signal reception time can be expressed as (1), which is is expanded by the Taylor series at $t=t_p$ and retained to the quadratic term for approximation.

$$R\left(t\right)=\sqrt{R_p^2+{(v_{r}t-v_r{t}_p)}^2}=\sqrt{R_p^2+v_r^2{(t-t_p)}^2}\approx R_p+{\displaystyle \frac{v_r^2{(t-t_p)}^2}{2R_p}}.$$

(1)

where $v_r$ denotes the satellite effective velocity, t denotes the flight time of the satellite, $R_p$ denotes the range distance, and $t_p$ denotes the azimuth time.

The signal of the 5G radiation source is an OFDM signal, which can be expressed as

$$s\left(t\right)=\sum _{m=0}^{\infty }\sum _{l=0}^{L-1}\sum _{k=0}^{K-1}{c}_{mlk}{e}^{j2\pi f_{k}t}rect\left\{t-l{T}_s-mL{T}_s\right\}$$

(2)

where

• $m,l,k$ denote the slot, OFDM symbol and subcarrier number, respectively;
• $L,K$ denote the number of OFDM symbols per slot and the number of subcarriers;
• $c_{mlk}$ denotes the modulation symbols of subcarriers;
• $f_k$ denotes the subcarrier frequency;
• $T_s$ denotes the duration of an OFDM symbol;
• $\mathrm{rect}\{·\}$ denotes a rectangular function representing the duration of a symbol.

The received signal, $s_r\left(t\right)$, is expressed as

$$s_r\left(t\right)=s(t-\tau \left(t\right))=s(t-{\displaystyle \frac{R\left(t\right)}{c}})$$

(3)

According to the principle of the OFDM signal, the carrier-frequency Doppler information can be extracted by Fast Fourier Transform (FFT). The general processing process is as follows [21]. First, intercept the baseband received signal in time slots to form a received signal matrix; each row corresponds to a slot signal. Each subcarrier signal can be extracted by FFT along the row. The reference signal of the 5G signal can be used for channel estimation to compensate the phase of the modulation symbol. After the above processing, the azimuth domain signal at frequency $f_0$ is expressed as

$$s_m\left(t\right)={\left|C_m\right|}^{2}exp\{-j2\pi f_0{\displaystyle \frac{R\left(t\right)}{c}}\}$$

(4)

where $C_m={\displaystyle \sum _{l=0}^{L-1}}{c}_{ml0}$. The Doppler frequency is

$$f_d={\displaystyle \frac{d}{dt}}\left(-f_0{\displaystyle \frac{R\left(t\right)}{c}}\right)=-{\displaystyle \frac{v_r^2{f}_0}{R_{p}c}}(t-t_p)$$

(5)

Thus, $s_m\left(t\right)$ is an LFM signal with the Doppler rate $K=-f_0{v}_r^2/c{R}_p$ and the Doppler center time $t_p$. Since the radiation source location can be determined by $R_p$ and $t_p$, the estimation of Doppler information can realize the location. In addition, the azimuth sampling frequency is $f_a={\displaystyle \frac{1}{T_{slot}}}=2^{\mu }\left[\mathrm{kHz}\right]$, and the virtual synthetic aperture time is $T_a=L_a/v_r=\theta R_p/v_r=kc{R}_p/v_r{f}_{0}D$, where D is the antenna aperture and k is the beam width factor.

2.2. Doppler Estimation Based on Improved GSS-FRFT

Since FRFT is performed on a set of orthogonal LFM bases, FRFT has good focusing properties for LFM signals and good performance on parameter estimation of LFM signals.

The mathematical representation of the FRFT [22] for the signal $f\left(t\right)$ is shown as (6)–(9).

$$F_{\alpha }\left(u\right)={\mathcal{F}}^{\alpha }\left\{f\left(t\right)\right\}\left(u\right)={\int }_{-\infty }^{+\infty }f\left(t\right)K_{\alpha }(t,u)dt$$

(6)

where $\alpha ={\displaystyle \frac{\pi }{2}}p$ is the rotation angle of the time–frequency plane, p is the order of FRFT, ${\mathcal{F}}^{\alpha }$ is the operator of FRFT, and $K_{\alpha }(t,u)$ is the kernel of FRFT, expressed as

$$K_{\alpha }(t,u)=\left\{\begin{array}{cc}{A}_{\alpha }{e}^{j\pi \left(t^2+u^2\right)cot\alpha -j2\pi utcsc\alpha },\hfill & \alpha \ne n\pi \hfill \\ \delta (t-u),\hfill & \alpha =2n\pi \hfill \\ \delta (t+u),\hfill & \alpha =(2n\pm 1)\pi \hfill \end{array}\right.$$

(7)

where $A_{\alpha }=\sqrt{1-jcot\alpha }$, $\delta \left(t\right)$ is the Dirac function.

Figure 2 shows the time, frequency and fractional Fourier domains for LFM signals. The signals can be focused in fractional domains at the optimal angle, ${\alpha }_0$. The normalized chirp rate, $k_r$, initial frequency, $f_{p0}$, and Doppler center time, $t_{p0}$, can be estimated by the optimal angle, ${\alpha }_0$, and the coordinate, $u_0$, corresponding to the FRFT peak at this angle. The normalized scale of FRFT is $S=\sqrt{T/B}$, where T and B are the time and frequency width of the LFM signal. In the model of the paper, the time width is equal to the virtual synthetic aperture, and the frequency width is equal to the azimuth sampling frequency, that is, $S=\sqrt{T_a/f_a}$. The actual chirp rate, K, initial frequency, $f_p$, and Doppler center time, $t_p$, are:

$$\begin{array}{cc}\hfill & K=k_r/S^2,k_r=-cot{\alpha }_0\hfill \\ \hfill & f_p=f_{p0}/S,f_{p0}=u_{0}csc{\alpha }_0\hfill \\ \hfill & t_p=t_{p0}S,t_{p0}=u_{0}sec{\alpha }_0\hfill \end{array}$$

(8)

${\alpha }_0$ and $u_0$ can be obtained by searching for the maximum value of FRFT under different rotation angles:

$$\left\{{\widehat{\alpha }}_0,{\widehat{u}}_0\right\}=\underset{\alpha ,u}{\arg \max }\left\{\left|F^{\alpha }\left(u\right)\right|\right\}$$

(9)

The search for the maximum value by (9) requires a two-dimensional search in the FRFT domain, which requires a large amount of computation [23]. To improve the computation speed and reduce the amount of computation, scholars have proposed various improved algorithms. Aldimashki et al. used the GSS iterative algorithm to search for the optimal order of FRFT [22]. The algorithm used the golden ratio $r=\frac{\sqrt{5}-1}{2}$ for interval division and simplified two-dimensional search into one-dimensional search, which could effectively reduce the amount of computation, complete the optimal order estimation with the least number of iterations, and approach CRLB under low SNR. To further improve the resolution and reduce the influence of noise, an improved GSS-FRFT method is proposed in this paper, which uses 4-order origin moment instead of the maximum to search the optimal rotation angle. Since the period of $\alpha$ for LFM signals is $\pi$ and the Doppler rate, K, is a negative number, the initial interval of $\alpha$ is $\alpha \in (0,\frac{\pi }{2})$. The flow is shown in Figure 3. First, initialize ${\alpha }_1$ and ${\alpha }_2$ according to the initial search interval $(0,\frac{\pi }{2})$. Then, FRFT is performed under the angles ${\alpha }_1$ and ${\alpha }_2$, respectively, and the corresponding 4-order origin moments $v_1$ and $v_2$ are obtained. Compare $v_1$ and $v_2$, and retain the angle corresponding to the larger value of the 4-order origin moment and update the other angle. Cycle the above operation until the interval length is less than the set accuracy. The optimal rotation angle is the angle corresponding to the larger value of the 4-order origin moment of the FRFT.

After the FRFT under the estimated optimal rotation angle, $\widehat{{\alpha }_0}$, the estimation of the Doppler chirp rate, $\widehat{K}$, and Doppler center time, $\widehat{t_p}$, can be obtained by (8).

2.3. Effective Velocity and Location Estimation Method

The range distance can be estimated by the estimation of the Doppler chirp rate, $\widehat{K}$; the estimation of range distance is

$$\widehat{R_p}=-{\displaystyle \frac{f_0{v}_r^2}{c\widehat{K}}}$$

(10)

The method to solve the radiation source position in ECEF by the estimated $\widehat{t_p}$ and $\widehat{R_p}$ is given as follows. In the distance model in Figure 1, at the Doppler center time, $t_p$, the distance between the satellite and the radiation source is $R_p$, and the radial velocity of the satellite is 0. And the radiation source is a ground target. So, the radiation source position in ECEF can be solved by the function (11).

$$\begin{array}{cc}\hfill & {\mathit{V}}_{\mathit{T}}·{\left({\mathit{S}}_{\mathit{T}}-\mathit{U}\right)}^T=0\hfill \\ \hfill & \left({\mathit{S}}_{\mathit{T}}-\mathit{U}\right)·{\left({\mathit{S}}_{\mathit{T}}-\mathit{U}\right)}^T={\widehat{R}}_p^2\hfill \\ \hfill & diag\left(1,1,{(1-f)}^{-2}\right)·\mathit{U}·{\mathit{U}}^T=R_e^2\hfill \end{array}$$

(11)

where ${\mathit{S}}_{\mathit{T}}$ and ${\mathit{V}}_{\mathit{T}}$ are the position and velocity of the satellite at $\widehat{t_p}$, which is known. $R_e=6378.137$ km is the radius of the Earth and $f=1/298.257223563$ is the oblateness of the Earth.

The effective velocity is introduced to correct the location model, and an estimation method based on signal focusing is shown in Algorithm 1. The orbital velocity of the satellite, $v_s$, is taken as the initial effective velocity, and the range distance corresponding to the effective velocity can be estimated by (10). The target position in the Earth-centered Earth-fixed (ECEF) coordinate system $\widehat{\mathit{U}}$ can be solved by the satellite position at $\widehat{t_p}$ and the range distance, $\widehat{R_p}$. The ECEF position of the satellite in the virtual aperture time $\widehat{\mathit{S}}$ is known, which is used to construct the filters. The signal $s_m\left(t\right)$ is filtered to obtain the peak value. Since the effective velocity of the satellite is less than the orbital velocity, the above process is repeated with a decreasing interval of 50 m/s until the velocity corresponding to the maximum peak value is found. To further improve the estimation accuracy, we can take 5 points near $\widehat{v_r}$ with a 10 m/s interval and repeat the above process to find the peak of the maximum, which corresponds to the effective velocity, $\widehat{v_r}$.

Algorithm 1: Principle of effective velocity estimation method.

Initialize:            $\widehat{v_r}=v_s, \widehat{R_p}=-f_0{\widehat{v_r}}^2/c\widehat{K}$, $(\widehat{t_p},\widehat{R_p})\to \widehat{\mathbf{U}}$    Set the filters: $H=exp\{j2\pi f_0{\displaystyle \frac{R_t}{c}}\}, R_t=\left|\right|\mathbf{S}-\widehat{\mathbf{U}}\left|\right|$    Filter the processed signal and find the peak:    $P_k=max\left\{\right|s_m\left(t\right)\otimes H\left|\right\}$    if $P_k<P$    break    else       $\widehat{v_r}=\widehat{v_r}-50 [\mathrm{m}/\mathrm{s}]$, $P=P_k, k=k+1$    end if    return $\widehat{v_r}$

The complete process of the proposed method is as follows. First, the received 5G baseband signal is rearranged into range and azimuth domains. Then, FFT is performed along the range domain to extract the signal at a particular frequency and the phase of the data symbol is compensated. Thus, an LFM signal in the azimuth domain containing the location information is obtained. Improved GSS-FRFT is used for Doppler analysis. Combining the location model, the effective velocity and the radiation source location can be estimated.

3. Analysis of the Method Performance

3.1. Analysis of Resolutions

The amplitude of the results at different rotation angles has Fresnel function characteristics, and the resolution of the rotation angle for the LFM signal is ref. [24]

$${\rho }_{\alpha }=arctan\left({\displaystyle \frac{6.9485T_a^2}{\left(K^2+1\right)T_a^4-12.0704}}\right)$$

(12)

The range resolution ${\rho }_r=|R_1-R_2|$ can be calculated as:

$$\begin{array}{c}\hfill {\displaystyle \frac{K_1}{2}}-{\displaystyle \frac{K_2}{2}}={\displaystyle \frac{f_0{v}_r^2}{2c{R}_1}}-{\displaystyle \frac{f_0{v}_r^2}{2c{R}_2}},{\rho }_r=\left|R_1-R_2\right|\approx {\displaystyle \frac{2c{R}_p^2}{f_0{v}_r^2}}{\rho }_k\end{array}$$

(13)

where ${\rho }_k=k_{\alpha }{\rho }_{\alpha }$ is the resolution of the chirp rate, and $k_{\alpha }$ is the slope of the curve $y=-cotx$ at ${\alpha }_0$.

The range resolution of the existing method based on matched filters is ref. [21]

$${\rho }_{r_0}={\displaystyle \frac{6.9485c{R}_p^2}{f_0{v}_r^2{T}_a^2}}$$

(14)

The amplitude envelope of the Fractional Fourier domain (FRFD) is an Sinc function, and the resolution in FRFD is

$${\delta }_u\approx {\displaystyle \frac{0.886}{T_a}}|sin{\alpha }_0|$$

(15)

According to (8), the azimuth distance resolution is

$${\delta }_x\approx {\displaystyle \frac{0.886}{T_{a}K}}{v}_r$$

(16)

The azimuth of the existing method is ${\delta }_{x_0}=c{R}_p/v_r{f}_0{T}_a$ [21], since $K=-f_0{v}_r^2/c{R}_p$, ${\delta }_{x_0}=v_r/T_{a}K$, so the azimuth resolution of the proposed method is better than the existing method.

Since the improved GSS-FRFT algorithm uses higher-order statistics, the azimuth resolution is consistent with the basic FRFT algorithm, but it is difficult to express the distance resolution directly by mathematical formula. Therefore, Monte Carlo experiment simulation is used to verify the superiority of the proposed algorithm in resolution. The specific explanation and results are shown in Figure 4.

3.2. Analysis of Computation Complexity

According to the principle of the proposed method, the received signal is first transformed into a two-dimensional matrix, whose size is $M\times N$, and FFT along the row of the matrix is done. Since the complexity of N-points FFT is $\mathcal{O}\left(N{log}_{2}N\right)$, the complexity of this process is $\mathcal{O}\left(MN{log}_{2}N\right)$.

For phase compensation, if the number of DM-RS symbols is K in a slot, the complexity of the least square method is $\mathcal{O}\left(K\right)$, and the complexity of the interpolation method is $\mathcal{O}\left(N{log}_{2}N\right)$. So, the complexity of the process is $\mathcal{O}\left(MN{log}_{2}N\right)$.

Then, extract the signal at a particular frequency, obtaining an M-point LFM signal in the azimuth domain. The complexity of improved GSS-FRFT for Doppler analysis is $\mathcal{O}\left(K_{f}N{log}_{2}N\right)$, and $K_f$ is the times of FRFT.

In summation, the computation complexity of the proposed algorithm is $\mathcal{O}\left(MN{log}_{2}N\right)$. Compared with the passive virtual aperture location method based on matched filters [21], whose computation complexity is $\mathcal{O}(MN{log}_{2}N+N{M}^2)$, the complexity is lower.

4. Simulation and Results

The parameters of the simulation are shown in

Table 1. Parameters of signal and satellite.

Parameters	Values
Center frequency	29 GHz
Subcarrier interval	30 kHz
Bandwidth	50 MHz
Sampling frequency	122.88 MHz
Modulation	16QAM
Antenna aperture	5 m
SNR	5 dB
Inclination	49 deg
Semimajor	6876 km
Eccentricity	0
Source location	(−1821.6, 3766.26, 4799.15) km

. The spectrum of the 5G signal ranges from 450 MHz to 6 GHz and 24 GHz to 52 GHz, and the frequency of the signal is 29 GHz in the paper. After the simulation by STK, the virtual aperture time is $T_a=0.1845\mathrm{s}$.

Figure 5 shows the estimation results of the Doppler. Figure 5a shows GSS-FRFT based on maximum search and 4-order moments results, respectively; the optimal rotation angle of the FRFT is $\widehat{{\alpha }_0}=0.86058$. The range resolution for maximum search GSS-FRFT is 23.25 km, and for improved GSS-FRFT is 6.25 km. So, improved GSS-FRFT can improve the resolution of range distance. Figure 5b shows the FRFT result at $\widehat{{\alpha }_0}$. The azimuth distance resolution is 3.308 m. So, the chirp rate and the Doppler center time can be calculated by (8), which are $\widehat{K}=-9.3214\mathrm{kHz}$ and $\widehat{t_p}=0\mathrm{s}$. The location of the satellite at $\widehat{t_p}$ and the estimation, $\widehat{K}$, are used to estimate the effective velocity and realize the location. The satellite velocity is $v_s=7.2849\mathrm{km}/\mathrm{s}$, and the estimated effective velocity is $\widehat{v_r}=6.9549\mathrm{km}/\mathrm{s}$. The location error is 1.398 km.

Figure 6 shows the comparison of FRFT times between the improved GSS-FRFT method and other FRFT search methods [22,23] under a different search accuracy and SNR, where SNR = 5 dB in Figure 6a and search accuracy $L_{\alpha }={10}^{-5}$ in Figure 6b. Compared with other search methods, the improved GSS-FRFT algorithm requires fewer search times, and only needs about 20 times to achieve a high-precision search.

In addition, the paper gives the resolution comparison curves of the existing passive virtual aperture location method based on matched filters [21], GSS-FRFT and improved GSS-FRFT. The Monte Carlo simulation results are shown in Figure 4. The results show that the resolutions can be better with the longer virtual aperture. In addition, the method based on improved GSS-FRFT can effectively improve the azimuth and range resolutions compared with the matched filters method, and improve the range resolution compared with the GSS-FRFT method.

The proposed passive virtual aperture location method based on improved GSS-FRFT is compared with the DOA, Multi-RTT and the passive location method based on matched filters via 500 Monte Carlo simulations. The DOA method uses the phase interferometer with 10 m baselines, and the phase ambiguity is solved. The Multi-RTT method of the simulation uses three times the measurement of the round-trip time between the satellite and the radiation source with the interval of 10 s. The location error curves with SNR is shown in Figure 7a; the virtual aperture time of the passive virtual aperture location method is 100 ms. The result shows that the proposed method has a better performance than the DOA and Multi-RTT methods. Figure 7b shows the error curves with the virtual aperture time of the passive virtual aperture location methods based on matched filters and improved GSS-FRFT, respectively. The curves show that the method based on improved GSS-FRFT is more sensitive to the virtual aperture time and has better performance, with a long virtual aperture time (>50 ms).

5. Conclusions

This paper proposed a novel passive location method based on a virtual aperture for 5G OFDM signals, using low-orbit communication satellites to locate ground-based 5G radiation sources, which helps the realization of integrated sensing and communication and satellite–Earth interconnection. The method uses the long virtual aperture formed by the satellite motion in space and coherently accumulates the continuous signals received during the virtual aperture time to improve the location accuracy. To improve the resolution and search accuracy, an improved GSS-FRFT algorithm is proposed, which uses the 4-order origin moment instead of the maximum value to search the optimal order. The improved GSS-FRFT algorithm is used to analyze the accumulated azimuth signals to obtain the location information. Combined with the satellite orbit model and the Earth model, the effective velocity of the satellite is introduced to establish a linear location model, and the location coordinates of the target are estimated. Compared with the existing passive virtual aperture location method based on matched filters, the simulation results show that the proposed algorithm can effectively improve the range and azimuth resolution, and the algorithm complexity is lower by theoretical analysis. In addition, the simulation results show that the passive virtual aperture location method has higher precision than the single-satellite DOA and Multi-RTT methods. In the subsequent research, the algorithm performance will continue to be optimized according to the characteristics of 5G signals, and the impact of multi-path problems on location during signal propagation will be analyzed and solved.