Doppler Modeling and Simulation of Train-to-Train Communication in Metro Tunnel Environment

The communication system of urban rail transit is gradually changing from train-to-ground (T2G) to train-to-train (T2T) communication. The subway can travel at speeds of up to 200 km/h in the tunnel environment, and communication between trains can be conducted via millimeter waves with minimum latency. A precise channel model is required to test the reliability of T2T communication over a non-line-of-sight (NLoS) Doppler channel in a tunnel scenario. In this paper, the description of the ray angle for a T2T communication terminal is established, and the mapping relationship of the multipath signals from the transmitter to the receiver is established. The channel parameters including the angle, amplitude, and mapping matrix from the transmitter to the receiver are obtained by the ray-tracing method. In addition, the channel model for the T2T communication system with multipath propagations is constructed. The Doppler spread simulation results in this paper are consistent with the RT simulation results. A channel physics modelling approach using an IQ vector phase shifter to achieve Doppler spread in the RF domain is proposed when paired with the Doppler spread model.

Sensors 2022, 22, 4289 3 of 13 speeds of more than 200 km/h along a given track in a tunnel environment cause higher Doppler shifts. Thus far, the channel modeling work in subway tunnels has mainly studied the influence of the LoS path, and the single-bounced and double-bounced signal on the channel in the same coordinate space in the V2G communication scene [38][39][40]. In the T2T communication system, the transceiver ends are located in different locations, so it is difficult to apply the same coordinate space analysis. In addition, the movement of the antenna causes rapid changes in the channel environment, complicating the signal propagation process. The influence of multi-bounced signals and the movement of the transceiver antenna on the Doppler shift must be considered, so a Doppler spread model suited for the movement of two-terminal terminals in the tunnel must be established.
In this paper, the receiver (Rx) and transmitter (Tx) coordinate systems are established, and the Doppler spread model of the multipath signals from the transmitter to the receiver is established in their respective coordinate systems. The mapping matrix approach is proposed as an innovative solution to the problem of signal matching at the receiver and transmitter, as well as a method for obtaining the mapping matrix. In order to verify the proposed Doppler model for T2T communication in the tunnel, the ray-tracing (RT) [41] approach is utilized to obtain the angle and amplitude of the signals at the transmitting and receiving ends. By comparing the simulation results of the RT approach with the simulation results of the Doppler spread model, the validity of the Doppler spread model is proved. A channel physical simulation method using IQ vector phase shifters [42,43] is proposed to execute the T2T communication channel simulation in the tunnel environment, which can be used for future tunnel environments when combined with the T2T channel model and test data analysis in the tunnel [44][45][46]. It can provide a reference for 5G millimeter wave physical channel simulation in the future tunnel environment.

Article Structure
The rest of this paper is organized as follows: In Section 2, the Doppler shift models for transmitted and received signals are established, followed by the solution method for the multipath signal mapping relationship at the transmit and receive ends and the multipath signal's Doppler spread model. In Section 3, the RT simulation method is used to obtain the angle, amplitude, and mapping relationship of the transmitted and received signals, and the Doppler spread simulation of the theoretical model is discussed. In Section 4, combined with the analysis of the communication signal in the tunnel, a method to realize physical channel simulation using an IQ vector phase shifter is proposed. Finally, Section 5 provides the conclusion of this paper. Figure 1 depicts a T2T communication scenario in which the front and rear trains run through a tunnel with a width W and a height H. The complicated propagation process of multipath signals through straight or curved tunnels, such as reflection and scattering, is represented by the multipath link between two trains. The space where the multipath link is located represents the complex channel environment, such as straight or curved tunnels. A three-dimensional coordinate system is established at the transceiver antennas, with the tunnel depth as the x-axis, the height as the z-axis, and the horizontal direction as the y-axis. The downlink of the T2T communication consists of the transmitting antenna Tx located in the rear train and the receiving antenna Rx located in the front train. In addition, v t and v r represent the moving speed of the transmitting antenna and the receiving antenna, and the moving direction follows the same path as the x-axis. The received signal consists of the NLoS signal that reaches the receiving antenna after multiple reflections and scattering. In the LoS scenario, it includes the LoS signal from the transmitting antenna to the receiving antenna. In order to study the doppler spread of T2T communication in the tunnel environment, it is assumed that the receiving and the transmitting antennas are omnidirectional uniform antennas. signal consists of the NLoS signal that reaches the receiving antenna after multiple re tions and scattering. In the LoS scenario, it includes the LoS signal from the transmi antenna to the receiving antenna. In order to study the doppler spread of T2T comm cation in the tunnel environment, it is assumed that the receiving and the transmi antennas are omnidirectional uniform antennas.  where , represents the angle between the signal ( , , , , , ) and the mo direction of Tx. ̂, and ̂ represent the unit vector in the direction of the transm signal and the unit vector in the direction of Tx movement. 0 is the signal carrier w length, and (•) represents the transpose of the matrix. Due to the movement of th ceiving antenna, the Doppler shift , of the signal ( , , , , , ) at the recei end can be expressed as

Wireless Channel Model of T2T Communication
and I = M, I and M represent the number of multipaths of transmitted and receiving signals. Let P t,i denote the transmit power of the i-th path signal, and P r,m denote the receive power of the m-th path signal. Then the spherical coordinate form of the transmitter signal and the receiver signal can be expressed as (P t,i , θ ZOD,i , φ AOD,i ) and (P r,m , θ ZOA,m , φ AOA,m ). Due to the movement of the transmitting antenna, the Doppler shift f i d,t of the signal (P t,i , θ ZOD,i , φ AOD,i ) can be expressed as where ψ t,i represents the angle between the signal (P t,i , θ ZOD,i , φ AOD,i ) and the moving direction of Tx.r t,i andv t represent the unit vector in the direction of the transmitted signal and the unit vector in the direction of Tx movement. λ 0 is the signal carrier wavelength, and (·) T represents the transpose of the matrix. Due to the movement of the receiving antenna, the Doppler shift f m d,r of the signal (P r,m , θ ZOA,m , φ AOA,m ) at the receiving end can be expressed as cos(ψ r,m ) =r T r,m ·v r (6) where ψ r,m represents the angle between the signal (P r,m , θ ZOA,m , φ AOA,m ) and the moving direction of Rx.r r,m andv r represent the unit vector of the received signal direction and the unit vector of the Rx moving direction. where , represents the angle between the signal ( , , , , , ) and the moving direction of Rx. ̂, and ̂ represent the unit vector of the received signal direction and the unit vector of the Rx moving direction.

Matching of Receiving and Transmitting Rays
In the proposed system, the transmitted and the received signals have a one-to-one mapping relationship, which means that for each received signal, a unique corresponding transmitted signal can always be located, completing a full signal chain from Tx to Rx. According to the roughness of the sidewall of the tunnel, the mapping relationship between the transmitted and receiving signals can be solved by the spatial mirror method and the random scatterer distribution method. The space mirror method is shown in  For the NLoS propagation path in the tunnel, this method solely considers reflection, and the mirror space is formed with the reflection surface as the axis. For the signal reflected for k (k = 0, 1, 2, …, K) times, the mirror image point Tx' of transmitting antenna Tx needs to be obtained through k times of mirror image.
The scatterers' location at the tunnel's size wall follows a uniform random distribution, as shown in Figure 4. In this model, scatterers are randomly distributed along the inner wall of the tunnel. When the NLoS signal passes through the scatterer, the rough

Matching of Receiving and Transmitting Rays
In the proposed system, the transmitted and the received signals have a one-to-one mapping relationship, which means that for each received signal, a unique corresponding transmitted signal can always be located, completing a full signal chain from Tx to Rx. According to the roughness of the sidewall of the tunnel, the mapping relationship between the transmitted and receiving signals can be solved by the spatial mirror method and the random scatterer distribution method. The space mirror method is shown in Figure 3.
where , represents the angle between the signal ( , , , , , ) and the moving direction of Rx. ̂, and ̂ represent the unit vector of the received signal direction and the unit vector of the Rx moving direction.

Matching of Receiving and Transmitting Rays
In the proposed system, the transmitted and the received signals have a one-to-one mapping relationship, which means that for each received signal, a unique corresponding transmitted signal can always be located, completing a full signal chain from Tx to Rx. According to the roughness of the sidewall of the tunnel, the mapping relationship between the transmitted and receiving signals can be solved by the spatial mirror method and the random scatterer distribution method. The space mirror method is shown in Fig  For the NLoS propagation path in the tunnel, this method solely considers reflection, and the mirror space is formed with the reflection surface as the axis. For the signal reflected for k (k = 0, 1, 2, …, K) times, the mirror image point Tx' of transmitting antenna Tx needs to be obtained through k times of mirror image.
The scatterers' location at the tunnel's size wall follows a uniform random distribution, as shown in Figure 4. In this model, scatterers are randomly distributed along the inner wall of the tunnel. When the NLoS signal passes through the scatterer, the rough For the NLoS propagation path in the tunnel, this method solely considers reflection, and the mirror space is formed with the reflection surface as the axis. For the signal reflected for k (k = 0, 1, 2, . . . , K) times, the mirror image point Tx' of transmitting antenna Tx needs to be obtained through k times of mirror image.
The scatterers' location at the tunnel's size wall follows a uniform random distribution, as shown in Figure 4. In this model, scatterers are randomly distributed along the inner wall of the tunnel. When the NLoS signal passes through the scatterer, the rough scatterer surface leads to a certain randomness in the direction of the secondary radiation wave. When the signal is repeatedly scattered, the mapping between the transmitted signal and the received signal can be considered as random mapping. scatterer surface leads to a certain randomness in the direction of the secondary radiation wave. When the signal is repeatedly scattered, the mapping between the transmitted signal and the received signal can be considered as random mapping. The mapping relationship between the transmitter multipath signal and the receiver multipath signal can be expressed as where A is the mapping matrix with I rows and M columns. The element in the mapping matrix represents the mapping relationship between the signal ( , , , , , ) at the receiving end and the signal ( , , , , , ) at the transmitting end. Let the transmitter signal ( , , , , , ) and the receiver signal ( , , , , , ) be the same signal, where 1 ≤ ≤ , 1 ≤ ≤ , then the element is The matrix N is the subscript matrix of the multipath signal at the receiving end. After rearranging the mapping matrix, the subscript matrix Γ corresponding to the signal at the transmitting end is obtained.

Doppler Effect at the Transmitter and Receiver
Rearrange the Doppler shifts of each ray at the receiver so that they are in the same order as the corresponding ray at the transmitter When both the receiving and transmitting ends move, the Doppler shift of the communication signal can be expressed as Assuming that the transmitted signal is ( ) = cos (2 ), the bandpass form ( ) of the i-th path received signal can be expressed as where and represent the power normalized amplitude and time delay of the i-th path signal, so the baseband form ( ) of the i-th path received signal is expressed as The mapping relationship between the transmitter multipath signal and the receiver multipath signal can be expressed as where A is the mapping matrix with I rows and M columns. The element a im in the mapping matrix represents the mapping relationship between the signal (P r,m , θ ZOA,m , φ AOA,m ) at the receiving end and the signal (P t,i , θ ZOD,i , φ AOD,i ) at the transmitting end. Let the transmitter signal (P t,x , θ ZOD,x , φ AOD,x ) and the receiver signal P r,y , θ ZOA,y , φ AOA,y be the same signal, where 1 ≤ x ≤ M, 1 ≤ y ≤ M, then the element a im is The matrix N is the subscript matrix of the multipath signal at the receiving end. After rearranging the mapping matrix, the subscript matrix Γ corresponding to the signal at the transmitting end is obtained.

Doppler Effect at the Transmitter and Receiver
Rearrange the Doppler shifts of each ray at the receiver so that they are in the same order as the corresponding ray at the transmitter When both the receiving and transmitting ends move, the Doppler shift f i d of the communication signal can be expressed as Assuming that the transmitted signal is x p (t) = cos(2π f c t), the bandpass form R i p (t) of the i-th path received signal can be expressed as where c i and τ i represent the power normalized amplitude and time delay of the i-th path signal, so the baseband form R i b (t) of the i-th path received signal is expressed as thus, the baseband form of the multipath received signal can be expressed as When the number of rays I → ∞ , the received signal can be expressed as the integral function of all frequency components from the minimum Doppler frequency f d,min to the maximum Doppler frequency f d,max where P( f d ) represents the continuous Doppler spectral function.

Simulation Model and Parameter Settings of RT
In order to verify the Doppler model proposed in this paper, the RT simulation method is used in the Wireless Insite (WI) simulation software to obtain the angle and amplitude characteristics of the transmitted and received signals, and the mapping relationship of the transmitted and received signals is extracted. The 3D model of the tunnel is built using the 3D modeling software Inventor. The tunnel is a rectangular straight tunnel with a length of 300 m, a width of 5 m, and a height of 5 m. In the simulation, the signal carrier frequency is 28 GHz, and both the transmitting antenna and the receiving antenna are omnidirectional antennas, located in the center of the tunnel 100 m and 200 m away from the tunnel entrance. The distance between the antenna and the tunnel ground is 2 m, as shown in Figure 5. The tunnel structure and transmit and receive antenna parameters are listed in Table 1.
where = 2 ( + ), when ≫ , ≈ 2 ; thus, the baseband form of the multipath received signal can be expressed as When the number of rays → ∞, the received signal can be expressed as the integral function of all frequency components from the minimum Doppler frequency , to the maximum Doppler frequency , where ( ) represents the continuous Doppler spectral function.

Simulation Model and Parameter Settings of RT
In order to verify the Doppler model proposed in this paper, the RT simulation method is used in the Wireless Insite (WI) simulation software to obtain the angle and amplitude characteristics of the transmitted and received signals, and the mapping relationship of the transmitted and received signals is extracted. The 3D model of the tunnel is built using the 3D modeling software Inventor. The tunnel is a rectangular straight tunnel with a length of 300 m, a width of 5 m, and a height of 5 m. In the simulation, the signal carrier frequency is 28 GHz, and both the transmitting antenna and the receiving antenna are omnidirectional antennas, located in the center of the tunnel 100 m and 200 m away from the tunnel entrance. The distance between the antenna and the tunnel ground is 2 m, as shown in Figure 5. The tunnel structure and transmit and receive antenna parameters are listed in Table 1.  The tunnel material and simulation ray parameter settings are shown in Table 2. The tunnel material is concrete, and the parameters such as the permittivity and conductivity of the tunnel material are calibrated according to the measured data of Shanghai Metro  The tunnel material and simulation ray parameter settings are shown in Table 2. The tunnel material is concrete, and the parameters such as the permittivity and conductivity of the tunnel material are calibrated according to the measured data of Shanghai Metro Line 7 [10]. Moreover, the signal's maximum reflection time in the tunnel is set to 10, its maximum scattering time is set to 2, and its transmission time is set to 0.

Simulation Results and Analysis
The angles and powers of 250 multipath signals are obtained through the RT simulation, and the propagation paths of the multipath signals in the tunnel are shown in Figure 6. The polar coordinate form of the multipath signal angle is shown in Figure 7, in which the pitch departure angle and pitch arrival angle are concentrated around 90 • , while the horizontal departure angle and horizontal arrival angle are around 0 • and 180 • . The angular range of the arrival angle is greater than the angular range of the departure angle. The angles and powers of the five largest energy paths in the simulation results are shown in Table 3. Line 7 [10]. Moreover, the signal's maximum reflection time in the tunnel is set to 10, its maximum scattering time is set to 2, and its transmission time is set to 0.

Simulation Results and Analysis
The angles and powers of 250 multipath signals are obtained through the RT simulation, and the propagation paths of the multipath signals in the tunnel are shown in Figure  6. The polar coordinate form of the multipath signal angle is shown in Figure 7, in which the pitch departure angle and pitch arrival angle are concentrated around 90°, while the horizontal departure angle and horizontal arrival angle are around 0° and 180°. The angular range of the arrival angle is greater than the angular range of the departure angle. The angles and powers of the five largest energy paths in the simulation results are shown in Table 3.  The transceiver signal mapping matrix extracted from the RT simulation results can be represented as an identity matrix with 250 rows and 250 columns Line 7 [10]. Moreover, the signal's maximum reflection time in the tunnel is set to 10, its maximum scattering time is set to 2, and its transmission time is set to 0.

Simulation Results and Analysis
The angles and powers of 250 multipath signals are obtained through the RT simulation, and the propagation paths of the multipath signals in the tunnel are shown in Figure  6. The polar coordinate form of the multipath signal angle is shown in Figure 7, in which the pitch departure angle and pitch arrival angle are concentrated around 90°, while the horizontal departure angle and horizontal arrival angle are around 0° and 180°. The angular range of the arrival angle is greater than the angular range of the departure angle. The angles and powers of the five largest energy paths in the simulation results are shown in Table 3.  The transceiver signal mapping matrix extracted from the RT simulation results can be represented as an identity matrix with 250 rows and 250 columns  Table 3. Angle and power of 5 maximum energy paths. The transceiver signal mapping matrix extracted from the RT simulation results can be represented as an identity matrix with 250 rows and 250 columns

Number of Multipath
In order to verify the spatial mirroring method proposed in this paper and the random matching method for scattered signals, after randomly arranging the transmitted signals, first determine the mapping relationship of the reflected signals between the transceivers according to the spatial mirroring principle, and then perform random matching on the unmatched signals. The complete transceiver signal mapping matrix is shown in Figure 8. In order to verify the spatial mirroring method proposed in this paper and the ran dom matching method for scattered signals, after randomly arranging the transmitted sig nals, first determine the mapping relationship of the reflected signals between the trans ceivers according to the spatial mirroring principle, and then perform random matching on the unmatched signals. The complete transceiver signal mapping matrix is shown in Figure 8.  After obtaining the angle, power information, and mapping relationship of the transmitting and receiving signals, the normalized Doppler power spectrum of the transmitting and receiving antennas at different moving speeds is obtained through the Doppler model, as shown in Figure 9. The normalized amplitude in the graph is defined as the ratio of the power of each single path to the total power of the multipath. When the moving speeds of the receiving and transmitting antennas are 160 km/h and 80 km/h, the Doppler shift of the LoS signal in the RT simulation results is 2.074 KHz, and the Doppler spread is

Physical Simulation Model of T2T Communication Channel in Tunnel
In a complex propagation environment, two kinds of fading channels will be generated due to the delay spreading effect of multipath channels, namely, the frequency flat fading channel and the frequency selective fading channel. Multipath effects cause the amplitude of the received signal to shift over time when the signal bandwidth is smaller than the coherence bandwidth , but the signal spectrum does not. In this case, the duration of the symbol is greater than the maximum time delay of multipaths, and this channel is called the flat fading channel. In a flat fading channel, the influence of the time delay on the communication system can be ignored. Existing test results show that the multipath delay in tunnel scenarios is tens of nanoseconds [11][12][13][14], that is, < , so the bandpass form of Equation (17) where ( ) = tan −1 ( ( ) ( ) ⁄ ) is the phase shift caused by the Doppler shift of multipaths.
The circuit structure of the IQ vector phase shifter [15,16] is shown in Figure 10. The phase shifter circuit consists of a quadrature splitter (QS), a variable gain amplifier (VGA), and a quadrature combiner (QC). The input RF signal generates the in−phase component = √2 ⁄ and the quadrature component = √2 ⁄ after passing through the quadrature splitter. After and pass through independent VGAs, they are summed in the combiner, and the output signal is a function of the VGA gains and where the gain range of VGA is {−1,1}, the amplitude of the output signal and the input signal remain unchanged, and phase difference ∆ = tan −1 ( ⁄ ). Compared to (21) and (22), make = , then , = √2 ⁄ , , = √2 ⁄ , = , = − . Therefore, the physical simulation of the channel can be theoretically realized

Physical Simulation Model of T2T Communication Channel in Tunnel
In a complex propagation environment, two kinds of fading channels will be generated due to the delay spreading effect of multipath channels, namely, the frequency flat fading channel and the frequency selective fading channel. Multipath effects cause the amplitude of the received signal to shift over time when the signal bandwidth B s is smaller than the coherence bandwidth B c , but the signal spectrum does not. In this case, the duration of the symbol T s is greater than the maximum time delay τ max of multipaths, and this channel is called the flat fading channel. In a flat fading channel, the influence of the time delay on the communication system can be ignored. Existing test results show that the multipath delay in tunnel scenarios is tens of nanoseconds [11][12][13][14], that is, τ max < T s , so the bandpass form of Equation (17) can be expressed as the product of the bandpass transmit signal x p (t) and the multiplicative spreading factor H(t) c i e j2π f i d t (20) where x p (t) = x p,I (t) + jx p,Q (t), H(t) = |H(t)|e jϕ(t) = H I (t) + jH Q (t), then Equation (20) can be expressed as where ϕ(t) = tan −1 H I (t)/H Q (t) is the phase shift caused by the Doppler shift of multipaths. The circuit structure of the IQ vector phase shifter [15,16] is shown in Figure 10. The phase shifter circuit consists of a quadrature splitter (QS), a variable gain amplifier (VGA), and a quadrature combiner (QC). The input RF signal RF in generates the in−phase component V I = RF in / √ 2 and the quadrature component V Q = jRF in / √ 2 after passing through the quadrature splitter. After V I and V Q pass through independent VGAs, they are summed in the combiner, and the output signal RF out is a function of the VGA gains A I and A Q where the gain range of VGA is {−1,1}, the amplitude of the output signal RF out and the input signal RF in remain unchanged, and phase difference ∆ϕ = tan −1 A I /A Q . Compared to (21) and (22), make x p = RF in , then x p,I = RF in / √ 2, x p,Q = jRF in / √ 2, A I = H I , A Q = −H Q . Therefore, the physical simulation of the channel can be theoretically realized by using the program-controlled IQ vector phase shifter. The physical simulation model is shown in Figure 11. In Figure 11, the IQ vector phase shifter is a programcontrolled phase shifter that can be controlled in real time. by using the program-controlled IQ vector phase shifter. The physical simulation model is shown in Figure 11. In Figure 11, the IQ vector phase shifter is a program-controlled phase shifter that can be controlled in real time.

Conclusions
In this paper, the Doppler shift and Doppler spread of T2T communication in a tunnel environment are studied. Independent coordinate systems are established at the receiving and transmitting antennas. According to the angle and amplitude characteristics of the receiving and transmitting signals, the Doppler spread caused by the movement of the receiving and transmitting antennas is analyzed. The use of the mapping matrix approach to solve the matching problem of the transmitting and receiving signals is presented as an innovative solution, and two methods for obtaining the mapping matrix are described and verified. In order to verify the T2T Doppler spread simulation model proposed in this paper, the RT method is used to simulate the T2T communication channel in the tunnel, and the angle and amplitude information of the transmitted and received signals are obtained. By comparing the Doppler results of the simulation model with those of WI simulation, the correctness of the T2T Doppler spread simulation model is proved. Based on the Doppler spread model, a physical channel simulation method using an IQ vector phase shifter to complete T2T communication in a tunnel environment is proposed, which can provide a reference for the physical channel simulation of 5G mmWave T2T communication in a tunnel environment in the future.
Author Contributions: Conceptualization, P.Z. and G.Z.; data curation, P.Z. and X.W.; formal analysis, P.Z.; funding acquisition, G.Z. and Y.J.; investigation, P.Z. and X.W.; methodology, P.Z. and G.Z.; project administration, P.Z. and K.Z.; resources, P.Z. and G.Z.; software, P.Z.; validation, P.Z.; by using the program-controlled IQ vector phase shifter. The physical simulation model is shown in Figure 11. In Figure 11, the IQ vector phase shifter is a program-controlled phase shifter that can be controlled in real time.

Conclusions
In this paper, the Doppler shift and Doppler spread of T2T communication in a tunnel environment are studied. Independent coordinate systems are established at the receiving and transmitting antennas. According to the angle and amplitude characteristics of the receiving and transmitting signals, the Doppler spread caused by the movement of the receiving and transmitting antennas is analyzed. The use of the mapping matrix approach to solve the matching problem of the transmitting and receiving signals is presented as an innovative solution, and two methods for obtaining the mapping matrix are described and verified. In order to verify the T2T Doppler spread simulation model proposed in this paper, the RT method is used to simulate the T2T communication channel in the tunnel, and the angle and amplitude information of the transmitted and received signals are obtained. By comparing the Doppler results of the simulation model with those of WI simulation, the correctness of the T2T Doppler spread simulation model is proved. Based on the Doppler spread model, a physical channel simulation method using an IQ vector phase shifter to complete T2T communication in a tunnel environment is proposed, which can provide a reference for the physical channel simulation of 5G mmWave T2T communication in a tunnel environment in the future.

Conclusions
In this paper, the Doppler shift and Doppler spread of T2T communication in a tunnel environment are studied. Independent coordinate systems are established at the receiving and transmitting antennas. According to the angle and amplitude characteristics of the receiving and transmitting signals, the Doppler spread caused by the movement of the receiving and transmitting antennas is analyzed. The use of the mapping matrix approach to solve the matching problem of the transmitting and receiving signals is presented as an innovative solution, and two methods for obtaining the mapping matrix are described and verified. In order to verify the T2T Doppler spread simulation model proposed in this paper, the RT method is used to simulate the T2T communication channel in the tunnel, and the angle and amplitude information of the transmitted and received signals are obtained. By comparing the Doppler results of the simulation model with those of WI simulation, the correctness of the T2T Doppler spread simulation model is proved. Based on the Doppler spread model, a physical channel simulation method using an IQ vector phase shifter to complete T2T communication in a tunnel environment is proposed, which can provide a reference for the physical channel simulation of 5G mmWave T2T communication in a tunnel environment in the future.
Funding: This work was supported by National Natural Science Foundation of China (61871261) and Natural Science Foundation of Shanghai (22ZR1422200).