High-speed rail tunnel communication and perception integrated information transmission method based on movable antenna

Abstract

The invention discloses a high-speed rail tunnel communication sensing integrated information transmission method based on a movable antenna, and belongs to the technical field of wireless communication, and the method comprises the steps: constructing a high-speed rail tunnel communication sensing integrated system architecture assisted by the movable antenna for a high-speed rail tunnel scene, and designing an information transmission protocol; mathematical modeling is carried out according to movable antenna model features and tunnel scene channel features, a communication transmission model and a sensing transmission model are fused, and a communication and sensing integrated information transmission model is established. Aiming at the problems that the communication stability is limited and spectrum resources are deficient in a tunnel scene, a movable antenna and communication sensing integrated technology is adopted, dual-function coordination of base station communication and radar sensing in the tunnel is realized, and the spectrum utilization rate is improved and the total communication transmission rate of a train is maximized on the premise of meeting a sensing interference power threshold value.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication technology and relates to a high-speed railway tunnel communication and perception integrated information transmission method based on a movable antenna. The method specifically includes an integrated communication system model, an integrated transmission protocol, a movable antenna and beamforming technology, and solves the problems of limited communication stability, track foreign object intrusion and spectrum resource shortage in tunnel scenarios. Background Art

[0002] With the rapid expansion of my country's high-speed rail network, it has become an essential means of transportation for daily commutes. Tunnels occupy a significant proportion of high-speed rail routes. However, the unique electromagnetic characteristics of tunnel environments present significant challenges for wireless communications. First, tunnels are typically closed or semi-closed structures. The reflection, scattering, and multipath propagation of electromagnetic waves within these enclosed spaces create an extremely complex tunnel channel environment. Furthermore, the high speeds of high-speed trains (over 300 km / h) introduce significant Doppler shift, further significantly reducing the link stability of traditional communication systems and severely impacting stable communication between trains and base stations.

[0003] To address these issues, existing technologies typically rely on fixed leaky cable systems or distributed antenna systems. While these solutions provide basic coverage, they suffer from significant performance bottlenecks in tunnel environments. While leaky cable systems offer continuous coverage, they suffer from low spectral efficiency and high deployment costs. Furthermore, traditional fixed distributed antennas are limited by their installation locations and struggle to effectively address the rapid localized fading caused by multi-scattering electromagnetic waves within tunnels.

[0004] In recent years, movable antenna (MA) technology has become a key research area for improving wireless communication quality due to its unique spatial freedom of adjustment capabilities. MA technology achieves real-time dynamic adjustment of antenna position through micro-scale mechanical displacement or liquid medium adjustment of the antenna, effectively avoiding deep valleys of channel fading, reconfiguring wireless channels, and significantly improving link stability. Furthermore, MA technology eliminates the need for additional RF links. By jointly optimizing position diversity and beamforming, it reduces system cost and energy consumption while improving the robustness of communication systems.

[0005] At the same time, the development of sixth-generation mobile communications has proposed a new vision of integrated sensing and communication (ISAC), which aims to achieve real-time and accurate environmental perception while ensuring efficient communication. In high-speed rail tunnels, ISAC not only meets communication needs but can also be used in applications such as tunnel environmental safety monitoring, train running posture detection, and obstacle identification, possessing great application value. Combining movable antenna technology with ISAC not only enables the synergy of communication and radar perception in tunnel scenarios, but also improves spectrum resource utilization and communication link quality.

[0006] Therefore, studying the integrated information transmission technology of synaesthesia based on movable antennas in high-speed rail tunnel scenarios has important theoretical value and practical application prospects. It can provide new technical solutions and theoretical basis for the design of highly reliable and efficient wireless communication systems in tunnels, and has practical application value. Summary of the Invention

[0007] In view of this, the present invention provides a high-speed railway tunnel communication perception integrated information transmission method based on movable antennas, which realizes beamforming vector optimization and movable antenna position configuration according to the channel model in the tunnel to achieve the purpose of maximizing the total communication transmission rate.

[0008] In order to achieve the above object, the present invention adopts the following technical solutions:

[0009] A high-speed railway tunnel communication perception integrated information transmission method based on a movable antenna includes the following steps:

[0010] S1: Targeting high-speed rail tunnel scenarios, construct an integrated high-speed rail tunnel interawareness system architecture assisted by movable antennas and design an information transmission protocol;

[0011] S2: Based on the characteristics of the movable antenna model and the channel characteristics of the tunnel scenario, mathematical modeling is performed, and the communication transmission model and the perception transmission model are integrated to establish a synaesthesia integrated information transmission model;

[0012] S3: With the goal of maximizing the total communication transmission rate, the movable antenna position, the beamforming vector transmit power, and the perceived interference link power as constraints, an optimization problem is constructed. Fractional programming is used to perform an equivalent transformation of the objective function and simplify the optimization problem.

[0013] S4: The simplified optimization problem is decomposed into two sub-problems: communication beamforming vector optimization and movable antenna position vector optimization. The communication beamforming vector optimization is solved by the manifold optimization linear search method, and the movable antenna position optimization is converted into a convex optimization problem by quadratic transformation and first-order Taylor expansion approximation. Finally, the system beamforming vector and movable antenna position vector are updated through alternating optimization iterative updates to achieve the goal of maximizing the total communication transmission rate.

[0014] Furthermore, the content of step S1 includes:

[0015] (1) System Architecture

[0016] The system consists of three components: an ISAC (Integrated Sensing and Communication) base station assisted by a movable antenna (MA) deployed on the top of the tunnel, K omnidirectional single-antenna mobile relays (MR) on the top of the high-speed rail cars, and track sensing targets to be detected in the tunnel. Devices inside any high-speed rail car communicate with the base station via the mobile relay on the car top. The base station is an MA-assisted ISAC base station, and its antenna array is divided into two groups: one group, a uniform linear array (ULA) composed of M fixed antennas, is used to sense obstacles in the tunnel, such as rolling stones and animals that have strayed into the tunnel; the other group, a movable antenna communication array composed of N antennas, is used for downlink communication between the base station and the high-speed rail. The communication group antennas utilize the emerging technology of movable antennas, which allows multiple antennas to flexibly move within the restricted area of ​​the transmitter and receiver to reconfigure the optimal wireless channel, thereby improving system communication performance. To alleviate the spectrum shortage problem in high-speed rail operations, the system is designed to share the same frequency band for communication and sensing functions, improving the system's spectrum utilization efficiency.

[0017] (2) Information transmission protocol

[0018] Movable antenna communication uses the New Radio-Time Division Duplexing (NR-TDD) frame structure. Multiple users transmit information through spatial multiplexing, and one frame consists of five subframes. The subframe structure consists of five parts: MA-Pilot (Moveable Antenna–Pilot), CSI-DL (Channel State Information–Downlink), Opt (Optimization), Move, and Data. MA-Pilot is the movable antenna subframe pilot, used by the base station to perform orthogonal sounding sequences and for users to transmit coarse information status information. CSI-DL is the user uploading fine-grained downlink channel state information for channel modeling and system optimization. Opt is the system optimization process, which calculates the optimal beamforming vector and antenna position information. Move is the MA execution displacement process, during which the base station's power-limited data channel remains silent. Data is the information transmission process, during which the base station transmits data to multiple users according to the optimal beamforming vector and antenna position vector.

[0019] Furthermore, the content of step S2 includes:

[0020] (1) Movable antenna model

[0021] The movable antenna adjusts the position of the antenna within the linear array area to dynamically optimize the communication link. The antenna array area is denoted as C. t , the coordinate of the center of the movable antenna is marked as x0, and the coordinate of the position of the nth movable antenna is marked as x n , for any x n , all have x n ∈C t ,in The antenna position vector (APV) is expressed as:

[0022] x=[x1,x2,…,x N ] T

[0023] (2) Tunnel scenario channel model

[0024] Due to the unique electromagnetic wave propagation characteristics of the tunnel environment, the fading pattern of the wireless signal is different from that of free space propagation. The wireless signal in the tunnel will encounter more reflections, diffractions and scattering. The system tunnel scenario channel model consists of three parts: the channel link h from the ISAC base station communication antenna group to the kth mobile relay; k , the interference link g from the uniform linear array to the kth mobile relayk And the communication part perceives the interference link H s ;

[0025] The channel link h between the ISAC base station communication antenna group and the kth mobile relay k The wireless channel model is composed of line-of-sight (LoS) and non-line-of-sight (NLoS) components. The NLoS component includes single-hop reflection (SB) components from the tunnel ceiling, ground, and walls on both sides. The effective scatterers are randomly distributed within the single-hop reflection range. L clusters of SB components are distributed on the inner surface of the tunnel. The channel link h from the ISAC base station communication antenna group to the kth mobile relay is k , expressed as:

[0026]

[0027] in, represents the kth mobile relay, is the LoS component between the ISAC base station and the kth mobile relay on the high-speed railway; represents the lth cluster single-hop reflection, is the lth cluster single-hop reflected NLoS component;

[0028] LoS component from ISAC base station to high-speed rail mobile relay Expressed as:

[0029]

[0030] Among them, PL k represents large-scale fading, The unit is dB, represents the path loss at a reference distance of 1 meter, α d,k represents the path loss index, D represents the distance of a single link; K R Represents the Rice factor, which represents the ratio of the LoS component power to the scattered component power; is the MA antenna array steering vector. Unlike traditional linear uniform antenna arrays, it is not only related to the angle between the signal direction and the array axis (x-axis), but also to the antenna position vector, which can be expressed as:

[0031]

[0032] in, represents the communication transmission transmission angle from the base station communication antenna to the kth mobile relay, x is the antenna position vector of the movable antenna; λ is the carrier wavelength; is the maximum Doppler shift, given by the train speed vR , carrier frequency f c Determination; t is the observation time variable, in the discrete baseband symbol model, t = nT s , T s is the symbol interval, n=0,1,2,… is the symbol number;

[0033] Single-hop reflection component Expressed as

[0034]

[0035] Among them, P l is the ratio of the power of the lth scattering cluster to the total scattering component power, N l is the number of scatterers in the lth cluster, assuming N l →∞, For nth l The random phases of the scatterers are uniformly distributed at (-π,π);

[0036] Similarly, the interference link g from the uniform linear array to the kth mobile relay is sensed k It consists of LoS component and NLoS component, and its mathematical form is expressed as:

[0037]

[0038] Among them, PL g represents the large-scale fading of the sensing link to the kth mobile relay, The unit is dB, represents the path loss at a reference distance of 1 meter, D represents the distance of a single link, and α d,g represents the path loss exponent; represents the steering vector from the sensing uniform linear array to the kth mobile relay, and its mathematical expression is:

[0039]

[0040] in, represents the communication transmission transmission angle of the base station sensing antenna to the kth mobile relay, and M represents the number of ULA antennas in the sensing part;

[0041] Interference link H of the communication part to the perception part s It is composed of NLoS components, and its mathematical expression is:

[0042]

[0043] Among them, PL i represents large-scale fading; K R represents the Rice factor; P lis the ratio of the power of the lth scattering cluster to the total scattering component power; a MA (x,θ c ) is the communication MA antenna array steering vector, θ c is the emission angle of the interference link; a FA (θ s ) is the sensing FA antenna array steering vector, θ s is the arrival angle of the interference link; N l is the number of scatterers in the lth cluster; For nth l The random phases of the scatterers are uniformly distributed at (-π,π);

[0044] (3) Communication model

[0045] Based on the channel model of the tunnel scenario, the communication signal y received by the kth mobile relay is k Expressed as:

[0046]

[0047] in, and They represent the communication channel response of the ISAC base station communication antenna array to the kth mobile relay and the interference channel response of the sensing antenna array to the kth mobile relay, respectively. is a complex field, and h k and g k The conjugate transpose of represents the beamforming vector of the ISAC base station communication array to the kth mobile relay, s k represents the communication symbols required by the k-th mobile relay, Orthogonal emission waveform vector for sensing signal; Indicates that the mean at the kth mobile relay is zero and the variance is Additive White Gaussian Noise (AWGN);

[0048] Therefore, the signal to interference plus noise ratio (SINR) of the kth mobile relay is expressed as:

[0049]

[0050] in, is the beamforming signal power received by the kth mobile relay; is the beamforming interference power of other mobile relays, that is, the interference power of other users; is the interference power of the sensing link to the kth mobile relay; is the Gaussian white noise power;

[0051] Assuming that all mobile relays use the same bandwidth, the normalized total communication rate of K mobile relays is:

[0052]

[0053] (4) Perception Model

[0054] In the sensing uniform linear antenna array part, the echo signal received by the sensing radar after detecting the target is expressed as:

[0055]

[0056] Among them, α represents the echo signal loss coefficient, and its value depends on the radar cross section (RCS, Radar Cross Section) and the channel loss coefficient between the base station and the detection target. It is defined as vector and They represent the transmitting direction vector and receiving direction vector of the radar antenna array respectively. The specific expressions are:

[0057]

[0058] in, is the orthogonal transmission waveform vector of the perception signal; matrix It represents the interference channel between the communication part and the sensing part, that is, the link where the communication signal is scattered by the target or other reflectors during the propagation process. is the transmit beam matrix of the base station, is the symbol vector sent by the base station, means the mean is zero and the variance is Additive Gaussian white noise;

[0059] The interference power of the ISAC base station communication link to the sensing link is expressed as:

[0060]

[0061] Furthermore, the content of step S3 includes:

[0062] (1) Construction of overall optimization problem

[0063] With the optimization goal of maximizing the total communication rate R of the mobile relay, the optimization problem is constructed as follows:

[0064]

[0065] stC1:|x i -x j |≥d min ,1≤i≠j≤N

[0066]

[0067] C3:||w k || 2 =1

[0068] C4:P int ≤p0

[0069] Among them, constraint C1 means that the minimum distance between each pair of movable antennas is greater than the minimum antenna coupling distance d min ; Constraint C2 ensures that the movable antenna's range of motion is within the restricted area C t Constraint C3 is the beamforming vector power constraint w k , the beamforming vector of the kth mobile relay needs to be normalized to ensure the consistency of the total transmit power distribution; constraint C4 is the interference power constraint, the interference power of the communication link to the sensing link must be lower than the threshold p0 to ensure the normal operation of the radar;

[0070] (2) Equivalent transformation of optimization problems

[0071] Introducing the Fractional Programming (FP) method to solve the objective function Perform Lagrangian dual transform and transform the objective function into:

[0072]

[0073] Among them, an auxiliary variable ν is introduced k , for R1(w k ,x,ν k )About ν k Find the partial derivative, since the function R1(w k ,x,ν k ) is a monotonically decreasing function, then the point where the partial derivative is 0 is the function R1(w k ,x,ν k ), that is, The optimal solution is:

[0074]

[0075] The optimization problem P1 is equivalently transformed into:

[0076]

[0077] Furthermore, the content of step S4 includes:

[0078] (1) Communication beamforming vector optimization

[0079] The complex problem is split into the beamforming vector optimization sub-problem and the antenna position optimization sub-problem by using the alternating optimization method; in order to solve the optimal base station communication end beamforming vector w k , fixing the antenna position vector x in the original optimization problem P2, the communication beamforming optimization sub-problem can be expressed as:

[0080]

[0081] stC1:||w k || 2 =1

[0082] C2:P int ≤p0

[0083] The interference power constraint C2 is added to the objective function as a penalty term. The square error between the interference power and the threshold is added to the objective function, that is, the sum-square penalty. The sum-square penalty is calculated as follows:

[0084] φ(P int )=(p0-P int ) 2

[0085] The objective function is reshaped into P4 using the sum-square penalty technique:

[0086]

[0087] st||w k || 2 =1

[0088] For this non-convex optimization problem, the manifold optimization method is used to solve it. The oblique manifold (OM) structure is used to constrain the variable value range, and a linear search is performed within the constraint set to obtain a feasible solution. The mathematical definition formula of the oblique manifold is

[0089]

[0090] The manifold is the product of spheres, and its physical meaning is: if each column in X is in the complex field There is a unit norm on , then That is, the set of X is a slant flow So the beamforming matrix in, Defined as an oblique manifold Its mathematical formula is:

[0091]

[0092] Furthermore, the optimization problem P4 can be restated as the following unconstrained problem:

[0093]

[0094] Introduce the selection column vector e k =[0,…,1,…,0] T , that is, the kth row is 1 and the other items are 0, then w k =We k , the objective function can be restated as follows:

[0095]

[0096] Find the Euclidean gradient of it, that is

[0097]

[0098] oblique manifold The tangent space and normal space are defined at point W on and oblique manifold Tangent space at point W The mathematical expression is:

[0099]

[0100] The mathematical meaning of this formula is: tangent space Depend on The Δ matrix satisfies diag(W T Δ)=0, that is, Δ is orthogonal to W;

[0101] oblique manifold Normal space at point W The mathematical expression is:

[0102]

[0103] The mathematical meaning of this formula is: normal space It is composed of DW, where D is a diagonal matrix, that is, the normal direction of each column is the direction of the vector of the column at point W, that is, the spherical normal, and the normal space is composed of the combination of these radial directions;

[0104] The Riemann gradient of f(W) at point W is given by its Euclidean gradient in the tangent space The projection on is obtained, which is expressed as:

[0105]

[0106] Based on the above, we designed an algorithm to solve the communication beamforming vector optimization subproblem, namely the Line Search Approach-oblique manifold (LSA-OM) algorithm. Line search on the manifold can be regarded as an extension of line search in Euclidean space. The solution process is as follows:

[0107] First, let W (t) is the beamforming matrix at the tth iteration, then the t+1th iteration point is:

[0108]

[0109] Where α(t) is the search step size, which is assumed to be the Armijo step size;

[0110] Secondly, the iteration point W (t+1) Projection onto the oblique manifold The iterative point after projection is recorded as To ensure that each step is run on the oblique manifold, the projection formula is:

[0111]

[0112] Then, the step size update process satisfies:

[0113]

[0114] Among them, η t W (t) The Riemann gradient on the oblique manifold M is vec(η t ) represents the matrix η t Stack by column into column vectors;

[0115] Finally, when the gradient at iteration t+1 meets the algorithm termination criterion, the iterative algorithm ends. The termination criterion of the manifold optimization linear search algorithm is defined as:

[0116] ||vec(η t+1 )|| ∞ <ε(1+||vec(η t )|| ∞ )

[0117] Among them, ||vec(η t+1 )|| ∞ Represents the infinite norm, that is, the column vector vec(η t+1 ), ε is the precision parameter;

[0118] (2) Optimization of movable antenna position

[0119] To optimize the base station communication end antenna position vector x, the fixed beamforming vector w k , the movable antenna position vector problem can be expressed as:

[0120]

[0121] stC1:|x i -x j |≥d min ,1≤i≠j≤N

[0122]

[0123] Transform the objective function and constraint C1, and perform a quadratic transformation on the objective function to convert it into the following formula:

[0124]

[0125] Among them, μ k is the auxiliary variable introduced, the optimal value The mathematical expression is:

[0126]

[0127] To avoid the problem of non-differentiable norm at zero point, transform the constraint condition C1 in P6 into Then, the first-order Taylor expansion is introduced to transform the non-convex feasible domain of the constraint into a convex feasible domain;

[0128] Let δ = x i -x j , let function |x i -x j | 2 For ψ(δ)=|δ| 2 , the initial point is recorded as Then its first-order Taylor expansion is:

[0129] ψ(δ)≥ψ(δ r )+▽ψ(δ r )(δ-δ r )

[0130] =|δ r | 2 +2δ r (δ-δ r )

[0131] =-|δ r | 2 +2δ r δ

[0132] Right now,

[0133] Therefore, constraint C1 becomes the following inequality:

[0134]

[0135] This inequality is an affine inequality, and its corresponding feasible domain is a convex set. Therefore, the original optimization subproblem P6 is transformed into a convex optimization problem of the following form, and the existing optimization tool CVX is used for efficient solution;

[0136]

[0137] (3) Alternating optimization performs a fractional programming equivalent transformation on the objective function of the optimization problem, decomposing the problem into two sub-problems: communication beamforming vector optimization and movable antenna position vector optimization. The communication beamforming vector is solved by the linear search method in manifold optimization, and the movable antenna position is approximately solved by quadratic transformation and first-order Taylor expansion. An alternating optimization strategy is adopted to fix other variables, optimize the current variables and update the parameters, and repeat in sequence until the preset number of iterations is reached or the convergence conditions are met, and the joint optimization result is obtained.

[0138] Compared with the prior art, the present invention has the following beneficial effects:

[0139] This paper addresses the unique challenges of high-speed rail tunnels, where wireless channel models exhibit significant fading variations, communication stability is limited, and spectrum resources are scarce. By constructing a more accurate wireless channel model and designing an ISAC base station architecture suitable for this scenario, the paper introduces movable antenna technology to improve communication link stability, and employs integrated telepathy technology to enable communication and perception to share the same frequency spectrum, improving spectrum utilization and alleviating spectrum resource constraints. A method for integrated communication and perception information transmission in high-speed rail tunnels based on movable antennas is proposed. This method maximizes the overall communication transmission rate by optimizing the beamforming vectors and movable antenna positions of the tunnel ISAC base station. BRIEF DESCRIPTION OF THE DRAWINGS

[0140] Figure 1 Schematic diagram of the process of the method proposed in the present invention.

[0141] Figure 2 Schematic diagram of the high-speed railway tunnel synaesthesia integrated model based on movable antennas in the present invention.

[0142] Figure 3 This is a schematic diagram of the synaesthesia integrated base station model in the present invention.

[0143] Figure 4 Schematic diagram of the transmission protocol in the present invention. DETAILED DESCRIPTION

[0144] Example 1 System Architecture and Information Transmission Protocol of the Present Invention

[0145] (1) System Architecture

[0146] An MA-assisted ISAC base station is deployed on the top of the tunnel, along with K omnidirectional single-antenna mobile relays (MRs) on the top of the high-speed rail cars, and track sensing targets to be detected within the tunnel. Devices inside any high-speed rail car communicate with the base station via the MRs on the top of the cars. The base station is a MA-assisted, integrated telepathic base station with two antenna arrays. One is a uniform linear array (ULA) consisting of M fixed antennas, used to sense obstacles in the tunnel, such as rolling stones and animals that have strayed into the tunnel. The other is a movable antenna communication array consisting of N antennas, used for downlink communication between the base station and the high-speed rail.

[0147] (2) Information transmission protocol

[0148] Movable antenna communication adopts the New Radio-Time Division Duplexing (NR-TDD) frame structure. Multiple users transmit information through spatial multiplexing. Five subframes constitute a frame, and the subframe structure consists of five parts: movable antenna pilot (MA-Pilot), downlink channel state information (CSI-DL), optimization (Opt), movement (Move) and data transmission (Data).

[0149] Example 2: Establishing a Synaesthesia Integrated Information Transmission Model

[0150] (1) Establishing a movable antenna model

[0151] The movable antenna adjusts the position of the antenna within the linear array area to dynamically optimize the communication channel. The antenna array area is denoted as C. t , the coordinate of the center of the movable antenna is marked as x0, and the coordinate of the position of the nth movable antenna is marked as x n , for any x n , all have x n ∈C t ,in The antenna position vector (APV) of MA is recorded as:

[0152] x=[x1,x2,…,x N ] T

[0153] (2) Establishing a channel model

[0154] Due to the unique electromagnetic wave propagation characteristics of the tunnel environment, the fading pattern of the wireless signal is different from that of free space propagation. The wireless signal in the tunnel will encounter more reflections, diffractions and scattering. The channel link from the ISAC base station communication antenna group to the kth mobile relay is denoted as h k , the interference link g from the uniform linear array to the kth mobile relay k , the communication part perceives the interference link H s :

[0155] (3) Build a communication model

[0156] Based on the channel model of the tunnel scenario, the communication signal y received by the kth mobile relay is k It can be expressed as:

[0157]

[0158] Therefore, the signal-to-interference-and-noise ratio of the kth mobile relay can be expressed as:

[0159]

[0160] Assuming that all mobile relays use the same bandwidth, the normalized total communication rate of K mobile relays is:

[0161]

[0162] (4) Building a perception model

[0163] In the sensing uniform linear antenna array part, the echo signal received by the sensing radar after detecting the target is expressed as:

[0164]

[0165] The interference power of ISAC base station communication transmission to sensing transmission can be expressed as:

[0166]

[0167] Example 3: Constructing an optimization problem

[0168] (1) Construction of overall optimization problem

[0169] With the optimization goal of maximizing the total communication rate R of the mobile relay, the optimization problem is constructed as follows:

[0170]

[0171] stC1:|x i -xj |≥d min ,1≤i≠j≤N

[0172]

[0173] C3:||w k || 2 =1

[0174] C4:P int ≤p0

[0175] (2) Equivalent transformation of optimization problems

[0176] The introduction of the Fractional Programming (FP) method can transform it into a more easily tractable form. Perform Lagrangian dual transform and convert the objective function to:

[0177]

[0178] The auxiliary variable ν is introduced k The optimal solution is:

[0179]

[0180] When fixed {w k ,x}, find the optimal The best Substitute into the function R1(w k ,x,ν k ), the objective function value and the original rate expression R(w k ,x) is completed, so the Lagrange dual transformation of the optimization objective is an equivalent transformation and will not introduce relaxation or error. Therefore, the optimization problem P1 is equivalently transformed into:

[0181]

[0182] stC1:|x i -x j |≥d min ,1≤i≠j≤N

[0183]

[0184] C3:||w k || 2 =1

[0185] C4:P int ≤p0

[0186] Example 4: Breaking down the problem to maximize communication transmission efficiency

[0187] (1) Optimization and solution of communication beamforming vector

[0188] Fixing the antenna position vector x in the original optimization problem P2, the communication beamforming optimization sub-problem can be expressed as:

[0189]

[0190] stC1:||w k || 2 =1

[0191] C2:P int ≤p0

[0192] First, the interference power constraint C2 is added to the objective function as a penalty term. Penalty-based methods approximate the constrained optimization problem by using parts of the objective function as penalty terms. Specifically, the squared error between the interference power and the threshold, or the sum-of-squares penalty, is added to the objective function. The sum-of-squares penalty is calculated as follows:

[0193] φ(P int )=(p0-P int ) 2

[0194] The objective function is reshaped into P4 using the sum-square penalty technique:

[0195]

[0196] st||w k || 2 =1

[0197] Secondly, the constraints are redefined as oblique manifolds (OM). Manifold optimization can exploit the structure of the constraints, reduce the degrees of freedom of the variables, and effectively find a good local optimal solution.

[0198] The mathematical definition formula of oblique manifold is

[0199]

[0200] The manifold is the product of spheres, and its physical meaning is: if each column in X is in the complex field There is a unit norm on , then The set of X is a slant flow. Therefore, the present invention uses the beamforming matrix in, Defined as an oblique manifold Its mathematical formula is:

[0201]

[0202] Furthermore, the optimization problem P4 can be restated as the following unconstrained problem:

[0203]

[0204] Furthermore, we introduce the selection column vector e k =[0,…,1,…,0] T , that is, the kth row is 1 and the other items are 0, then w k =We k , the objective function can be restated as follows:

[0205]

[0206] Find the Euclidean gradient of it, that is

[0207]

[0208] Then, the Euclidean gradient is converted to the Riemann gradient, and the Riemann gradient of f(W) at point W is given by its Euclidean gradient in the tangent space The projection on is obtained, which is expressed as:

[0209]

[0210] Finally, the Line Search Approach-oblique manifold (LSA-OM) algorithm is used to solve the problem. The solution steps are as follows:

[0211] ① Let W (t) is the beamforming matrix at the tth iteration, then the t+1th iteration point is:

[0212]

[0213] Where α(t) is the search step size, which is assumed to be the Armijo step size.

[0214] ② Set the iteration point W (t+1) Projection onto the oblique manifold The iterative point after projection is recorded as To ensure that each step is run on the oblique manifold, the projection formula is:

[0215]

[0216] ③The step size update process satisfies:

[0217]

[0218] Among them, η t W (t) Point on oblique manifold The Riemann gradient on vec(η t ) represents the matrix η t Stack columns into column vectors.

[0219] ④ Algorithm termination criterion: When the gradient at iteration t+1 meets the algorithm termination criterion, the iterative algorithm stops and ends. The termination criterion of the manifold optimization linear search algorithm is defined as:

[0220] ||vec(η t+1 )|| ∞ <ε(1+||vec(η t )|| ∞ )

[0221] Among them, ||vec(η t+1 )|| ∞ Represents the infinite norm, that is, the column vector vec(η t+1 ), ε is the precision parameter.

[0222] (2) Optimization of movable antenna position

[0223] To optimize the base station communication end antenna position vector x, the fixed beamforming vector w k , the optimization subproblem of the movable antenna position vector x is expressed as:

[0224]

[0225] stC1:|x i -x j |≥d min ,1≤i≠j≤N

[0226]

[0227] Transform the objective function and constraint C1, and perform a quadratic transformation on the objective function to convert it into the following formula:

[0228]

[0229] where μ k is the auxiliary variable introduced, the optimal value The mathematical expression is:

[0230]

[0231] To avoid the problem of non-differentiable norm at zero point, transform the constraint condition C1 in P6 into However, the set that satisfies the constraint is still a non-convex set. In order to transform the non-convex set into a convex feasible domain that is easy for the algorithm to handle, a first-order Taylor expansion is introduced.

[0232] Therefore, constraint C1 becomes the following inequality

[0233]

[0234] This inequality is an affine inequality, and its corresponding feasible domain is a convex set. Therefore, the original optimization subproblem P6 is transformed into a convex optimization problem of the following form, and is efficiently solved using the existing optimization tool CVX.

[0235]

[0236] (3) Alternating Optimization

[0237] Fractional programming techniques are introduced to perform an equivalent transformation on the objective function of the optimization problem, simplifying it. The simplified optimization problem is decomposed into two subproblems: communication beamforming and movable antenna position vector. Communication beamforming vector optimization is solved using a manifold optimization linear search method, while movable antenna position optimization can be approximated using quadratic transformation and first-order Taylor expansion. Based on the above analysis, an alternating optimization method can be used to iteratively update each optimization variable. The key idea is that in each iteration, all optimization variables except the current variable are first treated as fixed values. The optimal value of the current variable is solved and the common parameters are updated. The remaining variables are then optimized sequentially using this method, completing an alternating optimization cycle. This process is repeated until the preset number of optimizations is reached or the algorithm converges, resulting in the final parameters for the joint optimization problem.

Claims

1. A method for integrated information transmission of high-speed railway tunnel communication and perception based on a movable antenna, comprising the following steps: The specific steps are as follows: S1: Targeting high-speed rail tunnel scenarios, construct an integrated high-speed rail tunnel interawareness system architecture assisted by movable antennas and design an information transmission protocol; S2: Based on the characteristics of the movable antenna model and the channel characteristics of the tunnel scenario, mathematical modeling is performed, and the communication transmission model and the perception transmission model are integrated to establish a synaesthesia integrated information transmission model; S3: With the goal of maximizing the total communication transmission rate, the movable antenna position, the beamforming vector transmit power, and the perceived interference link power as constraints, an optimization problem is constructed. Fractional programming is used to perform an equivalent transformation of the objective function and simplify the optimization problem. S4: The simplified optimization problem is decomposed into two sub-problems: communication beamforming vector optimization and movable antenna position vector optimization. The communication beamforming vector optimization is solved by the manifold optimization linear search method, and the movable antenna position optimization is converted into a convex optimization problem by quadratic transformation and first-order Taylor expansion approximation. Finally, the system beamforming vector and movable antenna position vector are updated through alternating optimization iterative updates to achieve the goal of maximizing the total communication transmission rate.

2. The method for integrated information transmission of high-speed railway tunnel communication and perception based on a movable antenna according to claim 1, characterized in that: The contents of step S1 include: (1) System Architecture The system consists of the following three parts: a telepathy integrated base station assisted by a movable antenna deployed on the top of the tunnel, K omnidirectional single-antenna mobile relays on the top of the high-speed rail carriage, and track sensing targets to be detected in the tunnel; the internal equipment of any high-speed rail carriage communicates with the base station through the mobile relay on the top of the carriage; the base station is a telepathy integrated base station assisted by a movable antenna, and its antenna array is divided into two groups: one group consists of a uniform linear array composed of M fixed antennas, which is used to sense obstacles in the tunnel; the other group consists of a movable antenna communication array composed of N antennas, which is used for downlink communication between the base station and the high-speed rail; the communication group antenna uses the emerging technology of movable antennas, which enables multiple antennas to be flexibly moved within the restricted area of ​​the transmitter and receiver to reconfigure the optimal wireless channel and improve the system communication performance; to alleviate the problem of spectrum shortage during high-speed rail operation, the system is designed to share the spectrum of the same frequency band for communication and perception functions, thereby improving the system spectrum utilization efficiency; (2) Information transmission protocol Movable antenna communication adopts the new air interface time division duplex frame structure. Multiple users transmit information through spatial multiplexing. Five subframes constitute one frame, and the subframe structure consists of five parts: MA-Pilot, CSI-DL, Opt, Move and Data. MA-Pilot is the subframe pilot of the movable antenna, which is used by the base station to perform orthogonal detection sequence, and the user returns coarse information status information. CSI-DL is the user uploading fine-grained downlink channel state information for channel modeling and system optimization. Opt is the system optimization process, which calculates the optimal beamforming vector and antenna position information. Move is the process of displacement of the movable antenna, during which the base station power-limited data channel remains silent. Data is the information transmission process, and the base station transmits data to multiple users according to the optimal beamforming vector and antenna position vector.

3. The method for integrated information transmission of high-speed railway tunnel communication and perception based on a movable antenna according to claim 1, characterized in that: The contents of step S2 include: (1) Movable antenna model The movable antenna adjusts the position of the antenna within the linear array area to dynamically optimize the communication link. The antenna array area is denoted as C. t , the coordinate of the center of the movable antenna is marked as x0, and the coordinate of the position of the nth movable antenna is marked as x n , for any x n , all have x n ∈C t ,in The antenna position vector is expressed as: x=[x1,x2,…,x N ] T (2) Tunnel scenario channel model Due to the unique electromagnetic wave propagation characteristics of the tunnel environment, the fading pattern of the wireless signal is different from that of free space propagation. The wireless signal in the tunnel will encounter more reflections, diffractions and scattering. The system tunnel scenario channel model consists of three parts: the channel link h from the ISAC base station communication antenna group to the kth mobile relay; k , the interference link g from the uniform linear array to the kth mobile relay k And the communication part perceives the interference link H s ; The channel link h between the ISAC base station communication antenna group and the kth mobile relay k The wireless channel model is composed of LoS and NLoS components. The LoS component is the line-of-sight component, and the NLoS component is the non-line-of-sight component. The NLoS component includes the SB component from the tunnel ceiling, ground, and walls on both sides, i.e., the single-hop reflection component. The effective scatterers are randomly distributed within the single-hop reflection range. L clusters of SB components are distributed on the inner surface of the tunnel. The channel link h from the ISAC base station communication antenna group to the kth mobile relay is k , expressed as: in, represents the kth mobile relay, is the LoS component between the ISAC base station and the kth mobile relay on the high-speed railway; represents the lth cluster single-hop reflection, is the lth cluster single-hop reflected NLoS component; LoS component from ISAC base station to high-speed rail mobile relay Expressed as: Among them, PL k represents large-scale fading, The unit is dB, represents the path loss at a reference distance of 1 meter, α d,k represents the path loss index, D represents the distance of a single link; K R Represents the Rice factor, which represents the ratio of the LoS component power to the scattered component power; is the MA antenna array steering vector. Unlike traditional linear uniform antenna arrays, it is not only related to the angle between the signal direction and the array axis (x-axis), but also to the antenna position vector, which can be expressed as: in, represents the communication transmission transmission angle from the base station communication antenna to the kth mobile relay, x is the antenna position vector of the movable antenna; λ is the carrier wavelength; is the maximum Doppler shift, given by the train speed v R , carrier frequency f c Determination; t is the observation time variable, in the discrete baseband symbol model, t = nT s , T s is the symbol interval, n=0,1,2,… is the symbol number; Single-hop reflection component Expressed as Among them, P l is the ratio of the power of the lth scattering cluster to the total scattering component power, N l is the number of scatterers in the lth cluster, assuming N l →∞, For nth l The random phases of the scatterers are uniformly distributed at (-π,π); Similarly, the interference link g from the uniform linear array to the kth mobile relay is sensed k It consists of LoS component and NLoS component, and its mathematical form is expressed as: Among them, PL g represents the large-scale fading of the sensing link to the kth mobile relay, The unit is dB, represents the path loss at a reference distance of 1 meter, D represents the distance of a single link, and α d,g represents the path loss exponent; represents the steering vector from the sensing uniform linear array to the kth mobile relay, and its mathematical expression is: in, represents the communication transmission transmission angle of the base station sensing antenna to the kth mobile relay, and M represents the number of ULA antennas in the sensing part; Interference link H of the communication part to the perception part s It is composed of NLoS components, and its mathematical expression is: Among them, PL i represents large-scale fading; K R represents the Rice factor; P l is the ratio of the power of the lth scattering cluster to the total scattering component power; a MA (x,θ c ) is the communication MA antenna array steering vector, θ c is the emission angle of the interference link; a FA (θ s ) is the sensing FA antenna array steering vector, θ s is the arrival angle of the interference link; N l is the number of scatterers in the lth cluster; For nth l The random phases of the scatterers are uniformly distributed at (-π,π); (3) Communication model Based on the channel model of the tunnel scenario, the communication signal y received by the kth mobile relay is k Expressed as: in, and They represent the communication channel response of the ISAC base station communication antenna array to the kth mobile relay and the interference channel response of the sensing antenna array to the kth mobile relay, respectively. is a complex field, and h k and g k The conjugate transpose of represents the beamforming vector of the ISAC base station communication array to the kth mobile relay, s k represents the communication symbols required by the k-th mobile relay, Orthogonal emission waveform vector for sensing signal; Indicates that the mean at the kth mobile relay is zero and the variance is Additive Gaussian white noise; Therefore, the signal to interference and noise ratio of the kth mobile relay is expressed as: in, is the beamforming signal power received by the kth mobile relay; is the beamforming interference power of other mobile relays, that is, the interference power of other users; is the interference power of the sensing link to the kth mobile relay; is the Gaussian white noise power; Assuming that all mobile relays use the same bandwidth, the normalized total communication rate of K mobile relays is: (4) Perception Model In the sensing uniform linear antenna array part, the echo signal received by the sensing radar after detecting the target is expressed as: Among them, α represents the echo signal loss coefficient, and its value depends on the radar scattering cross section and the channel loss coefficient between the base station and the detection target. It is defined as vector and They represent the transmitting direction vector and receiving direction vector of the radar antenna array respectively. The specific expressions are: in, is the orthogonal transmission waveform vector of the perception signal; matrix It represents the interference channel between the communication part and the sensing part, that is, the link where the communication signal is scattered by the target or other reflectors during the propagation process. is the transmit beam matrix of the base station, is the symbol vector sent by the base station, means the mean is zero and the variance is Additive Gaussian white noise; The interference power of the ISAC base station communication link to the sensing link is expressed as:

4. The method for integrated information transmission of high-speed railway tunnel communication and perception based on a movable antenna according to claim 1, characterized in that: The contents of step S3 include: (1) Construction of overall optimization problem With the optimization goal of maximizing the total communication rate R of the mobile relay, the optimization problem is constructed as follows: s.t.C1:|x i -x j |≥d min ,1≤i≠j≤N C3:||in k || 2 =1 C4:P int ≤p0 Among them, constraint C1 means that the minimum distance between each pair of movable antennas is greater than the minimum antenna coupling distance d min ; Constraint C2 ensures that the movable antenna's range of motion is within the restricted area C t Constraint C3 is the beamforming vector power constraint w k , the beamforming vector of the kth mobile relay needs to be normalized to ensure the consistency of the total transmit power distribution; constraint C4 is the interference power constraint, the interference power of the communication link to the sensing link must be lower than the threshold p0 to ensure the normal operation of the radar; (2) Equivalent transformation of optimization problems Introducing the fractional programming FP method, the objective function Perform Lagrange dual transformation and convert the objective function into: Among them, an auxiliary variable ν is introduced k , for R1(w k ,x,ν k )About ν k Find the partial derivative, since the function R1(w k ,x,ν k ) is a monotonically decreasing function, then the point where the partial derivative is 0 is the function R1(w k ,x,ν k ), that is, The optimal solution is: The optimization problem P1 is equivalently transformed into:

5. The method for integrated information transmission of high-speed railway tunnel communication and perception based on a movable antenna according to claim 1, characterized in that: The contents of step S4 include: (1) Communication beamforming vector optimization The complex problem is split into the beamforming vector optimization sub-problem and the antenna position optimization sub-problem by using the alternating optimization method; in order to solve the optimal base station communication end beamforming vector w k , fixing the antenna position vector x in the original optimization problem P2, the communication beamforming optimization sub-problem can be expressed as: s.t.C1:||w k || 2 =1 C2:P int ≤p0 The interference power constraint C2 is added to the objective function as a penalty term. The square error between the interference power and the threshold is added to the objective function, that is, the sum-square penalty. The sum-square penalty is calculated as follows: φ(P int )=(p0-P int ) 2 The objective function is reshaped into P4 using the sum-square penalty technique: s.t.||w k || 2 =1 For this non-convex optimization problem, the manifold optimization method is used to solve it. The oblique manifold structure is used to constrain the variable value range, and a linear search is performed within the constraint set to obtain a feasible solution. The mathematical definition formula of the oblique manifold is The manifold is the product of spheres, and its physical meaning is: if each column in X is in the complex field There is a unit norm on , then That is, the set of X is a slant flow So the beamforming matrix in, Defined as an oblique manifold Its mathematical formula is: Furthermore, the optimization problem P4 can be restated as the following unconstrained problem: Introduce the selection column vector e k =[0,…,1,…,0] T , that is, the kth row is 1 and the other items are 0, then w k =We k , the objective function can be restated as follows: Find the Euclidean gradient of it, that is oblique manifold The tangent space and normal space are defined at point W on and oblique manifold Tangent space at point W The mathematical expression is: The mathematical meaning of this formula is: tangent space Depend on The Δ matrix satisfies diag(W T Δ)=0, that is, Δ is orthogonal to W; oblique manifold Normal space at point W The mathematical expression is: The mathematical meaning of this formula is: normal space It is composed of DW, where D is a diagonal matrix, that is, the normal direction of each column is the direction of the vector of the column at point W, that is, the spherical normal, and the normal space is composed of the combination of these radial directions; The Riemann gradient of f(W) at point W is given by its Euclidean gradient in the tangent space The projection on is obtained, which is expressed as: Based on the above content, an algorithm for solving the communication beamforming vector optimization subproblem is designed, namely the manifold optimization linear search algorithm. The line search on the manifold can be regarded as an extension of the line search in Euclidean space. Its solution process is as follows: First, let W (t) is the beamforming matrix at the tth iteration, then the t+1th iteration point is: Where α(t) is the search step size, which is assumed to be the Armijo step size; Secondly, the iteration point W (t+1) Projection onto the oblique manifold The iterative point after projection is recorded as To ensure that each step is run on the oblique manifold, the projection formula is: Then, the step size update process satisfies: Among them, η t W (t) The Riemann gradient on the oblique manifold M is vec(η t ) represents the matrix η t Stack by column into column vectors; Finally, when the gradient at iteration t+1 meets the algorithm termination criterion, the iterative algorithm stops and ends. The termination criterion of the manifold optimization linear search algorithm is defined as: ||vec(n t+1 )|| ∞ <ε(1+||vec(η t )|| ∞ ) Among them, ||vec(η t+1 )|| ∞ Represents the infinite norm, that is, the column vector vec(η t+1 ), ε is the precision parameter; (2) Optimization of movable antenna position To optimize the base station communication end antenna position vector x, the fixed beamforming vector w k , the movable antenna position vector problem can be expressed as: s.t.C1:|x i -x j |≥d min ,1≤i≠j≤N Transform the objective function and constraint condition C1, perform a secondary transformation on the objective function, and transform it into the following formula: Among them, μ k is the auxiliary variable introduced, the optimal value The mathematical expression is: To avoid the problem of non-differentiable norm at zero point, transform the constraint condition C1 in P6 into Then, the first-order Taylor expansion is introduced to transform the non-convex feasible domain of the constraint into a convex feasible domain; Let δ = x i -x j , let function |x i -x j | 2 For ψ(δ)=|δ| 2 , the initial point is recorded as Then its first-order Taylor expansion is: Right now, Therefore, constraint C1 becomes the following inequality: This inequality is an affine inequality, and its corresponding feasible domain is a convex set. Therefore, the original optimization subproblem P6 is transformed into a convex optimization problem of the following form, and the existing optimization tool CVX is used for efficient solution; (3) Alternating optimization performs a fractional programming equivalent transformation on the objective function of the optimization problem, decomposing the problem into two sub-problems: communication beamforming vector optimization and movable antenna position vector optimization. The communication beamforming vector is solved by the linear search method in manifold optimization, and the movable antenna position is approximately solved by quadratic transformation and first-order Taylor expansion. An alternating optimization strategy is adopted to fix other variables, optimize the current variables and update the parameters, and repeat in sequence until the preset number of iterations is reached or the convergence conditions are met, and the joint optimization result is obtained.

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