Full-space intelligent metasurface-assisted vehicle tracking method and system

Abstract

The invention provides a full-space intelligent metasurface-assisted vehicle tracking method and system. The system comprises a roadside unit RSU, a vehicle top IOS and an in-vehicle communication receiver CR. The RSU comprises an MIMO (Multiple Input Multiple Output) multi-antenna system; the IOS assists the RSU to communicate with the CR in the vehicle and track the vehicle, and high-precision vehicle tracking is realized by designing a customized extended Kalman filter (EKF) method and utilizing position side information provided by the IOS. According to the method, the IOS is utilized to assist the MIMO multi-antenna ISAC system, and the transmitting beam forming and IOS configuration of the RSU are jointly optimized, so that the sensing performance is remarkably improved, the CR communication rate is ensured, and particularly, excellent performance is shown under the conditions of high power and a large number of IOS units.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless communication. Specifically, it relates to a vehicle tracking method and system assisted by a full-space intelligent metasurface, and more specifically, to a vehicle tracking method and a communication-sensing integrated ISAC system assisted by a full-space intelligent metasurface IOS. Background Art

[0002] Due to the high dependence on the environment, limited coverage, and weak radar cross-section (RCS) in urban environments, the collaborative gain provided by ISAC technology in vehicle-to-everything (V2X) communication has decreased significantly. To overcome this challenge, intelligent metasurfaces are introduced into the ISAC system to enhance the system coverage through their ability to effectively and adaptively reconstruct wireless channels. Existing research mainly focuses on the potential of intelligent reflecting surface (IRS) to simultaneously enhance communication and sensing performance in the ISAC system, while the present invention proposes a communication-sensing integrated ISAC system assisted by a full-space intelligent metasurface IOS to further improve the system performance.

[0003] IOS is an emerging technology. Compared with the traditional IRS that can only serve receivers on the same side, IOS can achieve full-space coverage by simultaneously reflecting and refracting incident signals, which enables IOS to adjust the phase shift and power ratio of the reflected and refracted signals, providing a new degree of freedom for the popularization of wireless communication. Different from traditional relays, IOS does not require additional radio frequency links and energy consumption, thus having the advantages of low cost and low energy consumption. Most existing research on IOS-assisted ISAC systems focuses on the optimization of IOS, while its application in V2X communication is more challenging, especially in vehicle tracking method design and resource allocation.

[0004] Previous research mainly focused on tracking vehicles as point targets. However, in actual scenarios, vehicles usually occupy multiple grids in the range and angle domains. This "point target" assumption may lead to significant performance losses. To solve this problem, the present invention installs IOS on the top surface of an extended vehicle. By reflecting and refracting the ISAC signals transmitted from a roadside unit (RSU) through IOS, the sensing accuracy and communication performance can be improved simultaneously. However, in V2X communication, IOS-assisted ISAC technology faces a series of technical challenges, including how to design a vehicle tracking method to accurately predict and track vehicle states, how to optimize the transmit beamforming of the RSU, and how to optimize the reflection / refraction amplitude and phase of IOS.

[0005] Patent document CN112767475B (application number: 202011607167.6) discloses an intelligent roadside perception system based on C-V2X, radar and vision. The system integrates modules such as C-V2X communication, target recognition, multi-source information fusion, target positioning, and RSU message forwarding. For visual target detection and radar multi-target tracking, a lightweight target detection neural network model and a weighted neighborhood data association multi-target tracking algorithm based on unscented Kalman filter are designed. A multi-source information fusion weight allocation method based on information gain is designed. For the problem of asynchronous acquisition data of different sensors, a multi-sensor fusion time synchronization method based on interpolation and extrapolation is designed. Then, combined with C-V2X communication, the fusion result is corrected and compensated through vehicle-road collaborative data, and a multi-source information fusion correction method based on C-V2X is designed. Finally, combined with high-precision positioning, the target information after fusion perception is broadcast to vehicles and pedestrians, making up for the deficiencies of in-vehicle perception.

[0006] The present invention proposes a vehicle tracking method and system assisted by a full-space intelligent metasurface. By designing a customized extended Kalman filter (EKF) method, the perception and prediction of vehicle states are realized. At the same time, based on the predicted vehicle states given by the customized EKF method, for the RSU transmission beamforming and IOS configuration that affect the perception accuracy in the ISAC system, a zero-order optimization-based augmented penalty dual decomposition (ZO-IPDD) algorithm is adopted to efficiently optimize the RSU transmission beamforming and IOS configuration, and enable the customized EKF method to give higher-precision vehicle predicted states in the following. Compared with traditional tracking methods and optimization methods, the present invention shows higher superiority in vehicle tracking and resource allocation, providing new ideas and methods for the design of the next-generation wireless communication system. Summary of the Invention

[0007] Aiming at the defects in the prior art, the purpose of the present invention is to provide a vehicle tracking method and system assisted by a full-space intelligent metasurface.

[0008] According to a vehicle tracking method assisted by a full-space intelligent metasurface provided by the present invention, it includes:

[0009] Step S1: A roadside unit (RSU) communicates with an in-vehicle communication receiver (CR) through an in-vehicle object (IOS) on the top of the vehicle to obtain the reflected signal from the IOS;

[0010] Step S2: Based on the reflected signal from the IOS, the vehicle state is predicted and tracked by a customized extended Kalman filter method;

[0011] The customized extended Kalman filter method realizes the perception and prediction of vehicle states through the construction of vehicle state evolution and measurement models.

[0012] Preferably, step S1 includes: the roadside unit RSU sends an ISAC signal to the vehicle, where part of the signal is refracted by the in-vehicle optical sensor (IOS) on the vehicle top to the in-vehicle communication receiver (CR), and part of the signal is reflected back to the roadside unit RSU by the IOS on the vehicle top, and the reflected signal from the IOS is acquired.

[0013] Preferably, the method further includes: optimizing the transmit beamforming of the roadside unit RSU and the configuration of the IOS on the vehicle top based on the zero-order optimization augmented penalty dual decomposition (ZO-IPDD) algorithm to obtain an optimal resource allocation scheme; obtaining the reflected signal from the IOS under the optimized resource allocation scheme;

[0014] The roadside unit RSU includes a MIMO multi-antenna array; the IOS on the vehicle top includes a plurality of full-space units and a controller;

[0015] Controlling the amplitude and phase of the MIMO multi-antenna array through the optimized transmit beamforming;

[0016] Optimizing the configuration of the IOS on the vehicle top based on the ZO-IPDD algorithm includes: respectively optimizing the reflection / refraction amplitude and phase of each full-space unit in the IOS on the vehicle top.

[0017] Preferably, the optimizing the transmit beamforming of the roadside unit RSU and the configuration of the IOS on the vehicle top based on the zero-order optimization augmented penalty dual decomposition (ZO-IPDD) algorithm to obtain an optimal resource allocation scheme includes:

[0018] The zero-order optimization augmented penalty dual decomposition (ZO-IPDD) algorithm adopts a double-loop structure; in the inner loop, the transmission beam and the IOS configuration are jointly optimized through the ZO algorithm; in the outer loop, the IPDD framework is used to update the penalty factor and the dual variable to solve the non-linear variable coupling problem;

[0019] For the power allocation ratio, in the optimal solution of the proposed optimization problem, the power allocation ratio of reflection / refraction should satisfy and represents the optimal refraction amplitude response of the m-th element of the k-th IOS; represents the optimal refraction amplitude response of the m'-th element of the k-th IOS, represents the optimal reflection amplitude response of the m-th element of the k-th IOS, represents the optimal reflection amplitude response of the m'-th element of the k-th IOS; for all All elements of the k-th IOS share the same reflection and refraction power allocation ratios, denoted as and Therefore, the reflection / refraction amplitude vector of IOS is simplified to To handle the non-convex communication rate constraint, define:

[0020]

[0021] Thus, the communication rate constraint is rewritten as:

[0022]

[0023] where β TR denotes the aggregated refraction amplitude vector, denotes the aggregated refraction phase shift vector, and f denotes the transmit beamforming vector of the RSU;

[0024] To handle this rewritten constraint, further consider the augmented Lagrangian form of the optimization problem:

[0025]

[0026] where

[0027]

[0028] denotes all optimization variables, ζ is the Lagrangian dual variable, and λ is the penalty factor;

[0029] Next, adopt the IPDD framework, which adopts a double-loop structure. The inner loop solves the augmented Lagrangian problem, while the outer loop updates the dual variable ζ and the penalty factor λ; among them, the ratio of the reflection and refraction amplitudes must satisfy the energy conservation condition; therefore, once the reflection amplitude vector β R is optimized, the corresponding refraction amplitude vector β TR is obtained through ; therefore, in the following text, by replacing β TR with only the optimization of β R will be considered without loss of optimality;

[0030] Propose a zero-order optimization algorithm with adaptive momentum. The main idea of this zero-order algorithm is to approximate the full gradient through the difference in function values at random query points; the proposed zero-order algorithm with adaptive momentum is an iterative algorithm, where i represents the inner-loop iteration index, and each iteration mainly includes the following four steps:

[0031] 1) Derive the ZO gradient: By setting and fixing ζ and λ in the inner loop, construct the function The ZO gradient estimate is obtained by the forward difference of two function values in a random unit direction:

[0032]

[0033] where u1 is a random vector uniformly distributed on the unit sphere, μ1>0 is a perturbation radius, which can be regarded as a smoothing parameter, and is the dimension-dependent factor related to the above uniform distribution; N t represents the number of RSU transmit antennas, K represents the number of subarrays of the IOS, and M represents the number of elements in each subarray;

[0034] Since the RSU-IOS and IOS-CR channels are mainly LoS links, a dimension reduction strategy is proposed to reduce the dimension of, mainly by reconstructing the original refraction / reflection phase shift vector of the k-th IOS into the form of ; Therefore, the aggregated refraction / reflection phase shift vectors of the K IOSs to be optimized, and are expressed as:

[0035]

[0036] After adopting this form, the dimension of the optimization variable is significantly reduced from N t +K+2KM to N t +5K, because the number of IOS elements M is usually much larger than K and N t ; Based on the above dimension reduction strategy, the overall optimization variable vector is redefined as Then the ZO gradient estimator is reformulated as:

[0037]

[0038] where the definitions of u2 and μ2 are similar to those of u1 and μ1, and is related to the dimension;

[0039] 2) Update the second momentum: The next step of the ZO algorithm is to update the second momentum v i in the i-th iteration, which is defined as the exponential moving average of the cumulative history and the squared gradient of the current iteration; Update v i can be achieved by the following:

[0040]

[0041] where η∈[0,1) controls the exponential decay rate of v i ;

[0042] 3) Keep the maximum value of the second momentum: Use to keep the maximum value of v j ,j ∈ {1, 2, …, i} up to the i-th iteration for normalizing the running average of the gradient, and the expression is as follows:

[0043]

[0044] 4) Update variables using Mahalanobis projection: Adopt Mahalanobis projection to update the optimization variables The expression is as follows:

[0045]

[0046] where

[0047]

[0048] represents the projection of a onto the feasible set with respect to α i is the step size determined by the Armijo rule;

[0049] The IPDD framework is used to update the dual variable ζ and the penalty factor λ; let r denote the external iteration index of the IPDD framework; then, the dual variable ζ r in the r-th external iteration is updated as follows:

[0050]

[0051] Meanwhile, the penalty factor λ r is updated as follows:

[0052] λ r = c λ λ r-1

[0053] to gradually increase the cost of constraint violation in each iteration, where 0 < c λ < 1 is a constant controlling the penalty growth rate; in this framework, λ r is initially set to a large value that meets the preset requirements; subsequently, it is gradually decreased in each iteration to accelerate the process of satisfying the equality constraint.

[0054] Preferably, the step S2 includes:

[0055] In the n-th iteration, using to represent the state parameters of the vehicle, the state evolution model is expressed as:

[0056]

[0057] v n = v n-1 + ω v

[0058] wherein, represents the estimated vehicle angle relative to the RSU along the x-axis in the nth period, d n represents the distance between the vehicle and the RSU in the nth period, v n represents the vehicle speed in the nth period, ΔT represents the duration of each time period, ω d and ω v represent the corresponding noises, which follow a Gaussian distribution with a mean of zero and variances of and Let represent the measurement parameters at the RSU, where wherein, represents the normalized output signal corresponding to the kth IOS in the nth period, τ k,n represents the time delay at the kth IOS in the nth period, μ k,n represents the Doppler shift at the kth IOS in the nth period; K represents the number of sub-arrays of the IOS; then, the state evolution model and the measurement model are restated as:

[0059] State evolution model: x n = g(x n-1 ) + ω n ,

[0060] Measurement model: y n = t(x n ) + z n

[0061] wherein, g(·) reflects the mapping relationship in the state evolution model, t(·) reflects the mapping relationship in the measurement model, x n represents the vehicle state parameters in the nth period, and at the same time ω n and z n both follow a Gaussian distribution with a zero mean, and their covariance matrices are as follows:

[0062]

[0063] wherein, represents the normalized measurement noise, 1 Nr represents an N r -dimensional vector with all elements being 1, The measured Gaussian noise representing the delay at the k-th IOS, The measured Gaussian noise representing the Doppler shift at the k-th IOS;

[0064] Next, a customized EKF method is proposed. Using the location side information provided by the IOS, the measurement parameter y n and the vehicle parameter x n are related; To linearize these models, first calculate the Jacobian matrices of g(x n ) and t(x n ); The Jacobian matrix of t(x n ) is derived as:

[0065]

[0066] where v represents the speed of the vehicle and d represents the distance between the vehicle and the RSU;

[0067] Next, to derive the Jacobian matrix of t(x n ), denoted as the relative static position between the IOS and the vehicle needs to be utilized; Therefore, T n is obtained through the chain rule:

[0068]

[0069] where the first term is expressed as:

[0070]

[0071] and n r,t = 2 - n r - n t and

[0072] where f represents the transmit beamforming vector of the RSU, represents the complex reflection coefficient at the k-th IOS, β k represents the amplitude response of the k-th IOS, n r,t represents the index of the RSU antenna, represents the estimated angle of the k-th IOS relative to the RSU along the x-axis, M represents the number of elements in each subarray, m y (m) = m - m x (m)M y - 1, φ k represents the estimated angle of the k-th IOS relative to the RSU along the y-axis, θ k,m represents the phase shift of the m-th element of the k-th IOS;

[0073] The second term is expressed as:

[0074]

[0075] where d k,n represents the distance between the k-th IOS and the RSU in the n-th period, x k,n represents the state parameter of the k-th IOS in the n-th period, v k,n represents the speed of the k-th IOS in the n-th period, f c represents the carrier frequency, and c represents the speed of light;

[0076] The third term is expressed as:

[0077]

[0078] where 1 K represents a K-dimensional vector with all elements being 1, and I3 represents a 3rd-order identity matrix;

[0079] The fourth term is expressed as:

[0080]

[0081] According to G n and T n , a customized EKF method is given and outlined as follows:

[0082] 1) State prediction:

[0083] 2) Linearization:

[0084] 3) MSE matrix prediction:

[0085] 4) Kalman gain calculation:

[0086] 5) State tracking:

[0087] 6) MSE matrix update: M n =(I - K n T n )M n|n-1 .

[0088] At the n-th iteration, the RSU updates the predicted state n based on the measurement parameter y to obtain This state will be used as the input for the (n + 1)-th state prediction step; in the state prediction step, the predicted state is used for Cramer-Rao bound (CRB) optimization.

[0089] A vehicle tracking system assisted by a full-space intelligent metasurface according to the present invention includes:

[0090] Step S1: The roadside unit RSU communicates with the in-vehicle communication receiver CR through the in-vehicle optical sensor (IOS) on the vehicle top to obtain the reflected signal from the IOS.

[0091] Step S2: Based on the reflected signal from the IOS, the state of the vehicle is predicted and tracked by a customized extended Kalman filtering method.

[0092] The customized extended Kalman filtering method realizes the perception and prediction of the vehicle state through the construction of the vehicle state evolution and measurement models.

[0093] Preferably, step S1 includes: The roadside unit RSU sends an integrated sensing and communication (ISAC) signal to the vehicle, where part of the signal is refracted by the IOS on the vehicle top to the in-vehicle communication receiver CR, and part of the signal is reflected back to the roadside unit RSU by the IOS on the vehicle top, and the reflected signal from the IOS is obtained.

[0094] Preferably, the method further includes: optimizing the transmit beamforming of the roadside unit RSU and the configuration of the IOS on the vehicle top based on the zero-order optimization-based incremental penalty dual decomposition (ZO-IPDD) algorithm to obtain an optimal resource allocation scheme; under the optimized resource allocation scheme, obtaining the reflected signal from the IOS.

[0095] The roadside unit RSU includes a multiple-input multiple-output (MIMO) antenna array; the IOS on the vehicle top includes multiple full-space units and a controller.

[0096] Controlling the amplitude and phase of the MIMO antenna array through the optimized transmit beamforming.

[0097] Optimizing the configuration of the IOS on the vehicle top based on the ZO-IPDD algorithm includes: optimizing the reflection / refraction amplitude and phase of each full-space unit in the IOS on the vehicle top respectively.

[0098] Preferably, optimizing the transmit beamforming of the roadside unit RSU and the configuration of the IOS on the vehicle top based on the zero-order optimization-based incremental penalty dual decomposition (ZO-IPDD) algorithm to obtain an optimal resource allocation scheme includes:

[0099] The zero-order optimization-based incremental penalty dual decomposition (ZO-IPDD) algorithm adopts a double-loop structure; in the inner loop, the transmission beam and the IOS configuration are jointly optimized through the ZO algorithm; in the outer loop, the IPDD framework is used to update the penalty factor and the dual variable to solve the non-linear variable coupling problem.

[0100] For the power splitting ratio, in the optimal solution of the proposed optimization problem, the power splitting ratio of reflection / refraction should satisfy and denotes the optimal refraction amplitude response of the m-th element of the k-th IOS; denotes the optimal refraction amplitude response of the m'-th element of the k-th IOS, denotes the optimal reflection amplitude response of the m-th element of the k-th IOS, denotes the optimal reflection amplitude response of the m'-th element of the k-th IOS; for all all elements of the k-th IOS share the same reflection and refraction power splitting ratios, denoted as and Therefore, the reflection / refraction amplitude vector of the IOS is simplified to To handle the non-convex communication rate constraint, define:

[0101]

[0102] Thereby, the communication rate constraint is rewritten as:

[0103]

[0104] where, β TR denotes the aggregated refraction amplitude vector, denotes the aggregated refraction phase shift vector, f denotes the transmit beamforming vector of the RSU;

[0105] To handle this rewritten constraint, further consider the augmented Lagrangian form of the optimization problem:

[0106]

[0107] where

[0108]

[0109] denotes all optimization variables, ζ is the Lagrangian dual variable, and λ is the penalty factor;

[0110] Next, adopt the IPDD framework, which adopts a double-loop structure, where the inner loop solves the augmented Lagrangian problem, and the outer loop updates the dual variable ζ and the penalty factor λ; among them, the ratio of reflection and refraction amplitudes must satisfy the energy conservation condition; therefore, once the reflection amplitude vector β R is optimized, the corresponding refraction amplitude vector β TR is obtained through ; therefore, hereinafter, by replacing β TR with Only the optimization of β will be considered R without sacrificing optimality;

[0111] A zero-order optimization algorithm with adaptive momentum is proposed. The main idea of this zero-order algorithm is to approximate the full gradient by the function value differences at random query points. The proposed zero-order algorithm with adaptive momentum is an iterative algorithm, where i represents the inner-loop iteration index, and each iteration mainly consists of the following four steps:

[0112] 1) Derive the ZO gradient: By setting and fixing ζ and λ in the inner loop, construct the ZO gradient estimate of the function at the i-th iteration, which is obtained by the forward difference of two function values in a random unit direction:

[0113]

[0114] where u1 is a random vector uniformly distributed on the unit sphere, μ1>0 is a perturbation radius, which can be regarded as a smoothing parameter, and is the dimension-dependent factor related to the above uniform distribution; N t represents the number of RSU transmit antennas, K represents the number of subarrays of the IOS, and M represents the number of elements in each subarray;

[0115] Since the RSU-IOS and IOS-CR channels are mainly LoS links, a dimensionality reduction strategy is proposed to reduce the dimension, mainly by reconstructing the original refraction / reflection phase shift vector of the k-th IOS into the form of ; Therefore, the aggregated refraction / reflection phase shift vector of the K IOSs to be optimized, and are expressed as:

[0116]

[0117] After adopting this form, the dimension of the optimization variable is significantly reduced from N t +K+2KM to N t +5K, because the number of IOS elements M is usually much larger than K and N t ; Based on the above dimensionality reduction strategy, the overall optimization variable vector is redefined as Then the ZO gradient estimator is reformulated as:

[0118]

[0119] where the definitions of u2 and μ2 are similar to those of u1 and μ1, and is related to the dimension;

[0120] 2) Update the second momentum: The next step of the ZO algorithm is to update the second momentum v in the i-th iteration i , which is defined as the exponential moving average of the squared gradients of the cumulative history and the current iteration; update v i can be achieved in the following way:

[0121]

[0122] where η ∈ [0, 1) controls the exponential decay rate of v i .

[0123] 3) Retain the maximum value of the second momentum: Use to retain the maximum value of v up to the i-th iteration j , j ∈ {1, 2, …, i}, in order to normalize the running average of the gradients, and the expression is as follows:

[0124]

[0125] 4) Update the variable using Mahalanobis projection: Adopt Mahalanobis projection to update the optimization variable and its expression is as follows:

[0126]

[0127] where

[0128]

[0129] represents the projection of a onto the feasible set of under the Mahalanobis distance relative to α i is the step size, determined by the Armijo rule;

[0130] The IPDD framework is used to update the dual variable ζ and the penalty factor λ; let r denote the external iteration index of the IPDD framework; then, the dual variable ζ in the r-th external iteration r is updated as follows:

[0131]

[0132] Meanwhile, the penalty factor λ r is updated as follows:

[0133] λ r = c λ λ r-1

[0134] By gradually increasing the cost of constraint violation in each iteration, where 0 < c λ <1 is a constant that controls the growth rate of the penalty; in this framework, λ r is initially set to a large value that meets the preset requirements; subsequently, it is gradually decreased in each iteration to accelerate the process of satisfying the equality constraints.

[0135] Preferably, the step S2 includes:

[0136] In the nth iteration, using to represent the state parameters of the vehicle, the state evolution model is expressed as:

[0137]

[0138] v n = v n-1 + ω v

[0139] where, represents the estimated angle of the vehicle along the x-axis relative to the RSU in the nth period, d n represents the distance between the vehicle and the RSU in the nth period, v n represents the speed of the vehicle in the nth period, ΔT represents the duration of each time period, ω d and ω v represent the corresponding noises, following a Gaussian distribution with a mean of zero and variances of and Let represent the measurement parameters at the RSU, where where, represents the normalized output signal corresponding to the kth IOS in the nth period, τ k,n represents the time delay at the kth IOS in the nth period, μ k,n represents the Doppler shift at the kth IOS in the nth period; K represents the number of sub-arrays of the IOS; then, the state evolution model and the measurement model are restated as:

[0140] state evolution model: x n = g(x n-1 ) + ω n ,

[0141] measurement model: y n = t(x n ) + z n

[0142] Among them, g(·) reflects the mapping relationship in the state evolution model, t(·) reflects the mapping relationship in the measurement model, and x n represents the vehicle state parameters in the nth period. Meanwhile, ω n and z n both follow zero-mean Gaussian distributions, and their covariance matrices are shown as follows:

[0143]

[0144] Among them, represents the normalized measurement noise, and 1 Nr represents an N r -dimensional vector with all elements being 1. represents the measurement Gaussian noise of the time delay at the kth IOS, and

[0145] Next, a customized EKF method is proposed. Using the location side information provided by the IOS, the measurement parameter y n is related to the vehicle parameter x n . To linearize these models, the Jacobian matrices of g(x n ) and t(x n ) are first calculated. The derivation of the Jacobian matrix of t(x n ) is as follows:

[0146]

[0147] Among them, v represents the vehicle speed, and d represents the distance between the vehicle and the RSU.

[0148] Next, to derive the Jacobian matrix of t(x n ), denoted as , the relative static position between the IOS and the vehicle needs to be utilized. Therefore, T n is obtained through the chain rule:

[0149]

[0150] Among them, the first term is expressed as:

[0151]

[0152] And n r,t = 2 - n r - n t and

[0153] Among them, f represents the transmit beamforming vector of the RSU, represents the complex reflection coefficient at the kth IOS, and βk denotes the amplitude response of the k-th IOS, n r,t denotes the index of the RSU antenna, denotes the estimated angle of the k-th IOS relative to the RSU along the x-axis, M denotes the number of elements in each subarray, m y (m) = m - m x (m)M y -1, φ k denotes the estimated angle of the k-th IOS relative to the RSU along the y-axis, θ k,m denotes the phase shift of the m-th element of the k-th IOS;

[0154] The second term is expressed as:

[0155]

[0156] where, d k,n denotes the distance between the k-th IOS and the RSU in the n-th period, x k,n denotes the state parameter of the k-th IOS in the n-th period, v k,n denotes the speed of the k-th IOS in the n-th period, f c denotes the carrier frequency, c denotes the speed of light;

[0157] The third term is expressed as:

[0158]

[0159] where, 1 K denotes a K-dimensional vector with all elements being 1, I3 denotes the 3rd-order identity matrix;

[0160] The fourth term is expressed as:

[0161]

[0162] According to G n and T n , a customized EKF method is given as follows:

[0163] 1) State prediction:

[0164] 2) Linearization:

[0165] 3) MSE matrix prediction:

[0166] 4) Kalman gain calculation:

[0167] 5) State tracking:

[0168] 6) MSE matrix update: M n = (I - K n T n )M n|n-1 .

[0169] In the nth iteration, the RSU updates the predicted state according to the measurement parameter y n to obtain This state will be used as the input for the (n + 1)th state prediction step; in the state prediction step, the predicted state is used for Cramér-Rao bound (CRB) optimization.

[0170] Compared with the prior art, the present invention has the following beneficial effects:

[0171] 1. Improve tracking accuracy: By incorporating the known relative positions between various parts of the IOS and the vehicle, the present invention designs a customized EKF method, significantly improving the accuracy of vehicle state prediction and tracking accuracy; at the same time, by optimizing the transmit beamforming of the RSU and the configuration of the IOS, the accuracy is further improved;

[0172] 2. Optimized algorithm is efficient: The joint optimization algorithm proposed by the present invention can effectively design the transmit beamforming of the RSU and allocate the reflection / refraction amplitude and phase of each element of the IOS, further improving the performance and efficiency of the ISAC system; through the ZO-IPDD algorithm, the complex multi-dimensional optimization problem can be quickly converged to find the optimal solution;

[0173] 3. Low deployment cost: The architecture proposed by the present invention is simple and easy to deploy, and has significant advantages in terms of hardware cost and power consumption. Compared with traditional antenna arrays and other signal enhancement technologies, the IOS has a lower hardware cost and excellent signal enhancement effect, and is suitable for the next-generation high-efficiency wireless communication system; in addition, the system proposed by the present invention does not require dedicated downlink pilots because the entire ISAC signal block is used for sensing and communication.

[0174] 4. Green communication: The IOS device used in the present invention has the characteristics of low power consumption and is a new type of green auxiliary sensing device; through reasonable configuration and optimization, it can significantly reduce the system energy consumption while maintaining high performance, meeting the development needs of modern communication systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0175] By reading the detailed description of the non-limiting embodiments with reference to the following drawings, other features, objects, and advantages of the present invention will become more apparent:

[0176] Figure 1 For the IOS-assisted ISAC system.​

[0177] Figure 2 The variation of CRB with transmission power under different IOS configurations and different numbers of IOS elements.

[0178] Figure 3 The variation of CRB with the number of IOS elements under different IOS configurations and different transmission powers. Detailed implementation manners

[0179] The present invention will be described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several changes and improvements can still be made. These all belong to the protection scope of the present invention.

[0180] Embodiment 1

[0181] An embodiment of the present invention discloses a vehicle tracking method assisted by a full-space intelligent metasurface, as Figure 1 shown, including an integrated sensing and communication (ISAC) system; the integrated sensing and communication (ISAC) system is equipped with an RSU with a multi-antenna system, an IOS on the top of the vehicle, and an in-vehicle communication receiver CR;

[0182] The RSU is equipped with a MIMO multi-antenna system, and the in-vehicle CR is equipped with a single-antenna system. The RSU is equipped with multiple transmitting antennas and receiving antennas, and the in-vehicle CR is equipped with one antenna;

[0183] By designing the vehicle tracking method and resource allocation, the sensing accuracy of the RSU for the vehicle and the communication performance for the in-vehicle CR are improved.

[0184] The IOS includes multiple full-space units, and the IOS is equipped with an intelligent controller for controlling the reflection / refraction amplitude and phase of each full-space unit;

[0185] The RSU sends an ISAC signal to the vehicle, and a part of the signal is refracted by the IOS to the CR inside the vehicle, so that a communication link is established between the CR and the RSU and the information transmitted by the RSU to it is obtained, while the other part is reflected back to the RSU by the IOS. The RSU senses and predicts the vehicle state according to the echo signal, so as to realize the fusion of the communication function and the sensing function in the system.

[0186] The vehicle tracking method assisted by the full-space intelligent metasurface includes:

[0187] Vehicle tracking step: A customized EKF method is used to perform high-precision prediction and tracking of the vehicle state;

[0188] Cramer-Rao Bound (CRB) Optimization Steps: Using the ZO-IPDD algorithm, based on the vehicle state predicted by the vehicle tracking method, solve the problem of joint RSU transmission beamforming and IOS configuration optimization, and perform efficient resource allocation.

[0189] In the IOS-assisted ISAC system during signal transmission, the RSU receives the echo signal from the IOS, and uses the customized EKF method to achieve the prediction and tracking of the vehicle state. At the same time, the in-vehicle CR receives the refraction signal from the IOS to improve the communication performance; the IOS-assisted ISAC system jointly performs beamforming, conducts RSU transmission beamforming design and IOS configuration, and obtains the CRB of the minimized vehicle estimation parameters.

[0190] In the IOS-assisted ISAC system, the RSU needs to complete the prediction and tracking of the vehicle state based on the echo signal from the IOS and complete the transmission beamforming; the IOS enhances the ISAC signal quality by adjusting the reflection / refraction amplitude and phase of each IOS element. In the IOS-assisted ISAC system, the joint optimization design of the RSU and the IOS is considered. The RSU conducts the transmission beamforming design, and the IOS conducts the configuration adjustment.

[0191] Optimization of RSU transmission beamforming: Considering that the transmission power of the RSU is p n and the beamforming vector is f n after the beamforming design, the vehicle tracking accuracy and the communication quality of the in-vehicle CR are improved.

[0192] Optimization of IOS reflection / refraction amplitude and phase: The IOS adjusts the amplitude and phase of the incident signal, controls the coefficient matrix of the IOS to design the amplitude and phase of all IOS elements, so that the reflected signal can minimize the CRB of the vehicle estimation parameters and improve the communication quality of the in-vehicle CR.

[0193] Optimization scheme of the IOS-assisted ISAC system: Taking the minimization of the CRB of the vehicle estimation parameters as the performance index, and ensuring the communication performance requirements of the in-vehicle CR and the configuration constraints of the IOS. By constructing an optimization problem with the minimization of the CRB of the vehicle estimation parameters as the objective and the communication quality of the in-vehicle CR, the energy conservation condition and the configuration condition of each unit of the IOS as the constraints, the present invention realizes the scheme design of the IOS-assisted ISAC system.

[0194] Scheme design of the IOS-assisted ISAC system: The IOS device introduced in this scheme is passive and does not require an additional radio frequency chain to process signals. It realizes signal reflection and refraction in a passive manner and can achieve better performance at a lower cost.

[0195] Optimization Algorithm Design for IOS-Assisted ISAC System: The constructed CRB minimization optimization problem is a non-convex optimization problem, and the global optimal solution cannot be directly obtained. In the following, based on the ZO-IPDD algorithm, the present invention optimizes all optimization variables and obtains a local optimal solution of relatively high quality.

[0196] For the requirements of the next-generation wireless communication for the performance and system complexity of the ISAC system, the present invention provides a novel IOS-assisted vehicle tracking method and ISAC system design.

[0197] According to the IOS-assisted ISAC system provided by the present invention, a joint design scheme for high-precision vehicle tracking scheme design, RSU transmission beamforming design, and IOS configuration is provided.

[0198] The RSU needs to consider beamforming when transmitting ISAC signals. By adjusting the beamforming vector, the communication and sensing performance of the ISAC signals can be improved. At the same time, the RSU needs to use a customized vehicle tracking method based on the echo signals from the IOS to achieve high-precision prediction and tracking of the vehicle state. The IOS needs to control the amplitude and phase of each full-space unit when assisting in reflecting / refracting signals to improve the communication performance of the in-vehicle CR and the sensing performance of the echo signals.

[0199] The RSU adopts a uniform linear array (ULA) arranged along the x-axis, equipped with N t transmitting antennas and N r receiving antennas. We solve the complex scenario where the top of the vehicle is a metal panel, resulting in significant penetration loss. In the system deployment, a vehicle moves along a road parallel to the x-axis, and the RSU simultaneously performs vehicle tracking and communication with the in-vehicle CR. The IOS is divided into K parts, indexed as The k-th part of each IOS has M = M x ×M y elements, which are arranged in a uniform planar array (UPA) along the x-axis and y-axis. Among them, there are M x elements along the x-axis and M y elements along the y-axis. Without loss of generality, the spacing between the antennas / elements is set to half-wavelength. In addition, we assume that the IOS is uniformly deployed around the center of the top surface of the vehicle.

[0200] We define T as the maximum duration of interest, which is divided into smaller time slots (or epochs), and the duration of each time slot is ΔT. The indices of these time slots are where For convenience, let and φ n (φ k,n) represent the estimated angles of the vehicle (the k-th IOS) relative to the RSU along the x-axis and y-axis in the n-th period. Additionally, let d n (d k,n ) and v n (v k,n ) represent the distance and speed between the vehicle (the k-th IOS) and the RSU, respectively. We assume that the motion parameters and the communication channel remain approximately constant within each period, i.e., within a coherence block.

[0201] We use the energy splitting model to describe the simultaneous refraction and reflection of the IOS. Specifically, for the k-th IOS, in the n-th time slot, the incident signal power acting on each element is divided into two parts: the refracted power and the reflected power. The power ratio of these components must satisfy the following energy conservation condition:

[0202]

[0203] where and represent the refraction and reflection amplitude responses of the m-th element of the k-th IOS in the n-th time slot. Then, the refraction and reflection coefficient matrix of the k-th IOS is modeled as:

[0204]

[0205] where i ∈ {TR, R}, and and are the phase responses of the m-th element of the k-th IOS to the refracted and reflected components in the n-th time slot.

[0206] In the n-th iteration, the RSU receives the echo reflected by the IOS, and the received signal can be expressed as:

[0207]

[0208] where p n is the transmit power of the RSU, μ k,n and τ k,n represent the Doppler frequency and round-trip delay of the k-th IOS in the n-th time slot, respectively. f n is the transmit beamforming vector of the RSU, s n (t) is the transmitted ISAC signal, satisfying while z(t) is complex additive white noise with zero mean and covariance matrix . The downlink channel from the RSU to the k-th IOS, denoted by , can be modeled as:

[0209]

[0210] where represents the complex reflection coefficient, which is determined by the signal propagation distance d k,n and the radar cross-section α of the vehicle at the nth moment r . The vectors and are the beamforming vectors of the RSU and the kth IOS respectively, and their form expressions are as follows:

[0211]

[0212] where the mth element of is:

[0213]

[0214] and m y (m) = m - m x (m)M y - 1,

[0215] Similarly, the uplink channel from the kth IOS to the RSU at the nth moment is modeled as:

[0216]

[0217] where

[0218] To solve for distance and velocity in the delay-Doppler domain, we employ a standard matched filtering technique. Then, the output signal of the matched filter at the RSU can be expressed as:

[0219]

[0220] where is the normalized matched filtering output function, obtained by performing time and frequency reversal and conjugate operations on the complex ISAC signal s n (t), G is the matched filtering gain, represents the noise output of the matched filter. The estimated delay and Doppler shift of the kth IOS are determined by locating the peak position in the output, and the specific expressions are as follows:

[0221]

[0222] where c is the speed of light, f c is the carrier frequency, and are zero-mean and have variances of and Measured Gaussian noise. Specifically, these measurement noise variances are inversely proportional to the SNR received by the RSU, i.e.:

[0223]

[0224] where represents the beamforming gain factor, and ρ i , i ∈ {τ, μ} are known constants related to the system configuration and specific signal processing algorithms.

[0225] Since the IOS is divided into K parts, by substituting and into the output signal and normalizing the measurement noise, the normalized output signal corresponding to the k-th IOS can be expressed as:

[0226]

[0227] where represents the measurement noise normalized by the transmit power p n and the matched filtering gain G, with a mean of zero and a variance of (ρ z is a known constant, whose definition is similar to ρ i , i ∈ {τ, μ}).

[0228] The CR in the vehicle mainly receives signals through the RSU-IOS-CR link. Therefore, in the n-th time slot, the signal received by the CR is:

[0229]

[0230] where z c (t) is the channel noise with zero mean and variance of Since the k-th IOS and the in-vehicle CR are relatively stationary, the channel h k from the k-th IOS to the CR can be modeled as:

[0231]

[0232] where represents the LoS channel gain, and can be expressed as:

[0233]

[0234] where and represent the CR angles with respect to the k-th IOS along the x and y axes. Then, the achievable rate in the n-th period is given by the following formula:

[0235]

[0236] The present invention provides a vehicle tracking method in the IOS-assisted ISAC system. Based on the known relative positions between various parts of IOS and the vehicle, a customized EKF method is designed to achieve accurate prediction of the vehicle state and high-precision tracking.

[0237] (1) Design a customized EKF method to achieve vehicle tracking

[0238] To improve the tracking performance of the vehicle, we incorporate the known relative positions between various parts of IOS and the vehicle, and use a customized EKF method for vehicle prediction and tracking:

[0239] In the nth iteration, we use to represent the state parameters of the vehicle. Then, the state evolution model can be expressed as:

[0240]

[0241] v n = v n-1 + ω v

[0242] where ω d and ω v represent the corresponding noises, which follow a Gaussian distribution with a mean of zero and variances of and Let represent the measurement parameters at the RSU, where Then, the state evolution model and the measurement model can be restated as:

[0243] state evolution model: x n = g(x n-1 ) + ω n ,

[0244] measurement model: y n = t(x n ) + z n

[0245] where g(·) reflects the mapping relationship in the state evolution model, t(·) reflects the mapping relationship in the measurement model, and at the same time ω n and z n both follow a zero-mean Gaussian distribution, and their covariance matrices are as follows:

[0246]

[0247] Next, we propose a customized EKF method that utilizes the location side information provided by IOS to establish the relationship between the measurement parameter y n and the vehicle parameter x n . To linearize these models, we first calculate the Jacobian matrices of g(x n ) and t(x n ). Specifically, the Jacobian matrix of t(x n ) can be derived as follows:

[0248]

[0249] Next, to derive the Jacobian matrix of t(x n ), denoted as , the relative static position between IOS and the vehicle needs to be utilized. Therefore, T n can be obtained through the chain rule:

[0250]

[0251] where the first term can be expressed as:

[0252]

[0253] and n r,t = 2 - n r - n t and the second term can be expressed as:

[0254]

[0255] The third term can be expressed as:

[0256]

[0257] The fourth term can be expressed as:

[0258]

[0259] Based on G n and T n , we present the customized EKF method, outlined as follows:

[0260] 1) State prediction:

[0261] 2) Linearization:

[0262] 3) MSE matrix prediction:

[0263] 4) Kalman gain calculation:

[0264] 5) State tracking:

[0265] 6) MSE matrix update: M n = (I - K n T n )M n|n-1 .

[0266] At the n-th iteration, the RSU updates the predicted state n based on the measurement parameter y to obtain This state will be used as the input for the (n + 1)-th state prediction step. In the state prediction step, the predicted state is used for CRB optimization.

[0267] The present invention provides the RSU transmission beamforming and IOS configuration design in the IOS-assisted ISAC system. Based on the vehicle state predicted by the vehicle tracking method, the transmission beamforming of the RSU and the reflection / refraction amplitude and phase of each element of the IOS are designed to minimize the CRB of the vehicle estimation parameters.

[0268] (2) Solve the RSU transmission beamforming and IOS configuration

[0269] While ensuring the CR communication rate, jointly optimize the RSU transmission beamforming and IOS configuration to minimize the CRB of the estimated vehicle parameters:

[0270] To evaluate the estimation accuracy of the vehicle parameters, we use the posterior CRB as the performance metric. For simplicity, we omit the time index n. To calculate the posterior CRB of the vehicle parameters, we first derive the posterior Fisher information matrix (FIM) Its expression is:

[0271] F K = F p + F m

[0272] where F p represents the prior FIM, while F m represents the measurement FIM. In the linearization step of the EKF process, x n-1 and ω n are both Gaussian distributions and independent of each other. Therefore, x n also follows a Gaussian distribution, and then F p can be expressed as:

[0273]

[0274] Next, we derive the IOS parameters The FIM (defined as F mm ). The measured FIM of vehicle parameter x (F m ) can be obtained by applying a transformation matrix to relate these two FIMs, expressed as:

[0275]

[0276] where K t can be expressed as:

[0277]

[0278]

[0279] By reconstructing the measurement covariance matrix R z in the following order, we obtain the FIM related to ξ, i.e., F mm , which can be expressed as:

[0280]

[0281] where each element can be specifically expressed as:

[0282]

[0283] According to the above discussion, the posterior CRB for estimating vehicle parameter x is defined as the trace of the inverse matrix of F K :

[0284]

[0285] Define and to represent the phase offset and amplitude vector of the k-th IOS, respectively. Define the aggregated phase offset vector and the aggregated amplitude vector Our goal is to jointly optimize the transmit beam vector f, the refraction / reflection amplitudes {β TR , β R}, and the refraction / reflection phase offset vector to minimize the CRB while satisfying the communication rate requirement and the IOS-related constraints. Therefore, the optimization problem is:

[0286]

[0287] We propose an efficient ZO-IPDD optimization algorithm to obtain high-quality solutions to the problem. The proposed algorithm adopts a double-loop structure. In the inner loop, by jointly optimizing the transmission beamforming and IOS configuration, the ZO algorithm is used to address the challenges posed by the implicit CRB expression. In the outer loop, the IPDD framework is applied to solve the non-linear variable coupling problem by updating the penalty factor and dual variables.

[0288] For the power splitting ratio, we note that in the optimal solution of the proposed optimization problem, the power splitting ratio of reflection / refraction should satisfy and For all i.e., for the k-th IOS all elements share the same reflection and refraction power splitting ratios, which can be simply expressed as and Therefore, the reflection / refraction amplitude vector of the IOS can be simplified to To handle the non-convex communication rate constraint, we define:

[0289]

[0290] Thereby rewriting the communication rate constraint as:

[0291]

[0292] To handle this rewritten constraint, we further consider the augmented Lagrangian form of the optimization problem:

[0293]

[0294] where

[0295]

[0296] denotes all the optimization variables, ζ is the Lagrangian dual variable, and λ is the penalty factor. Next, we adopt the IPDD framework, which has a double-loop structure, where the inner loop appropriately solves the augmented Lagrangian problem, and the outer loop updates the dual variable ζ and the penalty factor λ. Note that the ratio of the reflection and refraction amplitudes must satisfy the energy conservation condition. Therefore, once the reflection amplitude vector β R is optimized, the corresponding refraction amplitude vector β TR can be obtained by Thus, in the following, by substituting β TR with we will only consider optimizing β R without loss of optimality.

[0297] We propose a zero-order optimization algorithm with adaptive momentum. The main idea of this zero-order algorithm is to approximate the full gradient by the difference in function values at random query points. The proposed zero-order algorithm with adaptive momentum is an iterative algorithm, where \(i\) represents the inner-loop iteration index, and each iteration mainly consists of the following four steps:

[0298] 1) Derive the ZO gradient: By setting and fixing \(\zeta\) and \(\lambda\) in the inner loop, we can construct an estimate of the ZO gradient of the function at the \(i\)-th iteration. This estimate is obtained by the forward difference of two function values in a random unit direction:

[0299]

[0300] where \(u_1\) is a random vector uniformly distributed on the unit sphere, \(\mu_1>0\) is a perturbation radius, which can be regarded as a smoothing parameter, and is the dimension-dependent factor related to the above uniform distribution.

[0301] Since the RSU-IOS and IOS-CR channels are mainly LoS links, we propose a dimensionality reduction strategy to reduce the dimension, which is mainly achieved by reconstructing the original refraction / reflection phase shift vector of the \(k\)-th IOS into the form of . Therefore, the aggregated refraction / reflection phase shift vector of the \(K\) IOSs to be optimized, namely and can be expressed as After adopting this form, the dimension of the optimization variable is significantly reduced from \(N\) t +\(K\)+2\(KM\) to \(N\) t +5\(K\), because the number \(M\) of IOS elements is usually much larger than \(K\) and \(N\) t . Based on the above dimensionality reduction strategy, we now redefine the overall optimization variable vector as Then the ZO gradient estimator can be reformulated as:

[0302]

[0303] where \(u_2\) and \(\mu_2\) are defined similarly to \(u_1\) and \(\mu_1\), and is related to the dimension.

[0304] 2) Update the second momentum: The next step of the ZO algorithm is to update the second momentum \(v\) i , which is defined as the exponential moving average of the cumulative history and the squared gradient of the current iteration. Updating \(v\) i can be achieved as follows:

[0305]

[0306] where η ∈ [0, 1) controls the exponential decay rate of v i of the exponential decay rate.

[0307] 3) Retain the maximum value of the second momentum: Then, we use to retain the maximum value of v j , j ∈ {1, 2, …, i} up to the i-th iteration, in order to normalize the running average of the gradient, and the expression is as follows:

[0308]

[0309] 4) Update variables using Mahalanobis projection: We adopt Mahalanobis projection to update the optimization variables and its expression is as follows:

[0310]

[0311] where

[0312]

[0313] represents the projection of a (at this time ) onto the feasible set of in terms of the Mahalanobis distance with respect to Here, α i is the step size, which is determined by the Armijo rule.

[0314] Next, the IPDD framework is used to update the dual variable ζ and the penalty factor λ. Let r denote the external iteration index of the IPDD framework. Then, the dual variable ζ r in the r-th external iteration is updated as follows:

[0315]

[0316] Meanwhile, the penalty factor λ r is updated as follows:

[0317] λ r = c λ λ r-1

[0318] to gradually increase the cost of constraint violation in each iteration, where 0 < c λ < 1 is a constant that controls the penalty growth rate. In this framework, λ r is initially set to a large value to help find a good starting point. Subsequently, it is gradually decreased (thereby increasing the penalty) in each iteration to accelerate the process of satisfying the equality constraints.

[0319] The present invention particularly provides a novel IOS-assisted vehicle tracking method and an ISAC system. By applying IOS to assist the ISAC system, a vehicle tracking method is designed to predict and track the vehicle state with high precision. On the premise of ensuring the CR communication rate inside the vehicle, the system resource allocation is optimized to minimize the lower bound of the tracking error, thereby achieving the desired improvement in tracking accuracy and communication performance.

[0320] The novel IOS-assisted vehicle tracking method and ISAC system include the design of a tracking scheme and the minimization of the CRB of vehicle estimation parameters. Figure 1 The basic structural composition of the invention is described. Figure 2 and Figure 3 The sensing performance of the invention under different IOS configurations and different system parameters is compared, where "E-IOS" is the proposed scheme of the present invention.

[0321] Intelligent metasurfaces have recently received extensive attention for their ability to effectively and adaptively reconstruct the propagation environment, becoming a promising technology for next-generation wireless communication. For MIMO systems, intelligent metasurfaces can reconstruct the wireless channel environment, providing sufficient multipath components to improve the spatial multiplexing ability of the system. In addition, intelligent metasurfaces can also solve the coverage problem caused by the occlusion of line-of-sight links in communication. In the ISAC system, intelligent metasurfaces also have considerable potential. First, intelligent metasurfaces can achieve passive beamforming to improve the accuracy of signal coverage, align the users to be communicated with and the targets to be sensed, and enhance the strength of useful signals. Second, intelligent metasurfaces generally contain a large number of elements and can realize multipath signal regulation, bringing a high spatial degree of freedom to the system. Compared with the IRS-assisted system, the IOS-assisted system can achieve full-space coverage by simultaneously reflecting and refracting incident signals, enabling IOS to adjust the phase and power ratio of the reflected and refracted signals, providing a new degree of freedom for the popularization of wireless communication. Therefore, using IOS to improve the performance of the ISAC system is efficient and low-cost, and has important value in next-generation wireless communication.

[0322] The present invention provides a novel IOS-assisted vehicle tracking method, the design of an ISAC system, and the design of a joint optimization method under this system. The novel system includes an RSU equipped with a multi-antenna system, an IOS on the top of the vehicle, a customized EKF method, an optimization algorithm, and a target CRB. The core of the customized EKF method is to effectively incorporate the known relative positions between various parts of IOS and the vehicle and a series of non-linear transformations. The core of the optimization algorithm is the ZO-IPDD algorithm and the dimension reduction strategy.

[0323] In the ISAC system, the RSU receives the echo signal from the IOS, realizes the prediction and tracking of the vehicle state, and jointly optimizes the transmission design of the ISAC signal with the IOS. The RSU beamforming and IOS configuration information are respectively sent to the multi-antenna array and the IOS to minimize the CRB of the vehicle estimation parameters.

[0324] Considering that the vehicle tracking accuracy in this system is greatly affected by the RSU transmission beamforming and IOS configuration, the present invention takes the minimization of the CRB of the vehicle estimation parameters as the performance index, and ensures the communication performance of the in-vehicle CR and the energy conservation of the IOS, and jointly optimizes the design of the new IOS-assisted ISAC system.

[0325] Compared with the traditional ISAC system, the IOS-assisted ISAC system provided by the present invention does not additionally increase a large number of radio frequency links and complex signal processing units. Compared with the traditional IRS device, it can provide full-space coverage, and is a design with lower cost, lower power consumption and better performance. Through the joint beamforming design and coefficient adjustment matrix design of the RSU and the IOS, the vehicle tracking accuracy of the present invention is significantly improved.

[0326] The embodiment of the present invention also discloses a method for minimizing the CRB of vehicle estimation parameters in an IOS-assisted ISAC system. Applying the IOS-assisted ISAC system, the IOS device assists the RSU multi-antenna system to jointly optimize the design, realizes the minimization of the CRB of vehicle estimation parameters, and obtains the optimal RSU transmission beamforming and IOS configuration scheme.

[0327] The method includes the following steps:

[0328] Optimization of RSU transmission beamforming: Considering that the transmission power of the RSU is p n , and the beamforming vector is f n , after the beamforming design, the vehicle tracking accuracy and the communication quality of the in-vehicle CR are improved.

[0329] Optimization of the reflection / refraction amplitude and phase of the IOS: The IOS adjusts the amplitude and phase of the incident signal, controls the coefficient matrix of the IOS to design the amplitude and phase of all IOS elements, so that the reflected signal can minimize the CRB of the vehicle estimation parameters and improve the communication quality of the in-vehicle CR.

[0330] The present invention also provides a vehicle tracking system assisted by a full-space intelligent metasurface. The vehicle tracking system assisted by the full-space intelligent metasurface can be realized by executing the process steps of the vehicle tracking method assisted by the full-space intelligent metasurface. That is, those skilled in the art can understand the vehicle tracking method assisted by the full-space intelligent metasurface as the preferred implementation manner of the vehicle tracking system assisted by the full-space intelligent metasurface.

[0331] Those skilled in the art know that, in addition to implementing the systems, devices, and their respective modules provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the systems, devices, and their respective modules provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc., to achieve the same program. Therefore, the systems, devices, and their respective modules provided by the present invention can be considered as a kind of hardware component, and the modules included therein for implementing various programs can also be regarded as the structures within the hardware component; the modules for implementing various functions can also be regarded as either software programs for implementing the methods or the structures within the hardware component.

[0332] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A vehicle tracking method assisted by a full-space intelligent metasurface, characterized in that: include: Step S1: The roadside unit RSU communicates with the in-vehicle communication receiver CR through the vehicle top IOS to obtain the reflected signal from the IOS; Step S2: Based on the reflection signal from the IOS, the vehicle state is predicted and tracked by a customized extended Kalman filter method; The customized extended Kalman filter method realizes the perception and prediction of the vehicle state through the construction of the vehicle state evolution and measurement model.

2. The vehicle tracking method assisted by the full-space intelligent metasurface according to claim 1 is characterized in that: The step S1 includes: the roadside unit RSU sends an ISAC signal to the vehicle, wherein part of the signal is refracted to the in-vehicle communication receiver CR through the vehicle top IOS, and part of the signal is reflected back to the roadside unit RSU through the vehicle top IOS to obtain a reflected signal from the IOS.

3. The vehicle tracking method assisted by the full-space intelligent metasurface according to claim 1 is characterized in that: The method further includes: optimizing the transmission beamforming of the roadside unit RSU and the IOS configuration on the top of the vehicle based on the zero-order optimization added penalty dual decomposition ZO-IPDD algorithm to obtain the optimal resource allocation scheme; obtaining the reflected signal from the IOS under the optimized resource allocation scheme; The roadside unit RSU includes a MIMO multi-antenna array; the vehicle top IOS includes multiple full-space units and a controller; controlling the amplitude and phase of the MIMO multi-antenna array through optimized transmit beamforming; Optimizing the IOS configuration on the top of the vehicle based on the ZO-IPDD algorithm includes optimizing the reflection / refraction amplitude and phase of each full-space unit in the IOS on the top of the vehicle respectively.

4. The vehicle tracking method assisted by the full-space intelligent metasurface according to claim 3 is characterized in that: The zero-order optimization-based added penalty dual decomposition ZO-IPDD algorithm optimizes the transmission beamforming of the roadside unit RSU and the IOS configuration on the top of the vehicle to obtain the optimal resource allocation solution, including: The zero-order optimization-based added penalty dual decomposition ZO-IPDD algorithm adopts a double loop structure; in the inner loop, the transmission beam and IOS configuration are jointly optimized by the ZO algorithm; in the outer loop, the IPDD framework is used to update the penalty factor and the dual variable to solve the nonlinear variable coupling problem; For the power distribution ratio, in the optimal solution of the proposed optimization problem, the power distribution ratio of reflection / refraction should satisfy and represents the optimal refraction amplitude response of the mth element of the kth IOS; represents the optimal refraction amplitude response of the m'th element of the kth IOS, represents the optimal reflection amplitude response of the mth element of the kth IOS, represents the optimal reflection amplitude response of the m'th element of the kth IOS; for all All elements of the k-th IOS share the same reflected and refracted power distribution ratio, expressed as and Therefore, the reflection / refraction amplitude vector of the IOS simplifies to To handle non-convex communication rate constraints, define: The communication rate constraint is thus rewritten as: Among them, β TR represents the aggregate refraction magnitude vector, represents the aggregate refraction phase offset vector, and f represents the transmit beamforming vector of the RSU; To handle this rewritten constraint, we further consider the augmented Lagrangian form of the optimization problem: in represents all optimization variables, ζ is the Lagrangian dual variable, and λ is the penalty factor; Next, we adopt the IPDD framework, which adopts a double loop structure, where the inner loop solves the augmented Lagrangian problem, while the outer loop updates the dual variable ζ and the penalty factor λ; where the ratio of the reflected and refracted amplitudes must satisfy the energy conservation condition; therefore, once the reflected amplitude vector β R is optimized, the corresponding refraction amplitude vector β TR pass Therefore, in the following text, by TR Replace with Only optimization of β R without losing optimality; A zero-order optimization algorithm with adaptive momentum is proposed. The main idea of ​​the zero-order algorithm is to approximate the full gradient by the difference of function values ​​at random query points. The proposed zero-order algorithm with adaptive momentum is an iterative algorithm, where i represents the inner loop iteration index, and each iteration mainly includes the following four steps: 1) Derivation of ZO gradient: By letting And fix ζ and λ in the inner loop, construct the function in the i-th iteration The ZO gradient estimate is obtained by forward differencing the two function values ​​in a random unit direction: Among them, u1 is a random vector uniformly distributed on the unit sphere, μ1>0 is a perturbation radius, which can be regarded as a smoothing parameter, and is the dimension-dependent factor related to the above uniform distribution; N t represents the number of RSU transmitting antennas, K represents the number of IOS subarrays, and M represents the number of elements in each subarray; Since the RSU-IOS and IOS-CR channels are mainly LoS links, a dimensionality reduction strategy is proposed to reduce The dimension is mainly obtained by shifting the original refraction / reflection phase of the k-th IOS by the vector Refactored to Therefore, the aggregate refraction / reflection phase offset vector of the K IOSs that need to be optimized is and It is expressed as: After adopting this form, the dimension of the optimization variable increases from N t +K+2KM significantly reduced to N t +5K, because the number of IOS elements M is usually much larger than K and N t ; Based on the above dimensionality reduction strategy, the overall optimization variable vector is redefined as The ZO gradient estimator is then reformulated as: where u2 and μ2 are defined similarly to u1 and μ1, and Related to dimensions; 2) Update the second momentum: The next step of the ZO algorithm is to update the second momentum v in the i-th iteration i , which is defined as the exponential moving average of the squared gradients of the accumulated history and the current iteration; update v i This can be achieved by: where η∈[0,1) controls v i The exponential decay rate of . 3) Keep the maximum value of the second momentum: use To retain v up to the i-th iteration j ,j∈{1,2,…,i}, in order to normalize the running average of the gradient, the expression is as follows: 4) Update variables using Mahalanobi projection: Use Mahalanobi projection to update optimization variables Its expression is as follows: in Indicates that under the Mahalanobis distance, a is projected to The feasible set Relative to α i is the step length, determined by Armiho’s rule; The IPDD framework is used to update the dual variable ζ and the penalty factor λ; let r represent the external iteration index of the IPDD framework; then, the dual variable ζ in the rth external iteration r The update method is as follows: At the same time, the penalty factor λ r The update method is as follows: l r =c λ l r-1 to gradually increase the cost of constraint violation in each iteration, where 0 <c λ <1 is a constant that controls the rate at which the penalty increases; in this framework, λ r It is initially set to a large value that meets the preset requirements; then, it is gradually reduced in each iteration to speed up the process of satisfying the equality constraints.

5. The vehicle tracking method assisted by the full-space intelligent metasurface according to claim 1, characterized in that: The step S2 comprises: In the nth iteration, use represents the state parameters of the vehicle, then the state evolution model is expressed as: v n =v n-1 +ω v in, represents the estimated angle of the vehicle along the x-axis relative to the RSU in the nth period, d n represents the distance between the vehicle and the RSU in the nth period, v n represents the speed of the vehicle in the nth period, ΔT represents the duration of each time period, ω d and ω v Represents the corresponding noise, which obeys a Gaussian distribution with a mean of zero and variances of and make represents the measurement parameters at the RSU, where in, represents the normalized output signal corresponding to the kth IOS in the nth period, τ k,n represents the delay at the kth IOS in the nth period, μ k,n represents the Doppler shift at the kth IOS in the nth period; K represents the number of subarrays of the IOS; then, the state evolution model and the measurement model are restated as: state evolution model:x n =g(x n-1 )+ω n , measurement model:y n =t(x n )+z n Among them, g(·) reflects the mapping relationship in the state evolution model, t(·) reflects the mapping relationship in the measurement model, and x n represents the vehicle state parameters in the nth period, and ω n and z n They are all zero-mean Gaussian distributions, and their covariance matrices are as follows: in, represents the normalized measurement noise, 1 Nr N represents all elements are 1 r dimensional vector, represents the measured Gaussian noise of the delay at the kth IOS, represents the measured Gaussian noise of the Doppler shift at the kth IOS; Next, a customized EKF method is proposed to use the position information provided by IOS to establish the measurement parameter y n With vehicle parameters x n To linearize these models, we first calculate g(x n ) and t(x n )’s Jacobian matrix; t(x n ) is derived as: Where v represents the speed of the vehicle, and d represents the distance between the vehicle and the RSU; Next, in order to derive t(x n ), denoted by The relative static position between the IOS and the vehicle needs to be used; therefore, T n Using the chain rule we get: The first term is expressed as: And n r,t =2-n r -n t and Where, f represents the transmit beamforming vector of RSU, represents the complex reflection coefficient at the kth IOS, β k represents the magnitude response of the kth IOS, n r,t Indicates the index of the RSU antenna, represents the estimated angle of the kth IOS relative to the RSU along the x-axis, M represents the number of elements in each subarray, m y (m) = mm x (m)M y -1, φk represents the estimated angle of the kth IOS along the y-axis relative to the RSU, and θk,m represents the phase offset of the mth element of the kth IOS; The second term is expressed as: Among them, d k,n represents the distance between the kth IOS and the RSU in the nth period, x k,n represents the state parameter of the kth IOS in the nth period, v k,n represents the speed of the kth IOS in the nth period, f c represents the carrier frequency, c represents the speed of light; The third term is expressed as: Among them, 1 K represents a K-dimensional vector whose elements are all 1, and I3 represents a 3rd-order identity matrix; The fourth term is expressed as: According to G n and T n , a customized EKF method is given, which is summarized as follows: 1) State prediction: 2) Linearization: 3) MSE matrix prediction: 4) Kalman gain calculation: 5) Status tracking: 6) MSE matrix update: M n =(IK n T n )M n|n-1 . In the nth iteration, RSU calculates the measured parameter y n Forecast status Update and get This state will be used as the input of the (n+1)th round of state prediction step; in the state prediction step, the predicted state Used for Cramer-Rao Bound (CRB) optimization.

6. A full-space intelligent metasurface-assisted vehicle tracking system, characterized in that: include: Step S1: The roadside unit RSU communicates with the in-vehicle communication receiver CR through the vehicle top IOS to obtain the reflected signal from the IOS; Step S2: Based on the reflection signal from the IOS, the vehicle state is predicted and tracked by a customized extended Kalman filter method; The customized extended Kalman filter method realizes the perception and prediction of the vehicle state through the construction of the vehicle state evolution and measurement model.

7. The full-space intelligent metasurface-assisted vehicle tracking system according to claim 6, characterized in that: The step S1 includes: the roadside unit RSU sends an ISAC signal to the vehicle, wherein part of the signal is refracted to the in-vehicle communication receiver CR through the vehicle top IOS, and part of the signal is reflected back to the roadside unit RSU through the vehicle top IOS to obtain a reflected signal from the IOS.

8. The full-space intelligent metasurface-assisted vehicle tracking system according to claim 6, characterized in that: The method further includes: optimizing the transmission beamforming of the roadside unit RSU and the IOS configuration on the top of the vehicle based on the zero-order optimization added penalty dual decomposition ZO-IPDD algorithm to obtain the optimal resource allocation scheme; obtaining the reflected signal from the IOS under the optimized resource allocation scheme; The roadside unit RSU includes a MIMO multi-antenna array; the vehicle top IOS includes multiple full-space units and a controller; controlling the amplitude and phase of the MIMO multi-antenna array through optimized transmit beamforming; Optimizing the IOS configuration on the top of the vehicle based on the ZO-IPDD algorithm includes optimizing the reflection / refraction amplitude and phase of each full-space unit in the IOS on the top of the vehicle respectively.

9. The full-space intelligent metasurface-assisted vehicle tracking system according to claim 8, characterized in that: The zero-order optimization-based added penalty dual decomposition ZO-IPDD algorithm optimizes the transmission beamforming of the roadside unit RSU and the IOS configuration on the top of the vehicle to obtain the optimal resource allocation solution, including: The zero-order optimization-based added penalty dual decomposition ZO-IPDD algorithm adopts a double loop structure; in the inner loop, the transmission beam and IOS configuration are jointly optimized by the ZO algorithm; in the outer loop, the IPDD framework is used to update the penalty factor and the dual variable to solve the nonlinear variable coupling problem; For the power distribution ratio, in the optimal solution of the proposed optimization problem, the power distribution ratio of reflection / refraction should satisfy and represents the optimal refraction amplitude response of the mth element of the kth IOS; represents the optimal refraction amplitude response of the m'th element of the kth IOS, represents the optimal reflection amplitude response of the mth element of the kth IOS, represents the optimal reflection amplitude response of the m'th element of the kth IOS; for all All elements of the k-th IOS share the same reflected and refracted power distribution ratio, expressed as and Therefore, the reflection / refraction amplitude vector of the IOS simplifies to To handle non-convex communication rate constraints, define: The communication rate constraint is thus rewritten as: Among them, β TR represents the aggregate refraction magnitude vector, represents the aggregate refraction phase offset vector, and f represents the transmit beamforming vector of the RSU; To handle this rewritten constraint, we further consider the augmented Lagrangian form of the optimization problem: in represents all optimization variables, ζ is the Lagrangian dual variable, and λ is the penalty factor; Next, we adopt the IPDD framework, which adopts a double loop structure, where the inner loop solves the augmented Lagrangian problem, while the outer loop updates the dual variable ζ and the penalty factor λ; where the ratio of the reflected and refracted amplitudes must satisfy the energy conservation condition; therefore, once the reflected amplitude vector β R is optimized, the corresponding refraction amplitude vector β TR pass Therefore, in the following text, by TR Replace with Only optimization of β R without losing optimality; A zero-order optimization algorithm with adaptive momentum is proposed. The main idea of ​​the zero-order algorithm is to approximate the full gradient by the difference of function values ​​at random query points. The proposed zero-order algorithm with adaptive momentum is an iterative algorithm, where i represents the inner loop iteration index, and each iteration mainly includes the following four steps: 1) Derivation of ZO gradient: By letting And fix ζ and λ in the inner loop, construct the function in the i-th iteration The ZO gradient estimate is obtained by forward differencing the two function values ​​in a random unit direction: Among them, u1 is a random vector uniformly distributed on the unit sphere, μ1>0 is a perturbation radius, which can be regarded as a smoothing parameter, and is the dimension-dependent factor related to the above uniform distribution; N t represents the number of RSU transmitting antennas, K represents the number of IOS subarrays, and M represents the number of elements in each subarray; Since the RSU-IOS and IOS-CR channels are mainly LoS links, a dimensionality reduction strategy is proposed to reduce The dimension is mainly obtained by shifting the original refraction / reflection phase of the k-th IOS by the vector Refactored to Therefore, the aggregate refraction / reflection phase offset vector of the K IOSs that need to be optimized is and It is expressed as: After adopting this form, the dimension of the optimization variable increases from N t +K+2KM significantly reduced to N t +5K, because the number of IOS elements M is usually much larger than K and N t ; Based on the above dimensionality reduction strategy, the overall optimization variable vector is redefined as The ZO gradient estimator is then reformulated as: where u2 and μ2 are defined similarly to u1 and μ1, and Related to dimensions; 2) Update the second momentum: The next step of the ZO algorithm is to update the second momentum v in the i-th iteration i , which is defined as the exponential moving average of the squared gradients of the accumulated history and the current iteration; update v i This can be achieved by: where η∈[0,1) controls v i The exponential decay rate of . 3) Keep the maximum value of the second momentum: use To retain v up to the i-th iteration j ,j∈{1,2,…,i}, in order to normalize the running average of the gradient, the expression is as follows: 4) Update variables using Mahalanobi projection: Use Mahalanobi projection to update optimization variables Its expression is as follows: in Indicates that under the Mahalanobis distance, a is projected to The feasible set Relative to α i is the step length, determined by Armiho’s rule; The IPDD framework is used to update the dual variable ζ and the penalty factor λ; let r represent the external iteration index of the IPDD framework; then, the dual variable ζ in the rth external iteration r The update method is as follows: At the same time, the penalty factor λ r The update method is as follows: l r =c λ l r-1 to gradually increase the cost of constraint violation in each iteration, where 0 <c λ <1 is a constant that controls the rate at which the penalty increases; in this framework, λ r It is initially set to a large value that meets the preset requirements; then, it is gradually reduced in each iteration to speed up the process of satisfying the equality constraints.

10. The full-space intelligent metasurface-assisted vehicle tracking system according to claim 6, characterized in that: The step S2 comprises: In the nth iteration, use represents the state parameters of the vehicle, then the state evolution model is expressed as: v n =v n-1 +ω v in, represents the estimated angle of the vehicle along the x-axis relative to the RSU in the nth period, d n represents the distance between the vehicle and the RSU in the nth period, v n represents the speed of the vehicle in the nth period, ΔT represents the duration of each time period, ω d and ω v Represents the corresponding noise, which obeys a Gaussian distribution with a mean of zero and variances of and make represents the measurement parameters at the RSU, where in, represents the normalized output signal corresponding to the kth IOS in the nth period, τ k,n represents the delay at the kth IOS in the nth period, μ k,n represents the Doppler shift at the kth IOS in the nth period; K represents the number of subarrays of the IOS; then, the state evolution model and the measurement model are restated as: state evolution model:x n =g(x n-1 )+ω n , measurement model:y n =t(x n )+z n Among them, g(·) reflects the mapping relationship in the state evolution model, t(·) reflects the mapping relationship in the measurement model, and x n represents the vehicle state parameters in the nth period, and ω n and z n They are all zero-mean Gaussian distributions, and their covariance matrices are as follows: in, represents the normalized measurement noise, 1 Nr N represents all elements are 1 r dimensional vector, represents the measured Gaussian noise of the delay at the kth IOS, represents the measured Gaussian noise of the Doppler shift at the kth IOS; Next, a customized EKF method is proposed to use the position information provided by IOS to establish the measurement parameter y n With vehicle parameters x n To linearize these models, we first calculate g(x n ) and t(x n )’s Jacobian matrix; t(x n ) is derived as: Where v represents the speed of the vehicle, and d represents the distance between the vehicle and the RSU; Next, in order to derive t(x n ), denoted by The relative static position between the IOS and the vehicle needs to be used; therefore, T n Using the chain rule we get: The first term is expressed as: And n r,t =2-n r -n t and Where, f represents the transmit beamforming vector of RSU, represents the complex reflection coefficient at the kth IOS, β k represents the magnitude response of the kth IOS, n r,t Indicates the index of the RSU antenna, represents the estimated angle of the kth IOS relative to the RSU along the x-axis, M represents the number of elements in each subarray, m y (m) = mm x (m)M y -1,φ k represents the estimated angle of the kth IOS along the y-axis relative to the RSU, θ k,m represents the phase offset of the mth element of the kth IOS; The second term is expressed as: Among them, d k,n represents the distance between the kth IOS and the RSU in the nth period, x k,n represents the state parameter of the kth IOS in the nth period, v k,n represents the speed of the kth IOS in the nth period, f c represents the carrier frequency, c represents the speed of light; The third term is expressed as: Among them, 1 K represents a K-dimensional vector whose elements are all 1, and I3 represents a 3rd-order identity matrix; The fourth term is expressed as: According to G n and T n , a customized EKF method is given, which is summarized as follows: 1) State prediction: 2) Linearization: 3) MSE matrix prediction: 4) Kalman gain calculation: 5) Status tracking: 6) MSE matrix update: M n =(IK n T n )M n|n-1 . In the nth iteration, RSU calculates the measured parameter y n Forecast status Update and get This state will be used as the input of the (n+1)th round of state prediction step; in the state prediction step, the predicted state Used for Cramer-Rao Bound (CRB) optimization.

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