Robust secure beamforming and target tracking method and device for full-duplex sensing-integrated system

Abstract

The application discloses a kind of robust security beamforming and target tracking method and equipment of full duplex sensing integration system, by dual-function radar communication base station is executed.Step includes: base station receives radar echo signal, with extended Kalman filter real-time tracking estimation downlink mobile user motion state, obtain predicted channel state information;Based on this information, design downlink beamforming matrix, construct uplink receive beamforming vector, optimize artificial noise signal covariance matrix;With Cramer-Rao bound quantification potential eavesdropper angle estimation error, construct uncertainty set;Under the requirements such as satisfying secrecy rate, angle estimation error, beam tracking mean square error, construct the joint optimization problem of minimizing system total transmit power;Non-convex semi-infinite constraint is converted into linear matrix inequality and is solved iteratively, and optimal parameter is obtained;Accordingly control base station, realize robust security beamforming and target tracking, solve the problem of safe communication under dynamic environment.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, specifically to a robust and secure beamforming and target tracking method and device for a full-duplex integrated sensing system. Background Technology

[0002] With the rapid development of sixth-generation (6G) wireless communication technology, Integrated Sensing and Communication (ISAC) technology, which integrates communication and sensing functions, is considered a key supporting technology for next-generation intelligent wireless networks. ISAC aims to utilize a unified radio frequency platform to achieve synergistic coexistence and mutually beneficial cooperation between communication and sensing functions, thereby significantly improving overall system performance in terms of spectrum utilization and energy efficiency. Leveraging its high-throughput communication capabilities and high-resolution sensing capabilities, ISAC technology demonstrates broad application prospects in dynamic and complex wireless communication environments.

[0003] In dynamic wireless communication scenarios, channel states change rapidly over time. Traditional channel estimation methods relying on pilot and feedback mechanisms suffer from high overhead and feedback lag, limiting the system's communication efficiency and robustness. To address this, researchers have proposed a perception-assisted beam tracking technique. This technique utilizes the radar sensing capabilities of the ISAC system to estimate user motion state parameters (such as angle, distance, and velocity) in real time, enabling dynamic adjustment and tracking of the communication link. However, due to the spectrum sharing mechanism of the ISAC system and the broadcast characteristics of wireless channels, its communication security faces serious threats. Especially during target perception, some perceived targets may be malicious eavesdroppers attempting to obtain confidential information during downlink or uplink communication.

[0004] Furthermore, communication waveforms in ISAC systems typically exhibit stronger directivity. While this improves link quality, it also increases the risk of signal leakage towards the target, further enhancing the security vulnerability of information leakage. Nevertheless, sensing capabilities offer new possibilities for building robust and secure communication mechanisms in ISAC systems. Some existing research utilizes sensing information to accurately estimate the location of eavesdroppers and channel state information, thereby assisting in the design of targeted secure beamforming strategies to achieve dual protection of communication security and sensing performance. However, most current research on secure ISAC is still based on static user scenarios and assumes that the base station can perfectly obtain the channel state information or incident angle information of the eavesdropper, which is difficult to achieve in real dynamic environments. Since users and eavesdroppers may be in motion, channel state information cannot be accurately obtained, leading to a decrease in the effectiveness of secure beamforming strategies and an inability to adapt to rapidly changing wireless conditions. Therefore, current technologies struggle to solve robust security problems in dynamic environments, necessitating the development of joint sensing and communication optimization methods for dynamic scenarios to improve the practical deployment capability and security performance of the system. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a robust and secure beamforming and target tracking method and device for a full-duplex inductive integrated system. Its purpose is to solve the problems of decreased effectiveness of secure beamforming strategies in dynamic environments, difficulty in solving robust security issues, inability to adapt to rapidly changing wireless conditions, and difficulty in achieving secure communication in real dynamic environments.

[0006] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution:

[0007] According to a first aspect of the present invention, a robust and secure beamforming and target tracking method for a full-duplex integrated sensing system is provided, the method being executed by a dual-function radar communication base station, comprising the following steps:

[0008] S1. The base station receives radar echo signals and, based on the radar echo signals, uses an extended Kalman filter to perform real-time tracking and estimation of the motion state of the downlink mobile user to obtain the predicted channel state information of the downlink mobile user. The predicted channel state information includes at least angle, distance, and speed parameters.

[0009] S2. The base station designs the downlink beamforming matrix based on the predicted channel state information and constructs the uplink receiving beamforming vector, while optimizing the design of the covariance matrix of the artificial noise signal.

[0010] S3. Based on the radar echo signal, the base station uses Cramer-Rao bounded quantization to quantify the angle estimation error of potential eavesdroppers, and constructs a norm-bounded uncertainty set characterizing the channel uncertainty of eavesdroppers based on the angle estimation error.

[0011] S4. Under the premise of satisfying the minimum confidentiality rate constraint of the downlink and uplink communication links, the angle estimation error of the eavesdropper not exceeding the preset sensing accuracy requirement, and the beam tracking mean square error based on the extended Kalman filter meeting the dynamic tracking accuracy requirement, a joint optimization problem is constructed with the goal of minimizing the total system transmit power; wherein, the optimization variables of the joint optimization problem include the downlink beamforming matrix, the covariance matrix of the artificial noise signal, the uplink receiving beamforming vector, and the uplink communication user power allocation strategy;

[0012] S5. Transform the non-convex semi-infinite constraint caused by the eavesdropper channel uncertainty in the joint optimization problem into a linear matrix inequality, and iteratively solve the joint optimization problem to obtain the optimal beamforming and resource allocation parameters.

[0013] S6. Control the base station according to the optimal beamforming and resource allocation parameters to realize robust and secure beamforming and target tracking of the full-duplex sensing integrated system.

[0014] In one possible implementation of the first aspect, the step of using an extended Kalman filter to perform real-time tracking and estimation of the motion state of the downlink mobile user based on the radar echo signal to obtain the predicted channel state information of the downlink mobile user includes:

[0015] S101. Construct a state-space model containing downlink mobile user angle, distance and speed parameters. The state-space model includes a state transition function, an observation function, a measurement noise covariance matrix, a process noise covariance matrix and a state error covariance matrix.

[0016] S102. Predict the motion state of the downlink mobile user at the current moment based on the state transition function;

[0017] S103. Calculate the Jacobian matrix of the state transition function and the observation function;

[0018] S104. Based on the Jacobian matrix of the state transition function and the observation function, the process noise covariance matrix, and the state error covariance matrix of the previous time step, calculate the prediction error covariance matrix of the current time step.

[0019] S105. Calculate the Kalman gain based on the prediction error covariance matrix and the measurement noise covariance matrix at the current moment.

[0020] S106. Combining the observed values ​​in the radar echo signal with the Kalman gain, correct the motion state of the downlink mobile user at the current moment, and use the corrected motion state of the downlink mobile user at the current moment as the predicted channel state information of the downlink mobile user.

[0021] S107. Update the state error covariance matrix at the current moment based on the Kalman gain, and repeat S102 and S106.

[0022] In one possible implementation of the first aspect, the state transition function is specifically:

[0023]

[0024] In the formula, v l,n v represents the speed of the l-th downlink mobile user at the current moment. l,n-1 u represents the speed of the l-th downlink mobile user at the previous time step. v For velocity process noise; θ l,n θ is the angle between the l-th downlink mobile user at the current moment and the horizontal direction of the base station antenna; l,n-1d is the angle between the l-th downlink mobile user at the previous moment and the horizontal direction of the base station antenna; ΔT is the duration of a communication time slot; d l,n-1 The distance between the l-th downlink mobile user and the base station at the previous time step; u θ For angular process noise; d l,n The distance between the l-th downlink mobile user and the base station at the current moment; u d This refers to distance process noise.

[0025] In one possible implementation of the first aspect, the observation function includes an angle measurement model, a distance measurement model, and a velocity measurement model;

[0026] The angle measurement model is specifically as follows:

[0027]

[0028] The distance measurement model is specifically as follows:

[0029]

[0030] The speed measurement model is specifically as follows:

[0031]

[0032] In the formula, The radar echo signal of the l-th downlink mobile user at the current time, after time delay and Doppler compensation; r l,n (t) represents the radar echo signal of the l-th downlink mobile user at the current time; This is the conjugate component of the signal transmitted by the base station at the current moment; The current time delay measurement of the radar echo; j is the imaginary unit; This is the Doppler measurement of the radar echo at the current moment; Antenna gain; The reflection coefficient of the l-th downlink mobile user at the current time; G is the matched filter gain; a H (θ l,n ) represents the transmit antenna array steering vector of the l-th downlink mobile user at the current time; v l,n This is the transmit beamforming vector for the l-th downlink mobile user at the current time; For angle measurement noise; z τ For time delay measurement noise; z μ Noise for Doppler measurement.

[0033] In one possible implementation of the first aspect, the Jacobian matrix of the state transition function is specifically:

[0034]

[0035] The Jacobian matrix of the observation function is specifically:

[0036]

[0037] In the formula, denoted as the Jacobian matrix of the state transition function; θ is the angle between the downlink mobile user and the base station antenna in the horizontal direction; ΔT is the duration of a communication time slot; and d is the distance between the downlink mobile user and the base station. γ is the Jacobian matrix of the observation function; α is the transmit antenna gain; γ is the channel coefficient between the downlink mobile user and the base station; G is the matched filter gain; v is the transmit beamforming vector; f c is the carrier frequency; c is the speed of light.

[0038] In one possible implementation of the first aspect, the base station, based on the radar echo signal, employs Cramer-Rao bounded quantization to quantize the angle estimation error of a potential eavesdropper, and constructs a norm-bounded uncertainty set characterizing the channel uncertainty of the eavesdropper based on the angle estimation error, including:

[0039] S301. Based on multiple time-domain snapshots in the radar echo signal, and combining the base station transmitted signal covariance matrix and the eavesdropper reflection coefficient, calculate the Cramer-Rao threshold for estimating the angle of the potential eavesdropper.

[0040] S302. Based on the Cramer-Rao threshold estimated from the angle of the potential eavesdropper, construct the angle uncertainty region with three times the standard deviation of the Cramer-Rao threshold as the confidence limit, and complete the quantification of the angle estimation error of the potential eavesdropper.

[0041] S303. Taking into account the channel disturbance errors caused by angle estimation error, preset distance estimation error, and multipath fading, the channel uncertainty of potential eavesdroppers is modeled as a norm-bounded uncertainty set Φ. p The definition is as follows:

[0042]

[0043] In the formula, ν p The upper bound of the channel disturbance is characterized by the combined effects of angle estimation error, preset distance estimation error, and channel disturbance error caused by multipath fading; Δh b,p The channel uncertainty vector for the eavesdropper; For dimension N t A complex vector with 1 row and 1 column; N t The number of base station transmit antennas; ||Δh b,p ||2 is the Euclidean norm of the eavesdropper's channel uncertainty vector; For the Hermitian transpose of the eavesdropper's channel uncertainty vector; For the preset base station and the nth... t Upper bound on the uncertainty of multipath; κ p Let the Rice factor be the p-th eavesdropper; For the nth base station and the eavesdropper t Phase uncertainty of multiple paths; The true angle between the eavesdropper and the base station; Δθ p The angle estimation error between the eavesdropper and the base station; h b,p α is the complete channel vector between the base station and the p-th eavesdropper; p Let be the reference distance path loss for the p-th eavesdropper channel; Δd represents the true distance from the base station to the eavesdropper. b,p Error in estimating the distance from the base station to the eavesdropper; For the multi-radial quantity from the base station to the eavesdropper; For the Nth t Multipath components; This represents the actual channel value from the base station to the eavesdropper.

[0044] In one possible implementation of the first aspect, the joint optimization problem P1, which aims to minimize the total system transmit power, specifically includes:

[0045]

[0046] stC1:SR DL ≥ρ DL ,

[0047] C2:SR UL ≥ρ UL ,

[0048]

[0049] C4:Tr(M n )≤Γ MSE ,

[0050] C5:Rank(V l,n )≤1,

[0051]

[0052] In the formula, F is the uplink receiving beamforming matrix; V l,n The beamforming matrix for the l-th downlink mobile user in the n-th time slot; R w is the covariance matrix of the artificial noise; p is the power allocation vector for all uplink communication users; The trace of the downlink beamforming matrix and the sum of the downlink beamforming matrix; L is the number of downlink mobile users; Tr(R) w) represents the trace of the artificial noise covariance matrix; SR DL ρ is the downlink communication security rate; DL The minimum threshold for the set downlink communication security rate; SR UL For uplink communication security rate; ρ UL This is the minimum threshold for the preset uplink communication security rate. Cramer-Rao threshold value estimated from the eavesdropper's perspective; Γ CRB The upper limit of the Cramer-Rhodes boundary estimated from the specified eavesdropper's angle; Tr(M n ) represents the trace of the beam tracking mean square error matrix; Γ MSE The threshold for the trace of the beam tracking mean square error matrix is ​​set; Rank(V) l,n ) represents the rank of the downlink beamforming matrix.

[0053] In one possible implementation of the first aspect, the step of transforming the non-convex semi-infinite constraint caused by the eavesdropper channel uncertainty in the joint optimization problem into a linear matrix inequality, and iteratively solving the joint optimization problem to obtain the optimal beamforming and resource allocation parameters, includes:

[0054] S501. By introducing auxiliary variables, the joint optimization problem P1 is equivalently transformed into optimization problem P2, specifically:

[0055]

[0056] C2.5:C3-C8

[0057] S502. Using the S-lemma method, the non-convex semi-infinite constraints caused by the eavesdropper's channel uncertainty in optimization problem P2 are transformed into linear matrix inequalities. Combined with the Schur complement condition, the eavesdropper's angle estimation error constraint and the beam tracking mean square error constraint of the extended Kalman filter are reconstructed into convex form, forming optimization problem P3, specifically:

[0058]

[0059] stC3.1:C5-C8

[0060]

[0061] S503. Using the generalized Rayleigh quotient solution method, obtain the closed-form optimal solution for the uplink receiving beamforming vector. Eliminating the non-convexity related to the uplink receive beamforming vector in optimization problem P3, specifically:

[0062]

[0063] S504. Based on the successive convex approximation and semi-definite relaxation method, the optimization problem P3 is relaxed to obtain the optimization problem P4. The optimization problem P4 is then iteratively solved using convex optimization tools to obtain the optimal beamforming and resource allocation parameters, specifically:

[0064]

[0065] C4.2:C6-C8,C3.2,C3.4-C3.10

[0066] In the formula, R l,n The downlink achievable rate for the l-th downlink mobile user in the n-th time slot; The minimum downlink achievable rate limit for the l-th downlink mobile user in the n-th time slot; For any l downlink mobile users; R k,n The uplink achievable rate for the k-th uplink communication user in the n-th time slot; This is the preset minimum uplink achievable rate limit for the k-th uplink communication user in the n-th time slot; For any k uplink communication users; Let Δh be the set of the number of eavesdroppers. b,p Let Δd be the channel uncertainty vector for the eavesdropper; b,p Error in estimating the distance from the base station to the eavesdropper; Φ p D is a norm-bounded set of uncertainties; b,p The upper bound of the distance estimation error from the base station to the eavesdropper is set as the preset value; Let be the signal-to-interference-plus-noise ratio (SIR) received by the p-th eavesdropper from the l-th downlink mobile user; The maximum achievable rate limit for the p-th eavesdropper to the l-th downlink mobile user in the n-th time slot is defined. Let be the signal-to-interference-plus-noise ratio (SIR) received by the p-th eavesdropper from the k-th uplink user; ζ is the maximum achievable rate limit set for the p-th eavesdropper to the k-th uplink user in the n-th time slot; l,p ζ represents the maximum received signal-to-interference-plus-noise ratio (SINNR) limit for the p-th eavesdropper to the l-th downlink mobile user; k,p The maximum received signal-to-interference-plus-noise ratio (SINNR) limit for the p-th eavesdropper to the k-th uplink user; l l,p , ψ k,p z j λ is an auxiliary variable. l,n This represents the minimum downlink achievable rate limit for the l-th downlink mobile user in the n-th time slot; V is the Hermitian transpose of the downlink channel vector of the l-th downlink mobile user in the nth time slot; l,nThe beamforming matrix for the l-th downlink mobile user in the nth time slot; h l,n V is the downlink channel vector of the l-th downlink mobile user in the nth time slot; l′,n For the beamforming matrix of all downlink mobile users except the l-th downlink mobile user in the nth time slot; λ represents the signal-to-noise power of the l-th downlink mobile user. k,n p represents the minimum uplink achievable rate limit for the k-th uplink communication user in the n-th time slot. k p represents the power of the k-th uplink user. k′ The power of all uplink users except the k-th uplink user; h is the Hermitian transpose of the uplink receive beamforming vector for the k-th uplink communication user; k,b Let be the communication channel vector from the k-th uplink communication user to the dual-function radar communication base station; h is the Hermitian transpose of the communication channel vector from the k-th uplink communication user to the dual-function radar communication base station; k′,b f is the communication channel vector from the dual-function radar communication base station to all uplink communication users except the k-th uplink communication user; k For the uplink receive beamforming vector of the kth uplink communication user; R is the Hermitian transpose of the communication channel vectors from all uplink users except the k-th uplink user to the dual-function radar communication base station; Q is the interference term matrix; R is the interference term matrix. x Q is the covariance matrix of the base station's transmitted signal; H R is the Hermitian transpose of the interference term matrix; c Here is the clutter covariance matrix; To be with V l,n Relevant process optimization variables; The actual channel value between the base station and the eavesdropper; This is the Hermitian transpose of the true channel values ​​between the base station and the eavesdropper. For dimension N t The identity matrix; To be with p k Relevant process optimization variables; This represents the actual distance from the base station to the eavesdropper. To be with R x Relevant process optimization variables; To be with p k Relevant process optimization variables; The Hermitian transpose of the antenna array steering vector with respect to the angular partial derivative; t0 is the partial derivative of the antenna array steering vector with respect to the angle; t0 is a constant. A is the Hermitian matrix of the antenna array steering vector;p The antenna array steering vector matrix; e is the inverse of the beam tracking mean square error matrix; j Γ is the j-th column of an identity matrix of dimension 3; MSE The threshold value for the beam tracking mean square error matrix trace is set. For dimension N r The identity matrix; Ψ is the intermediate solution obtained in the r-th successive convex approximation iteration; k To optimize the variable matrix.

[0067] According to a second aspect of the present invention, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the robust and secure beamforming and target tracking method for a full-duplex inductive integrated system.

[0068] According to a third aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium storing a computer program, which, when executed by a processor, implements the robust and secure beamforming and target tracking method for a full-duplex inductive integrated system.

[0069] Compared with the prior art, the present invention has at least the following beneficial effects:

[0070] (1) This invention addresses the shortcomings of existing secure beamforming schemes, which generally rely on ideal channel information and are difficult to adapt to user movement and rapid changes in wireless channels, resulting in significant performance degradation in dynamic environments. It proposes a robust secure beamforming and target tracking method for a full-duplex integrated sensing system. By utilizing an extended Kalman filter to achieve real-time tracking of the downlink mobile user's motion state, and combining this with the Cramer-Rao boundary to quantify the angle estimation error of potential eavesdroppers, a channel uncertainty set is established, thereby achieving effective prediction of dynamic channels and accurate characterization of eavesdropper uncertainty. This invention can guarantee channel tracking accuracy and communication security in dynamic environments without requiring completely accurate channel information, overcoming the poor reliability of existing technologies in dynamic and complex environments.

[0071] (2) This invention jointly optimizes the downlink beamforming matrix, the artificial noise covariance matrix, the uplink receiving beamforming vector, and the user power allocation strategy. The non-convex constraints caused by the eavesdropper's channel uncertainty are transformed into equivalent linear matrix inequalities, thus constructing an optimization model that can be solved efficiently. This method, while satisfying constraints such as uplink and downlink security rates, sensing accuracy, and tracking accuracy, aims to minimize the total system transmit power, achieving efficient joint optimization of beamforming and resource allocation. Compared with existing technologies, this invention exhibits significant advantages in transmit power overhead, convergence speed, and secure communication performance, making it suitable for low-overhead, high-reliability, and secure communication systems in multi-user dynamic environments such as vehicle-to-everything (V2X) and smart cities.

[0072] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0073] To more clearly illustrate the technical solutions in the specific embodiments of the present invention, the drawings used in the description of the specific embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0074] Figure 1 This is a flowchart of a robust and secure beamforming and target tracking method for a full-duplex inductive integrated system according to the present invention;

[0075] Figure 2 A schematic diagram of the full-duplex integrated sensing system structure used in this embodiment of the invention;

[0076] Figure 3 This is a schematic diagram comparing the dynamic target tracking performance under different sensing accuracy constraints according to an embodiment of the present invention;

[0077] Figure 4 The simulation diagram shows the performance of the robust secure beamforming method and the comparative method in terms of secure communication in this invention. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0079] Combination Figure 2As shown, the full-duplex inductive integrated system includes a system with N t One transmitting antenna array and N r A dual-function radar communication base station with a receiving antenna array supports simultaneous radar sensing and full-duplex communication functions, serving K uplink communication users and L downlink mobile users. Meanwhile, in the full-duplex sensing integrated system, there are P eavesdroppers attempting to illegally obtain confidential information in the uplink and downlink, each using a set of... and Indicates. N t One transmit antenna array is used to transmit integrated sensing signals to achieve downlink communication and radar target perception, N r A single receiving antenna array is used to simultaneously receive communication signals from uplink communication users and radar echo signals.

[0080] Total observation time T of the full-duplex inductive integrated system tot The system is discretized into N time slots at equal intervals, with each time slot lasting for a duration of ΔT. Within any nth time slot, the motion state parameters of the lth downlink mobile user relative to the dual-function radar communication base station include the angle θ. l,n Distance d l,n and speed v l,n .

[0081] In the nth time slot, the dual-function radar communication base station transmits an integrated sensing signal x. n (t), used to simultaneously realize radar sensing and downlink communication, is expressed as:

[0082] x n (t)=V n s n (t)+w n (t)

[0083] Among them, V n For the downlink beamforming matrix, the l-th column v of the downlink beamforming matrix l,n Beamforming vector corresponding to the l-th downlink mobile user; s n (t) represents the downlink data symbol vector that satisfies unity power; w n (t) is a zero-mean circularly symmetric complex Gaussian artificial noise vector that satisfies And with s n (t) Statistically independent. Therefore, the synesthetic signal x n The covariance matrix of (t) is:

[0084]

[0085] A dual-function radar communication base station simultaneously transmits a sensing-integrated signal and receives communication signals and radar echo signals from uplink communication users. The uplink user's transmitted signal is d. k Satisfying power constraints

[0086] Consider a strong and dominant line-of-sight channel between the dual-function radar communication base station and each downlink mobile user, which facilitates high-precision positioning and tracking. The signal received by the l-th downlink mobile user from the dual-function radar communication base station in the nth time slot is represented as:

[0087]

[0088] in, Represents the antenna gain factor; γ l,n The channel gain coefficient depends on the distance d between the dual-function radar communication base station and the l-th downlink mobile user. l,n Furthermore, the Doppler frequency shift caused by user mobility is Among them, f c Let θ be the carrier frequency; c be the speed of light. a(θ) represents the direction vector of the transmitting antenna array. Assuming the spacing between adjacent transmitting antennas in a dual-function radar communication base station is half a wavelength, its expression is:

[0089]

[0090] Finally, n l,n (t) represents additive white Gaussian noise, which follows the... The Gaussian distribution.

[0091] Therefore, the received signal-to-interference-plus-noise ratio (SINR) of the l-th downlink mobile user in the n-th time slot is:

[0092]

[0093] in, Let represent the equivalent downlink channel vector. Then the downlink achievable rate for the l-th user in the n-th time slot is:

[0094]

[0095] Suppose there are P passive eavesdroppers in a full-duplex integrated sensing system, attempting to simultaneously eavesdrop on downlink signals transmitted by a dual-function radar communication base station and uplink signals transmitted by K legitimate users. Therefore, the signal received by the p-th eavesdropper in the n-th time slot can be expressed as:

[0096]

[0097] Among them, h k,pLet h represent the complex channel gain coefficient between the k-th uplink user and the p-th eavesdropper, modeled as a Rayleigh fading channel. b,p Let h represent the channel vector between the dual-function radar communication base station and the p-th eavesdropper. Considering the prevalent signal scattering in the ground environment, non-negligible multipath fading effects must be taken into account. Therefore, h b,p Modeled as a Ricean fading channel containing line-of-sight components and multipath scattering components, the expression is:

[0098]

[0099] Where, α p κ represents the path loss at the reference distance; p d is the Rice factor associated with the p-th eavesdropper; b,p This represents the distance between the dual-function radar communication base station and the p-th eavesdropper. The line-of-sight component of the Ricean fading channel. Defined as the guiding vector a(θ) p ), where θ p Let be the angle of incidence of the eavesdropping signal at the p-th eavesdropper. The multipath scattering component of a Ricean fading channel is denoted as . in The nth multipath scattering component t There are n elements. Finally, n p,n (t) represents additive white Gaussian noise with variance . Therefore, the signal-to-interference-plus-noise ratio (SINNR) received by the p-th eavesdropper from the k-th uplink user can be expressed as:

[0100]

[0101] To ensure secure communication performance under worst-case conditions, the full-duplex integrated sensing system adopts a conservative assumption: that an eavesdropper can first eliminate multi-user interference before decoding the information of a specific downlink mobile user. Therefore, the signal-to-interference-plus-noise ratio (SNR) received by the p-th eavesdropper from the l-th downlink mobile user can be expressed as:

[0102]

[0103] A dual-function radar communication base station aims to simultaneously track the motion status of L downlink mobile users and directionally transmit radar beams to P potential eavesdroppers. Therefore, in the nth time slot, the radar echo signal received by the dual-function radar communication base station can be expressed as:

[0104]

[0105] in, μ represents the gain factor of the antenna array. l,n With τ l,nLet represent the Doppler frequency shift and signal propagation delay for the l-th downlink mobile user in the nth time slot, respectively. The array steering vector of the receiving antenna array is denoted as b(θ), and its form is similar to that of the transmitting antenna array steering vector a(θ). The reflection coefficient is... Where ξ l,n Characterizing the combined effect of small-scale fading and the target's radar cross section. The complex reflection amplitude of the p-th potential eavesdropper is represented by γ. p .also, This represents the environmental clutter term, including echo interference from uplink communication users. Clutter covariance matrix. It is set to a constant value throughout the entire observation period to describe the statistical characteristics of the surrounding clutter environment.

[0106] In a full-duplex inductive integrated system, self-interference is not negligible, and the receiver will be affected by residual self-interference components, which are modeled as follows: Where β represents the residual self-interference power. The self-interference channel matrix H... SI Defined as Where d i,j Let be the distance between the i-th receiving antenna and the j-th transmitting antenna. Finally, the signal received by the dual-function radar communication base station in the n-th time slot is:

[0107]

[0108] The communication channel from the k-th uplink communication user to the dual-function radar communication base station is denoted as h. k,b It follows the Rice fading channel model and is determined by the Rice factor κ. k Characterization; This represents an additive white Gaussian noise vector.

[0109] Dual-function radar communication base stations improve uplink signal reception performance and suppress interference by designing uplink beamforming. For the k-th uplink communication user, the dual-function radar communication base station employs an uplink receiving beamforming vector... Therefore, the received signal-to-noise ratio of the k-th uplink communication user in the nth time slot is:

[0110]

[0111] The interference term matrix is ​​defined as follows: The achievable transmission rate of the k-th uplink communication user can be expressed as:

[0112]

[0113] In secure communication, the worst-case security rate is used as a key indicator to measure the security performance of a full-duplex sensing system. This indicator is used to evaluate the lowest achievable security rate among all users, thus reflecting the performance of the full-duplex sensing system under the most stringent security conditions. Specifically, two worst-case security rate indicators are defined: the worst-case security rate SR for downlink mobile users. DL Worst security rate SR with uplink communication users UL .

[0114] The worst-case confidentiality rate for downlink mobile users is defined as follows:

[0115]

[0116] Similarly, the worst-case confidentiality rate for uplink communication users is defined as:

[0117]

[0118] Radar sensing has two main functions in a full-duplex integrated sensing system: (1) extracting the motion state information of downlink mobile users from the received radar echo signal, thereby achieving more accurate beam prediction and tracking; (2) obtaining the channel state information of potential eavesdroppers to assist in the design of secure communication strategies.

[0119] like Figure 1 As shown, this invention provides a robust and secure beamforming and target tracking method for a full-duplex integrated sensing system. This method is executed by a dual-function radar communication base station and specifically includes the following steps:

[0120] S1. The base station receives radar echo signals and, based on the radar echo signals, uses an extended Kalman filter to perform real-time tracking and estimation of the motion state of downlink mobile users, thereby obtaining the predicted channel state information of downlink mobile users. The predicted channel state information includes at least angle, distance, and velocity parameters.

[0121] In one possible implementation, the specific implementation process of step S1 is as follows:

[0122] S101. Construct a state-space model containing downlink mobile user angle, distance, and speed parameters. The state-space model includes a state transition function, an observation function, a measurement noise covariance matrix, a process noise covariance matrix, and a state error covariance matrix.

[0123] Specifically, the state transition function is as follows:

[0124]

[0125] In the formula, v l,nv represents the speed of the l-th downlink mobile user at the current moment. l,n-1 u represents the speed of the l-th downlink mobile user at the previous time step. v For velocity process noise; θ l,n θ is the angle between the l-th downlink mobile user at the current moment and the horizontal direction of the base station antenna; l,n-1 d is the angle between the l-th downlink mobile user at the previous moment and the horizontal direction of the base station antenna; ΔT is the duration of a communication time slot; d l,n-1 The distance between the l-th downlink mobile user and the base station at the previous time step; u θ For angular process noise; d l,n The distance between the l-th downlink mobile user and the base station at the current moment; u d This refers to distance process noise.

[0126] Specifically, the observation functions include angle measurement models, distance measurement models, and velocity measurement models, among which:

[0127] The angle measurement model is as follows:

[0128]

[0129] The distance measurement model is as follows:

[0130]

[0131] The speed measurement model is as follows:

[0132]

[0133] In the formula, The radar echo of the l-th downlink mobile user at the current time, after time delay and Doppler compensation; r l,n (t) represents the radar echo of the l-th downlink mobile user at the current time; This is the conjugate component of the signal transmitted by the base station at the current moment; The current time delay measurement of the radar echo; j is the imaginary unit; This is the Doppler measurement of the radar echo at the current moment; Antenna gain; The reflection coefficient of the l-th downlink mobile user at the current time; G is the matched filter gain; a H (θ l,n ) represents the transmit antenna array steering vector of the l-th downlink mobile user at the current time; v l,n This is the transmit beamforming vector for the l-th downlink mobile user at the current time; For angle measurement noise; z τ For time delay measurement noise; z μ Noise for Doppler measurement.

[0134] The construction of the observation function in the state-space model is explained in detail below:

[0135] By utilizing the massive MIMO antenna array equipped in dual-function radar communication base stations, full-duplex integrated sensing systems can achieve extremely narrow transmit and receive beams, making inter-beam interference between multiple downlink mobile users negligible. According to massive MIMO antenna theory, the steering vectors corresponding to different angles of arrival will tend to be orthogonal as the number of antennas approaches infinity. Specifically, for different angles of arrival θ... l,n and θ l′,n Its inner product b H (θ l,n )b(θ l′,n The approximate value is zero, and it is assumed that... Right now in This represents the echo reception beamforming vector, whose incident angle is obtained using existing angle-of-arrival estimation methods. Therefore, through spatial filtering, the echo signal from the l-th downlink mobile user in the n-th time slot can be extracted, and its expression is:

[0136]

[0137] in, This represents the filtered additive white Gaussian noise, with a variance of .

[0138] Furthermore, the full-duplex integrated sensing system can process radar echo signals using the classic matched filtering method to estimate the signal delay. and Doppler shift In the already estimated and Based on this, and combined with the assumption that artificial noise and secure signals are independent of each other, the following angle measurement model can be constructed:

[0139]

[0140] Where G represents the matched filter gain, which can significantly improve the signal-to-noise ratio, thereby improving the accuracy of angle and distance estimation.

[0141] It is complex Gaussian noise.

[0142] The signal-to-noise ratio of the received radar echo signal can be expressed as:

[0143]

[0144] By applying matched filtering to the signal after delay and Doppler shift, the distance and velocity of the l-th downlink mobile user can be accurately estimated. The distance and velocity measurement models are as follows:

[0145]

[0146] Among them, z τ and z μ Let represent the measurement noise, respectively, with a mean of 0 and variances of . and The Gaussian distribution of the signal is used. Specifically, the measurement noise variance is inversely proportional to the signal-to-noise ratio of the radar echo signal, i.e.:

[0147] as well as The constants a1 and a2 depend on the specific signal processing algorithm.

[0148] The construction of state transition functions in state-space models is explained in detail below:

[0149] according to Figure 2 Based on the geometric model and kinematic principles shown, the motion state of the l-th downlink mobile user can be described as follows:

[0150]

[0151] Where, Δd=v l,n-1 ΔT, Δθ=θ l,n -θ l,n-1 Let represent the distance and angle changes within each time slot, respectively. Assume all downlink mobile users travel at a constant speed along a straight path parallel to the base station antenna array. Then the state transition function for the downlink mobile users can be expressed as:

[0152]

[0153] Among them, u v u θ u d The process noise term, used to characterize modeling error and system uncertainty, both have a mean of 0 and variances of [missing information]. The Gaussian distribution.

[0154] S102. Predict the motion state of the downlink mobile user at the current moment based on the state transition function;

[0155] X n∣n-1 =g(X) n-1 )

[0156] S103. Calculate the Jacobian matrix of the state transition function and the observation function to achieve linearization.

[0157]

[0158] Extended Kalman Filtering Process: Let the measurement vector be... The motion state vector is It can then be modeled as:

[0159]

[0160] Where h(·) and g(·) are nonlinear functions defined in the above equation, z l,n with u l,n The measurement noise and process noise are respectively represented by their covariance matrices. and To linearize the nonlinear model within the extended Kalman filter framework, its Jacobian matrix needs to be constructed.

[0161] Specifically, the Jacobian matrix of the state transition function is as follows:

[0162]

[0163] The Jacobian matrix of the observation function is specifically:

[0164]

[0165] In the formula, denoted by α, which is the Jacobian matrix of the state transition function; θ is the angle between the downlink mobile user and the base station antenna in the horizontal direction; ΔT is the duration of a communication time slot; d is the distance between the downlink mobile user and the base station; α is the transmit antenna gain; γ is the channel coefficient between the downlink mobile user and the base station; G is the matched filter gain; v is the transmit beamforming vector; f c is the carrier frequency; c is the speed of light.

[0166] S104. Based on the Jacobian matrix of the state transition function and the observation function, the process noise covariance matrix, and the state error covariance matrix of the previous time step, calculate the prediction error covariance matrix of the current time step.

[0167] S105. Calculate the Kalman gain based on the prediction error covariance matrix and the measurement noise covariance matrix at the current moment.

[0168]

[0169] S106. Combining the observed values ​​in the radar echo signal with the Kalman gain, correct the motion state of the downlink mobile user at the current moment, and use the corrected motion state of the downlink mobile user at the current moment as the predicted channel state information of the downlink mobile user.

[0170]

[0171] S107. Update the state error covariance matrix at the current moment based on the Kalman gain, and repeat S102 and S106.

[0172] S2. The base station designs the downlink beamforming matrix based on the predicted channel state information and constructs the uplink receiving beamforming vector, while optimizing the covariance matrix of the artificial noise signal.

[0173] S3. Based on radar echo signals, the base station uses the Cramér-Rao bound (CRB) to quantify the angle estimation error of potential eavesdroppers, and constructs a norm-bounded uncertainty set to characterize the channel uncertainty of eavesdroppers based on the angle estimation error.

[0174] In one possible implementation, the specific implementation process of step S3 is as follows:

[0175] S301. Based on multiple time-domain snapshots in the radar echo signal, and combining the base station transmitted signal covariance matrix and the eavesdropper reflection coefficient, calculate the Cramer-Rao threshold for estimating the angle of a potential eavesdropper.

[0176] S302. Based on the Cramer-Rao threshold estimated from the angle of the potential eavesdropper, construct the angle uncertainty region with three times the standard deviation of the Cramer-Rao threshold as the confidence limit, and complete the quantification of the angle estimation error of the potential eavesdropper.

[0177] S303. Taking into account the channel disturbance errors caused by angle estimation error, preset distance estimation error, and multipath fading, the channel uncertainty of potential eavesdroppers is modeled as a norm-bounded uncertainty set Φ. p , defined as follows.

[0178]

[0179] In the formula, v p The upper bound of the channel disturbance is characterized by the combined effects of angle estimation error, preset distance estimation error, and channel disturbance error caused by multipath fading; Δh b,p The channel uncertainty vector for the eavesdropper; For dimension N t A complex vector with 1 row and 1 column; N t The number of base station transmit antennas; ||Δh b,p ||2 is the Euclidean norm of the eavesdropper's channel uncertainty vector; For the Hermitian transpose of the eavesdropper's channel uncertainty vector; For the preset base station and the nth... t Upper bound on the uncertainty of multipath; κ p Let the Rice factor be the p-th eavesdropper; For the nth base station and the eavesdroppert Phase uncertainty of multiple paths; The true angle between the eavesdropper and the base station; Δθ p The angle estimation error between the eavesdropper and the base station; h b,p α is the complete channel vector between the base station and the p-th eavesdropper; p Let be the reference distance path loss for the p-th eavesdropper channel; Δd represents the true distance from the base station to the eavesdropper. b,p The estimated distance error from the base station to the eavesdropper, obtained through radar sensing; For the multi-radial quantity from the base station to the eavesdropper; For the Nth t Multipath components; This represents the actual channel value from the base station to the eavesdropper.

[0180] In detail, another key function of radar sensing is estimating the channel state information of potential eavesdroppers. Through signal processing techniques such as spatial filtering and interference cancellation, a full-duplex integrated sensing system can extract reflected signals related to eavesdroppers from radar echoes, thereby achieving relatively accurate channel state information estimation. Radar sensing relies on multiple sampling analyses of received radar echo signals. In this study, each communication time slot is set to last 100 milliseconds, while typical radar snapshot times are usually completed within a few milliseconds; therefore, multiple radar snapshot samples can be collected within a single time slot.

[0181] Based on this, within any time slot, the data matrix at the radar receiver... Expressed as:

[0182]

[0183] in, This represents the transmitted integrated sensing signal matrix; The covariance matrix of the superimposed interference and additive white Gaussian noise terms is: Furthermore, B = [b(θ1),…,b(θ)] P A = [a(θ1), ..., a(θ)] and A = [a(θ1), ..., a(θ)] P )] are the receive and transmit steering matrices, respectively; Ξ=diag(γ1,…,γ P ) is a diagonal matrix composed of the reflection coefficients of the eavesdropper.

[0184] The focus of this radar sensing analysis is to accurately estimate the angle information of the eavesdropper to assist in the design of a secure beamforming strategy. This involves evaluating the angle θ of the p-th eavesdropper. p To improve the estimation accuracy, this method uses CRB as a performance benchmark for parameter estimation. Specifically, in multi-eavesdropper detection scenarios, when the directions of other targets are known, θ...p The CRB expression is:

[0185]

[0186] Among them, A p =b(θ) p )a H (θ p ),and

[0187] A trajectory tracking model based on the extended Kalman filter: For L downlink mobile users, real-time tracking in dynamic movement scenarios is crucial for maintaining communication reliability and sensing accuracy. Accurate beamforming highly depends on precise angle information. Furthermore, combining range and velocity estimates from radar echoes can further improve the accuracy of positioning and trajectory tracking. The extended Kalman filter achieves efficient beam tracking and state estimation with extremely low pilot overhead by fusing radar measurements and kinematic models.

[0188] To elaborate, unlike traditional CRB which relies solely on observation data, state estimation for downlink mobile users requires the integration of a state evolution model. Therefore, a posterior Cramer-Rao bound (PCRB) can be constructed. According to Bayesian theory, its predicted value is consistent with the updated error covariance matrix in the Kalman filter, i.e.:

[0189] Uncertainty Bounds Regarding Eavesdropper Channel State Information: In radar sensing, a primary objective is to acquire the channel state information of potential eavesdroppers. However, due to unavoidable estimation errors, dual-function radar communication base stations may not be able to accurately obtain the distance and angle information of eavesdroppers. To address this issue, these uncertainties need to be considered within a robust and secure beamforming design framework.

[0190] Specifically, the distance between the p-th eavesdropper and the dual-function radar communication base station is modeled as follows:

[0191] in, Δd is the estimated distance obtained through radar sensing. b,p Let |Δd| be the error corresponding to the estimated distance obtained through radar sensing, satisfying |Δd| b,p |≤D b,p Similarly, the angle parameter is modeled as in To estimate the angle, Δθ pThis represents the angle estimation error. To achieve secure communication under channel uncertainty, beamforming design must consider all possible directions within the region of angle uncertainty. The inherent sensing capability of a full-duplex sensing system helps eliminate the uncertainty of channel state information. Specifically, the angle estimation error can be modeled as a variance of... It follows a zero-mean Gaussian distribution. Therefore, Δθ p Falling within the range The probability is approximately 99.73%. Therefore, the upper bound for the angular uncertainty is... Furthermore, the multipath fading components are modeled as perturbations in the line-of-sight channel, where each sub-channel component... satisfy Based on the above error modeling, the complete channel vector h of the p-th eavesdropper is... b,p It can be reformulated as:

[0192]

[0193] Among them, h b,p It includes three types of error terms: Δd b,p , Δθ p as well as Among them, the composite uncertainty vector The effects of angular deviation and multipath interference are also considered.

[0194] nth t Uncertain components corresponding to each antenna Satisfy the following upper bound:

[0195]

[0196] in,

[0197]

[0198] Specifically, this angular uncertainty is measured by CRB. For ease of calculation, the overall channel uncertainty for the p-th eavesdropper satisfies:

[0199]

[0200] Therefore, we define the continuous uncertain set Φ. p as follows:

[0201]

[0202] This set includes all possible small-scale fading perturbation components. Thus, an explicit relationship has been established between sensing performance and the uncertainty of channel state information from eavesdroppers. It is worth emphasizing that while increasing the transmit power towards the eavesdropper can improve the accuracy of channel state information estimation, it may also increase the risk of information leakage. Therefore, the inherent contradiction between sensing accuracy and communication security must be carefully weighed in beam design.

[0203] S4. Under the premise of satisfying the minimum confidentiality rate constraints of downlink and uplink communication links, the angle estimation error of the eavesdropper not exceeding the preset sensing accuracy requirement, and the mean square error of beam tracking based on the extended Kalman filter meeting the dynamic tracking accuracy requirement, a joint optimization problem is constructed with the goal of minimizing the total transmit power of the system. The optimization variables of the joint optimization problem include the downlink beamforming matrix, the covariance matrix of the artificial noise signal, the uplink receiving beamforming vector, and the uplink communication user power allocation strategy.

[0204] In this embodiment, firstly, the beamforming matrix is ​​defined as follows: The receiving beamforming matrix The kth column is f k The k-th component of the uplink power vector p is p k This problem aims to minimize the total system transmit power within each time slot while ensuring the minimum security rate requirements for uplink and downlink communication. Furthermore, to guarantee sensing quality, constraints are imposed on the CRB of the p-th eavesdropper's angle estimation and the covariance matrix of the beam tracking error. The full-duplex integrated sensing system jointly optimizes the beamforming matrix, the covariance matrix of artificial noise, and the uplink communication user power allocation strategy, i.e., {F, V...} l,n ,R w Given the following optimization problem P1:

[0205]

[0206] stC1:SR DL ≥ρ DL ,

[0207] C2:SR UL ≥ρ UL ,

[0208]

[0209] C4:Tr(M n )≤Γ MSE ,

[0210] C5:Rank(V l,n )≤1,

[0211]

[0212] In the formula, F is the uplink receiving beamforming matrix; V l,n The beamforming matrix for the l-th downlink mobile user in the n-th time slot; R w is the covariance matrix of the artificial noise; p is the power allocation vector for all uplink communication users; The trace of the downlink beamforming matrix and the sum of the downlink beamforming matrix; L is the number of downlink mobile users; Tr(R) w ) represents the trace of the artificial noise covariance matrix; SR DL ρ is the downlink communication security rate; DL The minimum threshold for the set downlink communication security rate; SR UL For uplink communication security rate; ρ UL This is the minimum threshold for the preset uplink communication security rate. Cramer-Rao threshold value estimated from the eavesdropper's perspective; Γ CRB The upper limit of the Cramer-Rhodes boundary estimated from the specified eavesdropper's angle; Tr(M n ) represents the trace of the beam tracking mean square error matrix; Γ MSE The threshold for the trace of the beam tracking mean square error matrix is ​​set; Rank(V) l,n ) represents the rank of the downlink beamforming matrix.

[0213] Among them, constraint C1 is the downlink secure rate constraint, which requires that the secure communication rate of all downlink mobile users must not be lower than the set minimum threshold ρ. DL Constraint C2 is an uplink secure communication rate constraint, stipulating that the secure communication rate of all uplink users shall not be lower than a preset minimum threshold ρ. UL Constraint C3 is a precision constraint on the angle estimation of eavesdroppers, requiring that the CRB corresponding to the angle estimation error of all potential eavesdroppers does not exceed the specified upper limit value Γ. CRB Constraint C4 is a dynamic target tracking error constraint, whereby the trace of the state estimation error matrix output by the extended Kalman filter is not greater than a set threshold Γ for the trace of the beam tracking mean square error matrix. MSE To ensure the accuracy of dynamic target trajectory tracking; constraints C5 and C6 are downlink beamforming matrix structure constraints, requiring the downlink beamforming matrix to be a positive semi-definite matrix with a rank not greater than 1; constraint C7 is a legality constraint for the artificial noise matrix, requiring the artificial noise covariance matrix to be a positive semi-definite matrix; constraint C8 is a power non-negativity constraint, stipulating that the power allocation vector of all uplink users must be a non-negative real vector.

[0214] S5. The non-convex semi-infinite constraint caused by the eavesdropper channel uncertainty in the joint optimization problem is transformed into a linear matrix inequality, and the joint optimization problem is solved iteratively to obtain the optimal beamforming and resource allocation parameters.

[0215] In this embodiment, the specific implementation process of step S5 is as follows:

[0216] S501. By introducing auxiliary variables, the joint optimization problem P1 is equivalently transformed into optimization problem P2, specifically:

[0217] First, define and These represent the minimum signal-to-interference-plus-noise ratio (SINORR) thresholds required for the l-th downlink mobile user and the k-th uplink communication user, respectively. To limit information leakage and ensure communication security, [the following is introduced]. and Let represent the maximum signal-to-interference-plus-noise ratio (SNR) allowed for the p-th eavesdropper to eavesdrop on the downlink signal emitted by the dual-function radar communication base station and the uplink signal emitted by the k-th uplink communication user, respectively.

[0218] Therefore, the original problem P1 is equivalently reconstructed as follows to obtain problem P2:

[0219]

[0220] C2.5:C3-C8

[0221] S502. Using the S-lemma method, the non-convex semi-infinite constraints caused by the eavesdropper's channel uncertainty in optimization problem P2 are transformed into linear matrix inequalities. Combined with the Schur complement condition, the eavesdropper's angle estimation error constraint and the extended Kalman filter's beam tracking mean square error constraint are reconstructed into convex form, forming optimization problem P3, as follows:

[0222] To illustrate the equivalence between problems P1 and P2, we define... And assume And require Based on the definition of the worst-case downlink security rate, applying it to the first constraint in P1 yields: Therefore, R is constrained by the first constraint C2.1 in P2. l,n The lower bound of the signal-to-interference-plus-noise ratio (SIR) for the eavesdropper, and the upper bound of the SIR for the eavesdropper, constrained by the third constraint C2.3, satisfy the first constraint in P1. Using a similar method and the definition of the worst-case uplink security rate, the second and fourth constraints in P2 can be derived, thus achieving an equivalent reconstruction with P2.

[0223] To further advance the reconstruction of constraints C2.1 and C2.2, two auxiliary variables λ are introduced. l,n , Constraint C2.1 can be equivalently rewritten as the formula The constraint C2.2 is equivalently rewritten as the formula. The correspondence between the above auxiliary variables and the signal-to-interference-plus-noise ratio (SIN / N) threshold is defined as follows: To further address the semi-infinite constraint problem, a new auxiliary variable η is introduced. l,n , And rewrite it equivalently as:

[0224]

[0225] in, Next, to decouple the uncertainty variables nested in the signal-to-interference-plus-noise ratio (SIR) expression, both the numerator and denominator of the SIR are multiplied by a factor. Subsequently, a slack variable ζ was further introduced. l,p , The above equation is rewritten as:

[0226]

[0227] However, this process introduces new semi-infinite constraints. To address this issue, we apply the S-lemma to transform these semi-infinite constraints into equivalent linear matrix inequalities. Using the S-lemma, the above equation can be further reconstructed into the following linear matrix inequality expression:

[0228]

[0229] Among them, l l,p , ψ k,p Values ​​≥0 are introduced auxiliary slack variables. (Matrix) Defined as and In addition, the intermediate variable is defined as:

[0230]

[0231] Furthermore, according to the Schul complement condition, constraint C3 is equivalent to the following form:

[0232]

[0233] in,

[0234] To solve the non-convexity problem in constraint C4, based on the extended Kalman filter structure, M is derived. n Inverse matrix form:

[0235]

[0236] in, It is important to note that, through H n and Perform matrix operations, matrix It can be represented as an affine function of the optimization variable.

[0237] To further reconstruct this constraint, Schul's complement lemma is applied to transform the original nonconvex constraint into a linear matrix inequality. An auxiliary variable z is introduced for this purpose. j If ≥0, j∈{1,…,3}, then constraint C3 can be equivalently rewritten as:

[0238]

[0239] Among them, e j Let J represent the j-th column vector of the identity matrix I3.

[0240] Combining the above transformations, the robust and secure beamforming and target tracking problem can be reformulated as follows:

[0241]

[0242] stC3.1:C5-C8

[0243]

[0244] S503. Using the generalized Rayleigh quotient solution method, obtain the closed-form optimal solution for the uplink receiving beamforming vector. To eliminate the non-convexity related to the uplink receive beamforming vector in optimization problem P3, the specific steps are as follows:

[0245] Since the only quantity that depends on F in the problem is And receive the beamforming vector f k They are user-specific and independent of each other, therefore each f k Each of these can be optimized individually. Therefore, the first step is to maximize the received beamforming vector for the k-th uplink user based on its signal-to-interference-plus-noise ratio (SIR), i.e. Based on the generalized Rayleigh quotient theory, the optimal beamforming vector for the k-th user can be expressed as:

[0246]

[0247] S504. Based on the successive convex approximation and semi-definite relaxation method, the optimization problem P3 is relaxed to obtain the optimization problem P4. The optimization problem P4 is then solved iteratively using convex optimization tools to obtain the optimal beamforming and resource allocation parameters, as follows:

[0248] Optimal receive vector After substituting the constraints, it can be rewritten in a form without F:

[0249]

[0250] in,

[0251]

[0252] We use a first-order Taylor expansion to... Perform a lower bound approximation:

[0253]

[0254] in, This is an intermediate solution obtained in the r-th successive convex approximation iteration. Therefore, the only nonconvexity in P3 comes from the rank constraint C5. To solve this problem, a positive semidefinite relaxation technique is employed. Therefore, problem P3 can be further reconstructed as:

[0255]

[0256] C4.2:C6-C8,C3.2,C3.4-C3.10

[0257] The relaxed problem P4 is convex, therefore it can be solved efficiently using convex optimization tools. It is worth noting that the structure of problem P4 has an optimal solution of rank one. Therefore, by optimizing the optimal solution... Perform Cholesky decomposition to recover the optimal beamforming vector.

[0258] In the formula, R l,n Let l be the downlink achievable rate for the l-th downlink mobile user in the n-th time slot; The minimum downlink achievable rate limit for the l-th downlink mobile user in the n-th time slot; For any l downlink mobile users; R k,n The uplink achievable rate for the k-th uplink communication user in the n-th time slot; This is the preset minimum uplink achievable rate limit for the k-th uplink communication user in the n-th time slot; For any k uplink communication users; Let Δh be the set of the number of eavesdroppers. b,p Let Δd be the channel uncertainty vector for the eavesdropper. b,p Error in estimating the distance from the base station to the eavesdropper; Φ p D is a norm-bounded set of uncertainties; b,p The upper bound of the distance estimation error from the base station to the eavesdropper is set as the preset value; Let be the signal-to-interference-plus-noise ratio (SIR) received by the p-th eavesdropper from the l-th downlink mobile user; The maximum achievable rate limit for the p-th eavesdropper to the l-th downlink mobile user in the n-th time slot is defined. Let be the signal-to-interference-plus-noise ratio (SIR) received by the p-th eavesdropper from the k-th uplink user; ζ is the maximum achievable rate limit set for the p-th eavesdropper to the k-th uplink user in the n-th time slot; l,p ζ represents the maximum received signal-to-interference-plus-noise ratio (SINNR) limit for the p-th eavesdropper to the l-th downlink mobile user; k,p The maximum received signal-to-interference-plus-noise ratio (SINNR) limit for the p-th eavesdropper to the k-th uplink user; l l,p , ψ k,p z j λ is an auxiliary variable. l,n This represents the minimum downlink achievable rate limit for the l-th downlink mobile user in the n-th time slot; V is the Hermitian transpose of the downlink channel vector of the l-th downlink mobile user in the nth time slot; l,n The beamforming matrix for the l-th downlink mobile user in the nth time slot; h l,n V is the downlink channel vector of the l-th downlink mobile user in the nth time slot; l′,n For the beamforming matrix of all downlink mobile users except the l-th downlink mobile user in the nth time slot; λ represents the signal-to-noise power of the l-th downlink mobile user. k,n p represents the minimum uplink achievable rate limit for the k-th uplink communication user in the n-th time slot. k p represents the power of the k-th uplink user. k′ The power of all uplink users except the k-th uplink user; h is the Hermitian transpose of the uplink receive beamforming vector for the k-th uplink communication user; k,b Let be the communication channel vector from the k-th uplink communication user to the dual-function radar communication base station; h is the Hermitian transpose of the communication channel vector from the k-th uplink communication user to the dual-function radar communication base station; k′,b f is the communication channel vector from the dual-function radar communication base station to all uplink communication users except the k-th uplink communication user; k For the uplink receive beamforming vector of the kth uplink communication user; R is the Hermitian transpose of the communication channel vectors from all uplink users except the k-th uplink user to the dual-function radar communication base station; Q is the interference term matrix; R is the interference term matrix. x Q is the covariance matrix of the base station's transmitted signal; H R is the Hermitian transpose of the interference term matrix; c Here is the clutter covariance matrix; To be with V l,n Relevant process optimization variables; The actual channel value between the base station and the eavesdropper; This is the Hermitian transpose of the true channel values ​​between the base station and the eavesdropper. For dimension N t The identity matrix; To be with p k Relevant process optimization variables; This represents the actual distance from the base station to the eavesdropper. To be with R x Relevant process optimization variables; To be with p k Relevant process optimization variables; The Hermitian transpose of the antenna array steering vector with respect to the angle; t0 is the partial derivative of the antenna array steering vector with respect to the angle; t0 is a constant. A is the Hermitian matrix of the antenna array steering vector; p The antenna array steering vector matrix; e is the inverse of the beam tracking mean square error matrix; j Γ is the j-th column of a 3-dimensional identity matrix; MSE The threshold value for the beam tracking mean square error matrix trace is set. For dimension N r The identity matrix; Ψ is the intermediate solution obtained in the r-th successive convex approximation iteration; k To optimize the variable matrix.

[0259] S6. Control the base station according to the optimal beamforming and resource allocation parameters to realize robust and secure beamforming and target tracking of the full-duplex inductive integrated system.

[0260] Figure 3 The proposed beam tracking framework based on a dual-function radar communication base station was evaluated under different mean square error thresholds Γ. MSE The performance of the extended Kalman filter was demonstrated. The results show that, thanks to the matched filter gain provided by the dual-function radar communication technology, the extended Kalman filter can successfully track changes in angle and distance. This highlights the ability of the full-duplex sensing system to extract accurate information from radar echoes. It can be observed that under stricter constraints (Γ... MSE =0.6), the predicted trajectory is very close to the actual paths of the two downlink mobile users. In contrast, under a more lenient threshold condition (Γ), MSE =1.2), and the tracking performance decreased slightly. These observations indicate that a smaller tracking error tolerance can lead to higher estimation accuracy, validating the effectiveness of using prediction error covariance as a tracking performance indicator.

[0261] Figure 4The robust secure beamforming and target tracking method of the full-duplex integrated sensing system of this invention was compared with several benchmark schemes. The first is the isotropic design (ISO) scheme, which uniformly distributes transmission power among uplink, downlink communication, and artificial noise generation. In this scheme, the covariance matrix of artificial noise is constructed as an orthogonal projection of the null space of the forward user channel, and the remaining power is allocated for transmission beamforming. The second benchmark is the No-Artificial-Noise (No-AN) design, specifically designed for communication scenarios. It employs zero-forcing (ZF) precoding in a dual-function radar communication base station and allocates uniform transmission power to all uplink users, serving as a reference scheme when security is not a primary concern. The third scheme is the Secure ISAC Design (SRCS), which represents an optimized ISAC strategy aimed at minimizing the eavesdropper's signal-to-noise ratio while satisfying communication signal-to-interference-plus-noise ratio constraints, radar sensing requirements, and total power budget. It should be noted that this scheme is only applicable to half-duplex communication systems. To ensure fair comparison, all methods use the power consumption achieved by the proposed method as a uniform power budget, and all benchmark schemes are evaluated under perfect channel state information conditions. To verify the performance of the proposed method, the second time slot is selected as a representative example for analysis.

[0262] Figure 4 The downlink noise power was studied under different secure transmission schemes. The impact of changes on downlink secure speed. The reachable speed requirement for legitimate users is fixed at [value missing]. The maximum achievable rate for eavesdroppers is set to This demonstrates strict confidentiality constraints. The robust secure beamforming and target tracking method of the full-duplex inductive integrated system of this invention can stably achieve a downlink security rate of approximately 6.99 bit / s / Hz under all noise levels. This stable performance reflects the strong robustness of the algorithm in effectively maintaining the required security rate even under varying noise conditions. The SRCS method also has a relatively stable security rate of approximately 4.9 bit / s / Hz, showing insensitivity to changes in noise power. However, its performance is slightly lower compared to the robust secure beamforming and target tracking method of the full-duplex inductive integrated system of this invention. This is because the SRCS method mainly focuses on minimizing the signal-to-noise ratio of the eavesdropper in a specific direction under power-constrained conditions, failing to perform more comprehensive power and direction optimization. The ISO method has an even lower and essentially constant security rate of approximately 3.88 bit / s / Hz. Due to the uniform power radiation and lack of directionality and optimization design, the security performance is significantly reduced. It is worth noting that the performance of the No-AN method varies with the noise level. In high signal-to-noise ratio (SNR) environments, its secure rate can reach approximately 4.5 bits / s / Hz. However, as noise increases, its secure rate rapidly drops to 1.2 bits / s / Hz. This is because the lack of artificial noise protection allows, in some cases, the SNR of an eavesdropper to even exceed that of a legitimate user. Overall, the robust secure beamforming and target tracking method of the full-duplex inductive integrated system of this invention outperforms all other benchmark schemes across the entire noise level range. This is due to its joint optimization of power allocation and beamforming strategies, effectively balancing communication performance and security requirements with minimal power consumption.

[0263] In another embodiment of the present invention, a computer device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions in the computer storage medium to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used in the operation of a robust and secure beamforming and target tracking method for a full-duplex integrated sensing system.

[0264] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the robust and secure beamforming and target tracking method for a full-duplex inductive integrated system described in the above embodiments.

[0265] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0266] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0267] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0268] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0269] This invention also provides a computer program product, which is used to execute any of the robust and secure beamforming and target tracking methods for a full-duplex inductive integrated system described above. Since the computer program product provided by this invention and the robust and secure beamforming and target tracking method for a full-duplex inductive integrated system described above belong to the same inventive concept, the computer program product provided by this invention possesses all the advantages of the robust and secure beamforming and target tracking method for a full-duplex inductive integrated system described above. Therefore, the beneficial effects of the computer program product provided by this invention will not be elaborated upon here.

[0270] In this invention, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0271] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit them. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the scope of the technology disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention.

Claims

1. A robust and secure beamforming and target tracking method for a full-duplex inductive integrated system, characterized in that, The method is executed by a dual-function radar communication base station and includes the following steps: S1. The base station receives radar echo signals and, based on the radar echo signals, uses an extended Kalman filter to perform real-time tracking and estimation of the motion state of downlink mobile users to obtain the predicted channel state information of downlink mobile users. The predicted channel state information includes angle, distance, and speed parameters. S2. The base station designs the downlink beamforming matrix based on the predicted channel state information and constructs the uplink receiving beamforming vector, while optimizing the design of the covariance matrix of the artificial noise signal. S3. Based on the radar echo signal, the base station uses Cramer-Rao bounded quantization to quantify the angle estimation error of potential eavesdroppers, and constructs a norm-bounded uncertainty set characterizing the channel uncertainty of eavesdroppers based on the angle estimation error. S4. Under the premise of satisfying the minimum confidentiality rate constraint of the downlink and uplink communication links, the angle estimation error of the eavesdropper not exceeding the preset sensing accuracy requirement, and the beam tracking mean square error based on the extended Kalman filter meeting the dynamic tracking accuracy requirement, a joint optimization problem is constructed with the goal of minimizing the total system transmit power; wherein, the optimization variables of the joint optimization problem include the downlink beamforming matrix, the covariance matrix of the artificial noise signal, the uplink receiving beamforming vector, and the uplink communication user power allocation strategy; The joint optimization problem with the objective of minimizing the total transmit power of the system. Specifically: In the formula, Beamforming matrix for uplink receiver; For the first The downlink mobile user in the first Beamforming matrix of time slots; Let be the covariance matrix of the artificial noise; Power allocation vectors for all uplink communication users; The trace of the downlink beamforming matrix and the sum; The number of downlink mobile users; The trace of the covariance matrix of artificial noise; For downlink communication security rate; The minimum threshold for the set downlink communication security rate; For uplink communication security rate; This is the minimum threshold for the preset uplink communication security rate. Cramer-Rao threshold value estimated from the eavesdropper's perspective; The upper limit of the Cramer-Rhodes boundary estimated for the specified eavesdropper angle; The trace of the beam tracking mean square error matrix; The threshold value for the beam tracking mean square error matrix trace is set. The rank of the downlink beamforming matrix; S5. Transform the non-convex semi-infinite constraint caused by the eavesdropper channel uncertainty in the joint optimization problem into a linear matrix inequality, and iteratively solve the joint optimization problem to obtain the optimal beamforming and resource allocation parameters. S6. Control the base station according to the optimal beamforming and resource allocation parameters to realize robust and secure beamforming and target tracking of the full-duplex sensing integrated system.

2. The robust and secure beamforming and target tracking method for a full-duplex inductive integrated system according to claim 1, characterized in that, The step of using an extended Kalman filter to perform real-time tracking and estimation of the motion state of downlink mobile users based on the radar echo signal to obtain the predicted channel state information of downlink mobile users includes: S101. Construct a state-space model containing downlink mobile user angle, distance and speed parameters. The state-space model includes a state transition function, an observation function, a measurement noise covariance matrix, a process noise covariance matrix and a state error covariance matrix. S102. Predict the motion state of the downlink mobile user at the current moment based on the state transition function; S103. Calculate the Jacobian matrix of the state transition function and the observation function; S104. Based on the Jacobian matrix of the state transition function and the observation function, the process noise covariance matrix, and the state error covariance matrix of the previous time step, calculate the prediction error covariance matrix of the current time step. S105. Calculate the Kalman gain based on the prediction error covariance matrix and the measurement noise covariance matrix at the current moment. S106. Combining the observed values ​​in the radar echo signal with the Kalman gain, correct the motion state of the downlink mobile user at the current moment, and use the corrected motion state of the downlink mobile user at the current moment as the predicted channel state information of the downlink mobile user. S107. Update the state error covariance matrix at the current moment based on the Kalman gain, and repeat S102 and S106.

3. The robust and secure beamforming and target tracking method for a full-duplex inductive integrated system according to claim 2, characterized in that, The state transition function is specifically: In the formula, For the current moment The speed of each downlink mobile user; For the previous moment The speed of each downlink mobile user; This refers to speed process noise; For the current moment The angle between the downlink mobile user and the horizontal direction of the base station antenna; For the previous moment The angle between the downlink mobile user and the horizontal direction of the base station antenna; The duration of a communication time slot; For the previous moment The distance between each downlink mobile user and the base station; This is noise from the angle process; For the current moment The distance between each downlink mobile user and the base station; This refers to distance process noise.

4. The robust and secure beamforming and target tracking method for a full-duplex inductive integrated system according to claim 2, characterized in that, The observation functions include an angle measurement model, a distance measurement model, and a velocity measurement model; The angle measurement model is specifically as follows: The distance measurement model is specifically as follows: The speed measurement model is specifically as follows: In the formula, The current time after time delay and Doppler compensation Radar echo signals of downlink mobile users; For the current moment Radar echo signals of downlink mobile users; This is the conjugate component of the signal transmitted by the base station at the current moment; This is the measured time delay of the radar echo at the current moment; The imaginary unit; This is the Doppler measurement of the radar echo at the current moment; Antenna gain; For the current moment Reflection coefficient of each downlink mobile user; For matched filter gain; For the current moment The transmit antenna array steering vector for each downlink mobile user; For the current moment Transmit beamforming vectors for each downlink mobile user; Noise for angle measurement; For time delay measurement noise; Noise for Doppler measurement.

5. A robust and secure beamforming and target tracking method for a full-duplex inductive integrated system according to claim 2, characterized in that, The Jacobian matrix of the state transition function is specifically: The Jacobian matrix of the observation function is specifically: In the formula, Let be the Jacobian matrix of the state transition function; The angle between the downlink mobile user and the horizontal direction of the base station antenna; The duration of a communication time slot; This refers to the distance between the downlink mobile user and the base station; Let be the Jacobian matrix of the observation function; This refers to the gain of the transmitting antenna; For downlink mobile users and base stations, the channel coefficients are used. For matched filter gain; Shape the transmitted beam with a vector; For carrier frequency; It is the speed of light.

6. The robust and secure beamforming and target tracking method for a full-duplex inductive integrated system according to claim 1, characterized in that, The base station, based on the radar echo signal, uses Cramer-Rao bounded quantization to quantize the angle estimation error of a potential eavesdropper, and constructs a norm-bounded uncertainty set characterizing the channel uncertainty of the eavesdropper based on the angle estimation error, including: S301. Based on multiple time-domain snapshots in the radar echo signal, and combining the base station transmitted signal covariance matrix and the eavesdropper reflection coefficient, calculate the Cramer-Rao threshold for estimating the angle of the potential eavesdropper. S302. Based on the Cramer-Rao threshold estimated from the angle of the potential eavesdropper, construct the angle uncertainty region with three times the standard deviation of the Cramer-Rao threshold as the confidence limit, and complete the quantification of the angle estimation error of the potential eavesdropper. S303. Taking into account the channel disturbance errors caused by angle estimation error, preset distance estimation error, and multipath fading, the channel uncertainty of potential eavesdroppers is modeled as a norm-bounded uncertainty set. The definition is as follows: In the formula, It is characterized as the upper bound of the channel disturbance caused by the combined effects of angle estimation error, preset distance estimation error, and channel disturbance error caused by multipath fading; The channel uncertainty vector for the eavesdropper; For dimension A complex vector with 1 row and 1 column; This refers to the number of transmitting antennas at the base station; Let be the Euclidean norm of the eavesdropper's channel uncertainty vector; For the Hermitian transpose of the eavesdropper's channel uncertainty vector; For the pre-set base station and the eavesdropper's first An upper bound on the uncertainty of multiple paths; For the first The Rice factor of an eavesdropper; For base stations and eavesdroppers Phase uncertainty of multiple paths; This represents the actual angle between the eavesdropper and the base station. The angle estimation error between the eavesdropper and the base station; For base station and the The complete channel vector between each eavesdropper; For the first Reference distance path loss for an eavesdropper channel; This represents the actual distance from the base station to the eavesdropper. Error in estimating the distance from the base station to the eavesdropper; For the multi-radial quantity from the base station to the eavesdropper; For the first Multipath components; This represents the actual channel value from the base station to the eavesdropper.

7. The robust and secure beamforming and target tracking method for a full-duplex inductive integrated system according to claim 1, characterized in that, The process involves transforming the non-convex semi-infinite constraint caused by the eavesdropper channel uncertainty in the joint optimization problem into a linear matrix inequality, and iteratively solving the joint optimization problem to obtain the optimal beamforming and resource allocation parameters, including: S501. By introducing auxiliary variables, the joint optimization problem P1 is equivalently transformed into optimization problem P2, specifically: S502. Using the S-lemma method, the non-convex semi-infinite constraints caused by the eavesdropper's channel uncertainty in optimization problem P2 are transformed into linear matrix inequalities. Combined with the Schur complement condition, the eavesdropper's angle estimation error constraint and the beam tracking mean square error constraint of the extended Kalman filter are reconstructed into convex form, forming optimization problem P3, specifically: S503. Using the generalized Rayleigh quotient solution method, obtain the closed-form optimal solution for the uplink receiving beamforming vector. To eliminate the non-convexity related to the uplink receive beamforming vector in optimization problem P3, specifically: S504. Based on the successive convex approximation and semi-definite relaxation method, the optimization problem P3 is relaxed to obtain the optimization problem P4. The optimization problem P4 is then iteratively solved using convex optimization tools to obtain the optimal beamforming and resource allocation parameters, specifically: In the formula, For the first The downlink mobile user in the first Downlink achievable rate per time slot; For the set number The downlink mobile user in the first The minimum downlink achievable rate limit for each time slot; For any One downlink mobile user; For the first The uplink communication user in the first Uplink achievable rate per time slot; For the preset first The uplink communication user in the first The minimum uplink achievable rate limit for each time slot; For any One uplink communication user; The set of the number of eavesdroppers; The channel uncertainty vector for the eavesdropper; Error in estimating the distance from the base station to the eavesdropper; It is a norm-bounded set of uncertainties; The upper bound of the distance estimation error from the base station to the eavesdropper is set as the preset value; For the first The eavesdropper on the first The received signal-to-interference-plus-noise ratio for each downlink mobile user; For the set number The eavesdropper on the first The downlink mobile user in the first The maximum achievable rate limit for each time slot; For the first The eavesdropper on the first The received signal-to-interference-plus-noise ratio of each uplink communication user; For the set number The eavesdropper on the first The uplink communication user in the first The maximum achievable rate limit for each time slot; For the first The eavesdropper on the first The maximum received signal-to-interference-plus-noise ratio limit for each downlink mobile user; For the first The eavesdropper on the first The maximum received signal-to-interference-plus-noise ratio limit for each uplink communication user; , , , , As an auxiliary variable, For the first The downlink mobile user in the first The minimum downlink achievable rate limit for each time slot; For the first The downlink mobile user in the first Hermitian transpose of the downlink channel vector of the time slot; For the first The downlink mobile user in the first Beamforming matrix of time slots; For the first The downlink mobile user in the first Downlink channel vector of the time slot; To exclude the first Other downlink mobile users besides the first downlink mobile user in the 1st Beamforming matrix of time slots; For the first Signal noise power of each downlink mobile user; For the first The uplink communication user in the first The minimum uplink achievable rate limit for each time slot; For the first Power of each uplink communication user; To exclude the first The power of other uplink users besides the one uplink communication user; For the first Hermitian transpose of the uplink receive beamforming vector of each uplink communication user; For the first Communication channel vector from an uplink communication user to a dual-function radar communication base station; For the first Hermitian transpose of the communication channel vector from an uplink communication user to a dual-function radar communication base station; To exclude the first Communication channel vectors from uplink users other than the existing uplink communication users to the dual-function radar communication base station; For the first Uplink receive beamforming vectors for each uplink communication user; To exclude the first Hermitian transpose of the communication channel vector from the dual-function radar communication base station to other uplink communication users besides the one uplink communication user; This is the interference term matrix; The covariance matrix of the base station's transmitted signal; This is the Hermitian transpose of the interference term matrix; Here is the clutter covariance matrix; To and Relevant process optimization variables; The actual channel value between the base station and the eavesdropper; This is the Hermitian transpose of the true channel values ​​between the base station and the eavesdropper. For dimension The identity matrix; To and Relevant process optimization variables; This represents the actual distance from the base station to the eavesdropper. To and Relevant process optimization variables; To and Relevant process optimization variables; The Hermitian transpose of the antenna array steering vector with respect to the angle; This represents the partial derivative of the antenna array steering vector with respect to the angle. It is a constant; The Hermitian matrix of the antenna array steering vector; The antenna array steering vector matrix; This is the inverse of the beam tracking mean square error matrix; The 3rd identity matrix of dimension 3 List; The threshold value for the beam tracking mean square error matrix trace is set. For dimension The identity matrix; For the first The intermediate solution obtained in each successive convex approximation iteration; To optimize the variable matrix.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements a robust and secure beamforming and target tracking method for a full-duplex inductive integrated system as described in any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements a robust and secure beamforming and target tracking method for a full-duplex inductive integrated system as described in any one of claims 1 to 7.

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