Method for optimization of active and passive beamforming and signal reception configuration of dual irss-assisted ISAC system

Abstract

The present invention provides a method for optimization of active and passive beamforming and signal reception configuration of a dual IRSs-assisted ISAC system. By jointly optimizing active beamforming at a base station, the reception of a sensing signal by the base station, and passive beamforming at an IRS, the achievable rate of communication users is maximized while ensuring that the signal-to-noise ratio of the sensing signal meets the minimum requirement. In the present invention, to solve the complex nonconvex problem generated, first, fractional programming is used to decouple an optimization problem, then, a successive convex approximation algorithm and an alternating direction method of multipliers are used to transform an intractable nonconvex problem into multiple tractable subproblems, and finally, an alternative optimization method is used to efficiently solve for a high-quality sub-optimal solution. Simulation results show that the provided solution has good convergence and effectiveness, and the solution can effectively improve the performance of IRS-assisted ISAC systems.

Description

Active and passive beamforming and received signal optimization configuration method for dual-irs-assisted ISAC system TECHNICAL FIELD

[0001] The application belongs to the field of beamforming of Integrated Sensing And Communications (ISAC) system, and relates to an active and passive beamforming and received signal base station optimization configuration method of algorithms such as fractional programming, successive convex approximation and alternating direction multiplier method. BACKGROUND

[0002] In practical applications, the ISAC system faces challenges such as high environmental dependence, limited coverage range, and high cost and power consumption. In order to compensate for the high path loss of high-frequency signals in the ISAC system, large-scale MIMO technology is used to design dual-function transmit waveforms to obtain higher integration and coordination gain. At the same time, in order to avoid the deterioration of system performance in severe propagation conditions, the Intelligent Reflecting Surface (IRS) technology is considered to be applied to the ISAC system to expand the system coverage range and improve the communication and sensing performance.

[0003] Intelligent Reflecting Surface (IRS) technology breaks through the limitations of traditional wireless communication by constructing an intelligent controllable wireless environment, bringing a new paradigm to future mobile communication networks. Existing research shows that IRS can improve the spatial multiplexing capability of the system through distributed deployment, and can solve the channel rank deficiency problem of high-frequency communication. Inspired by this, researchers have applied IRS technology to the ISAC system, using the Signal-to-Noise Ratio (SNR) index to evaluate the Quality of Service (QoS) of sensing and communication. However, in previous work, the Base Station (BS) only serves one user and does not fully consider all possible paths of the transmit waveform. In the ISAC system, in addition to enhancing the Quality of Service (QoS) of sensing and communication, IRS can also be used to reduce Multi-User Interference (MUI) and ensure sensing performance in terms of transmit beam direction and Cramér-Rao lower bound. Inspired by the above research, some researchers propose that the dual-function BS continuously detects multiple targets and simultaneously serves multiple users through direct links between the BS and the users and the help of IRS.

[0004] However, most of the existing works simplify the system model and only consider the single-IRS-assisted ISAC system, and the system performance will be severely impaired once the channel conditions between the IRS and the user and the target become poor. Moreover, the interference of the base station end clutter on the radar target detection is ignored in the simplified system model, and only the target detection scheme in the ideal case is considered. Therefore, it is necessary to jointly design the active and passive beamforming of the base station and the double-IRSs and the reception of the sensing signal by the base station. SUMMARY

[0005] To solve the above technical problems, the present application provides a double-IRSs-assisted ISAC system active and passive beamforming and received signal optimization configuration method, which first converts a difficult-to-solve non-convex optimization problem into multiple easy-to-solve sub-problems using fractional programming, successive convex approximation and alternating direction multiplier method, and finally obtains a high-quality suboptimal solution through alternating optimization.

[0006] To achieve the above purpose, the technical scheme adopted by the present application is:

[0007] The double-IRSs-assisted ISAC system active and passive beamforming and received signal optimization configuration method comprises the following steps:

[0008] S1, model construction:

[0009] A double-IRSs-assisted ISAC system model is built, in which a multi-antenna base station provides communication services for multiple users and performs target sensing, and an IRS is used to assist the multi-antenna base station to work. At the same time, two IRSs are distributed and deployed on the surface of a building to establish reliable channels between the multi-antenna base station and the communication target and the sensing target.

[0010] S2, alternating optimization:

[0011] S21: First, the communication and sensing reliable channel is used to derive the communication user's signal-to-interference-and-noise ratio and the sensing target's signal-to-noise ratio lower bound. On this basis, an optimization problem is established: by jointly designing the active beamforming w of the base station end and the reception u of the sensing signal by the multi-antenna base station and the passive beamforming θ1, θ2 of the double-IRSs, under the target of maximizing the sum rate of the communication users, the sensing signal-to-noise ratio is ensured to meet the minimum requirement, and the power constraint of the base station end and the constant modulus constraint of the IRS are met,

[0012] S22: auxiliary variables β and ρ are introduced, and the fractional programming method is used to decouple the optimization problem,

[0013] S23: the auxiliary variables β and ρ are updated by taking partial derivatives, and u is updated using the Lagrange multiplier under the premise of given w, θ1, θ2, ρ, β,

[0014] S24: Given u, ρ, β, θ1, θ2, reformulate the original optimization problem as a second-order cone constraint, and use the CVX toolbox to solve and update w.

[0015] S25: Introducing auxiliary variables Given u, ρ, β, w, θ2, and the dual variable μ, the alternating direction multiplier method is used to update them sequentially. Update θ2 using the same method.

[0016] S26: Repeat S25 until the values ​​of θ1 and θ2 converge.

[0017] S27: Repeat steps S23, S24, S25, and S26 until the algorithm converges, finally obtaining the optimal solution w. opt ,u opt ,

[0018] As a preferred technical solution of the present invention:

[0019] The specific ISAC system model with dual IRSs assistance in step S1 is as follows:

[0020] In the ISAC system model assisted by two IRSs, a multi-antenna base station simultaneously performs multi-user communication and target detection with the assistance of two N-ary IRSs, as detailed below:

[0021] A multi-antenna base station is equipped with M transmitting antennas and M receiving antennas, arranged in a uniform linear array with half-wavelength intervals. It transmits data to K single-antenna users while simultaneously detecting T sensing targets. The transmitted signal of the multi-antenna base station is expressed as: x = Ws = W c s c +W r s r

[0022] in These are the communication beamforming matrix and the sensing beamforming matrix, respectively, vector Indicates satisfaction Communication signals, vector Indicates satisfaction The perceived signals are assumed to be statistically independent and satisfy the following conditions: Define the entire beamforming matrix as The emitted symbol vector is

[0023] As a preferred technical solution of the present invention, the reliable channel in step S1 is specifically as follows:

[0024] Considering the ISAC system model assisted by double IRSs in a crowded environment, the BS-IRS channel can be modeled as a Rician fading channel, which is expressed as follows:

[0025] where ω R is the Rician factor of the BS-IRS link, when it tends to infinity, it degenerates into the LoS scenario, when it tends to zero, it becomes a Rayleigh channel, is the Rayleigh fading component, each item satisfies CN(0, 1) distribution, is the LoS channel component, because the multi-antenna base station and the IRS are modeled as a uniform linear array (ULA) and a uniform planar array (UPA) respectively, G LoS The channel matrix can be expressed as:

[0026] where α is the large-scale channel gain, θ is a random phase uniformly distributed in [0, 2π], a T is the transmit steering vector of the BS, a R is the receive steering vector of the IRS, then the steering vector is expressed as:

[0027] a(θ)=[e-j2πd sin(θ) / λ,...,e-j2πd(M-1)sin(θ) / λ] T where d is the distance between the array elements, usually set to half the wavelength, λ is the signal wavelength;

[0028] The channel between the multi-antenna base station and each user is composed of two parts: the direct link between the BS-user and the cascaded link between the BS-IRSs-user, so the received signal of the multi-antenna base station at the kth user can be expressed as:

[0029] where defines the effective channel between the BS and the kth user, between IRS1 and the kth user, between IRS2 and the kth user, between the BS and IRS1, and between the BS and IRS2, respectively, the reflection matrix of the IRS is defined as where θ i =[θ i1 ,…,θ iN ] Τ is the reflection coefficient vector satisfying |θ in |=1, .

[0030] As a preferred technical solution of the present application: in step S21, the signal-to-interference-and-noise ratio is specifically as follows,

[0031] The scalar is the additive white Gaussian noise at the kth user, thus, the signal-to-noise ratio of the kth user can be calculated as:

[0032] For simplicity, redefine where w j denotes the jth column of the beamforming matrix W, i.e.

[0033] Considering the link blockage of the multi-antenna base station to the tth target, the echo signal received through the intelligent reflecting surface assisted path can be represented as:

[0034] Considering target detection under far-field conditions, α t denotes the radar cross section (RCS) of the tth target, i.e. α t = 4πP Δ / S, where P Δ denotes the radiation power density of the target scattered wave, and S denotes the power density of the incident wave. It is known that the perceived target signal-to-noise ratio is calculated by expectation, for the sake of simplifying the formula expression, use to represent the expectation value of α t , i.e. denote the baseband channels between IRS1, IRS2 and the tth target, respectively, and the vector denotes the additive white Gaussian noise, assuming that the path between the IRS and the target is LoS, and the required angle of arrival / departure (AoA / AoD) is known, the equivalent channel matrix of the echo signal is redefined as H t :

[0035] Define to represent the vectorization of the matrix W, as the Kronecker product, then y r,t can be re-expressed as:

[0036] As a preferred technical solution of the present application: in step S21, the signal-to-noise ratio is specifically as follows,

[0037] The multi-antenna base station is configured to process the received perception signal y r,t ,

[0038] i.e.:

[0039] Therefore, the signal-to-noise ratio of the tth perceived target is:

[0040] The numerator in the formula is complex and difficult to optimize, first redefine: E{SS H} = IK+M By substituting the formula and using Jensen inequality, i.e., E{f(x)}≥f(E{x}), the lower bound of the signal-to-noise ratio is obtained as follows:

[0041] As a preferred technical solution of the present application:

[0042] The optimization problem in step S21 is specifically as follows: the multi-antenna base station configures the receiving signal u and the passive beamforming Θ1 and Θ2 at the double IRS to maximize the achievable rate of multi-user communication while satisfying the worst-case sensing signal-to-noise ratio Γ t , the transmit power budget P and the unit modulus characteristic of the reflection coefficient, so the optimization problem is expressed as:

[0043] As a preferred technical solution of the present application: the optimization problem is transformed and optimized through steps S22-S24, specifically as follows:

[0044] First, the Lagrange dual transformation is used to introduce auxiliary variables ρ=[ρ1,ρ2,…,ρ K ] T , and the objective function is transformed into the following form:

[0045] By introducing auxiliary variables β=[β1,β2,…,β K ] T , the objective function is expanded into a quadratic term:

[0046] The new objective function becomes f(w,θ,ρ,β), which is transformed into a more concise form through equivalent transformation:

[0047] In the above formula, define , wherein And by defining the permutation matrix , w is extracted from w j ; for simplicity of expression, θ is used to represent θ1 or θ2, and is applied to obtain the equivalent expression of f(w,θ,ρ,β), and the definitions of the remaining variables except w are as follows:

[0048] Similarly, the definitions of the remaining variables except θ are as follows:

[0049] As a preferred technical solution of the present application: in steps S24-S27, an alternating optimization method is used to iteratively solve each optimization variable, specifically as follows:

[0050] Before optimizing the configuration u of the multi-antenna base station to the received signal, two auxiliary variables p and b are optimized first. The optimization of the auxiliary variable p is a convex problem without constraints, given b, u, w, 0i and 0 2, and the optimal solution of p can be obtained by taking the partial derivative of the objective function with respect to p

[0051] Similarly, given u, w, 0i and 0 2, let Next, fix other variables and optimize the configuration u of the multi-antenna base station, as follows:

[0052] First, the maximization problem is defined as follows:

[0053] The optimal solution u opt can be obtained by using the relevant knowledge of the Lagrange multiplier, and the result is:

[0054] Given p, b, u, 0i and 0 2, the optimization of the transmit beamforming w can be represented as:

[0055] Where the objective function is a non-convex function with respect to the perceived constraint C1, to handle this non-convex constraint, C1 is expressed in the form of a second-order cone constraint:

[0056] The optimization problem is redefined as:

[0057] At this time, the optimization problem becomes a simple convex problem, which can be solved by the CVX toolbox,

[0058] Given p, b, u, w, 0 2, the optimization problem about the reflection coefficient 0i becomes:

[0059] Because there is a hidden function about 0i in the radar constraint and the non-convex unit modulus constraint, it cannot be solved directly, therefore, first handle the non-convex constraint C1, that is, rewrite the expression about 0i on the left side of C1, and then find the surrogate function of C1 by the method of SCA, as follows:

[0060] First, expand the expression of H t :

[0061]

[0062] ​​​By utilizing the equivalent transformation Θ1z 1,t = diag{z 1,t}θ1, Θ1z 2,t = diag{z 2,t}θ1, Θ2z 2,t = diag{z 2,t}θ2, Θ2z 1,t = diag{z 1,t}θ2and vectorized extraction sandwich formula: Will be re-expressed as:

[0063] To simplify the expression form, define

[0064] Given that θ2is fixed, and The constraint condition becomes:

[0065] Where: Since is a convex function about θ1, it can be represented as a lower bound by using the SCA algorithm:

[0066] Next, redefine Then the perception constraint condition C1 can be re-expressed as:

[0067] Next, use the ADMM algorithm to solve the constant modulus constraint problem, as follows:

[0068] First, introduce auxiliary variables The optimization problem of solving θ1 is converted to:

[0069] Using the ADMM algorithm, the problem is further converted by augmenting the Lagrangian function:

[0070] Where is the dual variable, ξ>0 is a pre-set penalty parameter, and this multi-variable problem is solved by updating each variable alternately given the other variables:

[0071] Update θ1: Given and μ, the optimization problem about θ1 is a convex problem, which can be solved by using various efficient algorithms,

[0072] Update Given θ1 and μ, can be obtained by phase alignment:

[0073] Update mu: Given theta1 and The update of the dual variable mu is:

[0074] Given rho, beta, u, w, theta1, the optimization problem about the reflection coefficient theta2 is the same as optimizing theta1.

[0075] Compared with the prior art, the present application has the beneficial effects that:

[0076] The present application designs a dual-IRSs assisted ISAC system active and passive beamforming and sensing signal base station optimization method, first, a difficult to solve non-convex optimization problem is transformed into multiple easy to solve sub-problems by using fractional programming, successive convex approximation and alternating direction multiplier method, and finally a high-quality suboptimal solution is obtained by the method of alternating optimization, the dual-IRSs enhances the communication and target detection performance at the same time through its higher degree of freedom, to maximize the user's communication and rate, while the configuration optimization of the base station brings better target detection effect to the ISAC system, through simulation experiment, the dual-IRSs assisted ISAC system active and passive beamforming and receiving signal optimization configuration method can significantly improve the overall performance of the system, the present application fully utilizes the array gain brought by the dual-IRSs and the suppression of interference by the base station, and good performance improvement is achieved. BRIEF DESCRIPTION OF DRAWINGS

[0077] Fig. 1 is a practical scene diagram of a dual-IRSs assisted ISAC system;

[0078] Fig. 2 is a simulation scene diagram of a dual-IRSs assisted ISAC system;

[0079] Fig. 3 is a curve of system sum rate and iteration number;

[0080] Fig. 4 is a curve of system sum rate and maximum base station transmit power P;

[0081] Fig. 5 is a curve of system sum rate and IRS element number N;

[0082] Fig. 6 is a curve of system sum rate and sensing signal SNR requirement;

[0083] Fig. 7 is a parameter setting table of the dual-IRSs assisted ISAC system active and passive beamforming and receiving signal optimization configuration method;

[0084] [Corrected according to Rule 91 on 07.02.2025] DETAILED DESCRIPTION

[0085] The present application will be further described in detail below in combination with the drawings and specific embodiments:

[0086] The application proposes a dual-IRSs assisted ISAC system active and passive beamforming and received signal optimization configuration method, including the following steps:

[0087] S1, model construction:

[0088] A dual-IRSs assisted ISAC system model is built, wherein a multi-antenna base station provides communication services for multiple users while perceiving targets, and an IRS is used to assist the multi-antenna base station to work, and meanwhile, two IRSs are distributed and deployed on the surface of a building to establish reliable channels between the multi-antenna base station and the communication targets and the perception targets;

[0089] S2, alternating optimization:

[0090] S21: First, the signal-to-interference-and-noise ratio of the communication users and the signal-to-noise ratio lower bound of the perception targets are derived according to the reliable channels for communication and perception, and on this basis, an optimization problem is established: by jointly designing the active beamforming w of the base station end and the reception u of the base station to the perception signal and the passive beamforming θ1, θ2 of the dual IRSs, the perception signal-to-noise ratio is ensured to meet the minimum requirement under the goal of maximizing the sum rate of the communication users, and the power constraint of the base station end and the constant modulus constraint of the IRS are met,

[0091] S22: auxiliary variables β and ρ are introduced, and the optimization problem is decoupled by using the fractional programming method,

[0092] S23: auxiliary variables β and ρ are updated by taking partial derivatives, and under the premise of given w, θ1, θ2, ρ, β, u is updated by using the Lagrange multiplier,

[0093] S24: under the condition of given u, ρ, β, θ1, θ2, the original optimization problem is re-expressed as a second-order cone constraint, and w is solved and updated by using the cvx toolbox,

[0094] S25: auxiliary variables and dual variables μ are introduced, and under the condition of given u, ρ, β, w, θ2, is sequentially updated by using the alternating direction multiplier method, is updated by using the same method,

[0095] S26: repeat S25 until the values of θ1, θ2 converge,

[0096] S27: repeat steps S23, S24, S25, and S26 until the algorithm converges, and finally obtain the optimal solution w opt , opt ,

[0097] The model construction is specifically as follows:

[0098] As shown in Figure 1, this invention constructs an ISAC system model assisted by dual IRSs. One of the multi-antenna base stations performs target detection while providing communication services to multiple users. Considering that there are obstacles between the target and the base station, a reliable link between the base station and the target is constructed using IRSs to realize the sensing function.

[0099] In the ISAC system model assisted by two IRSs, a multi-antenna base station simultaneously performs multi-user communication and target detection with the assistance of two N-ary IRSs, as follows: The multi-antenna base station is equipped with M transmit antennas and M receive antennas, arranged in a uniform linear array (ULA) with half-wavelength spacing. While transmitting data to K single-antenna users, it detects T sensed targets. The transmit signal of the multi-antenna base station is expressed as: x = Ws = W c s c +W r s r

[0100] in These are the communication beamforming matrix and the sensing beamforming matrix, respectively. (Vector) Indicates satisfaction Communication signals, vector Indicates satisfaction The perceived signals. Assume they are statistically independent and satisfy... For the sake of simplicity, the entire beamforming matrix is ​​defined as The emitted symbol vector is

[0101] In a real-world scenario, considering the ISAC system in a congested environment, the channel between the BS and IRS can be modeled as a Ricean fading channel, as follows:

[0102] Where ω R It is the Rice factor of the BS-IRS link. When it approaches infinity, it degenerates into the Loss of Space (LoS) scenario. When it approaches zero, it becomes a Rayleigh channel. For each of the Rayleigh fading components, the term satisfies the CN(0,1) distribution. For the line-of-sight channel components, since the base station and IRS are modeled as a uniform linear array (ULA) and a uniform area array (UPA) respectively, G LoS The channel matrix can be represented as:

[0103] Where α is the large-scale channel gain, and θ is a random phase uniformly distributed in [0, 2π]. T For the BS's transmission guidance vector, a R The steering vector is used to receive the IRS. Therefore, the steering vector is represented as:

[0104] a(θ) = [e-j2πd sin(θ) / λ,...,e-j2πd(M-1)sin(θ) / λ] T where d is the distance between the array elements, usually set to half wavelength, λ is the signal wavelength.

[0105] In the communication system model of the present application, the channel between the multi-antenna base station and each user is composed of two parts, the direct link of BS-user and the cascaded link of BS-IRSs-user, so the received signal of the multi-antenna base station at the kth user can be expressed as:

[0106] where define the effective channels between BS and the kth user, IRS1 and the kth user, IRS2 and the kth user, BS and IRS1, and BS and IRS2, respectively. The reflection matrix of IRS is defined as where θ i = [θ i1 ,..., θ iN ] Τ is the reflection coefficient vector satisfying |θ in | = 1, is the Additive White Gaussian Noise (AWGN) at the kth user. Therefore, the Signal and Interference to Noise Ratio (SINR) of the kth user can be calculated as:

[0107] For simplicity, redefine where w j denotes the jth column of the beamforming matrix W, i.e.

[0108] In the perception model of the present application, considering the link blockage of the multi-antenna base station to the tth target, the echo signal received through the intelligent reflecting surface assisted path can be expressed as:

[0109] The present application considers target detection under far-field conditions, α t denotes the Radar Cross Section (RCS) of the tth target, i.e. α t = 4πP Δ / S, where P Δ denotes the radiation power density of the target scattered wave, and S denotes the power density of the incident wave. It is known that the perception target signal-to-noise ratio is calculated by expectation, for simplicity of formula expression, the following is used​ denotes the expectation value of a t denote the baseband channels between IRS1, IRS2 and the t-th target, respectively, and denotes the additive white Gaussian noise. The present invention assumes LoS paths between the IRS and the targets, and the required angles of arrival / departure (AoA / AoD) are known. For simplicity, the equivalent channel matrix of the echo signal is redefined as t :

[0110] denote the baseband channels between IRS1, IRS2 and the t-th target, respectively, and denotes the vectorization of the matrix W, is the Kronecker product, then y r,t can be re-expressed as:

[0111] Meanwhile, the present invention considers the multi-antenna base station reception optimization of the sensing signal, because there are clutter signals in the received sensing signal at the multi-antenna base station end, in order to obtain satisfactory target detection performance, the multi-antenna base station configuration is further optimized in the present invention to process the received sensing signal y r,t , i.e.:

[0112] Therefore, the signal-to-noise ratio of the t-th sensing target is:

[0113] The numerator in this formula is complex and difficult to optimize, so first redefine: E{SS H} = I K+M Make formula substitution, and then use Jensen's inequality, i.e. E{f(x)} ≥ f(E{x}), so the obtained signal-to-noise ratio lower bound is:

[0114] The specific alternation optimization is as follows:

[0115] The object of the present invention is to jointly optimize the active beamforming W at the multi-antenna base station end, the reception configuration u of the sensing signal by the multi-antenna base station and the passive beamforming Θ1 and Θ2 at the double IRS to maximize the achievable sum rate of multi-user communication while satisfying the worst-case sensing signal-to-noise ratio Γ t , the transmit power budget P and the unit modulus characteristic of the reflection coefficient. Therefore, the problem is formulated as:

[0116] ​To address the aforementioned non-convex problem, this paper considers the joint optimization design of active and passive beamforming in a dual IRSs-assisted ISAC system and the reception of sensing signals by a multi-antenna base station, maximizing system communication performance while ensuring the sensing signal meets the minimum SNR requirement. However, due to the coupling variables between the objective function and the sensing signal SNR in constraint C1, and the unity modulus constraint problem caused by the IRS in constraint C3, the entire optimization problem is coupled and non-convex, making it difficult to solve. This invention proposes to transform the problem into multiple easily tractable subproblems using fractional programming (FP), successive convex approximation (SCA) algorithms, and the alternating direction multiplier method (ADMM), and then iteratively solve them based on the alternating optimization method.

[0117] Due to the presence of logarithmic and fractional terms, the objective function is quite complex, which can be simplified using the Closed-Form FP Approach. First, an auxiliary variable ρ = [ρ1, ρ2, ..., ρ] is introduced through Lagrange duality. K ] T The objective function is transformed into the following form:

[0118] By introducing auxiliary variables β = [β1, β2, ..., β] K ] T Expand the objective function using quadratic terms:

[0119] The new objective function becomes f(w,θ,ρ,β), which can be simplified to a more concise form through equivalent transformations:

[0120] In the above formula, we define in And by defining the permutation matrix Extract w from w j To simplify the expression, θ is used to represent θ1 or θ2. The equivalent expression for f(w,θ,ρ,β) is obtained, and the variables other than w are defined as follows:

[0121] Similarly, the other variables besides θ are defined as follows:

[0122] After transforming the problem into an optimization problem through the above steps, we will now use an alternating optimization method to iteratively solve for each optimization variable. Before optimizing the configuration u of the received signal for the multi-antenna base station, we will first optimize the two auxiliary variables ρ and β. Given β, u, w, θ1, and θ2, the optimization of the auxiliary variable ρ is an unconstrained convex problem, which can be solved by taking partial derivatives. Its optimal solution can be easily obtained.

[0123] Similarly, given u, w, θ1, and θ2, let be solved

[0124] Next, fix other variables to optimize u for multi-antenna base station. But in the actual optimization process, the method of solving the appropriate value of u by fixing other variables will lead to the lack of explicit target feasibility check problem. In order to accelerate convergence and create more degrees of freedom in subsequent iterations to maximize the system sum rate, the method of updating u by maximizing the lower bound of signal-to-noise ratio is proposed. First, the maximization problem is defined as follows:

[0125] The optimal solution u opt can be obtained by using the knowledge of the Rayleigh quotient, and the result is:

[0126] Given ρ, β, u, θ1, and θ2, the optimization of transmit beamforming w can be represented as:

[0127] Where the objective function is a non-convex function with respect to the perceived constraint C1, to handle this non-convex constraint, C1 is represented in the form of a second-order cone constraint:

[0128] The optimization problem is redefined as:

[0129] At this time, the optimization problem becomes a simple convex problem, which can be solved by CVX toolbox.

[0130] Given ρ, β, u, w, θ2, the optimization problem about the reflection coefficient θ1 becomes:

[0131] Because there are implicit functions about θ1 in the radar constraint and the non-convex unit modulus constraint, it cannot be solved directly. First, handle the non-convex constraint C1, that is, rewrite the expression about θ1 on the left side of C1, and then find the surrogate function of C1 by the method of SCA. First, expand the expression of H t :

[0132] By using the equivalent transformation Θ1z 1,t = diag{z 1,t}θ1, Θ1z 2,t = diag{z 2,t}θ1, Θ2z 2,t= diag{z 2,t}θ2, Θ2z 1,t = diag{z 1,t}θ2and vectorized extraction sandwich formula: will be restated as:

[0133] To simplify the expression, define

[0134] Given that θ2is fixed, and The constraint condition becomes:

[0135] where: Since is a convex function about θ1, its lower bound can be represented by using the SCA algorithm:

[0136] Therefore, its lower bound can be represented by using the SCA algorithm:

[0137] Next, redefine Then the perception constraint condition C1 can be re-expressed as:

[0138] Next, the ADMM algorithm is used to solve the constant modulus constraint problem. Specifically, first introduce auxiliary variables The optimization problem of θ1 is converted to:

[0139] Using the ADMM algorithm, the problem is further converted by augmenting the Lagrangian function:

[0140] where is the dual variable, and ξ > 0 is a pre-set penalty parameter. This multi-variable problem can be solved by updating each variable alternately given the other variables:

[0141] Update θ1: Given and μ, the optimization problem about θ1 is a convex problem, which can be easily solved by using various existing efficient algorithms.

[0142] Update Given θ1 and μ, can be easily obtained by phase alignment:

[0143] Update μ: Given θ1 and The update of the dual variable μ is: ​

[0144] Given ρ, β, u, w, θ1, the optimization problem about the reflection coefficient θ2 is the same as optimizing θ1.

[0145] [Corrected according to Rule 91 on 07.02.2025]

[0146] Experimental results:

[0147] The simulation experiments of the application are realized by MATLAB simulation software, as shown in FIG. 2, considering a 3D topology simulation area, and the parameter design of simulation is shown in FIG. 7. Firstly, the convergence of the proposed algorithm is verified by simulation and compared with other algorithms, then through the proposed algorithm, the relationship between the maximum reachable rate of communication users and the multi-antenna base station transmission power, the number of IRS elements and the minimum requirement of the sensing signal SNR is studied under the condition of ensuring the minimum requirement of the sensing signal SNR.

[0148] The simulation results are shown in FIGS. 3, 4, 5 and 6. FIG. 3 is a curve diagram of the system sum rate changing with the iteration number. It can be seen from the simulation results that when the transmitting and receiving antennas are both 16, the three schemes can all reach a stable state after 8 iterations. However, the design scheme proposed in the application can realize convergence after about 5 iterations, which proves that the scheme has good convergence performance. And compared with the single IRS optimization scheme and the double IRSs random phase scheme, the proposed algorithm can bring about 3dB of additional gain, further verifying the high efficiency of the scheme of the application.

[0149] FIG. 4 shows the influence of the transmission power P on the system sum rate. In order to verify the effectiveness of the proposed algorithm, the scheme is compared with the single IRS optimization, the double IRSs random phase shift and the optimization scheme considering only communication, wherein the scheme considering only communication is used as the benchmark of the upper limit of the system performance. The simulation results show that as the maximum transmission power of the multi-antenna base station increases, the system sum rate also increases. The scheme proposed in the application utilizes the double IRSs to provide a more stable transmission link, thereby bringing a performance improvement of more than 1dB compared with the single IRS optimization; and compared with the random IRS phase, it can bring a performance improvement of 3dB. At the same time, under the condition of the same maximum transmission power P, as the number of antennas M increases, the system sum rate under different schemes also increases, indicating the influence of spatial degrees of freedom on system performance, the higher the spatial degrees of freedom, the better the system performance. In addition, since the proposed algorithm needs to trade off between communication and sensing performance, there is a certain performance difference compared with the scheme considering only communication system.

[0150] Fig. 5 is a diagram of system sum rate and rate varying with the number of IRS elements N, which increases from 20 to 120. It can be seen from the simulation results that the system performance is improved with the increase of the number of IRS elements N, which further proves that the higher the spatial degrees of freedom of the system, the better the performance gain achieved. In the case of the same number of antennas M, the scheme proposed in the present application improves the propagation environment by utilizing more DoFs through double IRSs, and the performance is improved by 1.2 dB compared with the single IRS system. In the case of random phase for both double IRSs, because the IRS phase is not optimized, the system performance gain changes slowly, and the performance is reduced by about 2 dB compared with the single IRS scheme, which indicates the effectiveness of the algorithm proposed in the present application.

[0151] Finally, Fig. 6 shows the impact of the minimum requirement of sensing signal SNR on the system sum rate and rate. According to the simulation results, in the case of small minimum requirement of sensing signal SNR, whether assisted by double IRSs or single IRS, the user has a higher achievable sum rate and rate. However, with the increase of the minimum requirement of sensing signal SNR, the overall performance of the system is inhibited, resulting in a significant decrease in the achievable sum rate and rate of the user. Especially when the minimum requirement of sensing signal SNR increases to 14 dB, the gain effect of the single IRS assisted system is minimal, while the double IRSs rely on a better and more stable connection with the system, and still achieve a performance improvement of more than 1 dB compared with the single IRS scheme in the case of severe constraint on the system performance, which shows the superiority of the proposed scheme. From the simulation results, it can be clearly seen that there is a trade-off between multi-user communication performance and target detection. With the increase of the minimum requirement of sensing signal SNR, more resources need to be allocated for target detection, which will inevitably sacrifice the user communication performance. Therefore, in the ISAC system, the resource allocation between communication and radar needs to be reasonably considered. The above simulation results prove the superiority of double IRSs in improving the performance of the ISAC system and the effectiveness of the joint optimization scheme proposed in the present application.

[0152] The application researches the active and passive beamforming and receiving signal optimization configuration method of the double IRSs assisted ISAC system. The double IRSs enhance the communication and target detection performance at the same time through its higher degree of freedom, to maximize the user's communication and rate, and the configuration optimization of the base station brings better target detection effect to the ISAC system. Under the consideration of the radar signal-to-noise ratio, transmission power budget and IRS reflection coefficient and other constraint conditions, the application proposes a novel joint beamforming and reflection design scheme of the double IRSs assisted ISAC system, and solves the complex optimization problem by using fractional programming, successive convex approximation, alternating direction multiplier method and alternating optimization method. The simulation results show that the active and passive beamforming and receiving signal optimization configuration method of the double IRSs assisted ISAC system can significantly improve the overall performance of the system. In future work, we can further study the application of the IRS assisted ISAC system under the condition of imperfect channel and multiple targets.

[0153] The application designs an active and passive beamforming and perception signal base station optimization method of a double IRSs assisted ISAC system, first uses fractional programming, successive convex approximation and alternating direction multiplier method to transform a difficult to solve non-convex optimization problem into multiple easy to solve sub-problems, and finally obtains a high-quality suboptimal solution through the alternating optimization method, the double IRSs enhance the communication and target detection performance at the same time through its higher degree of freedom, to maximize the user's communication and rate, and the configuration optimization of the base station brings better target detection effect to the ISAC system, through simulation experiment, the active and passive beamforming and receiving signal optimization configuration method of the double IRSs assisted ISAC system can significantly improve the overall performance of the system, the application fully utilizes the array gain brought by the double IRSs and the interference suppression of the base station, and good performance improvement is achieved.

[0154] The above description is only a preferred embodiment of the application, and does not limit the application in any other form, and any modification or equivalent change made according to the technical essence of the application still belongs to the scope of the application claimed.

Claims

1. A method for active and passive beamforming and received signal optimization configuration of a dual-IRSs-assisted ISAC system, characterized in that: Comprising the following steps: S1, model construction: A dual-IRSs assisted ISAC system model is built, wherein a multi-antenna base station provides communication services for multiple users while performing target detection, and an IRS is used to assist the multi-antenna base station in operation, and meanwhile, reliable channels between the multi-antenna base station and the communication target and the detection target are established by deploying two IRSs on the surface of a building; S2, alternating optimization: S21: First, the signal-to-interference-and-noise ratio of the communication user and the signal-to-noise ratio lower bound of the detection target are derived based on the reliable channels for communication and detection, and an optimization problem is established: by jointly designing the active beamforming w of the base station end and the reception u of the multi-antenna base station to the detection signal and the passive beamforming θ1, θ2 of the dual IRSs, the sum rate of the communication users is maximized under the condition that the detection signal-to-noise ratio meets the minimum requirement and the power constraint of the base station end and the constant modulus constraint of the IRS are satisfied, S22: Auxiliary variables β and ρ are introduced, and the optimization problem is decoupled by using the fractional programming method, S23: The auxiliary variables β and ρ are updated by taking partial derivatives, and u is updated by using the KKT multiplier under the condition that w, θ1, θ2, ρ, β are given, S24: Under the condition that u, ρ, β, θ1, θ2 are given, the original optimization problem is represented as a second-order cone constraint, and w is updated by using the cvx toolbox, S25: Introducing auxiliary variables and the dual variable μ, given u, p, β, w, θ2, θ1is updated using the alternating direction method of multipliers, μ, θ2 is updated by using the same method, S26: Repeat S25 until the values of θ1, θ2 converge, S27: repeat steps S23, S24, S25, S26 until the algorithm converges, finally obtaining the optimal solution w opt u opt , 2. The dual-IRSs-aided ISAC system active-passive beamforming and received signal optimization configuration method of claim 1, wherein: In step S1, the dual-IRSs assisted ISAC system model is as follows, In the dual-IRSs assisted ISAC system model, a multi-antenna base station performs multi-user communication and target detection under the assistance of two N-element IRSs, which is as follows: The multi-antenna base station is equipped with M transmit antennas and M receive antennas arranged in a uniform linear array with half-wavelength spacing, and transmits data to K single-antenna users while detecting T detection targets, and the transmit signal of the multi-antenna base station is represented as: x = Ws = W c s c +W r s r wherein are a communication beamforming matrix and a sensing beamforming matrix, respectively, and vector satisfies communication signals, vector satisfies the perception signals of the other users, assuming that they are statistically independent from each other and satisfy The entire beamforming matrix is defined as The transmit symbol vector is 3. The dual-IRSs-aided ISAC system active-passive beamforming and received signal optimization configuration method of claim 1, wherein: In step S1, the reliable channel is as follows, Considering the dual-IRSs-assisted ISAC system model in a crowded environment, the BS and IRS can be modeled as a Rician fading channel, represented as follows: where ω R is the Rician factor of the BS-IRS link, which tends to infinity for the LoS scenario and to zero for the Rayleigh channel, for the Rayleigh fading component, each term satisfies CN(0, 1) distribution, For the line-of-sight channel component, since the multi-antenna base station and the IRS are modeled as a uniform linear array (ULA) and a uniform planar array (UPA), respectively, G LoS The channel matrix can be expressed as: where a is the large-scale channel gain, 0 is a random phase uniformly distributed in [0, 2p], a T is the transmit steering vector of the BS, a R is the receive steering vector of the IRS, then the steering vector is represented as: a(0) = [e-j2pdsin(0) / l,..., e-j2p d(M-1)sin(0) / l] T where d is the distance between the array elements, usually set to half the wavelength, l is the signal wavelength; The channel between the multi-antenna base station and each user is composed of two parts, the direct link of BS-user and the concatenated link of BS-IRSs-user, so the received signal at the multi-antenna base station to the kth user can be expressed as: wherein The effective channels between the BS and the k-th user, between IRS1 and the k-th user, between IRS2 and the k-th user, between the BS and IRS1, and between the BS and IRS2 are defined respectively, and the reflection matrix of the IRS is defined as where θ i = [θ i1 ,...,θ iN ] Τ satisfies The reflection coefficient vector of the IRS.

4. The dual-IRSs assisted ISAC system active and passive beamforming and received signal optimization configuration method of claim 1 or 3, wherein: In step S21, the signal-to-interference-and-noise ratio is as follows, scalar is the additive white Gaussian noise at the kth user, and thus the signal-to- interference-plus-noise ratio (SINR) of the kth user can be computed as: For brevity, redefined where w j denotes the jthcolumn of the beamforming matrix W, i.e. Considering the link blockage of the multi-antenna base station to the t-th target, the echo signal received through the intelligent reflecting surface assisted path can be represented as: Consider target detection in far field conditions, α t represents the radar cross section (RCS) of the tth target, i.e. α t = 4πP Δ / S, where P Δ represents the radiated power density of the target scattered wave, S represents the power density of the incident wave, it is known that the perception target signal-to-noise ratio is calculated by expectation, for the sake of simplifying the formula expression, use represents a t the desired value of respectively denote the baseband channels between IRS1, IRS2 and the t-th target, and the vector denotes additive white Gaussian noise, assuming the path between the IRS and the target is LoS, and the required angle of arrival / departure (AoA / AoD) is known, the equivalent channel matrix of the echo signal is redefined as H t : Definitions denotes vectorization of the matrix W, For the Kronecker product, then y r,t may be re-expressed as:

5. The dual-IRSs assisted ISAC system active and passive beamforming and received signal optimization configuration method of claim 1 or 3, wherein: In step S21, the signal-to-noise ratio lower bound is as follows, Multi-antenna base station configuration to process the received perception signal y r,t i.e. Thus, the signal-to-noise ratio of the tth perceived target is: The numerator of the formula is complex and difficult to optimize. Redefine: E{SS H} = I K+M Substitute the formula, and use Jensen's inequality, i.e., E{f(x)}≥f(E{x}), thus the lower bound of the signal-to-noise ratio is obtained as:

6. The dual-IRSs-aided ISAC system active-passive beamforming and received signal optimization configuration method of claim 1, wherein: The optimization problem in step S21 is formulated as follows, the multi-antenna base station receives the sensing signal configuration u and the passive beamforming Θ1 and Θ2 at the dual-IRS to maximize the achievable sum rate of multi-user communication while satisfying the worst-case sensing signal-to-noise ratio Γ t , the transmit power budget P and the unit modulus property of the reflection coefficient, so the optimization problem is expressed as:

7. The dual-IRSs-aided ISAC system active-passive beamforming and received signal optimization configuration method of claim 6, wherein: The optimization problem is transformed and optimized by steps S22-S24, which is as follows: First, by Lagrange dual transformation, introduce auxiliary variables ρ = [ρ1, ρ2,..., ρN]T, and the target function is transformed into the following form: K ] T , where the first term is the original target function, and the second term is the Lagrange function. By introducing auxiliary variables β = [β1, β2,..., β K ] T The objective function is quadraticly expanded: The new objective function becomes f(w, θ, p, β) which is reduced to a more compact form by an equivalent transformation: In the above formula, the definitions are wherein and by definition the permutation matrix Implementing extraction of w from w j ; for simplicity of expression, use θ to represent θ1 or θ2, apply An equivalent expression for f(w, θ, p, β) is obtained, with the remaining variables defined as follows: By analogy, the remaining variables, except θ, are defined as follows:

8. The dual-IRSs-aided ISAC system active-passive beamforming and received signal optimization configuration method of claim 6, wherein: In steps S24-S27, each optimization variable is iteratively solved by using the alternating optimization method, which is as follows: Before optimizing the configuration u of the multi-antenna base station to the received signal, two auxiliary variables p and β are optimized first. The optimization of the auxiliary variable p is a convex problem without constraints, by solving the partial derivative optimal solution can be obtained By analogy, in the case of a given u, w, θ1, and θ2, let obtained Next, fix other variables, and optimize the multi-antenna base station configuration u, which is as follows: First, the maximization problem is defined as follows: Optimal solution u opt This can be found by using the relevant knowledge of the Swinburne, and the result is: The optimization of the transmit beamforming w, given p, b, u, 0i and 0 2, can be expressed as: where the objective function is non-convex with respect to the constraint C1 of perception, to handle this non-convex constraint, C1 is expressed in the form of a second-order cone constraint: The optimization problem is redefined as: At this time, the optimization problem becomes a simple convex problem, which can be solved by the CVX toolbox. Given p, b, u, w, 0 2, the optimization problem about the reflection coefficient 0 1 becomes: Because there is a hidden function about θ1 in the radar constraint and the non-convex unit modulus constraint, it cannot be directly solved, therefore, first process the non-convex constraint C1, that is, rewrite the expression about θ1 on the left side of C1, and then find the proxy function of C1 by the SCA method, which is as follows: H t The expression is expanded: By utilizing the equivalence transformation Θ1z 1,t = diag{z 1,t}θ1, Θ1z 2,t = diag{z 2,t}θ1, Θ2z 2,t = diag{z 2,t}θ2, Θ2z 1,t = diag{z 1,t}θ2and the vectorized extraction sandwich formula: Will Rephrased as: To simplify the expression form, define θ2 is known to be fixed, and The constraint becomes: wherein: Due to is a convex function with respect to θ1, so its lower bound can be represented by SCA algorithm: Next, redefine So the perception constraint C1 will be re-expressed as: Next, the ADMM algorithm is used to solve the constant modulus constraint problem, which is as follows: First, introduce auxiliary variables The optimization problem to solve for θ1is transformed into: Using the ADMM algorithm, the problem is further transformed into: wherein is a dual variable, ξ>0 is a pre-set penalty parameter, and this multi-variable problem is solved by alternately updating each variable under the condition that other variables are given: Update θ1: Given and μ, the θ1 optimization problem about is a convex problem, which can be solved by using various existing efficient algorithms, update Given θ1and μ, may be obtained by phase alignment: Update μ: Given θ1and The update of the dual variable μ is: In the case of given p, b, u, w, 0i, the optimization problem about the reflection coefficient 0i is the same as the optimization of 0i.

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