Beam forming design method of active RIS-assisted ISAC system

Abstract

The invention relates to a beam forming design method of an active RIS-assisted ISAC system, and belongs to the field of communication perception integration. A multi-user large-scale multiple-input single-output system model assisted by communication and perception integration and a system model based on an ISAC system assisted by an active RIS are constructed, and a beam forming vector and a reflection coefficient of the active RIS are respectively optimized by adopting an alternating optimization algorithm. According to the method, the propagation blockage problem is solved, the system performance is further improved, the multiplicative fading effect problem of the passive RIS is solved by using the active RIS, the weighted minimum mean square error algorithm, the continuous convex approximation algorithm and the positive semidefinite relaxation algorithm are combined, the system effectiveness is improved to the maximum extent, and the system performance is improved to the maximum extent. The system utility is the sum of the weighted sum rate of the system and the target detection power, the target detection capability is remarkably enhanced while the weighted sum rate of the user is improved, and a new solution is provided for performance optimization of the ISAC system.

Description

Technical Field

[0001] The present invention belongs to the field of communication and sensing integration, and specifically relates to a method for beamforming design using an active RIS in a communication and sensing integrated system. Background Art

[0002] In recent years, with the rapid development of communication technologies, the communication rate has been continuously improved, and the boundary between communication and radar sensing in spectrum usage has become increasingly blurred, making the problem of scarce spectrum resources more prominent. This phenomenon has attracted extensive attention to communication and sensing integration technology. This technology integrates communication and sensing functions into the same system and effectively improves the spectrum utilization rate by sharing system resources and signal processing algorithms. Currently, communication and sensing integration technology is regarded as one of the important key technologies in the B5G and 6G eras.

[0003] With the continuous development of 5G massive multiple-input multiple-output (MIMO) antenna array technology and millimeter-wave communication technology, the communication and radar sensing capabilities of the networking system have been greatly enhanced. However, the problem of interference management conflicting with multi-user requirements remains intractable and needs to be optimized through beamforming design. How to ensure the efficient utilization of system resources and the robustness of the system has become the key. To solve this problem, researchers have begun to consider applying integrated sensing and communication (ISAC) technology to the networking system. By equipping base stations with communication and radar sensing functions to transmit ISAC signals, both communication with users and sensing target tasks can be carried out simultaneously, improving the spectrum resource utilization rate and the communication performance of the system. However, there are still many problems in the beamforming design of the ISAC system. First, most existing ISAC systems rely on direct channels for propagation. In complex urban environments or scenarios with severe blockages, the establishment of communication links and sensing capabilities are often greatly restricted. Therefore, reconfigurable intelligent surface (RIS) has become an important technical means to improve communication and sensing performance. By adjusting the amplitude and phase of the reflection units, it can construct an ideal channel environment and enhance the propagation performance of signals in complex scenarios. Passive RIS is an array composed of a large number of passive components. An important advantage of it is that the introduced noise can be ignored, thus achieving a high array gain. Second, although many researchers have used passive RIS to solve the above problems, in practice, it only observes significant performance gains in communication scenarios where the direct link between the transmitter and the receiver is completely blocked or very weak. In many cases where the direct link is not weak, passive RIS can only achieve limited performance gains because of the influence of the "multiplicative fading" effect introduced by RIS, that is, the equivalent path loss of the transmitter-RIS-receiver link is the product (rather than the sum) of the path losses of the transmitter-RIS and RIS-receiver links. To solve this problem, researchers have begun to consider applying active RIS to the ISAC system. Active RIS can overcome the performance bottleneck caused by the "multiplicative fading" effect of passive RIS. Different from passive RIS that only reflects signals without amplification, its key feature is to integrate a reflective amplifier into the reflection element to actively reflect and amplify signals, which not only effectively solves the common propagation blockage problem in traditional ISAC systems, but also breaks through the performance gain bottleneck of passive RIS. Therefore, it is very important to make better use of it in the beamforming design process to improve the signal transmission quality and sensing quality of the system. Summary of the Invention

[0004] The present invention provides a beamforming design method for an active RIS-assisted ISAC system, which is based on the beamforming design of a multi-user multiple-input single-output system empowered by ISAC with active RIS. Under the constraints of the total transmission power of the base station and the reflection power of the active RIS, a joint optimization problem model regarding the base station transmit beamforming vector and the reflection coefficient matrix of the active RIS is established to maximize the weighted sum rate of the users and the target detection power, and a convex optimization algorithm of weighted minimum mean square error, successive convex approximation, and semidefinite relaxation is used to solve the optimization problem. The signal transmission quality and sensing quality of the system can be significantly improved through the amplification mechanism of the active RIS.

[0005] The technical solution adopted by the present invention includes the following steps:

[0006] Step 1: Construct an ISAC-assisted multi-user large-scale multiple-input single-output (MU-MISO) system model:

[0007] Step 2: Construct a system model of an active RIS-assisted ISAC system:

[0008] Step 3: Under the constraints of the total transmission power of the base station and the reflection power of the active RIS, establish a joint optimization problem model regarding the base station beamforming vector and the reflection coefficient matrix of the active RIS to maximize the system weighted sum rate and the target detection power;

[0009] Step 4: Use an alternating optimization algorithm combining weighted minimum mean square error (WMMSE), successive convex approximation (SCA), and semidefinite relaxation (SDR) to solve the optimization problem in the joint optimization model.

[0010] In step 1 of the present invention, a base station BS equipped with M transmit and receive antennas serves K users simultaneously and detects the target. The M antennas are arranged in a uniform linear array (ULA) with a half-wavelength spacing. In addition, N active RIS elements are deployed near the users to improve the weighted sum rate.

[0011] The construction method in step 2 of the present invention includes: assuming perfect channel state information (CSI), adopting shared deployment, and using all antennas for communication and sensing simultaneously;

[0012] The communication model is:

[0013]

[0014] The above is the received signal of user k, where and respectively represent the channels from the RIS to the k-th user, from the BS to the RIS, and from the BS to the k-th user. The vector Denote the beamforming vector of user j, and the entire beamforming matrix is Since an additional reflective amplifier is integrated on the electromagnetic element, the reflection coefficient of the nth element of the active RIS can be expressed as where a n and represent the amplitude and phase shift respectively. Considering the actual amplification ability of the amplifier, assume that the amplitude a n is constrained by the maximum amplification gain, that is Let represent the reflection coefficient matrix of the active RIS, s j represents the communication symbol of user j, satisfying and are the dynamic noise introduced by the active RIS and the additive Gaussian white noise AWGN of the kth user respectively. Therefore, the signal-to-interference-plus-noise ratio SINR of the kth user is calculated as:

[0015]

[0016] where, define as the composite channel from the base station BS to the kth user. From formula (2), the signal-to-interference-plus-noise ratio of user k is obtained. The signal-to-interference-plus-noise ratio depends on the beamforming vector of the base station BS and the reflection coefficient matrix of the active RIS. Through the signal-to-interference-plus-noise ratio, the achievable rate of user k can be obtained, which is expressed as:

[0017] R k = log2(1 + γ k ) (3)

[0018] The weighted sum rate of the system is expressed as:

[0019]

[0020] The sensing metric is the detection power in the direction:

[0021]

[0022] where, is expressed as the covariance matrix of the beamforming vector, and the vector represents the transmission steering vector relative to the angle . Since the antennas are uniformly linearly arranged at the BS, the steering vector is:

[0023]

[0024] where d is the antenna spacing between the arrays, and λ represents the signal wavelength.

[0025] The joint optimization model established in step 3 of the present invention is expressed as:

[0026] Under the constraints of the total transmission power of the base station and the reflection power of the active RIS, a joint optimization model of the base station beamforming vector and the active RIS reflection coefficient matrix is established with the goal of maximizing the system weighted sum rate and the target detection power:

[0027]

[0028] Among them, ρ in the objective function c ≥0 and ρ r ≥0 are regularization parameters. By changing them, we can obtain the performance trade-off between communication and radar sensing. μ k ≥0 represents the weighting coefficient of each user, controlling the proportion of each user. P s is the power budget of the base station. Constraint C1 represents the transmission power allocation among antennas; Constraint C2 represents the power constraint of the active RIS, and P ris represents the maximum power budget of the active RIS; Constraint C3 represents the amplitude constraint of each active RIS, and a max represents the maximum amplitude of the reflection coefficient.

[0029] The steps of using the alternating optimization algorithm to solve the beamforming vector of the base station and the reflection coefficient matrix of the active RIS in step 4 of the present invention are as follows:

[0030] 1) Use the alternating optimization algorithm to find the optimal P and Φ by iteratively solving two sub-problems;

[0031] First, obtain the beamforming matrix P with the help of the WMMSE algorithm, and then update the reflection coefficient matrix Φ of the active RIS through the SCA algorithm;

[0032] 2) Fix Φ and optimize P. Introduce a linear receiver g k at user k, and the estimated communication symbol is written as:

[0033]

[0034] The mean square error MSE between the estimated symbol and the true symbol is derived as:

[0035]

[0036] The optimal MMSE receiver is obtained by solving as:

[0037]

[0038] Therefore, the received MSE using the optimal MMSE receiver can be expressed as follows:

[0039]

[0040] Construct another problem of minimizing the mean square error and maximizing the detection power:

[0041]

[0042] where, as long as the weight factor when, for a fixed Φ, problem (12) has the same optimal solution for {p1,…,p K} as problem (7). Since the second term of the objective function in problem (12) is still non-convex, transform the second term, which is equivalent to:

[0043]

[0044] Let It can be proved that is a positive semi-definite matrix and equation (13) is a convex function. Omitting the constant term, the problem becomes:

[0045]

[0046] First, it is necessary to homogenize this non-homogeneous quadratic constraint quadratic programming (QCQP) problem, e k can be written as:

[0047]

[0048] Ignoring the constant term and reconstructing,

[0049]

[0050] Similarly, the other term of the objective function is also transformed in the same way,

[0051]

[0052] Constraint C1 can be written as:

[0053]

[0054] Constraint C2 can be written as:

[0055]

[0056] Let L = G H Φ H ΦG, It is derived that:

[0057]

[0058] Based on the above transformation, the optimization problem (14) becomes an optimization problem with respect to :

[0059]

[0060] where

[0061] To solve problem (21), let The semi - definite relaxation (SDR) form of the homogeneous QCQP problem can be obtained:

[0062]

[0063] Due to the rank - one constraint C6, problem (22) is still non - convex. The semi - definite relaxation can be used to handle such a constraint. By removing the constraint C6, the problem becomes a convex problem and can be directly solved by the CVX toolbox to obtain T k After that, it cannot guarantee to satisfy the rank - one constraint. When the rank of T k is greater than 1, rank - one decomposition should be performed to obtain the optimal solution which can be given by the following formula:

[0064]

[0065] where

[0066] The beamforming matrix P is calculated using the weighted minimum mean - square error (WMMSE) algorithm combined with the semi - definite relaxation (SDR) algorithm, providing an initial value for the next - step optimization of the reflection coefficient matrix Φ of the active RIS;

[0067] 3) Fix P and optimize Φ. In this part, the beamforming vector P of the base station BS is a constant, and the reflection coefficient matrix Φ of the active RIS is optimized. The optimization problem (7) can be simplified to:

[0068]

[0069] where

[0070]

[0071] Due to the logarithmic - fractional form with respect to Φ, the optimization problem (24) is non - convex. To make the problem easier to handle, let

[0072] Then the objective function can be transformed into:

[0073]

[0074] Among them,

[0075]

[0076] By setting the objective function can be written as:

[0077] R k = log(tr(D 1,k V)) - log(tr(D 2,k V)) (28)

[0078] Constraint C1 changes to:

[0079]

[0080] Among them,

[0081] The optimization problem (7) can be reformulated as:

[0082]

[0083] Since the objective function of the optimization problem (30) is non-convex, the problem remains non-convex. The Successive Convex Approximation (SCA) algorithm is used to solve this problem. Specifically, at iteration n, the first-order Taylor series is used as the surrogate function, as shown in Equation (31):

[0084]

[0085] By omitting the rank constraint, the problem (30) is relaxed to:

[0086]

[0087] After relaxation, the optimization problem is directly solved using the CVX toolbox. If rank(V) = 1, the singular value decomposition or eigenvalue decomposition of V can be used to obtain the optimal v * , if rank(V) > 1, the rank-one decomposition is applied, but the solution v obtained at this time is only an approximate feasible solution. The reflection coefficient matrix Φ of the active RIS can be obtained through Φ = diag(v). The amplitude and phase of the nth element can be obtained through a n = |φ n | and obtained;

[0088] The active RIS reflection coefficient matrix Φ is calculated by using the Successive Convex Approximation (SCA) algorithm combined with the Semi-Definite Relaxation (SDR) algorithm. The optimized beamforming matrix P and reflection coefficient matrix Φ are used to maximize the system utility, which is more directional in the target direction.

[0089] Advantages of the present invention:

[0090] 1. The present invention considers the situation of limited spectrum resources in the network, integrates communication and sensing into the network, jointly optimizes the transmit beamforming vector of the base station and the reflection coefficient matrix of the active RIS, and maximizes the weighted sum rate of users and the detection power of the target. The beamforming design method of the ISAC system based on active RIS under the constraints of the total transmission power of the base station and the reflection power of the RIS transforms the original complex non-convex problem into a convex problem by using the method of alternating optimization. Compared with the traditional passive RIS-assisted ISAC system, the algorithm of the present invention achieves a performance improvement of more than 5 bps / Hz in terms of the system weighted sum rate, significantly improving the overall system utility. This innovation not only effectively solves the problem of system performance optimization in the scenario of limited spectrum resources, but also provides a new solution for the practical application of communication and sensing integration technology.

[0091] 2. Most existing ISAC systems rely on direct channels for propagation. In complex urban environments or scenarios with severe obstructions, the establishment of communication links and sensing capabilities are often greatly restricted. Therefore, the Reconfigurable Intelligent Surface (RIS) has become an important technical means to improve communication and sensing performance. By adjusting the amplitude and phase of the reflection units, it can construct an ideal channel environment and enhance the propagation performance of signals in complex scenarios. However, in practice, significant performance gains are only observed in communication scenarios where the direct link between the transmitter and the receiver is completely blocked or very weak. In many cases where the direct link is not weak, passive RIS can only achieve limited performance gains because of the influence of the "multiplicative fading" effect introduced by the RIS. To overcome the influence of the "multiplicative fading" effect, the present invention patent uses active RIS to assist the ISAC system, solving the performance bottleneck problem.

[0092] 3. The proposed alternating optimization algorithm combining WMMSE and SCA in the present invention is different from traditional algorithms. This algorithm not only utilizes the high efficiency of WMMSE for characteristic structures but also can handle complex non-convex problems with the convex approximation method of SCA. Experimental results show that this algorithm exhibits significant advantages in terms of optimization accuracy, convergence speed, and stability. Specifically, compared with passive RIS, the beamforming value of the algorithm proposed in the present invention at the target angle is increased by more than 3.5 dBm, significantly enhancing the performance gain of beamforming design in the system. This improvement not only verifies the effectiveness of the algorithm but also provides a new technical approach for the performance optimization of communication-sensing integrated systems. Description of the Drawings

[0093] Figure 1 is the implementation flowchart of the present invention;

[0094] Figure 2 is the model diagram of the active RIS-assisted ISAC system in the present invention;

[0095] Figure 3 is the flowchart of the alternating optimization algorithm in the present invention;

[0096] Figure 4 is the convergence diagram of the algorithm proposed in the present invention;

[0097] Figure 5 is the beamforming diagram of the present invention at the target angle;

[0098] Figure 6 is the simulation diagram of the achievable system rate of the present invention under different transmission powers;

[0099] Figure 7 is the simulation diagram of the achievable system rate of the present invention when the number N of active RIS elements changes. Detailed Embodiment

[0100] The present invention will be further described in detail below with reference to the drawings and specific examples. It should be understood that the specific examples described herein are only used to explain the present invention and are not used to limit the present invention.

[0101] As Figure 1 shown, it includes the following steps:

[0102] Step 1: Construct an ISAC-assisted multi-user massive multiple-input single-output (MU-MISO) system model:

[0103] Establish one as Figure 2The system model shown consists of a base station BS, K users, and a target. The base station is equipped with M transmit / receive antennas and is responsible for providing communication services to K users and performing target detection. These M antennas are arranged at half-wavelength intervals to form a uniform linear array ULA (Uniform Linear Array). In addition, N active RIS elements are deployed near the users to improve the weighted sum rate performance of the system;

[0104] Step 2: Construct the system model of the active RIS-assisted ISAC system:

[0105] All symbols involved hereinafter conform to the following definitions: lowercase and uppercase letters represent vectors and matrices respectively. denotes an M×K dimensional complex matrix. X≥0 means X is a positive semi-definite matrix, and Tr(X) represents the trace operation on X. I N denotes an N×N dimensional identity matrix, CN(0,σ 2 ) represents a circularly symmetric complex Gaussian random vector following a zero mean and variance of σ 2 , (·) * , (·) H , diag(·) and ||·|| represent complex conjugate operation, complex conjugate transpose operation, diagonalization operation, and Euclidean norm respectively.

[0106] Assume perfect channel state information CSI (Channel State Information). With shared deployment, all antennas are used for communication and sensing simultaneously;

[0107] The communication model is as follows:

[0108]

[0109] The above formula describes the received signal of user k, where, and represent the channels from the active RIS to user k, from the base station to the active RIS, and from the base station to user k respectively. The vector represents the beamforming vector of user j, and the entire beamforming matrix is denoted as Since the active RIS integrates an additional reflection amplifier on its electromagnetic elements, the reflection coefficient of the nth element can be expressed as where a n and represent the amplitude and phase of the reflection coefficient respectively. Considering the actual gain limitation of the amplifier, assume that the amplitude a n is subject to the maximum amplification gain constraint, i.e., The reflection coefficients of the active RIS elements form a matrix where In addition, s j represents the communication symbol of user j, satisfying and represent the dynamic noise introduced by the active RIS and the additive Gaussian white noise of user k, respectively. Based on the above model, the signal-to-interference-plus-noise ratio (SINR) of user k can be expressed as:

[0110]

[0111] wherein, it is defined that is the composite channel from the base station (BS) to the k-th user. Based on formula (2), the SINR of user k can be obtained. It can be seen that the SINR is closely related to the beamforming vector p k of the base station and the reflection coefficient matrix Φ of the active RIS. Further, through the SINR, the achievable rate of user k can be calculated, and its expression is:

[0112] R k = log2(1 + γ k ) (3)

[0113] The weighted sum rate of the system is expressed as:

[0114]

[0115] The sensing metric is the detection power in the direction:

[0116]

[0117] wherein, is expressed as the covariance matrix of the beamforming vector. The vector represents the transmission steering vector relative to the angle . Since the antennas are uniformly linearly arranged at the BS, the steering vector is:

[0118]

[0119] wherein, d is the antenna spacing between the arrays, and λ represents the signal wavelength;

[0120] Step 3: Under the constraints of the total transmission power of the base station and the reflection power of the active RIS, establish a joint optimization problem model for the base station beamforming vector and the active RIS reflection coefficient matrix to maximize the system weighted sum rate and the target detection power, so as to maximize the system utility:

[0121]

[0122] In the objective function, the parameters ρ c ≥ 0 and ρ r≥0 is the regularization parameter, and by adjusting their values, a trade-off can be achieved between communication performance and radar sensing performance. The parameter μ k represents the weighting coefficient of user k, which is used to control the priority or weight of each user in the system. In addition, the constraint C1 represents the power budget of the base station, that is, the limit on the distribution of transmission power among antennas, where P s is the maximum power budget of the base station; the constraint C2 represents the total power constraint of the active RIS, where P ris is the maximum power budget of the active RIS; the constraint C3 represents the amplitude constraint of each active RIS element, that is, the amplitude of the reflection coefficient shall not exceed the maximum value a max ;

[0123] Step 4: Adopt an alternating optimization algorithm that combines the weighted minimum mean square error (WMMSE), successive convex approximation (SCA), and semidefinite relaxation (SDR) to solve the optimization problem in the joint optimization model:

[0124] The weighted minimum mean square error algorithm WMMSE is an optimization algorithm widely used in communication systems proposed in 2011, and is usually used to optimize power allocation, beamforming, or resource allocation problems. The core idea of the WMMSE algorithm is to indirectly optimize the objective of the system by minimizing the weighted mean square error. Its advantages lie in strong applicability, excellent performance, and high flexibility. The successive convex approximation algorithm SCA is an iterative optimization algorithm widely used in solving non-convex optimization problems. The core idea of the SCA algorithm is to decompose complex non-convex problems into a series of convex sub-problems that are easy to solve. By gradually approaching the non-convex objective and constraints, a feasible solution or sub-optimal solution is finally found. Its advantage lies in ensuring convergence. The semidefinite relaxation algorithm SDR is an algorithm proposed in 2010 for optimizing non-convex optimization problems with quadratic constraints. The core idea of the SDR algorithm is to transform the non-convex constraints in the original problem into a semidefinite matrix convex constraint through "relaxation", thereby transforming the problem into a semidefinite programming (SDP) problem that can be efficiently solved.

[0125] This invention patent combines the weighted minimum mean square error algorithm, successive convex approximation algorithm, and semidefinite relaxation algorithm for the first time, and maximizes the system utility of the ISAC system based on the active RIS by alternately optimizing the base station transmit beamforming vector and the reflection coefficient matrix of the active RIS. The process of the alternating optimization algorithm is as Figure 3 shown:

[0126] 1) Adopt the alternating optimization algorithm to find the optimal P and Φ by iteratively solving two sub-problems;

[0127] First, obtain the beamforming matrix P with the help of the WMMSE algorithm, and then update the reflection coefficient matrix Φ of the active RIS through the SCA algorithm;

[0128] 2) Fix Φ and optimize P. Introduce a linear receiver g at user k k , and the estimated communication symbol can be written as:

[0129]

[0130] The mean square error (MSE) between the estimated symbol and the true symbol can be derived as:

[0131]

[0132] Optimal MMSE receiver By solving we obtain:

[0133]

[0134] Therefore, the received MSE using the optimal MMSE receiver can be expressed as:

[0135]

[0136] According to the relevant literature, it is proved that the problem of maximizing the sum rate is equivalent to the problem of minimizing the weighted mean square error, i.e., Another problem of minimizing the mean square error and maximizing the detection power can be constructed:

[0137]

[0138] where, as long as the weight factor when, for a fixed Φ, problem (12) has the same optimal solution for {p1,…,p K} as problem (7). Since the second term of the objective function in problem (12) is still non-convex, transform the second term, which is equivalent to:

[0139]

[0140] Let It can be proved that is a positive semi-definite matrix and equation (13) is a convex function. Omitting the constant term, the problem becomes:

[0141]

[0142] First, this non-homogeneous quadratic constraint quadratic programming (QCQP) problem needs to be homogenized, e k can be written as:

[0143]

[0144] Ignoring the constant term and reconstructing,

[0145]

[0146] Similarly, another term of the objective function is also transformed in the same way.

[0147]

[0148] The constraint C1 can be written as:

[0149]

[0150] The constraint C2 can be written as:

[0151]

[0152] Let L = G H Φ H ΦG, It can be deduced that:

[0153]

[0154] Based on the above transformation, the optimization problem (14) becomes an optimization problem about :

[0155]

[0156] where,

[0157] To solve problem (21), let The semidefinite relaxation (SDR) form of the homogenized QCQP problem can be obtained:

[0158]

[0159] Due to the existence of the rank-one constraint C6, problem (22) is still non-convex and difficult to solve directly. To solve this problem, the semidefinite relaxation (SDR) method can be used to handle this constraint. Specifically, removing the rank-one constraint C6, the problem is transformed into a convex problem, and at this time, optimization tools such as the CVX toolbox can be used to solve it directly. However, although a solution T k can be obtained through semidefinite relaxation, it cannot guarantee that it must satisfy the rank-one constraint. When the rank of T k is greater than 1, rank-one decomposition is required, and an approximate solution with rank 1 can be obtained through eigenvalue decomposition or Gaussian randomization method The optimal solution can be given by the following formula:

[0160]

[0161] where,

[0162] In summary, by combining the weighted minimum mean square error (WMMSE) algorithm and the semidefinite relaxation (SDR) algorithm, the beamforming matrix P can be calculated, providing a reliable initial value for optimizing the reflection coefficient matrix Φ of the active RIS in the next step.

[0163] 3) Fix P and optimize Φ. The beamforming vector P of this part of the base station (BS) is a constant, and the reflection coefficient matrix Φ of the active RIS is optimized. The optimization problem (7) can be simplified as:

[0164]

[0165] where

[0166]

[0167] It can be found that due to the logarithmic fractional form with respect to Φ, the optimization problem (24) is non-convex. To make the problem more tractable, Let

[0168] Then the objective function can be changed to:

[0169]

[0170] where

[0171]

[0172] By letting the objective function can be written as:

[0173] R k = log(tr(D 1,k V)) - log(tr(D 2,k V)) (28)

[0174] The constraint C1 changes to:

[0175]

[0176] where

[0177] The optimization problem (7) can be reconstructed as:

[0178]

[0179] However, due to the non-convex objective function of the optimization problem (30), the problem remains non-convex. The Successive Convex Approximation (SCA) algorithm is adopted to solve this problem. Specifically, at iteration n, we use the first-order Taylor series as the surrogate function, as shown in Equation (31):

[0180]

[0181] By omitting the rank constraint, Problem (30) is relaxed to:

[0182]

[0183] After relaxation, the optimization problem is directly solved by the CVX toolbox. If rank(V) = 1, the singular value decomposition or eigenvalue decomposition of V can be used to obtain the optimal v * , if rank(V) > 1, the rank-one decomposition is applied, but the solution v obtained at this time is only an approximate feasible solution. The reflection coefficient matrix Φ of the active RIS can be obtained through Φ = diag(v). The amplitude and phase of the nth element can be obtained through a n = |φ n | and obtained;

[0184] The continuous convex approximation SCA algorithm is combined with the semidefinite relaxation SDR algorithm to calculate the reflection coefficient matrix Φ of the active RIS. The optimized beamforming matrix P and the reflection coefficient matrix Φ are used to maximize the system utility, which is more directive in the target direction.

[0185] The technical effects of the present invention are further described in detail below in combination with simulation experiments:

[0186] The proposed scheme of the present invention is compared with the existing scheme in multiple dimensions such as beamforming gain, weighted sum rate, and system utility, so as to verify the effectiveness of the present invention.

[0187] (1) Simulation parameter settings

[0188] In the simulation experiment, the performance of the proposed algorithm is verified through computer simulation. In the simulation, the transmit / receive antennas of the base station are set to 8, the number of users is set to 4, the weight coefficient of the users is set to 1, the number of targets is set to 1, the number of elements of the active RIS is set to 50, and the user noise power and the noise power introduced by the active RIS are both -100 dBm.

[0189] (2) Simulation content and result analysis

[0190] Figure 4This is a schematic diagram of the convergence of the algorithm proposed in the present invention. It can be observed from the figure that under different communication weights, the algorithm proposed in the present invention has a fast convergence speed and few iteration times, and can converge within 10 times. As the communication weight ρ c increases, the objective function value also increases. This shows that the WMMSE combined with the SCA algorithm has a strong ability to handle non-convex problems, and the convergence speed has also been greatly improved.

[0191] Figure 5 This is the beamforming diagram of the present invention comparing different algorithms at the target angle. At this time, the communication weight is 10 and the sensing weight is 1. It can be observed from the figure that the main lobe beam value of the algorithm only used for radar sensing without communication is the largest near the target angle of 0°. The active RIS-assisted beamforming algorithm proposed in the present invention has a smaller beam value in the sidelobe and a larger main lobe beam value near the target angle of 0° compared with the passive RIS, random phase shift, and the beamforming algorithm without RIS assistance. This shows that the algorithm proposed in the present invention significantly improves the beam intensity at a specific azimuth angle, has strong directivity, and better performance.

[0192] Figure 6 This is the simulation diagram of the achievable rate of the system of the present invention under different transmission powers. The number of elements of the active RIS is set to 50, and the power budget of the active RIS is set to 0.1 times the transmission power. It can be observed from the figure that as the transmit power increases, the achievable rate of the system increases. In the case of a max = 8, when the transmission power is between 40 mW and 100 mW, the active RIS-assisted ISAC method always has a numerical improvement of more than 5 bps / Hz in the achievable rate of the system compared with the passive RIS-assisted beamforming method, and has a greater improvement compared with the random phase shift and the ISAC method without RIS assistance. When the transmit power increases to about 100 mW, the achievable rate of the system of the active RIS-assisted method gradually levels off. The reason for this is that even if the transmission power increases, the power budget P ris of the active RIS will also limit the performance improvement. In addition, even in the case of a max = 4, the active RIS-assisted ISAC method is still significantly better than other comparison algorithms.

[0193] Figure 7 This is the simulation diagram of the achievable rate of the system of the present invention when the number of elements N of the active RIS changes. The transmission power of the base station is set to 10 mW, and the power budget of the active RIS is 1 mW. It can be observed from the figure that as the number of elements N of the active RIS increases, the achievable rate of the system increases. The active RIS-assisted beamforming method proposed in the present invention, whether a max = 8 or a maxIn the case of =4, there is a significant improvement compared with the passive RIS-assisted beamforming method, and the growth rate is also significantly faster. For the passive RIS and random phase shift methods, as the number of elements N increases, the achievable rate of the system remains basically unchanged.

[0194] In summary, Figure 4 It effectively proves the effectiveness of combining the WMMSE algorithm with the SCA algorithm in the present invention, and its convergence speed is very fast. Figure 5 It verifies that the method proposed in the present invention has better directivity and reduces resource waste compared with other comparison methods. Figure 6 and Figure 7 It verifies the practicability of the active RIS-assisted beamforming method proposed in the present invention. Obviously, the method proposed in the present invention solves the problems of spectrum resource tension and propagation congestion, and realizes a significant improvement in the performance of the ISAC system.

Claims

1. A beamforming design method for an active RIS-assisted ISAC system, characterized in that: The following steps are involved: Step 1: Build an ISAC-assisted multi-user massive multiple-input single-output MU-MISO system model: Step 2: Construct a system model of the ISAC system based on active RIS assistance: Step 3: Under the constraints of the total transmission power of the base station and the active RIS reflection power, a joint optimization problem model of the base station beamforming vector and the active RIS reflection coefficient matrix is ​​established to maximize the system weighted sum rate and the target detection power; Step 4: Use the alternating optimization algorithm that combines weighted minimum mean square error (WMMSE), continuous convex approximation (SCA) and semi-positive definite relaxation (SDR) to solve the optimization problem in the joint optimization model.

2. The beamforming design method for an active RIS-assisted ISAC system according to claim 1, characterized in that: In the step 1, the base station BS equipped with M transmitting and receiving antennas serves K users at the same time and detects targets. The M antennas are arranged in a uniform linear array ULA with a half-wavelength spacing. In addition, N active RIS elements are deployed near the users to improve the weighted sum rate.

3. The beamforming design method for an active RIS-assisted ISAC system according to claim 1, characterized in that: The construction method in step 2 includes: assuming perfect channel state information CSI, adopting shared deployment, and all antennas are used for communication and sensing at the same time; The communication model is: The above formula is the received signal of user k, where and Respectively represent the channels from RIS to the kth user, BS to RIS, and BS to the kth user, and the vector represents the beamforming vector of user j, and the entire beamforming matrix is Since an additional reflection amplifier is integrated on the electromagnetic element, the reflection coefficient of the nth element of the active RIS can be expressed as where a n and Represent the amplitude and phase shift respectively. Considering the actual amplification capability of the amplifier, assuming that the amplitude a n Subject to the maximum amplification gain constraint, that is make represents the reflection coefficient matrix of active RIS, s j Represents the communication symbol of user j, satisfying and are the dynamic noise introduced by active RIS and the additive white Gaussian noise AWGN of the k-th user, so the signal to interference plus noise ratio SINR of the k-th user is calculated as: Among them, the definition As the composite channel from the base station BS to the kth user, the signal-to-interference-to-noise ratio of user k is obtained by formula (2). The signal-to-interference-to-noise ratio depends on the beamforming vector of the base station BS and the reflection coefficient matrix of the active RIS. The achievable rate of user k can be obtained through the signal-to-interference-to-noise ratio, which is expressed as: R k =log2(1+γ k ) (3) The weighted sum rate of the system is expressed as: The perception index is Detection power in direction: in, Expressed as the covariance matrix of the beamforming vector, the vector Represents the angle relative to The transmission steering vector is: Where d is the spacing between antennas in the array and λ is the signal wavelength.

4. The beamforming design method for an active RIS-assisted ISAC system according to claim 1, characterized in that: The joint optimization model established in step 3 is expressed as: Under the constraints of the total transmission power of the base station and the active RIS reflection power, a joint optimization model of the base station beamforming vector and the active RIS reflection coefficient matrix is ​​established with the goal of maximizing the system weighted sum rate and target detection power: Among them, ρ in the objective function c ≥0 and ρ r ≥0 are regularization parameters. By changing them, we can obtain the performance trade-off between communication and radar perception, μ k ≥0 indicates the weighted coefficient of each user, which controls the proportion of each user. s is the power budget of the base station, constraint C1 represents the transmission power allocation between antennas; constraint C2 represents the power constraint of active RIS, P ris represents the maximum power budget of active RIS; constraint C3 represents the amplitude constraint of each active RIS, a max Indicates the maximum amplitude of the reflection coefficient.

5. The beamforming design method for an active RIS-assisted ISAC system according to claim 1, characterized in that: The steps of using the alternating optimization algorithm in step 4 to solve the beamforming vector of the base station and the reflection coefficient matrix of the active RIS are as follows: 1) Using an alternating optimization algorithm, the optimal P and Φ are found by iteratively solving two sub-problems; Firstly, the beamforming matrix P is obtained by using the WMMSE algorithm, and then the reflection coefficient matrix Φ of the active RIS is updated by the SCA algorithm; 2) Fix Φ, optimize P, and introduce a linear receiver g at user k k , the estimated communication symbol is written as: The mean square error (MSE) between the estimated symbols and the true symbols is derived as: Best MMSE Receiver By solving Find: Therefore, the received MSE using the optimal MMSE receiver can be expressed as follows: Construct another problem of minimizing mean square error and maximizing detection power: Among them, as long as the weight factor When Φ is fixed, problem (12) has the same {p1,…,p K }, Problem (12) Since the second term of the objective function is still non-convex, the second term is transformed, which is equivalent to: make Provable is a semi-positive definite matrix, equation (13) is a convex function, omitting the constant term, the problem becomes: First, we need to homogenize this non-homogeneous quadratically constrained quadratic programming (QCQP) problem, e k It can be written as: Ignore the constant term and reformulate to get, Similarly, the other term of the objective function is transformed as well, Constraint C1 can be written as: Constraint C2 can be written as: Let L = G H Φ H ΦG, It is deduced that: Based on the above transformation, the optimization problem (14) becomes The optimization problem is: in, To solve problem (21), let The semidefinite relaxation (SDR) form of the homogeneous QCQP problem can be obtained: Due to the rank-one constraint C6, problem (22) is still non-convex. Semidefinite relaxation can be used to deal with such constraints. By removing constraint C6, the problem becomes convex and can be solved directly using the CVX toolbox to obtain T k After that, it cannot guarantee that the rank-one constraint is satisfied, when T k When the rank of is greater than 1, rank-one decomposition should be performed to obtain Optimal solution It can be given by the following formula: in, The beamforming matrix P is calculated by using the weighted minimum mean square error (WMMSE) algorithm combined with the semi-positive definite relaxation (SDR) algorithm, which provides the initial value for the next step of optimizing the reflection coefficient matrix Φ of the active RIS. 3) Fix P and optimize Φ. The beamforming vector P of the base station BS is a constant. Optimize the reflection coefficient matrix Φ of the active RIS. The optimization problem (7) can be simplified to: in, Due to the logarithmic fractional form of Φ, the optimization problem (24) is non-convex. In order to make the problem easier to handle, we have make So the objective function can be changed to: in, By order The objective function can be written as: R k =log(tr(D 1,k V))-log(tr(D 2,k V)) (28) Constraint C1 changes to: in, The optimization problem (7) can be reformulated as: Since the objective function of the optimization problem (30) is non-convex, the problem is still non-convex. The continuous convex approximation SCA algorithm is used to solve the problem. Specifically, when iterating n, the first-order Taylor series is used as the proxy function, as shown in formula (31): R k ≥log(tr(D 1,k V))-log(tr(D 2,k V (n) ))-tr(D 2,k (VV (n) ) / tr(D 2,k V (n) )·In2) (31) By omitting the rank constraint, problem (30) is relaxed to: After relaxation, the optimization problem is solved directly by the CVX toolbox. If rank(V) = 1, the optimal v can be obtained by performing singular value decomposition or eigenvalue decomposition on V. * If rank(V)>1, rank-1 decomposition is applied, but the solution v obtained at this time is only an approximate feasible solution. The reflection coefficient matrix Φ of the active RIS can be obtained by Φ=diag(v), and the amplitude and phase of the nth element can be obtained by a n =|φ n | and get; The active RIS reflection coefficient matrix Φ is calculated by combining the continuous convex approximation SCA algorithm with the semi-positive definite relaxation SDR algorithm. The optimized beamforming matrix P and reflection coefficient matrix Φ are used to maximize the system utility and make it more directional in the target direction.

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