Manifold optimization-based RIS auxiliary sensing integrated beam forming design

Abstract

The invention discloses an RIS auxiliary sensing integrated beamforming design based on manifold optimization, relates to the technical field of wireless communication, and aims to meet the requirement of high-precision sensing service in a 6G wireless communication system. By using the RIS technology, the invention provides an alternative optimization algorithm, which effectively improves the communication rate and reduces the interference between users. According to the method, the trade-off factor rho is introduced to balance communication and sensing performance, and dual optimization of the communication and sensing performance is realized. In the method, the communication sum rate of a'trade-off 'mode (rho = 0.2) reaches about 14 bit / s / Hz, the mean square error (MSE) of a beam pattern is controlled to be-4dB, and the system performance is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and particularly relates to a RIS-assisted integrated sensing and communication beamforming design scheme based on manifold optimization. Background Art

[0002] The future sixth-generation (6G) wireless communication system is expected to provide various high-precision sensing services, such as the precise positioning of indoor intelligent devices, Wi-Fi sensing in smart homes, and radar sensing in autonomous vehicles. These services pose higher requirements for the data transmission rate, latency, and positioning ability of wireless systems. These services pose higher requirements for the data transmission rate, latency, and positioning ability of wireless systems.

[0003] Due to the wide application of millimeter-wave and massive multiple-input multiple-output (MIMO) technologies, communication signals in future wireless systems often have high resolution in the time domain and angular domain, which makes it possible to use communication signals to achieve high-precision sensing. Therefore, it is desirable to jointly design communication and sensing systems so that they can share the same frequency band and hardware, and simultaneously perform communication and radar sensing functions to improve spectral efficiency and reduce hardware costs. This has promoted the research on integrated sensing and communication (ISAC) in related fields.

[0004] Reconfigurable intelligent surface (RIS) is an emerging electromagnetic material that plays an active role in ISCA waveform design. RIS technology is a promising new antenna technology that has emerged in recent years. Its essence is an artificial structure that can adjust the reflection, refraction, and scattering of electromagnetic waves, and is composed of a large number of carefully designed electromagnetic array units. RIS can adjust the amplitude, phase, polarization, focusing, attenuation, etc. of electromagnetic waves through programming, so as to intelligently control the spatial electromagnetic (EM) environment and signal transmission path, alleviate the interference problem between user ends (UEs), improve the coverage rate, spectral efficiency (SE), and energy efficiency (EE), etc., and can effectively solve the new problems brought by ISAC technology.

[0005] The present invention is to solve the problem of solving the parameters of the passive beam vector θ in the beamforming of the RIS-assisted communication perception integration (ISAC) system, and make full use of the alternating optimization algorithm AO-RTR based on the Riemann manifold to achieve the effect of improving the user communication rate and reducing the user interference (MUI). At the same time, the present invention proposes a method for weighing radar perception and communication performance, by comparing the 'strict' mode in the traditional method and the 'trade-off' mode of the new method, by introducing a trade-off factor ρ, to adjust the proportion of communication performance in the system, relax the strict constraints on the radar beam pattern, and allow a certain matching error between the designed beam pattern and the expected beam pattern, thereby achieving the goal of taking into account the radar perception performance while improving the user's communication and rate to a greater extent, so that it has good system performance. Summary of the invention

[0006] The present invention proposes an alternating algorithm based on Riemannian manifold optimization to solve the joint optimization problem of passive beamforming in a RIS-assisted ISAC system. This method utilizes the unique advantages of manifold optimization in dealing with non-convex constraint problems. Through the alternating optimization framework, the original problem is decomposed into easy-to-handle sub-problems, and the signal matrix and the phase shift matrix are optimized and solved respectively. Compared with the case without RIS, when RIS assistance is introduced, the communication rate at the user is up to 14bit / s / Hz, and the mean square error (MSE) of the beam pattern can be controlled at -4dB basically unchanged, which is significantly improved compared with the case without RIS. The Riemannian manifold trust region algorithm in the present invention can solve the problems of high coupling degree parameters being difficult to solve, slow convergence speed, and inaccurate optimal solution in the current traditional algorithm.

[0007] The method can be implemented by the following steps:

[0008] Step 1: Set parameters according to the actual needs of the system, establish a model of the RIS-assisted ISAC system, and set the number of base stations, communication users, RIS boards, and sensing targets.

[0009] Step 2: Define the communication channel and MIMO radar perception model according to the actual system requirements, and associate the beam pattern design with the signal covariance matrix design.

[0010] Step 3: Propose the original problem of parameter solution and calculate the communication and rate based on the general user communication formula Modeling and then using the alternating optimization algorithm to simplify the objective function

[0011] Step 4: Introduce a trade-off factor ρ to maximize the proportion of communication performance in the system by relaxing the strict constraints on the radar beam pattern and allowing a matching error between the designed beam pattern and the expected beam pattern.

[0012] Step 5: Perform iterative optimization by combining the Riemannian trust region method with a penalty function to solve the phase shift parameter configuration of the optimal RIS elements.

[0013] Step 6: Calculate the communication rate at the user according to the obtained phase shift parameters and waveform matrix.

[0014] Step 7: Analyze the influence of different signal-to-noise ratios and different numbers of RISs on the total communication rate, and further optimize the system configuration and algorithm parameters.

[0015] The advantages and beneficial effects of the present invention are as follows:

[0016] 1. The present invention provides a new communication and radar trade-off scheme. By introducing a trade-off factor ρ, the performance boundaries of communication and sensing are balanced, and dual optimization of communication and sensing performance is achieved.

[0017] 2. By using the alternating optimization technique on the Riemannian manifold, the present invention can effectively solve complex beamforming problems due to its advantage in dealing with non-convex constraint problems, solve the optimal passive beam vector Θ to achieve more accurate beam direction control, effectively reduce the multi-user interference (MUI), and improve the communication performance. Brief Description of the Drawings

[0018] Figure 1 It is the usage flow of the algorithm in the present invention.

[0019] Figure 2 It is a schematic diagram of the RIS-assisted ISAC system model.

[0020] Figure 3 It is the comparison curve of the total communication rate at the user under different signal-to-noise ratios in the simulation process of the present invention. Detailed Embodiment

[0021] The specific usage process of the present invention is realized by the following steps:

[0022] Step 1: Establish a system model through parameter settings. In the model establishment stage of the RIS-assisted ISAC system, we consider a system consisting of a base station equipped with M uniformly linear array antennas, K single-antenna communication users, a RIS board with L passive reflection units, and T point-like sensing targets. The RIS board is deployed near the users, maintaining a line-of-sight propagation path with the users to effectively assist user communication. At the same time, the RIS board can shape the energy beam to align with the users, and the echo signal reflected by the RIS can be ignored, thereby establishing an effective link between the base station and the users.

[0023] Step 2: Define the communication channel and the MIMO radar sensing model according to the actual situation required by the system, and associate the beam pattern design and the signal covariance matrix design. Among them, the communication channel is modeled as a Nakagami-m channel, and its probability density function is:

[0024]

[0025] where r is the signal envelope, m is the shape parameter of the Nakagami-m distribution, which defines the severity of the channel fading. Ω is the scale parameter, representing the average power of the signal envelope. Γ(m) is the Gamma function.

[0026] The MIMO radar sensing model is modeled as:

[0027]

[0028] where: is the angle of the signal transmitted from the base station to the target, and V H (θ) is the direction vector of the transmitted signal: λ g is the carrier wavelength of the transmitted signal, d is the antenna spacing, and the power of the transmitted signal can be expressed as:

[0029]

[0030] where: β 2 is the fading coefficient of the propagation path, XX H is the signal covariance matrix R X . This indicates that the larger the value, the greater the signal power transmitted in the direction of the target.

[0031] Step 3: Model the original problem of parameter solution and use the alternating optimization algorithm to simplify the objective function The passive beamforming vector Θ is subject to the constant modulus constraint, and X satisfies the maximum base station transmission power constraint. Therefore, the problem can be modeled as:

[0032]

[0033] C2: tr(XX H ) ≤ P max (6)

[0034]

[0035] where, P maxDenote the maximum transmit power of the base station. To ensure the communication quality of users, constraint C1 represents the minimum signal-to-noise ratio of the received signal at user K. Constraint C2 represents that the signal satisfies the maximum transmit power constraint of the base station, and constraint C3 represents that the phase shift parameter satisfies the constant modulus constraint. For a given covariance matrix R d , which satisfies the power constraint of P max . Combining the above relationship between MUI and communication sum rate, problem is then described as:

[0036]

[0037] For problem Note that in the original optimization problem, X and θ are highly coupled, and the original problem is a non-convex optimization problem with multiple constraints. It is not easy to directly obtain the analytical solutions of the signal matrix X and the passive beamforming vector θ. Therefore, the alternating optimization algorithm (AO) will be used to alternately solve the coupled variables:

[0038] 1) For the optimization problem When θ is given, the original optimization problem can be written as:

[0039]

[0040] After θ is given, the signal-to-noise ratio constraint C1 becomes a term only related to X, and then becomes a constant constraint term, which is a fixed value. We perform Cholesky decomposition on the given covariance matrix R d to get R d = FF H , where is a lower triangular matrix. Then the solution of the signal matrix X in problem can be expressed as where is the singular value decomposition (SVD) of , expressed as

[0041] 2) For the optimization problem When X is given, the original optimization problem can be written as:

[0042]

[0043] We expand the original formula to get:

[0044]

[0045] where: H bu is the direct link from the base station to the user, G is the direct link from the base station to the RIS board, U ruIt is the direct link from the RIS board to the user. Therefore, it is independent of Θ, and the above formula can be simplified as:

[0046]

[0047] Step 4: In previous studies, in order to balance the sensing performance of the radar, it was usually necessary to make the designed beam pattern exactly equal to the expected radar beam pattern. However, in such a process, it often seriously led to a loss of communication performance. Therefore, we introduce a trade-off factor ρ. By relaxing the strict constraint on the radar beam pattern and allowing a matching error between the designed and expected beam patterns, the proportion of communication performance in the entire system is made higher. Then the trade-off joint optimization problem is formulated as:

[0048]

[0049] where ρ ∈ [0, 1], and by adjusting the value of ρ, the requirements of radar matching and communication performance are balanced. U is the waveform template that matches the required radar beam direction.

[0050] Step 5: Iterative optimization. On the Riemannian manifold, the trust-region subproblem can be formulated as minimizing the model within the given trust-region radius Δ k as:

[0051]

[0052] where gradf(x k ), u represents the Riemannian gradient of the objective function. The Riemannian gradient is the projection of the Euclidean gradient onto the tangent space at a point on the manifold. Therefore, the Euclidean gradient must be calculated first and then projected onto the above manifold space. Using the orthogonal projection formula, the projection of the Euclidean gradient onto the manifold tangent space is:

[0053]

[0054] where, represents the inner product of the Euclidean gradient and the vector θ i on the manifold. After obtaining the Riemannian gradient, the second derivative of equation (28) is taken to obtain the Hessian matrix required by the trust-region algorithm. The obtained formula is substituted back into the original minimization model to obtain the actual decrease Δf k at the k-th iteration, and the predicted decrease Δq k . Then the ratio of the two is calculated By the value of r k , it is judged whether x k+1 := x k + u k is used as the new iteration point. If r k < 0, then Δfk <0,x k +u k cannot be used as the next iteration point, and the trust region radius needs to be reduced to re-solve the sub-problem. If r k is relatively close to 1, it indicates that the quadratic model and the objective function have a good approximation within the trust region. At this time, x k+1 := x k +u k can be used as the new iteration point, and the trust region radius can be increased during the next iteration. For other cases, the trust region radius can remain unchanged. Until the difference Δx between the two iteration points in this loop is less than the convergence threshold ∈ or the maximum number of iterations is reached, the output beamforming vector θ is output.

[0055] Step Six: After the above optimization is completed, the obtained output beamforming vector θ is brought back to the problem to solve for the waveform vector X, and then the value of the communication sum rate at the user is calculated according to the formula.

[0056] Step Seven: Evaluate the results based on the communication sum rate curve to further optimize the system configuration and algorithm parameters.

Claims

1. A RIS-assisted synaesthesia integrated beamforming design based on manifold optimization, which is implemented by the following steps: Step 1: Build an ISAC system model supported by RIS by adjusting relevant parameters, and determine the number of base stations, communication users, RIS panels, and sensing targets. Step 2: Define the communication channel and MIMO radar perception model according to the actual system requirements, and associate them with the beam pattern design and signal covariance matrix design. Step 3: Propose the original problem of parameter solution and calculate the formula based on the communication and rate at the user Modeling and using the alternating optimization algorithm to simplify the objective function Step 4: By introducing a trade-off factor ρ, the strict requirements on the radar beam pattern are relaxed, thereby allowing a certain deviation between the designed beam pattern and the target beam pattern. Step 5: Use the Riemann trust region method and penalty function method to perform iterative optimization to obtain the optimal RIS element phase shift parameter configuration. Step 6: Calculate the communication rate of the user end according to the obtained phase shift parameters and waveform matrix. Step 7: Analyze the impact of different signal-to-noise ratios and RIS numbers on the total rate, and further optimize the system configuration and algorithm parameters.

2. The RIS-assisted synaesthesia integrated beamforming design based on manifold optimization according to claim 1 is characterized by: In step 1, before simulating the communication system, the parameters of the system components need to be set. The specific parameters are set as follows: the base station is equipped with M uniform linear array antennas, the number of communication users is K, the number of passive reflection units of the RIS board is L, and the number of sensing targets is T. The RIS board is deployed near the user to maintain line-of-sight path propagation and can effectively align the user through beamforming technology. In order to simplify the model, the echo signal reflected by the RIS is ignored to ensure the effectiveness of the system link.

3. The RIS-assisted synaesthesia integrated beamforming design based on manifold optimization according to claim 1 is characterized in that: In step 2, the communication channel is modeled as a Nakagami-m channel, and its probability density function is: Where r is the signal envelope, m is the shape parameter of the Nakagami-m distribution, which defines the fading severity of the channel. Ω is the scale parameter, which represents the average power of the signal envelope. Γ(m) is the Gamma function. The MIMO radar perception model is modeled as: in: is the angle of the signal transmitted by the base station to the target, V H (θ) is the direction vector of the transmitted signal: λ g is the carrier wavelength of the transmitted signal, and d is the distance between the antennas.

4. The RIS-assisted synaesthesia integrated beamforming design based on manifold optimization according to claim 1 is characterized in that: In step 3, for a given covariance matrix R d , which satisfies P max The power constraint, combined with the relationship between MUI and communication rate, the original problem is It can be simplified as a problem For the problem Note that in the original optimization problem, X and θ are highly coupled, and the original problem is a non-convex optimization problem with multiple constraints. It is not easy to directly obtain the analytical solution of the signal matrix X and the passive beamforming vector θ. Therefore, the alternating optimization algorithm (AO) is used to alternately solve the coupling variables: 1) For optimization problems When θ is given, the original optimization problem can be written as: After θ is given, the signal-to-noise ratio constraint C1 becomes a term only related to X, and then becomes a constant constraint term. is a constant. We have a given covariance matrix R d Perform Cholesky decomposition into R d =FF H ,in is a lower triangular matrix, then the problem The solution of the signal matrix X can be expressed as in For The singular value decomposition (SVD) of is expressed as 2) For optimization problems When X is given, the original optimization problem can be written as: We expand the original formula to: Where: H bu is the direct link from the base station to the user, G is the direct link from the base station to the RIS board, H ru is the direct link from the RIS board to the user, so it has nothing to do with Θ, so the above formula can be simplified to:

5. The RIS-assisted synaesthesia integrated beamforming design based on manifold optimization according to claim 1 is characterized in that: In step 4, we usually strictly equalize the designed radar beam pattern with the expected beam pattern, but in this process, it often leads to serious loss of communication performance. Therefore, this scheme introduces a trade-off factor ρ, which relaxes the strict constraints on the radar beam pattern and allows matching errors between the designed and expected beam patterns. Then the trade-off joint optimization problem is expressed as: Where ρ∈[0,1], by adjusting the value of ρ, the requirements of radar matching and communication performance are balanced. U is the waveform template that matches the required radar beam direction.

6. The RIS-assisted synaesthesia integrated beamforming design based on manifold optimization according to claim 1 is characterized by: In step 5, through iterative optimization, on the Riemann manifold, the trust region subproblem can be expressed as k The minimization model is: Among them, gradf(x k ),u represents the Riemann gradient of the objective function. The Riemann gradient is the projection of the Euclidean gradient on the tangent space of a point on the manifold, so its Euclidean gradient must be calculated first. Then project it onto the above manifold space. Using the orthogonal projection formula, the projection of the Euclidean gradient into the manifold tangent space is: in, represents the Euclidean gradient and the vector θ on the manifold i The algorithm first calculates the Euclidean gradient and projects it into the tangent space of the manifold to obtain the Riemann gradient. Then, the trust region subproblem is solved by the quadratic model and the Hessian matrix, and the ratio of the actual drop to the predicted drop r is calculated. k to adjust the iteration direction. If the ratio is less than 0, reduce the trust region radius and solve again; if it is close to 1, accept the current iteration point and increase the trust region radius; otherwise, keep the trust region radius unchanged. This process continues to iterate until the convergence condition or the maximum number of iterations is reached, and then the optimized beamforming vector is output.

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