Intelligent metasurface-based wave beam forming robust design method for sensing integrated system

Abstract

The invention discloses an intelligent metasurface-based wave beam forming robust design method for a communication and induction integrated system, and belongs to the technical field of wireless communication. According to the method, aiming at the problems of imperfect channel state information and uncertainty of a target position in a communication and inductance integrated system, a worst-case robust optimization model is established by taking minimization of base station transmitting power as an optimization target. Firstly, an original non-convex problem is equivalently reconstructed by utilizing positive semidefinite programming; secondly, aiming at semi-infinite constraint introduced by uncertainty, solving by adopting a successive convex approximation method; meanwhile, interval uncertainty constraints are efficiently processed in combination with a sampling method; and finally, solving the coupling relationship among the optimization variables through an alternative optimization strategy. Simulation results show that the method can ensure the service quality of the communication and sensing target under multiple uncertainties, significantly improve the robustness of the system in an uncertain environment, and effectively reduce the transmitting power at the same time.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, in particular to a beamforming robust design method for an integrated sensing and communication system based on an intelligent metasurface. BACKGROUND

[0002] With the completion of commercial deployment and stable operation of the fifth generation (5G) mobile communication system worldwide, the sixth generation (6G) mobile communication technology aiming at the vision of "all things intelligent" has entered the stage of full research and development. 6G needs to focus on supporting five core demands of "super wireless broadband, extremely high reliability communication, super large-scale connection, inclusive intelligent services and communication-sensing fusion", which promotes the evolution of wireless networks towards "deep integration of communication, sensing and computing functions". Through multi-functional cooperation, it can not only meet the immersive interaction of human-centered, but also support efficient and reliable Internet of Things applications, becoming the core development trend of next-generation wireless technology.

[0003] Under this background, integrated sensing and communication (ISAC) technology has emerged. This technology realizes the joint design of radar sensing and data communication by sharing spectrum and hardware resources: on the one hand, communication signals can be reused as sensing waveforms, avoiding additional spectrum occupation and greatly improving spectrum utilization; on the other hand, there is no need to deploy radar hardware separately, which effectively reduces system complexity and cost. However, there are differences in functional requirements and waveform characteristics between radar and communication - radar needs high power and narrow beam to ensure detection accuracy, while communication needs wide coverage and low interference to ensure multi-user rate, which poses a great challenge to the performance optimization of integrated sensing and communication systems.

[0004] In recent years, reconfigurable intelligent surface (RIS) has gradually become a research hotspot in the field of wireless communication and sensing. This technology deploys a metasurface array composed of a large number of passive reflection units in the propagation environment, and programmably controls the amplitude and phase of each reflection unit, thereby realizing intelligent control of the propagation characteristics of incident electromagnetic waves. Compared with traditional technologies, RIS can effectively improve wireless channel quality, reduce system energy consumption and improve spectrum efficiency without increasing additional transmission power. With the continuous progress of hardware technology, RIS has shown practical value in signal coverage enhancement, interference suppression, energy efficiency improvement, etc. Especially in the field of integrated sensing and communication, it can optimize reflected beams and assist communication signal transmission and sensing target detection, providing a highly potential technical path to solve the mismatch problem of integrated sensing and communication functions.

[0005] However, although the RIS-enabled integrated sensing and communication system can bring significant performance gains, its actual design still faces two major challenges:

[0006] First, the impact of target position uncertainty on sensing performance. The target detection of the integrated sensing and communication system relies on the base station transmitting high-power beams to illuminate the target to obtain its state information. In actual scenarios, there is often a deviation between the estimated target angle and the true angle. This deviation not only leads to distorted detection results, but also significantly reduces energy utilization efficiency. At the same time, in complex scenarios such as multipath propagation, dynamic changes in target and user positions, and occlusion, the sensing and communication performance will be further affected, so it is necessary to consider the target angle uncertainty in system design.

[0007] Second, the constraints of imperfect channel state information on system optimization. The RIS-assisted integrated sensing and communication system highly depends on the cascade channel state information (CSI) of "base station-RIS-user" in beamforming, resource allocation, and other core links. However, as a passive device, RIS cannot actively transmit pilot signals or receive pilots for channel estimation, making it much more difficult to obtain cascade CSI than the direct channel from the base station to the user. This not only may reduce the quality of service of the base station to the user, but also causes additional transmission power overhead. Therefore, in the intelligent metasurface-enabled integrated sensing and communication system, it is necessary to fully consider the impact of imperfect CSI on system design.

[0008] Existing research attempts to improve to some extent in response to the above problems, such as using bounded error or statistical channel error modeling methods. However, most existing research still mainly focuses on improving communication performance, and pays insufficient attention to ensuring sensing performance, and generally considers the target position information obtained by the base station as ideal and known, without considering the angle deviation in actual scenarios, resulting in insufficient robustness of the design scheme in complex environments.

[0009] In summary, under the dual constraints of imperfect channel state information and target position uncertainty, how to jointly optimize system parameters to ensure the quality of service of communication and sensing while effectively reducing the transmission power of the base station is still a technical problem to be solved in the field of RIS-assisted integrated sensing and communication. SUMMARY

[0010] The purpose of the present application is to provide a robust design method for beamforming of an integrated sensing and communication system based on intelligent metasurfaces, which can effectively reduce the transmission power of the base station while meeting the user's communication rate demand and the requirement of target beamforming gain, and improve the robustness of the system under the dual constraints of "imperfect channel state information" and "uncertain target position", avoiding performance degradation caused by uncertainty.

[0011] To achieve the above object, the technical scheme adopted by the present application is:

[0012] The beamforming robust design method of the sensing-integrated system based on the intelligent metasurface comprises the following steps:

[0013] S1, an intelligent metasurface-assisted sensing-integrated system is constructed, the system comprising a dual-function base station equipped with a uniform linear array, a passive intelligent metasurface equipped with a plurality of reflecting units, a plurality of communication users, and a plurality of detection targets; the base station simultaneously transmits two types of data streams, one type of data stream being used to provide services for the communication users, and the other type of data stream being used exclusively for sensing the detection targets;

[0014] S2, the uncertainty in the system is characterized, considering the imperfect channel state information and the uncertainty of the target position, the channel from the base station to the user adopting a bounded error model, and the angle of arrival of the detection target adopting an interval uncertainty model;

[0015] S3, a robust optimization model is established, taking the minimization of the total transmission power of the base station as the optimization objective, and jointly optimizing the base station precoding matrix and the phase shift matrix of the intelligent metasurface, while satisfying the minimum rate constraint of all communication users, the minimum beamforming gain constraint of all detection targets, and the modulus-one constraint of the reflecting units of the intelligent metasurface;

[0016] S4, the robust optimization model is solved, for the minimum rate constraint of the communication users, a successive convex approximation method is used to linearize the non-convex term, and S-Procedure and Nemirovski's lemma are used to convert the bounded channel error constraint into a solvable linear matrix inequality; for the minimum beamforming gain constraint of the detection targets, a sampling method is used to convert the angle of arrival uncertainty interval into a constraint set on a finite number of sampling points, and then a successive convex approximation method is used to convert the non-convex constraint of the beamforming gain into a convex constraint; an alternating optimization strategy is used to decompose the robust optimization problem into two sub-problems about the base station precoding matrix and the phase shift matrix of the intelligent metasurface, and the two sub-problems are solved alternately until the change in the base station transmission power is less than a set threshold, and the optimal base station precoding matrix and the optimal phase shift matrix of the intelligent metasurface are obtained.

[0017] Further, in step S1, the base station is equipped with N uniform linear arrays, and the intelligent metasurface is equipped with M reflecting units; the total number of the two types of data streams transmitted by the base station is K+L, wherein K data streams are used to serve K single-antenna users, and L data streams are used exclusively for sensing L detection targets; the intelligent metasurface is a passive intelligent metasurface, and its phase shift matrix is a diagonal matrix, each diagonal element corresponding to a phase shift coefficient of a reflecting unit, and the modulus of each phase shift coefficient being 1.

[0018] Further, in step S1, the received signal-to-noise ratio of the communication user is:

[0019]

[0020] where h k is the channel state vector from the base station to the kth user, g k is the channel state vector from the intelligent metasurface to the kth user, Φ is the phase shift matrix of the intelligent metasurface, G is the channel state matrix from the base station to the intelligent metasurface, w k is the precoding vector allocated by the base station for the kth user, w i is the precoding vector allocated by the base station for other users or sensing targets except the kth user, σ 2 is the variance of additive white noise, and K+L is the total number of data streams simultaneously transmitted by the base station, of which K are for communication users and L are for sensing targets.

[0021] Further, in step S2, the modeling process of the bounded error model is: where g k is the real channel, is the estimated channel, Δg k is the channel error, ‖Δg k ‖2≤α k , α k is the bounded radius of the channel error; the direction of arrival of the sensing target is represented as: θ l ∈[θ l -Δθ,θ l +Δθ], and Δθ is the direction of arrival error.

[0022] Further, the beamforming gain at the sensing target l is:

[0023]

[0024] where, is the direction vector corresponding to the direction of arrival θ l , d0 is the interval between adjacent transmitting array elements, and λ represents the wavelength; x represents the signal transmitted by the base station; W represents the precoding matrix of the base station; W H represents the conjugate transpose matrix of the precoding matrix W.

[0025] Further, in step S3, the robust optimization model is:

[0026]

[0027] where, denotes the optimization objective of minimizing the total transmit power of the base station; constraints C1 denotes the minimum rate requirement that each communication user needs to meet, C2 denotes the minimum beamforming gain requirement that each probing target needs to meet, and C3 denotes the constraint that the phase shift coefficient of each reflecting element of the intelligent metasurface satisfies the modulus 1.

[0028] Further, in step S4, when processing the minimum rate constraint of the communication user, the specific implementation process is as follows:

[0029] (1) The constraint C1 is converted into the following equivalent form:

[0030]

[0031] wherein δ=[δ1,...,δ K ] T is a slack variable, W -k is a matrix obtained by removing the kth item of the beamforming matrix W; and

[0032] (2) The lower bound of formula (1) is linearly approximated by using the successive convex approximation method, and the following formula (2) is obtained:

[0033]

[0034] wherein E k ,e k and z k are respectively:

[0035]

[0036] wherein and Φ (n) are the optimal solution of the n th iteration;

[0037] The bounded error model is brought into formula (3), and the following formula (4) is further obtained:

[0038]

[0039] wherein

[0040] Finally, the S-Procedure theorem is used to convert the semi-infinite constraint of the channel error into a finite linear matrix inequality:

[0041]

[0042] wherein is a slack variable; I M is an M-dimensional unit matrix;

[0043] (2) For formula (2), the Schur complement is used to convert it into:

[0044]

[0045] in,

[0046] Will Substituting into formula (6) and applying Nemirovski's lemma, we can further transform it into a linear matrix inequality:

[0047]

[0048] In the formula, ξ=[ξ1,...,ξ K ] T As slack variables,

[0049] Furthermore, in step S4, when processing the minimum beamforming gain constraint of the detected target, the sampling method is used to handle the angle uncertainty. Specifically, multiple sampling points are selected within the uncertainty interval of the angle of arrival, and then the successive convex approximation method is used to achieve convexity by performing a first-order Taylor expansion on the quadratic term of the beamforming gain, so that the original infinite constraint is approximated as satisfying the beamforming gain constraint at all sampling points.

[0050] Further, in step S4, the specific process of the alternating optimization strategy is as follows: First, fix the phase shift matrix of the smart metasurface, solve the subproblem with the base station precoding matrix as the optimization variable, and obtain the optimal precoding matrix under the current phase shift matrix; then fix the optimal precoding matrix, solve the subproblem with the phase shift matrix of the smart metasurface as the optimization variable, and obtain the optimal phase shift matrix under the current precoding matrix; repeat the above process until the relative change in base station transmit power obtained in two adjacent iterations is less than the set threshold, and the iteration terminates.

[0051] Furthermore, in step S4, when solving the subproblem with the phase shift matrix of the intelligent metasurface as the optimization variable, the signal-to-noise ratio residual and penalty coefficient are introduced. The non-convex constraint of the mode 1 of the intelligent metasurface reflection unit is transformed into a convex constraint through concave-convex programming. At the same time, the relevant terms are approximated by combining the first-order Taylor expansion. After obtaining the convex optimization subproblem, the optimal phase shift matrix is ​​solved.

[0052] The beneficial effects of the above scheme are as follows:

[0053] 1. This invention directly addresses the practical problems of imperfect channel state information and target location deviations in real-world applications. By constructing a dual robust optimization model for coverage channel error and angle of arrival error, it ensures that the user's communication rate and the beamforming gain requirements of the sensed target can be met simultaneously within all possible error ranges. This effectively avoids communication interruptions or sensing failures caused by estimation errors, thereby significantly enhancing the stability and reliability of the system in actual deployment.

[0054] 2. The present application takes the minimization of base station transmit power as the core optimization goal, and by jointly optimizing the base station precoding matrix and the intelligent metasurface phase shift matrix, a low-power suboptimal solution can be found while strictly meeting the quality of service requirements of communication and sensing. This effectively avoids the conservative strategy of excessive use of transmit power to overcome uncertainty, improves the system energy efficiency, helps to reduce the energy consumption and operating cost of the base station, and ensures the overall communication quality of the network.

[0055] 3. For the complex problem of joint optimization of active and passive beams in the integrated communication and sensing system, the present application effectively solves the difficulty of solving caused by the high coupling between optimization variables and the non-convexity of constraints. An alternating optimization strategy is adopted to decompose the original complex problem into two solvable sub-problems and iteratively solve them, ensuring the realizability and effectiveness of the algorithm.

[0056] 4. For different forms of uncertainty such as channel error and angle error, the present application respectively adopts accurate transformation tools and sampling strategies for processing, and applies successive convex approximation methods to the solution of non-convex constraints, greatly reducing the computational complexity while ensuring the performance of suboptimal solutions, meeting the real-time optimization requirements in dynamic scenarios, and allowing ordinary base stations to run with embedded processors, facilitating engineering deployment. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 is a schematic diagram of the system model of the present application;

[0058] Figure 2 is a basic flowchart of the present application;

[0059] Figure 3 is a comparison curve of user outage probability varying with error level under different design schemes in the embodiment of the present application;

[0060] Figure 4 is a curve of beamforming gain varying with azimuth angle under different beamforming gain requirements in the embodiment of the present application;

[0061] Figure 5 is a comparison curve of base station transmit power varying with angle error under different design schemes and different beam gain requirements in the embodiment of the present application;

[0062] Figure 6 is a comparison curve of base station transmit power varying with channel error level under different design schemes and different rate requirements in the embodiment of the present application. DETAILED DESCRIPTION

[0063] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0064] It should be noted that all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs unless otherwise specifically defined.

[0065] As shown in Figure 1 、 Figure 2 The beamforming robust design method of the all-sensing integrated system based on the intelligent metasurface has the characteristics that it comprises the following steps:

[0066] S1, an intelligent metasurface assisted all-sensing integrated system is constructed, the system comprises a dual-function base station equipped with a uniform linear array, a passive intelligent metasurface equipped with a plurality of reflecting units, a plurality of communication users and a plurality of detection targets; the base station simultaneously transmits two types of data streams, one type is used to provide services for the communication users, and the other type is used to specifically sense the detection targets;

[0067] S2, the uncertainty in the system is characterized, considering the imperfect channel state information and the uncertainty of the target position, the channel from the base station to the user adopts a bounded error model, and the angle of arrival of the detection target adopts an interval uncertainty model;

[0068] S3, a robust optimization model is established, taking the minimum total transmission power of the base station as the optimization objective, and jointly optimizing the base station precoding matrix and the intelligent metasurface phase shift matrix, while satisfying the minimum rate constraint of all communication users, the minimum beamforming gain constraint of all detection targets, and the modulus one constraint of the intelligent metasurface reflecting unit;

[0069] S4, the robust optimization model is solved, for the minimum rate constraint of the communication user, a successive convex approximation method is used to linearize the non-convex term, and S-Procedure and Nemirovski's lemma are used to convert the bounded channel error constraint into a solvable linear matrix inequality; for the minimum beamforming gain constraint of the detection target, a sampling method is used to convert the angle of arrival uncertainty interval into a constraint set on a finite number of sampling points, and then a successive convex approximation method is used to convert the non-convex constraint of the beamforming gain into a convex constraint; an alternating optimization strategy is used to decompose the robust optimization problem into two sub-problems about the base station precoding matrix and the intelligent metasurface phase shift matrix, and the two sub-problems are solved alternately until the change amount of the base station transmission power is less than a set threshold, and the optimal base station precoding matrix and intelligent metasurface phase shift matrix are obtained.

[0070] The implementation process of the application will be described in detail as follows:

[0071] 1) An intelligent metasurface-assisted sensing and communication integrated system includes a dual-function base station equipped with N uniform linear arrays and an intelligent metasurface equipped with M reflecting elements. Among them, the base station simultaneously transmits K+L data streams, K data streams serve K single-antenna users with the assistance of the intelligent metasurface, and L data streams are exclusively used for sensing L detection targets, thereby increasing the degrees of freedom of the system and increasing the detection accuracy. The intelligent metasurface is a passive intelligent metasurface, and its phase shift matrix is a diagonal matrix, with each diagonal element corresponding to the phase shift coefficient of a reflecting element. The transmitted signal s satisfies independent complex Gaussian distribution, and E{ss H} = I K+L . Let W represent the precoding matrix of the base station, and Therefore, the transmitted signal of the base station can be represented as x = Ws.

[0072] In addition, it is assumed that the channel between the base station and the kth user it serves is characterized by PL = -30-10τlog10(d) decibels, where τ represents the path loss exponent and d is the link distance in meters. The small-scale fading follows the Ricean fading, and its complex gain is where G is the Ricean factor, h LOS represents the complex gain of the line-of-sight path, h NLOS is the complex gain of the non-line-of-sight component following the Rayleigh distribution, and h NLOS satisfies that the real part and the imaginary part respectively follow the Gaussian distribution with a mean of 0 and a variance of σ 2 . Therefore, the signal received by the kth user can be represented as n k is an additive white noise and follows the CN(0, σ 2 ) distribution, is the channel state vector from the base station to the user, is the channel state vector from the intelligent metasurface to the user, is the channel state matrix from the base station to the intelligent metasurface, is defined as the phase shift matrix of the intelligent metasurface. Thus, the received signal-to-noise ratio at the user k is:

[0073]

[0074] where h k is the channel state vector from the base station to the kth user, g k is the channel state vector from the intelligent metasurface to the kth user, Φ is the phase shift matrix of the intelligent metasurface, G is the channel state matrix from the base station to the intelligent metasurface, w k is the precoding vector allocated by the base station to the kth user, w i is the precoding vector allocated by the base station to other users or sensing targets except the kth user, and σ 2K+L is the total number of data streams transmitted by the base station at the same time, where K is used for communication users and L is used for detecting targets.

[0075] and its data rate (unit: bit / s) is: R k = log2(1+γ k ).

[0076] For the lth sensing target, define θ l , l ∈ {1,..., L} as its angle of arrival, and the communication data stream and the sensing data stream can be used for sensing of the target at the same time. Then the beamforming gain at the target l is:

[0077]

[0078] where, is the direction vector of the angle of arrival θ l , d0 is the interval between adjacent transmitting array elements, and λ represents the wavelength.

[0079] 2) Since the passive passive characteristic of the reflecting element, i.e. the intelligent metasurface can only reflect signals and cannot actively send or receive signals, it is more challenging to obtain the channel state information of the cascade channel than the direct channel. Therefore, the real channel g k can be modeled as where is the estimated channel, and Δg k is the channel error, a bounded error model is adopted, i.e. ‖Δg k ‖2≤α k .

[0080] Here, only the angle of arrival of the point target under the far-field assumption is concerned, and the deviation of the target angle of arrival direction is considered. The uncertain angle of arrival of the target l can be expressed as: θ l ∈ [θ l - Δθ, θ l + Δθ], and Δθ is the angle of arrival error.

[0081] 3) Under the conditions of imperfect channel state information and uncertain target position, the beamforming matrix and the phase shift matrix of the intelligent metasurface are jointly optimized to minimize the total transmit power of the base station, and the rate requirement of the communication user and the beamforming gain requirement of the detection target are ensured, and a robust optimization model for the intelligent metasurface assisted sensing and communication integrated system is established, which includes user rate constraints, beamforming gain constraints and phase shift matrix constraints of the intelligent metasurface, as follows:

[0082]

[0083] where, denotes the optimization objective of minimizing the total transmit power of the base station; constraints C1 denotes the minimum rate requirement of each user, C2 denotes the minimum beamforming gain requirement of each probing target, and C3 denotes the constraint that the phase shift coefficient of each reflecting element of the intelligent metasurface satisfies the modulus 1.

[0084] 4) Due to the high coupling of the optimization variables of the optimization problem in step 3) and the non-convex constraints C1, C2 and C3, the original problem belongs to a non-convex problem and cannot be directly solved. Therefore, a successive convex approximation method is used to alternately iterate and optimize to obtain a suboptimal solution of the original problem, and the specific process is as follows:

[0085] 5) In terms of meeting the user rate requirement, C1 in step 3) is converted into the following equivalent form:

[0086]

[0087] where δ = [δ1,..., δ K ] T is a slack variable, and W -k is a matrix obtained by removing the kth item of the beamforming matrix W. To satisfy the constraint C1, the above two non-convex inequalities need to be solved, therefore, inequalities (1) and (2) are solved separately.

[0088] 6.1) In order to solve the quadratic term problem on the left side of non-convex inequality (1) in step 5), a successive convex approximation method is used to linearly approximate the lower bound thereof, as follows:

[0089]

[0090] where E k ,e k and z k are respectively:

[0091]

[0092] Here, and Φ (n) are the optimal solutions of the n th iteration.

[0093] The channel error model is brought into inequality (3), which can be further converted into the following form:

[0094]

[0095] where

[0096] In order to solve the bounded channel error model, S-Procedure is used to further convert (4) into the following form:

[0097]

[0098] where are the slack variables.

[0099] 6.2) Substitute the channel error model into the non-convex inequality (2) in step 5) and convert it into the following form by using Schur complement:

[0100]

[0101] where

[0102] Substitute into equation (6) and apply Nemirovski’s lemma to further convert it into the following form:

[0103]

[0104] where ξ = [ξ1,...,ξ K ] T are the slack variables,

[0105] 7) In solving the requirement of beamforming gain for the detection target, the angle of arrival error in constraint C2 is converted into an uncertainty set Θ = [θ l - Δθ, θ l + Δθ] and the sampling method is used to solve the problem of this infinite continuous uncertainty set, with the following steps:

[0106] 7.1) Select S sampling points on the infinite continuous uncertainty set, and the error angle set is further converted into where

[0107] Thus, the beamforming gain for the detection target is

[0108] 7.2) Since the beamforming gain obtained in step 7.1) has a quadratic term, the successive convex approximation method is used to convert it into the following form by first-order Taylor expansion:

[0109]

[0110] 8) To solve the problem of high coupling between optimization variables W and Φ, the alternating optimization method is used to decompose the problem in step 3) into two sub-problems, with the following steps:

[0111] 8.1) Given the optimization variable Φ, the original problem P1 can be decomposed into a sub-problem P2, as follows:

[0112]

[0113] 8.2) Given the optimization variable W, the original problem P1 can be decomposed into subproblem P3 as follows:

[0114]

[0115] where a = [a1,..., a k ] T is the signal-to-noise ratio residual (introducing the signal-to-noise ratio residual can achieve better results in simulation), and (5)' is

[0116] The concave-convex programming is used to solve the modulus-one problem of the non-convex constraint C3. The constraint |φ m | 2 = 1, can be written as 1 ≤ |φ m | 2 ≤ 1. By using the first-order Taylor expansion, the lower bound of 1 ≤ |φ m | 2 part is By introducing the relaxation variable b = [b1,..., b 2M ] T and the penalty coefficient η [t] , the subproblem P3 is further converted into the following form:

[0117]

[0118] 9) The subproblems P2 and P4 are already non-convex, and the alternating iteration can be used to obtain the suboptimal solution of the original problem.

[0119] The effectiveness and superiority of the present application are illustrated by the simulation experiment as follows:

[0120] Figures 3-6 The related situations of the user communication interruption probability, the beamforming gain and the base station transmission power of the sensing-integrated system when the present method is used are presented. The simulation parameters are set as follows: the positions of the devices involved in the present application are modeled in two dimensions, the dual-function base station is located at (0m, 0m), and is equipped with 6 transmission antennas; the intelligent metasurface is located at (50m, 10m) and is composed of 16 reflecting units; the positions of the 3 communication users are randomly distributed with (70m, 0m) as the center and 5m as the radius; the estimated angles of the 2 probe targets are 50° and -50°, respectively. The noise power is -174dBm, the path loss exponent from the base station to the user is 4, the path loss exponent from the intelligent metasurface to the user is 2, and the path loss exponent from the base station to the intelligent metasurface is 2.2; the Rician factor index is 5. For the user k, the channel state information error is where ρ ∈ [0, 1) represents the error level; the angle error of the probe target is θ l ∈ [θ l- Δθ, θ l + Δθ], wherein Δθ is an angle deviation.

[0121] Figure 3 The contrast graph of user interruption probability changing with channel error level shows that the user interruption probability changes differently with the channel error level under different design schemes (robust design, non-robust design, etc.) and different rate requirements. The user interruption probability under the robust design scheme is significantly smaller than that under the non-robust design scheme. This shows that the robust design of the application can effectively cope with the adverse effects of channel errors, greatly improve the reliability of user communication, and reduce the possibility of communication interruption. Figure 4 The curve graph of beamforming gain changing with azimuth angle shows that the beamforming gain obtained by the method of the application has obvious peak values near the target azimuth angle and low side lobes under different beamforming gain requirements (0.8W, 1.0W, 1.2W). This shows that the application can accurately focus the beam on the azimuth of the detection target, effectively suppresses the interference to other azimuths while meeting different gain requirements, and ensures the accuracy and directivity of perception. Figure 5 The contrast graph of base station transmit power changing with angle error shows that the robust design scheme has a smaller rising amplitude of transmit power with angle error under different beam gain requirements than the random phase shift. Even if the angle error increases, the transmit power required by the robust design can still be well controlled within a reasonable range, which shows that the application can guarantee system performance with relatively low transmit power when dealing with angle errors, improving energy utilization efficiency. The "illusion" of performance stability of the non-robust design actually sacrifices the robustness to angle errors. Figure 6 The contrast graph of base station transmit power changing with channel error level shows that the rising amplitude of transmit power with channel error level of the robust design scheme is significantly smaller than that of the random phase shift under different rate requirements, and the transmit power of the robust design is lower under the same channel error level and rate requirement. This shows that the robust design of the application can reduce the consumption of base station transmit power when there are errors in the channel.

[0122] The simulation results show that the application can guarantee communication reliability and perception accuracy while optimizing transmit power when dealing with uncertain factors such as channel errors and angle errors, and has significant performance advantages in the integrated communication and sensing system.

[0123] Finally, it should be noted that the parts of the present application not described in detail are all prior art. Those skilled in the art can understand that the above only describes the preferred examples of the present application and is not used to limit the present application. Although the present application is described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions recorded in the foregoing examples or make equivalent replacements for some of the technical features. Any modification, equivalent replacement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A robust design method of beamforming for a system of integrated sensing and communication based on smart metasurface, characterized in that, Comprise the following steps: S1, construct an intelligent metasurface assisted integrated sensing and communication system, the system contains a dual-function base station equipped with a uniform linear array, a passive intelligent metasurface equipped with multiple reflecting elements, multiple communication users and multiple detection targets; The base station transmits two types of data streams, one type is used to provide services for communication users, and the other type is used to perceive detection targets; S2, characterize the uncertainty in the system, considering the imperfect channel state information and the uncertainty of the target position, the channel from the base station to the user adopts a bounded error model, and the angle of arrival of the detection target adopts an interval uncertainty model; S3, establish a robust optimization model to minimize the total transmit power of the base station as the optimization objective, jointly optimize the base station precoding matrix and the intelligent metasurface phase shift matrix, while satisfying the minimum rate constraint of all communication users, the minimum beamforming gain constraint of all detection targets, and the modulus one constraint of the intelligent metasurface reflecting elements; S4, solve the robust optimization model, for the minimum rate constraint of the communication user, linearize the non-convex term by successive convex approximation method, and convert the bounded channel error constraint into a solvable linear matrix inequality by using S-Procedure and Nemirovski's lemma; For the minimum beamforming gain constraint of the detection target, the interval of the angle of arrival uncertainty is converted into a constraint set on a finite number of sampling points by using the sampling method, and the non-convex constraint of the beamforming gain is converted into a convex constraint by using the successive convex approximation method; Adopt an alternating optimization strategy, decompose the robust optimization problem into two sub-problems about the base station precoding matrix and the intelligent metasurface phase shift matrix, and solve them alternately until the change of the base station transmit power is less than a certain threshold, to obtain the optimal base station precoding matrix and intelligent metasurface phase shift matrix.

2. The smart metasurface-based system-of-systems sensing and cognition integration system beamforming robust design method of claim 1, wherein In step S1, the base station is equipped with N uniform linear arrays, and the intelligent metasurface is equipped with M reflecting elements; The total number of two types of data streams sent by the base station is K+L, where K data streams are used to serve K single-antenna users, and L data streams are used to perceive L detection targets; The intelligent metasurface is a passive intelligent metasurface, and its phase shift matrix is a diagonal matrix, each diagonal element corresponds to the phase shift coefficient of a reflecting element, and the modulus of each phase shift coefficient is 1.

3. The smart metasurface-based system-of-systems sensing and communication integration beamforming robust design method of claim 2, wherein, In step S1, the received signal-to-noise ratio of the communication user is: where h k is the channel state vector from the base station to the kth user, g k is the channel state vector from the intelligent metasurface to the kth user, Φ is the phase shift matrix of the intelligent metasurface, G is the channel state matrix from the base station to the intelligent metasurface, w k is the precoding vector allocated by the base station for the kth user, w i is the precoding vector allocated by the base station for other users or sensing targets except the kth user, σ 2 is the variance of the additive white noise, K+L is the total number of data streams simultaneously transmitted by the base station, where K is for communication users and L is for probing targets.

4. The smart metasurface-based system-of-systems sensing and cognition integration system beamforming robust design method of claim 1, wherein In step S2, the modeling process of the bounded error model is: where g k is the real channel, is the estimated channel, Δg k is the channel error, ‖Δg k ‖2≤α k , α k is the bounded radius of the channel error; the direction of arrival of the probing target is denoted as: θ l ∈ [θ l - Δθ, θ l + Δθ], and Δθ is the direction of arrival error.

5. The smart metasurface-based system-of-systems sensing and communication integration beamforming robust design method of claim 4, wherein, The beamforming gain at the detection target l is: In the formula, is the angle of arrival θ l The corresponding direction vector, d0 is the interval between adjacent transmitting array units, λ represents the wavelength; x represents the signal transmitted by the base station; W represents the precoding matrix of the base station; W H represents the conjugate transpose matrix of the precoding matrix W.

6. The smart metasurface-based system-of-systems sensing and cognition integration system beamforming robust design method of claim 1, wherein In step S3, the robust optimization model is: C2: p(0 l ) ≥ Q l , 0 l ∈ [0 l - Δθ, 0 l + Δθ], C3: |φ m | 2 = 1, 1≤m≤M In the formula, represents the optimization goal of minimizing the total transmit power of the base station; the constraint C1 represents the minimum rate requirement that each communication user needs to meet, C2 represents the minimum beamforming gain requirement that each probe target needs to meet, and C3 represents the constraint that the phase shift coefficient of each reflecting element of the intelligent metasurface satisfies the modulus 1.

7. The smart metasurface-based system-of-systems sensing and cognition integration system beamforming robust design method of claim 1, wherein In step S4, when processing the minimum rate constraint of the communication user, the specific implementation process is: (1) Convert the constraint C1 to the following equivalent form: where δ = [δ1,..., δK] is the vector of the K beamforming weights. K ] T is the relaxed variable, W -k is the matrix obtained by removing the k-th entry from the beamforming matrix W. (2) Linearly approximate the lower bound of formula (1) by using the successive convex approximation method, to obtain: wherein E k , e k and z k are respectively: wherein and Φ (n) is the optimal solution of the n-th iteration; Further, by introducing the bounded error model into formula (3), we obtain: wherein Finally, the S-Procedure theorem is used to convert the semi-infinite constraint of the channel error into a finite linear matrix inequality: wherein is a slack variable; I M is an M-dimensional identity matrix; (2) For formula (2), convert it to by using Schur complement: wherein, Bringing into equation (6), and using Nemirovski's lemma, it is further converted into linear matrix inequality: Bringing into equation (6), and using Nemirovski's lemma, it is further converted into linear matrix inequality: where ξ = [ξ1,..., ξn]T. K ] T are the slack variables, 8. The smart metasurface-based system-of-systems sensing and cognition integration system beamforming robust design method of claim 1, wherein In step S4, when processing the detection target minimum beamforming gain constraint, a sampling method is used to process the angle uncertainty, specifically: a plurality of sampling points are selected in the angle of arrival uncertainty interval, and then a convex approximation method is used to realize convexization by first-order Taylor expansion of the quadratic term of the beamforming gain, and the original infinite constraint is approximated to the beamforming gain constraint to be satisfied at all sampling points.

9. The smart metasurface-based system-of-systems sensing and cognition integration system beamforming robust design method of claim 1, wherein In step S4, the specific process of the alternating optimization strategy is as follows: first, fix the intelligent metasurface phase shift matrix, solve the sub-problem taking the base station precoding matrix as the optimization variable, and obtain the optimal precoding matrix under the current phase shift matrix; then fix the optimal precoding matrix, solve the sub-problem taking the intelligent metasurface phase shift matrix as the optimization variable, and obtain the optimal phase shift matrix under the current precoding matrix; repeat the above process until the relative change of the base station transmission power obtained by adjacent two iterations is less than a set threshold, and the iteration is terminated.

10. The smart metasurface-based system-of-systems sensing and cognition integration beamforming robust design method of claim 1, wherein In step S4, when solving the sub-problem taking the intelligent metasurface phase shift matrix as the optimization variable, a signal-to-noise ratio residual and a penalty coefficient are introduced, the modulus non-convex constraint of the intelligent metasurface reflecting unit is converted into a convex constraint through concave-convex programming, and the related term is approximated by first-order Taylor expansion, and then the optimal phase shift matrix is solved after obtaining the convex optimization sub-problem.

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