Wireless sensing and communication method based on super diagonal reconfigurable smart surface

Abstract

The present invention discloses a wireless perception and communication method based on a super diagonal reconfigurable smart surface, which relates to the field of communication perception technology. The method includes constructing an ISAC system model, tracking and locating a perception target based on the ISAC system model using an echo signal received by a sensor communication base station, and proposing an optimization problem of minimizing a joint a posteriori Cramer-Rao bound according to the tracking and locating result; based on the optimization problem, decomposing a first sub-problem for optimizing the beamforming of the sensor communication base station and a second sub-problem for optimizing the reflection coefficient of the super diagonal reconfigurable smart surface, converting the first sub-problem into a convex problem for solution using a semi-positive definite relaxation algorithm, and solving the second sub-problem by quantizing the matrix using an augmented Lagrange multiplier method and a penalty dual decomposition framework. The present invention improves the estimation accuracy of perception target parameters by jointly optimizing the beamforming of the sensor communication base station and the reflection coefficient of the super diagonal reconfigurable smart surface.

Description

Technical Field

[0001] The present invention belongs to the technical field of communication perception, and in particular relates to a wireless perception and communication method based on a super diagonal reconfigurable smart surface. Background Art

[0002] With the continuous growth of wireless communication network applications, the next generation of wireless networks has an increasingly urgent need for high-quality wireless connections and high-precision sensing capabilities. As a key component of modern wireless networks, ISAC technology is gradually emerging. ISAC technology is committed to effectively integrating communication and sensing functions to support intelligent applications such as smart manufacturing and smart transportation. Its significant advantage is that it can use a shared platform to simultaneously transmit data and perceive the environment, thereby greatly improving spectrum utilization efficiency and reducing hardware costs and signaling overhead. At the same time, through the collaborative design of communication and sensing, ISAC technology achieves mutual benefit and win-win results for both parties, optimizes signal processing technology, meets a variety of communication and sensing performance indicators, and thus improves the overall performance and application flexibility of the system.

[0003] At present, Reconfigurable Intelligent Surface (RIS) is regarded as a revolutionary example of wireless networks. RIS acts as a relay for incoming signals by flexibly adjusting the propagation direction, signal superposition mode and phase shift of signals in three-dimensional space, significantly enhancing the spectrum efficiency. Although traditional RIS can manipulate incident electromagnetic waves through programmable reflection and phase conversion to achieve passive beamforming and reduce energy consumption, its reflection coefficients usually form a diagonal matrix, which limits the interaction between ports, thereby restricting the beamforming capability and system performance.

[0004] As an upgraded version of the traditional RIS, the super diagonal reconfigurable smart surface (BD-RIS) came into being. It represents a new type of reconfigurable scattering parameter network architecture. By introducing impedance connections between ports, a group-connected network structure is constructed, which significantly improves the signal reception quality and system energy efficiency. However, the existing perception communication methods using super diagonal reconfigurable smart surfaces are limited by the static channel modeling assumption, and the target tracking error in dynamic multipath scenarios is large. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention proposes a wireless sensing and communication method based on a super diagonal reconfigurable smart surface. This method cleverly combines the essence of super diagonal reconfigurable smart surface and ISAC technology, aiming to achieve more efficient wireless communication and more accurate environmental perception. By giving full play to the powerful beamforming capability of the super diagonal reconfigurable smart surface and combining the integration characteristics of ISAC, the present invention can flexibly adjust and jointly optimize the beamforming of the sensor communication base station and the super diagonal reconfigurable smart surface reflection coefficient in a multi-user dynamic multipath scenario, thereby greatly improving the spectrum utilization of the system, meeting the growing demand for wireless communications, and significantly improving the accuracy of perception parameter estimation, and ensuring the downlink and rate of communication users.

[0006] The technical solution of the present invention is:

[0007] A wireless sensing and communication method based on a super diagonal reconfigurable smart surface comprises the following steps:

[0008] S1, build a sensor communication base station, a super diagonal reconfigurable smart surface, a dynamic sensing target and ISAC system model consisting of 100 communication users;

[0009] S2. Based on the ISAC system model, the dynamic sensing target is tracked and located using the echo signal received by the sensor communication base station, and an optimization problem of minimizing the joint posterior Cramer-Rao bound is proposed according to the tracking and positioning results;

[0010] S3. Based on the optimization problem, decompose a first sub-problem for optimizing the beamforming of the sensor communication base station, and use a semi-positive definite relaxation algorithm to transform the first sub-problem into a convex problem for solution;

[0011] S4. Based on the optimization problem, decompose a second sub-problem for optimizing the reflection coefficient of the super diagonal reconfigurable smart surface, and solve the second sub-problem by using an augmented Lagrange multiplier method and a penalty dual decomposition framework vectorized matrix;

[0012] S5. Alternately solve the first subproblem and the second subproblem to obtain optimal beamforming and optimal reflection coefficient.

[0013] Furthermore, step S1 is specifically as follows:

[0014] S101, build a sensor communication base station, a super diagonal reconfigurable smart surface, a dynamic sensing target and The super diagonal reconfigurable intelligent surface is equipped with a rectangular uniform planar array composed of N antennas, and the N antennas are connected to a The super diagonal reconfigurable smart surface adopts a group connection architecture. The ports are divided into groups, ports belonging to the same group are fully connected, and ports between different groups are independent of each other; set the group index set to , and the The number of ports in the group is ; Reflection coefficient matrix of superdiagonal reconfigurable smart surface Modeled as:

[0015]

[0016]

[0017] in is the function for constructing a block diagonal matrix, For the A block diagonal matrix, for The identity matrix of order;

[0018] S102, setting the motion model of the dynamic sensing target to a constant speed model, and the sensor communication base station based on the first The posterior motion state of the dynamic perception target in each round To predict the Prior motion state estimation of dynamic sensing targets , and estimate the prior motion state , adjust the sensor communication base station beamforming, and at the same time the super diagonal reconfigurable smart surface changes the reflection coefficient matrix; the sensor communication base station communicates with the communication user and uses the detection signal to detect the dynamic perception target, based on the prior motion state estimation The sensor communication base station uses the echo signal received from the dynamic sensing target to obtain the measurement signal vector And estimate the The posterior motion state of the round ;

[0019] S103, based on the constructed ISAC system, determine the sensor communication base station at the Round and The superposition and sum of the communication and perception signals sent in the time slot;

[0020] Among them, in Round and Time slot, the signal transmitted by the sensor communication base station is expressed as:

[0021]

[0022] In the formula, represents the beamforming of the communication signal, It represents the beamforming of the sensing signal, and the superposition is recorded as ; Represents a communication signal serving a communication user, satisfying , Represents the detection signal used for perception, satisfying and , the superposition is recorded as ; is the K-order identity matrix, for The unit matrix, is the number of antennas of the sensor communication base station;

[0023] S104, based on the superposition obtained in step S103, determine the The communication user is in The signals and received in the round are determined according to the signals and Signal-to-interference-noise ratio of each communication user :

[0024]

[0025] in Representation Matrix No. List, Representation Matrix No. List, is the variance of the noise in the user received signal; , Indicates the sensor communication base station and the The channels between the communicating users, for The conjugate transposed matrix of Represents the super diagonal reconfigurable smart surface and the The channels between the communicating users, for The conjugate transposed matrix of Represents the channel between the sensor communication base station and the superdiagonal reconfigurable smart surface.

[0026] Further, in step S104,

[0027]

[0028]

[0029]

[0030] in represents the reference channel power gain, represents the distance between the sensor communication base station and the kth communication user, represents the azimuth from the sensor communication base station to the kth communication user, represents the distance between the superdiagonal reconfigurable smart surface and the kth communication user, represents the azimuth from the superdiagonal reconfigurable smart surface to the kth communication user, represents the distance between the sensor communication base station and the superdiagonal reconfigurable smart surface, represents the azimuth from the sensor communication base station to the superdiagonal reconfigurable smart surface, represents the azimuth angle from the super-diagonal reconfigurable smart surface to the sensor communication base station; represents the steering vector of the superdiagonal reconfigurable smart surface; Represents the steering vector of the sensor communication base station.

[0031] Furthermore, step S2 is specifically as follows:

[0032] S201, determining a state transition model of a dynamic sensing target according to the ISAC system model:

[0033]

[0034] in, is the state transition matrix, is the identity matrix, is a 0 matrix, To set the deviation, For the The posterior motion state of the dynamic perception target in each round, For the Prior motion state estimation of dynamic perception targets in rounds; is with The corresponding covariance matrix is ;

[0035] If you get the Dynamic perception target posterior motion state in rounds , then Prior motion state estimation of dynamic sensing targets in rounds for:

[0036]

[0037] No. The prior state covariance matrix in the round is defined as:

[0038]

[0039] in, It is The posterior state covariance matrix in the round;

[0040] S202, obtaining the sensor communication base station in the The received echo signals are subjected to two-dimensional estimation of Doppler frequency shift and time delay using the deconvolution of the generalized matched filter output, and the measurement model and signal-to-noise ratio of the dynamic sensing target are determined based on the two-dimensional estimation results;

[0041] Among them The echo signal received by the round-by-round sensor communication base station is:

[0042]

[0043] In the formula, is the array gain factor, represents the complex reflection coefficient, represents the Doppler shift of the dynamically sensed target, represents the delay of dynamic perception target, for The superposition of communication signal and detection signal at every moment, It means that the mean is zero and the variance is The complex additive Gaussian white noise, The response matrix is:

[0044]

[0045] in represents the channel between the super-diagonal reconfigurable smart surface and the dynamic sensing target;

[0046] The deconvolution of the generalized matched filter output is used to perform two-dimensional estimation of the Doppler frequency shift and time delay of the dynamic sensing target, which is expressed as:

[0047]

[0048] in for The adjoint matrix of

[0049] The measurement model for establishing dynamic perception targets is expressed as:

[0050]

[0051]

[0052]

[0053] In the formula, Indicates the carrier frequency, represents the speed of light, It has zero mean and variance The measured Gaussian noise, It has zero mean and variance The measured Gaussian noise, It has zero mean and variance The measurement Gaussian noise is defined as , then the measurement model of dynamic perception target is expressed as:

[0054]

[0055] in, is the measurement function, For the The motion state of the dynamic perception target in the round, is with Unrelated measurement noise, the corresponding covariance matrix is:

[0056]

[0057] The signal-to-noise ratio of the dynamic perception target is finally determined as:

[0058]

[0059] S203, linearize the measurement model using an extended Kalman filter, and track the state of the dynamic sensing target using a Kalman filter based on the state transition model, the measurement model, and the linearized measurement model; the specific Kalman gain is

[0060]

[0061] in for The Jacobian matrix of for The conjugate transposed matrix of ;

[0062] In the state tracking phase, The posterior motion state of the dynamic perception target in each round Given by:

[0063]

[0064] No. The posterior state covariance matrix in the round is:

[0065]

[0066] S204. Based on the tracking status, the optimization of the beamforming of the sensor communication base station and the reflection coefficient of the super diagonal reconfigurable smart surface is considered to construct an optimization problem of the joint PCRB to ensure the downlink and rate minimization of the communication user:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073] in, is the maximum transmit power, for The square of the F norm, For the The signal-to-interference-to-noise ratio of each communication user is represents the minimum signal-to-interference-noise ratio; C1 limits the maximum transmission power of the sensor communication base station, C2 guarantees the channel quality of the communication user, and C3, C4 and C5 describe the reflection coefficient characteristics of the super diagonal reconfigurable smart surface in a mathematical way; For dynamic perception target Prior motion state estimation in rounds Direction coordinates, express The corresponding joint posterior Cramér-Rao bound is, For dynamic perception target Prior motion state estimation in rounds Direction coordinates, express The corresponding joint posterior Cramér-Rao bound is, For dynamic perception target Prior motion state estimation in rounds Direction speed, express The corresponding joint posterior Cramér-Rao bound is, For dynamic perception target Prior motion state estimation in rounds Direction speed, express The corresponding joint posterior Cramér-Rao bound.

[0074] Further, in step S204,

[0075]

[0076]

[0077]

[0078]

[0079] in is the Fisher information matrix, for No. elements, for No. elements, for No. elements, for No. elements.

[0080] Furthermore, the first sub-problem is:

[0081]

[0082]

[0083]

[0084] in, is an intermediate variable of elements, yes of elements, for The adjoint matrix, intermediate variables , , is an orthogonal matrix containing the eigenvectors.

[0085] Furthermore, the first subproblem is transformed into a convex problem using a semi-positive definite relaxation algorithm for solution:

[0086] S301, introducing an auxiliary variable as the upper limit of the first sub-problem;

[0087] S302, using a semi-positive definite relaxation algorithm to relax the first sub-problem about constraints to transform the first subproblem from a concave problem to a convex problem for solution.

[0088] Furthermore, the second sub-problem is:

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] in,

[0095]

[0096]

[0097]

[0098] Indicates the trace operation. represents the real part operation, , , , as well as are all intermediate variables in the decomposition process. and are all intermediate coefficients in the decomposition process.

[0099] Furthermore, the augmented Lagrange multiplier method and the penalty dual decomposition framework are used to vectorize the matrix to solve the second subproblem:

[0100] S401, introducing a splitting variable to decouple the orthogonality constraint in the second sub-problem from other constraints;

[0101] S402. The decoupled second sub-problem is processed by augmented Lagrange multiplier method, and then the penalty dual decomposition framework is used to vectorize the matrix solution.

[0102] The present invention also proposes a wireless sensing and communication system using the above method, comprising:

[0103] Building blocks for building a system consisting of a sensor communication base station, a super diagonal reconfigurable smart surface, a sensing target and ISAC system model consisting of 100 communication users;

[0104] An optimization module is used to track and locate the perceived target based on the ISAC system model using the echo signal received by the sensor communication base station, and propose an optimization problem of minimizing the joint posterior Cramer-Rao bound according to the tracking and positioning results;

[0105] A solution module is used to decompose a first sub-problem for optimizing the beamforming of a sensor communication base station based on the optimization problem, and transform the first sub-problem into a convex problem for solution using a semi-positive definite relaxation algorithm; decompose a second sub-problem for optimizing the reflection coefficient of a superdiagonal reconfigurable smart surface based on the optimization problem, and solve the second sub-problem by vectorizing the matrix using an augmented Lagrange multiplier method and a penalty dual decomposition framework; alternately solve the first sub-problem and the second sub-problem to obtain an optimal beamforming and an optimal reflection coefficient.

[0106] Compared with the prior art, the wireless sensing and communication method based on super diagonal reconfigurable smart surface proposed in the present invention has at least the following significant beneficial effects:

[0107] 1) Significantly improve the accuracy of perception parameter estimation

[0108] The present invention achieves high-precision estimation of parameters such as the position and speed of the sensing target by jointly optimizing the beamforming of the sensing communication base station and the reflection coefficient of the superdiagonal reconfigurable smart surface. By tracking the sensing target and minimizing the joint a posteriori PCRB bound, the present invention significantly improves the accuracy and reliability of the perception parameter estimation, providing strong technical support for wireless sensing applications.

[0109] 2) Ensure the quality of communication user links

[0110] While optimizing the perception performance, the present invention fully considers the link conditions of the communication users. Through the carefully designed beamforming and reflection coefficient adjustment strategies, the present invention can improve the perception accuracy while ensuring that the downlink and rate of the communication users are not affected, thereby meeting the demand for high-quality communication services in wireless networks.

[0111] 3) Propose efficient algorithms to solve non-convex problems

[0112] In response to the non-convexity challenge in optimization problems, the present invention proposes an efficient algorithm based on alternating optimization and semi-positive relaxation. By decomposing sub-problems, relaxing constraints and using existing mathematical tools, the present invention can effectively solve complex non-convex optimization problems, improving the feasibility and practicality of the algorithm.

[0113] 4) Flexibly adapt to complex environments

[0114] The introduction of super diagonal reconfigurable smart surfaces provides wireless networks with higher flexibility and adaptability. By dynamically adjusting the reflection coefficient, super diagonal reconfigurable smart surfaces can respond intelligently according to different environmental conditions and perception requirements, thus achieving flexible adaptation and efficient perception of complex environments.

[0115] 5) Reduce system cost and complexity

[0116] The present invention realizes the integration and coordination of sensing and communication functions by jointly optimizing the configuration of sensor communication base stations and super diagonal reconfigurable smart surfaces. This integrated design not only improves the overall performance of the system, but also reduces hardware costs and signaling overhead, providing strong support for the sustainable development of wireless networks.

[0117] In summary, the present invention achieves a significant improvement in the accuracy of perception parameter estimation by deploying super diagonal reconfigurable smart surfaces and jointly optimizing the beamforming of the sensor communication base station and the reflection coefficient of the super diagonal reconfigurable smart surface, while ensuring the link quality of the communication users. Compared with traditional technologies, the present invention shows significant advantages in perception accuracy, communication performance, algorithm efficiency, environmental adaptability and system cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] In order to more clearly illustrate the specific implementation of the present invention or the technical solution in the prior art, the following is a brief introduction to the drawings required for the specific implementation or the prior art description. In all drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn according to the actual scale:

[0119] Figure 1 A flowchart of a wireless sensing and communication method based on a super diagonal reconfigurable smart surface provided in Embodiment 1 of the present invention;

[0120] Figure 2 A schematic diagram of the structure of the ISAC system provided in Example 1 of the present invention;

[0121] Figure 3 A PCRB comparison diagram of the group connection size of 2 and the size of 4 provided in Example 1 of the present invention under the condition of changing the number of superdiagonal reconfigurable smart surface elements;

[0122] Figure 4 A PCRB comparison diagram of a group connection size of 2 and a group connection size of 4 under the condition of changing the maximum transmission power of the sensor communication base station provided in Embodiment 1 of the present invention;

[0123] Figure 5 A system block diagram of a wireless sensing and communication system based on a super diagonal reconfigurable smart surface provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0124] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0125] In the description of the present invention, it should be understood that the terms “include” and “comprises” indicate the presence of described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0126] It should also be understood that the terms used in the present specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, the singular forms "a", "an" and "the" are intended to include plural forms unless the context clearly indicates otherwise.

[0127] It should be further understood that the term "and / or" used in the present specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes these combinations. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in the present invention generally indicates that the associated objects are in an "or" relationship.

[0128] The word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)", depending on the context.

[0129] Example 1

[0130] like Figure 1 As shown, the present invention provides a wireless sensing and communication method based on a super diagonal reconfigurable smart surface, the method comprising the following steps:

[0131] S1, build a sensor communication base station, a super diagonal reconfigurable smart surface, a dynamic sensing target and ISAC system model consisting of 3 communicating users.

[0132] In the embodiment of the present invention, step S1 is specifically:

[0133] S101, build a sensor communication base station, a super diagonal reconfigurable smart surface, a dynamic sensing target and The ISAC system is composed of communication users, wherein the sensor communication base station is equipped with multiple antennas, the dynamic sensing target and the communication user are equipped with a single antenna, and the super diagonal reconfigurable intelligent surface is equipped with a rectangular uniform planar array composed of N antennas, which can be modeled as N antennas connected to a The scattering parameter network of the ports. Assume that the vector and Respectively The input and output signals of the ports have The input and output relationship of the port network can be expressed as , the incident signal passes through the reflection coefficient matrix Processing, where the set of reflective elements (N antennas) is represented by The super-diagonal reconfigurable smart surface adopts a group connection architecture. Specifically, all The ports are divided into Groups. Ports belonging to the same group are fully connected, while ports in different groups are independent of each other. Set the group index set to , and the The number of ports in the group is For this class, the reflection coefficient matrix It can be modeled as:

[0134] (1)

[0135] (2)

[0136] in is the function for constructing a block diagonal matrix, For the A block diagonal matrix, for It can be seen that the group connection architecture can flexibly set the group size (i.e. the number of ports in each group), which is more flexible and balanced than traditional RIS. Assume that the location of the sensor communication base station is q b =[ x b , y b ] T ∈ R 2×1 , No. The position of each communicating user is recorded as q c =[ x c k , y c k ] T ∈ R 2×1 ( ), whose position is known a priori to the sensor communication base station, and the super diagonal reconfigurable position of the smart surface q r =[ x r , y r ] T ∈ R 2×1 , while the position of the dynamic sensing target is unknown and can be estimated by the sensing communication base station with sensing capability. The position and velocity of the dynamic sensing target are expressed as q (t)=[ x s (t), y s (t) ] T ∈ R 2×1 , q ̇ (t)=[ x ̇ s (t), y ̇ s (t) ] T ∈ R 2×1 Here, the position and speed of the dynamic perception target are all about time. Parameters, The range is [0,T] ,in is the maximum attention period. For ease of expression, the time period Discrete into several time slots and remain constant in one time slot , and , Recorded as the motion state of the dynamic perception target .

[0137] S102, Dynamic Perception The motion model is a constant speed model, and the sensor communication base station is based on the The posterior motion state of the dynamic perception target in each round To predict the Prior motion state estimation of dynamic sensing targets , and estimate the prior motion state , adjust the sensor communication base station beamforming, and at the same time the super diagonal reconfigurable smart surface changes the reflection coefficient matrix; the sensor communication base station communicates with the communication user and uses the detection signal to detect the dynamic perception target, based on the prior motion state estimation The sensor communication base station uses the echo signal received from the dynamic sensing target to obtain the measurement signal vector And estimate the The posterior motion state of the round .

[0138] S103, based on the constructed ISAC system, determine the sensor communication base station at the Round and The superposition and sum of the communication and perception signals sent in the time slot;

[0139] Specifically, in Round and Time slot, the signal transmitted by the sensor communication base station is expressed as:

[0140] (3)

[0141] In the formula, and They represent the beamforming of the communication signal and the beamforming of the perception signal respectively, and the superposition is recorded as . Represents a communication signal serving a communication user, satisfying , Represents the detection signal used for perception, satisfying and , the superposition is recorded as ; is the K-order identity matrix, for The identity matrix of order; is the number of antennas of the sensor communication base station.

[0142] S104, based on the superposition and determination of The communication user is in The signals and received in the round are determined according to the signals and The signal-to-interference-noise ratio of a communication user.

[0143] Specifically, in Round, No. The signal received by a communication user is expressed as:

[0144] (4)

[0145] in, represents additive white Gaussian noise. To simplify the notation, .

[0146] Indicates the sensor communication base station and the Channels between communicating users:

[0147]

[0148] represents the distance between the sensor communication base station and the kth communication user, Indicates the reference channel power gain at a distance of 1 meter, θ b,k ∈[- π 2 ， π 2 ] represents the azimuth from the sensor communication base station to the kth communication user, represents the steering vector of the sensor communication base station;

[0149] Represents the super diagonal reconfigurable smart surface and the Channels between communicating users:

[0150]

[0151] represents the distance between the superdiagonal reconfigurable smart surface and the kth communication user, θ r,k ∈[- π 2 ， π 2 ] represents the azimuth from the superdiagonal reconfigurable smart surface to the kth communication user, represents the steering vector of the superdiagonal reconfigurable smart surface;

[0152] Represents the channel between the sensor communication base station and the super diagonal reconfigurable smart surface:

[0153]

[0154] represents the distance between the sensor communication base station and the superdiagonal reconfigurable smart surface, θ b,r ∈[- π 2 ， π 2 ] represents the azimuth from the sensor communication base station to the superdiagonal reconfigurable smart surface, θ r,b ∈[- π 2 ， π 2 ] represents the azimuth angle from the super-diagonal reconfigurable smart surface to the sensor communication base station;

[0155] Steering vector of sensor communication base station and super-diagonal reconfigurable smart surfaces The expression is:

[0156] (5)

[0157] No. In round 1, The signal-to-interference-to-noise ratio (SINR) of a communication user is expressed as:

[0158] (6)

[0159] in Representation Matrix No. List, is the variance of the noise in the user received signal.

[0160] The above steps comprehensively construct an ISAC system model that integrates perception and communication functions, and carefully considers dynamic parameters, signal processing and the actual propagation environment, providing a solid foundation for subsequent performance optimization.

[0161] S2. Based on the ISAC system model, the dynamic sensing target is tracked and located using the echo signal received by the sensor communication base station, and an optimization problem of minimizing the joint a posteriori Cramer-Rao bound (PCRB) is proposed according to the tracking and positioning results.

[0162] In the embodiment of the present invention, step S2 is specifically:

[0163] S201, determining a state transition model of a dynamic sensing target according to the ISAC system model;

[0164] Specifically, the motion state variables of the dynamic sensing target are defined as ,According to the ISAC system model, the state transition model of the dynamic perception target is expressed as:

[0165] (7)

[0166] in, is the state transition matrix, is the identity matrix, is a 0 matrix, To set the deviation, For the The posterior motion state of the round, For the Prior motion state estimation of rounds; is with The corresponding covariance matrix is ;

[0167] If you get the Dynamic perception target posterior motion state in rounds , then Prior motion state estimation of dynamic sensing targets in rounds for:

[0168] (8)

[0169] No. The prior state covariance matrix in the round is defined as:

[0170] (9)

[0171] in, It is The posterior state covariance matrix in the epoch.

[0172] S202, obtaining the sensor communication base station in the The received echo signals are subjected to two-dimensional estimation of Doppler frequency shift and time delay using the deconvolution of the generalized matched filter output, and the measurement model and signal-to-noise ratio of the dynamic sensing target are determined based on the two-dimensional estimation results;

[0173] Specifically, the sensor communication base station works in full-duplex mode, transmitting signals and receiving echo signals at the same time. The echo signal received by the round-trip sensor communication base station is expressed as:

[0174] (10)

[0175] In the formula, is the array gain factor, represents the complex reflection coefficient, represents the Doppler shift of the dynamically sensed target, represents the delay of dynamic perception target, for The superposition of communication signal and detection signal at every moment, It means that the mean is zero and the variance is The complex additive Gaussian white noise, The response matrix is:

[0176]

[0177] in Represents the channel between the superdiagonal reconfigurable smart surface and the dynamic sensing target:

[0178]

[0179] represents the distance between the superdiagonal reconfigurable smart surface and the dynamic sensing target, Represents the azimuth from the super-diagonal reconfigurable smart surface to the dynamic sensing target.

[0180] The deconvolution of the generalized matched filter output is further used to perform two-dimensional estimation of the Doppler frequency shift and time delay of the dynamic sensing target, which is expressed as:

[0181] (11)

[0182] When When the maximum value is reached, the two-dimensional estimation of the Doppler frequency shift and time delay of the dynamic sensing target is obtained. ,in for The adjoint matrix of .

[0183] The measurement model for establishing dynamic perception targets is expressed as:

[0184] (12)

[0185] (13)

[0186] (14)

[0187] In the formula, and denote the carrier frequency and the speed of light respectively, , and Respectively represent zero mean and variance , and The measurement signal vector is defined as .

[0188] For the sake of simplicity, formulas (12)-(14) can be written as:

[0189] (15)

[0190] in, is the measurement function defined in equations (12)-(14), is with Unrelated measurement noise, the corresponding covariance matrix is:

[0191] (16)

[0192] Finally, the signal-to-noise ratio (SNR) of the dynamic perception target is determined as:

[0193] (17)

[0194] S203, linearizing the measurement model using an extended Kalman filter, based on the state transition model, the measurement model and the linearized measurement model, Kalman filtering tracks the state of dynamically sensed targets;

[0195] Specifically, to linearize the measurement model, calculate The Jacobian matrix , then the Kalman gain is .

[0196] In the state tracking stage, dynamically perceive the target's posterior motion state Given by:

[0197] (18)

[0198] No. The posterior state covariance matrix in the round is:

[0199] (19)

[0200] It should be noted that is the trace representing the prior mean square error, is the trace representing the posterior mean square error.

[0201] S204. Based on the tracking status, the optimization of the beamforming of the sensor communication base station and the reflection coefficient of the super diagonal reconfigurable smart surface is considered to construct an optimization problem of the joint PCRB that ensures the downlink of the communication user and minimizes the rate.

[0202] The goal of the present invention is to jointly optimize the beamforming of the sensor communication base station and the reflection coefficient of the superdiagonal reconfigurable smart surface to minimize the joint a posteriori Cramér-Rao bound (PCRB) while ensuring that the downlink and rate of the communication user meet the predetermined requirements. Therefore, the optimization problem constructed by the present invention is specifically:

[0203]

[0204]

[0205]

[0206]

[0207]

[0208] (20)

[0209] in, is the maximum transmit power, for The square of the F norm, For the The signal-to-interference-to-noise ratio of each communication user is represents the minimum signal-to-interference-noise ratio; C1 limits the maximum transmission power of the sensor communication base station, C2 guarantees the channel quality of the communication user, and C3, C4 and C5 describe the reflection coefficient characteristics of the super diagonal reconfigurable smart surface in a mathematical way; For dynamic perception target Prior motion state estimation in rounds Direction coordinates, express The corresponding joint posterior Cramér-Rao bound is, For dynamic perception target Prior motion state estimation in rounds Direction coordinates, express The corresponding joint posterior Cramér-Rao bound is, For dynamic perception target Prior motion state estimation in rounds Direction speed, express The corresponding joint posterior Cramér-Rao bound is, For dynamic perception target Prior motion state estimation in rounds Direction speed, express The corresponding joint posterior Cramér-Rao bound.

[0210] Since the Fisher information matrix The inverse lower order of is close to the predicted PCRB matrix, and the predicted PCRB matrix is ​​equal to the posterior state mean square error matrix in the Kalman iteration, so there is , It is The posterior state covariance matrix in the round. Tracked motion state The The PCRB of the parameters to be estimated is used as No. elements are obtained. Therefore, the joint PCRB of the dynamic perception target position and speed is obtained by the following formula:

[0211] (twenty one)

[0212] (twenty two)

[0213] (twenty three)

[0214] (twenty four)

[0215] for No. elements, for No. elements, for No. elements, for No. elements.

[0216] S3. Based on the optimization problem, decompose a first sub-problem for optimizing the beamforming of the sensor communication base station, and use a semi-positive definite relaxation algorithm to transform the first sub-problem into a convex problem for solution.

[0217] In order to solve the non-convex optimization problem with complex dependencies between variables, this embodiment decomposes the optimization problem into two suboptimal problems: the sensor communication base station beamforming optimization problem and the super diagonal reconfigurable smart surface reflection coefficient optimization problem.

[0218] Specifically, by deducing , , , and The relationship between is used to decompose the first sub-problem from the optimization problem.

[0219] More specifically, due to , then the Fisher information matrix can be expressed as:

[0220] (25)

[0221] The intermediate variable , , is the intermediate process matrix;

[0222] Furthermore, the inverse of the Fisher information matrix is ​​expressed as:

[0223] (26)

[0224] is the unit matrix, through Perform eigenvalue decomposition and set

[0225] (27)

[0226] In the formula, is an orthogonal matrix containing the eigenvectors, is a diagonal matrix of eigenvalues, so

[0227]

[0228] (28)

[0229] In the formula, the intermediate variable .according to The diagonal structure of

[0230] (29)

[0231] in , yes Therefore, No. The elements are calculated as:

[0232] (30)

[0233] in, is an intermediate variable of elements, yes of elements, for The adjoint matrix of . Therefore, the PCRB of each parameter is given as:

[0234] (31)

[0235] (32)

[0236] (33)

[0237] (34)

[0238] Therefore, the first sub-problem for optimizing the beamforming of the sensor communication base station can be expressed as:

[0239]

[0240]

[0241]

[0242] For the first sub-problem mentioned above, we can use the semi-positive definite relaxation algorithm to transform it into a convex problem and solve it:

[0243] S301, introduce auxiliary variables As the upper bound of the first subproblem;

[0244] S302, using a semi-positive definite relaxation algorithm to relax the first sub-problem about constraints to transform the first subproblem from a concave problem to a convex problem for solution.

[0245] Specifically, it can be expressed as: Convert the first sub-problem back to:

[0246]

[0247]

[0248]

[0249]

[0250]

[0251]

[0252] Clearly, this is a convex problem and can be easily solved by standard convex optimization algorithms.

[0253] S4. Based on the optimization problem, a second sub-problem for optimizing the reflection coefficient of the super diagonal reconfigurable smart surface is decomposed, and the second sub-problem is solved by using an augmented Lagrange multiplier method and a penalty dual decomposition framework vectorized matrix.

[0254] It should be noted that the process of decomposing the second sub-problem from the optimization problem is similar to the process of decomposing the first sub-problem from the optimization problem, and will not be repeated in this embodiment. The decomposed second sub-problem for optimizing the reflection coefficient of the super diagonal reconfigurable smart surface can be expressed as:

[0255]

[0256]

[0257]

[0258]

[0259] (35)

[0260] in,

[0261]

[0262]

[0263] .

[0264] Indicates the trace operation. represents the real part operation, , , , as well as are all intermediate variables in the decomposition process. and are all intermediate coefficients in the decomposition process.

[0265] For the second sub-problem mentioned above, in this embodiment, the augmented Lagrange multiplier method and the penalty dual decomposition framework vectorized matrix are used to solve the second sub-problem. Specifically, the following steps are included:

[0266] S401. Since the objective function of the second sub-problem is about The fourth term of and Decompose the originally difficult quartic function into and The quadratic function of , and decouple the orthogonal constraints;

[0267] S402, the sub-problem is processed by the augmented Lagrange multiplier method as follows:

[0268]

[0269]

[0270]

[0271]

[0272] (36)

[0273] In the formula, is the penalty factor, is the dual variable (Lagrange multiplier).

[0274] Then, following the PDD framework, we vectorize the matrix to solve the problem (36) using a two-layer iterative algorithm. The inner layer is updated alternately using a block coordinate descent algorithm. , and , the outer selective update Lagrange multiplier or penalty coefficient .

[0275] S5. Alternately solve the first subproblem and the second subproblem to obtain optimal beamforming and optimal reflection coefficient.

[0276] To verify the superiority of the present invention, we conducted a simulation comparison with the existing mechanism based on the same network parameters. In the simulation environment, the location of the sensor communication base station is set to , the location of the super diagonal reconfigurable smart surface is and the initial position of the perceived target , where the number of super diagonal reconfigurable smart surface elements is set to 12, the number of sensor communication base station antennas is 16, and its maximum transmission power is set to 25dBm.

[0277] During the simulation, we focused on counting and analyzing the impact of the following two key conditions on performance: the number of super-diagonal reconfigurable smart surface elements and the maximum transmission power of the sensor communication base station. Figure 3 and Figure 4 , Figure 3 and Figure 4 The comparison of each PCRB under the conditions of changing the number of super diagonal reconfigurable smart surface elements and the maximum transmission power of the sensor communication base station is shown respectively. Figure 2 The effect of the number of super diagonal reconfigurable smart surface elements on PCRB is plotted. It is obvious that a larger group connection size of the super diagonal reconfigurable smart surface contributes to a larger beamforming gain. Figure 3 The influence of the maximum transmission power of the sensor communication base station on PCRB is shown. It can be clearly seen from the figure that as the maximum transmission power of the sensor communication base station increases, more useful information is extracted from the echo signal, resulting in an increase in perception performance. The simulation results clearly show that in the BD-RIS-assisted integrated sensing and communication (ISAC) network environment, the scheme proposed in the present invention exhibits excellent performance. The present invention successfully achieves the goal of minimizing the joint PCRB by collaboratively optimizing multiple key parameters including the sensor communication base station beamforming matrix and the super diagonal reconfigurable smart surface reflection coefficient.

[0278] The simulation results clearly show that the proposed scheme shows excellent performance in the super-diagonal reconfigurable smart surface assisted integrated sensing and communication (ISAC) network environment. The scheme effectively optimizes the sensing performance by jointly designing the beamforming of the sensor communication base station and the reflection coefficient of the super-diagonal reconfigurable smart surface, and tracking the target state in real time. Specifically, the present invention successfully achieves the goal of minimizing the positioning and velocity perception error (PCRB) by collaboratively optimizing multiple key parameters including the sensor communication base station beamforming matrix and the super-diagonal reconfigurable smart surface reflection coefficient.

[0279] In summary, the present invention provides a wireless sensing and communication method based on a super diagonal reconfigurable smart surface, which adopts a new security sensing and communication control framework. In this scheme, the sensor communication base station beamforming sends communication information to the communication user, and sends sensing information to the target to track the target's position and speed. In order to achieve the goal of PCRB minimization, the scheme optimizes multiple parameters through collaborative optimization, including the beamforming matrix of the sensor communication base station and the super diagonal reconfigurable smart surface reflection coefficient. The performance of this scheme in sensing the position and speed of target tracking is better than existing work.

[0280] Example 2

[0281] like Figure 5 As shown, an embodiment of the present invention provides a wireless sensing and communication system based on a super diagonal reconfigurable smart surface, which is used to implement the wireless sensing and communication method based on the super diagonal reconfigurable smart surface. Specifically, the system includes:

[0282] Building blocks for building a system consisting of a sensor communication base station, a super diagonal reconfigurable smart surface, a dynamic sensing target and ISAC system model consisting of 100 communication users;

[0283] An optimization module is used to track and locate the dynamic sensing target based on the ISAC system model using the echo signal received by the sensor communication base station, and propose an optimization problem of minimizing the joint a posteriori Cramer-Rao bound (PCRB) according to the tracking and positioning results;

[0284] A solution module is used to decompose a first sub-problem for optimizing the beamforming of a sensor communication base station based on the optimization problem, and transform the first sub-problem into a convex problem for solution using a semi-positive definite relaxation algorithm; based on the optimization problem, decompose a second sub-problem for optimizing the reflection coefficient of a super-diagonal reconfigurable smart surface, and solve the second sub-problem by vectorizing the matrix using an augmented Lagrange multiplier method and a penalty dual decomposition framework, and alternately solve the first sub-problem and the second sub-problem to obtain an optimal beamforming and an optimal reflection coefficient.

[0285] It should be understood that the wireless sensing and communication system based on the super diagonal reconfigurable smart surface provided in the embodiment of the present invention and the wireless sensing and communication method based on the super diagonal reconfigurable smart surface provided in the above embodiment are based on the same inventive concept. For more specific working principles of each module in the wireless sensing and communication system based on the super diagonal reconfigurable smart surface in the embodiment of the present invention, please refer to the above embodiment and will not be repeated in this embodiment.

Claims

1. A wireless sensing and communication method based on a super diagonal reconfigurable smart surface, characterized in that: The following steps are involved: S1. Construct an ISAC system model consisting of 1 sensor communication base station, 1 super diagonal reconfigurable intelligent surface, 1 dynamic sensing target and k communication users; specifically: S101, construct an ISAC system consisting of a sensor communication base station, a super diagonal reconfigurable smart surface, a dynamic sensing target and k communication users; the super diagonal reconfigurable smart surface is equipped with a rectangular uniform planar array consisting of N antennas, and the N antennas are connected to a The super diagonal reconfigurable smart surface adopts a group connection architecture. The ports are divided into groups, ports belonging to the same group are fully connected, and ports between different groups are independent of each other; set the group index set to , and the The number of ports in the group is ; Reflection coefficient matrix of superdiagonal reconfigurable smart surface Modeled as: in is the function for constructing a block diagonal matrix, For the A block diagonal matrix, for The identity matrix of order; S102, setting the motion model of the dynamic sensing target to a constant speed model, and the sensor communication base station based on the first The posterior motion state of the dynamic perception target in each round To predict the Prior motion state estimation of dynamic sensing targets , and estimate the prior motion state , adjust the sensor communication base station beamforming, and at the same time the super diagonal reconfigurable smart surface changes the reflection coefficient matrix; the sensor communication base station communicates with the communication user and uses the detection signal to detect the dynamic perception target, based on the prior motion state estimation The sensor communication base station uses the echo signal received from the dynamic sensing target to obtain the measurement signal vector And estimate the The posterior motion state of the round ; S103, based on the constructed ISAC system, determine the sensor communication base station at the The superposition and sum of the communication and sensing signals sent in the round and the tth time slot; Among them, in In round t and time slot t, the signal transmitted by the sensor communication base station is expressed as: In the formula, represents the beamforming of the communication signal, It represents the beamforming of the sensing signal, and the superposition is recorded as ; Represents a communication signal serving a communication user, satisfying , Represents the detection signal used for perception, satisfying and , the superposition is recorded as ; is the K-order identity matrix, for The unit matrix, is the number of antennas of the sensor communication base station; S104, based on the superposition obtained in step S103, determining the kth communication user in the The signal sum received in the round, and the signal interference noise ratio of the kth communication user is determined according to the signal sum : in Representation Matrix No. List, Representation Matrix No. List, is the variance of the noise in the user received signal; , Indicates the sensor communication base station and the The channels between the communicating users, for The conjugate transposed matrix of represents the channel between the superdiagonal reconfigurable smart surface and the kth communication user, for The conjugate transposed matrix of represents the channel between the sensor communication base station and the super diagonal reconfigurable smart surface; S2. Based on the ISAC system model, the dynamic sensing target is tracked and located using the echo signal received by the sensor communication base station, and an optimization problem of minimizing the joint posterior Cramer-Rao bound is proposed according to the tracking and positioning results; S3. Based on the optimization problem, decompose a first sub-problem for optimizing the beamforming of the sensor communication base station, and use a semi-positive definite relaxation algorithm to transform the first sub-problem into a convex problem for solution; S4. Based on the optimization problem, decompose a second sub-problem for optimizing the reflection coefficient of the super diagonal reconfigurable smart surface, and solve the second sub-problem by using an augmented Lagrange multiplier method and a penalty dual decomposition framework vectorized matrix; S5. Alternately solve the first subproblem and the second subproblem to obtain optimal beamforming and optimal reflection coefficient.

2. According to claim 1, a wireless sensing and communication method based on a super diagonal reconfigurable smart surface is characterized in that: In step S104, in represents the reference channel power gain, represents the distance between the sensor communication base station and the kth communication user, represents the azimuth from the sensor communication base station to the kth communication user, represents the distance between the superdiagonal reconfigurable smart surface and the kth communication user, represents the azimuth from the superdiagonal reconfigurable smart surface to the kth communication user, represents the distance between the sensor communication base station and the superdiagonal reconfigurable smart surface, represents the azimuth from the sensor communication base station to the superdiagonal reconfigurable smart surface, represents the azimuth angle from the super-diagonal reconfigurable smart surface to the sensor communication base station; represents the steering vector of the superdiagonal reconfigurable smart surface; Represents the steering vector of the sensor communication base station.

3. According to claim 1, a wireless sensing and communication method based on super diagonal reconfigurable smart surface is characterized in that: Step S2 is specifically as follows: S201, determining a state transition model of a dynamic sensing target according to the ISAC system model: in, is the state transition matrix, is the identity matrix, is a 0 matrix, To set the deviation, For the The posterior motion state of the dynamic perception target in each round, For the Prior motion state estimation of dynamic perception targets in rounds; is with The corresponding covariance matrix is ; If you get the -1 round of dynamic perception target posterior motion state , then Prior motion state estimation of dynamic sensing targets in rounds for: No. The prior state covariance matrix in the round is defined as: in, It is -1 posterior state covariance matrix in round 1; S202, obtaining the sensor communication base station in the The received echo signals are subjected to two-dimensional estimation of Doppler frequency shift and time delay using the deconvolution of the generalized matched filter output, and the measurement model and signal-to-noise ratio of the dynamic sensing target are determined based on the two-dimensional estimation results; Among them The echo signal received by the round-by-round sensor communication base station is: In the formula, is the array gain factor, represents the complex reflection coefficient, represents the Doppler shift of the dynamically sensed target, represents the delay of dynamic perception target, for The superposition of communication signal and detection signal at every moment, It means that the mean is zero and the variance is The complex additive Gaussian white noise, The response matrix is: in represents the channel between the super-diagonal reconfigurable smart surface and the dynamic sensing target; The deconvolution of the generalized matched filter output is used to perform two-dimensional estimation of the Doppler frequency shift and time delay of the dynamic sensing target, which is expressed as: in for The adjoint matrix of The measurement model for establishing dynamic perception targets is expressed as: In the formula, Indicates the carrier frequency, represents the speed of light, It has zero mean and variance The measured Gaussian noise, It has zero mean and variance The measured Gaussian noise, It has zero mean and variance The measurement Gaussian noise is defined as , then the measurement model of dynamic perception target is expressed as: in, is the measurement function, For the The motion state of the dynamic perception target in the round, is with Unrelated measurement noise, the corresponding covariance matrix is: The signal-to-noise ratio of the dynamic perception target is finally determined as: S203, linearize the measurement model using an extended Kalman filter, and track the state of the dynamic sensing target using a Kalman filter based on the state transition model, the measurement model, and the linearized measurement model; the specific Kalman gain is in for The Jacobian matrix of for The conjugate transposed matrix of ; In the state tracking phase, The posterior motion state of the dynamic perception target in each round Given by: No. The posterior state covariance matrix in the round is: S204. Based on the tracking status, the optimization of the beamforming of the sensor communication base station and the reflection coefficient of the super diagonal reconfigurable smart surface is considered to construct an optimization problem of the joint PCRB to ensure the downlink and rate minimization of the communication user: in, is the maximum transmit power, for The square of the F norm, is the signal-to-interference-noise ratio of the kth communication user, represents the minimum signal-to-interference-noise ratio; C1 limits the maximum transmission power of the sensor communication base station, C2 guarantees the channel quality of the communication user, and C3, C4 and C5 describe the reflection coefficient characteristics of the super diagonal reconfigurable smart surface in a mathematical way; For dynamic perception target Prior motion state estimation in rounds Direction coordinates, express The corresponding joint posterior Cramér-Rao bound is, For dynamic perception target Prior motion state estimation in rounds Direction coordinates, express The corresponding joint posterior Cramér-Rao bound is, For dynamic perception target Prior motion state estimation in rounds Direction speed, express The corresponding joint posterior Cramér-Rao bound is, For dynamic perception target Prior motion state estimation in rounds Direction speed, express The corresponding joint posterior Cramér-Rao bound.

4. According to claim 3, a wireless sensing and communication method based on super diagonal reconfigurable smart surface is characterized in that: In step S204, Where is the Fisher information matrix, for The (1,1)th element of for The (2,2)th element of for The (3,3)th element of for The (4,4)th element of .

5. The wireless sensing and communication method based on super diagonal reconfigurable smart surface according to claim 4, characterized in that: The first sub-problem is: in, is an intermediate variable of elements, yes of elements, for The adjoint matrix, intermediate variables , , is an orthogonal matrix containing the eigenvectors.

6. The wireless sensing and communication method based on super diagonal reconfigurable smart surface according to claim 5, characterized in that: The first subproblem is transformed into a convex problem using the semi-positive definite relaxation algorithm for solution: S301, introducing an auxiliary variable as the upper limit of the first sub-problem; S302, using a semi-positive definite relaxation algorithm to relax the first sub-problem about constraints to transform the first subproblem from a concave problem to a convex problem for solution.

7. The wireless sensing and communication method based on super diagonal reconfigurable smart surface according to claim 4 is characterized in that: The second sub-problem is: in, Indicates the trace operation. represents the real part operation, , , , as well as are all intermediate variables in the decomposition process. and are all intermediate coefficients in the decomposition process.

8. The wireless sensing and communication method based on super diagonal reconfigurable smart surface according to claim 7, characterized in that: The second subproblem is solved by vectorizing the matrix using the augmented Lagrange multiplier method and the penalty dual decomposition framework: S401, introducing a splitting variable to decouple the orthogonality constraint in the second sub-problem from other constraints; S402. The decoupled second sub-problem is processed by augmented Lagrange multiplier method, and then the penalty dual decomposition framework is used to vectorize the matrix solution.

9. A wireless sensing and communication system using the method according to any one of claims 1 to 8, characterized in that: include: A building module is used to construct an ISAC system model consisting of 1 sensor communication base station, 1 superdiagonal reconfigurable smart surface, 1 sensing target and k communication users; An optimization module is used to track and locate the perceived target based on the ISAC system model using the echo signal received by the sensor communication base station, and propose an optimization problem of minimizing the joint posterior Cramer-Rao bound according to the tracking and positioning results; A solving module, used for decomposing a first sub-problem for optimizing the beamforming of the sensor communication base station based on the optimization problem, and converting the first sub-problem into a convex problem for solving by using a semi-positive definite relaxation algorithm; Based on the optimization problem, a second sub-problem for optimizing the reflection coefficient of the super diagonal reconfigurable smart surface is decomposed, and the second sub-problem is solved by using an augmented Lagrange multiplier method and a penalty dual decomposition framework vectorized matrix; the first sub-problem and the second sub-problem are solved alternately to obtain an optimal beamforming and an optimal reflection coefficient.

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