A ris-assisted integrated sensing and communication joint beamforming design method and system

Abstract

The application belongs to the technical field of wireless communication, and relates to a RIS-assisted integrated sensing and communication joint beamforming design method and system, which comprises the following steps: constructing an RIS-assisted ISAC system; initializing a digital beamforming matrix and a phase shift matrix according to a base station total power constraint; constructing an unconstrained optimization problem by using a penalty function method; designing a sending end phase shift matrix based on the unconstrained optimization problem; designing a sending end digital beamforming matrix based on the phase shift matrix; repeating the previous two steps until the change of the system objective function values before and after the two times is less than a preset threshold value, so that the optimal phase shift matrix and the corresponding digital beamforming matrix are obtained. The application effectively improves the performance of the overall system sensing mutual information by alternately optimizing the phase shift matrix and the digital beamforming matrix.

Description

Technical Field

[0001] This application belongs to the field of wireless communication technology, and in particular relates to a RIS-assisted integrated sensing and beamforming design method and system. Background Technology

[0002] As exploration of sixth-generation mobile communication systems (ISCs) progresses, ISAC, as one of the potential core technologies for sixth-generation mobile communication networks, can achieve deep integration of communication and sensing functions by sharing hardware platforms and spectrum resources, thereby improving spectrum efficiency while reducing system costs. Reconfigurable Intelligent Surface (RIS) technology has received widespread attention in ISAC system research due to its ability to dynamically control wireless channels. Traditional RISs have clear limitations: firstly, their single-layer physical structure restricts their potential for implementing more advanced signal processing functions; secondly, existing circuit architectures are relatively simple, mostly supporting only phase modulation with limited degrees of freedom in modulation.

[0003] Existing research addresses the limitations of single-layer structures. Researchers have proposed stacked RIS technology, which, by introducing a multi-layer structure similar to an artificial neural network design, achieves native signal processing of incident electromagnetic waves. See non-patent literature J. An, C. Xu, DWK Ng, GC Alexandropoulos, and C. Huang, “Stackedintelligent metasurfaces for multiuser downlink beamforming in the wavedomain,” IEEE Transactions on Wireless Communications, vol. 24, no. 7, pp.1234–1245, Jul. 2025. This research demonstrates that integrating stacked RIS into the transmitter can replace the analog beamforming module in traditional hybrid beamforming architectures, significantly reducing hardware costs while achieving near-fully digital beamforming performance. To address the limited degrees of freedom in control, researchers have begun exploring BeyondDiagonal Reconfigurable Intelligent Surfaces (BD-RIS) technology. This technology overcomes the limitations of the diagonal scattering matrix by introducing inter-coupling structures between units, thereby constructing more complex scattering matrix forms. Compared to conventional RIS with only phase modulation, BD-RIS significantly enhances the control over transmit and receive RF signals, providing additional performance improvements for the system. See non-patent literature Qiu Xia, Jun Zhang, Kaizhe Xu, Shaodan Ma, Shi Jin, and Chau Yuen, “Statistical CSI-Enabled Optimization for Beyond DiagonalSIM,” IEEE Wireless Communications Letters, vol. 14, no. 9, pp. 2972–2976, Jul. 2025. This research further combines the potential of stacked RIS in multi-layer signal processing with the advantages of BD-RIS in terms of modulation freedom, forming a stacked BD-RIS architecture. This breaks through the limitations of traditional stacked RIS diagonal structures, improves signal processing capabilities in the wave domain, and enables a more efficient communication system.

[0004] Based on the above development status, existing technologies still lack a stacked BD-RIS auxiliary system architecture and its joint optimization method suitable for downlink multi-user ISAC scenarios. The technical problem of how to fully exploit the multi-layer structure and off-diagonal control capabilities of stacked BD-RIS under multi-user communication constraints, thereby improving the system's perception performance, has not yet been solved. Summary of the Invention

[0005] The purpose of this application is to provide a RIS-assisted integrated sensing beamforming design method and system that can effectively improve the system's sensing performance while meeting the quality of service constraints of multi-user communication.

[0006] To achieve the above objectives, this application employs the following technical solution:

[0007] In a first aspect, this application provides a RIS-assisted integrated sensing joint beamforming design method, including:

[0008] S1, Construct a RIS-assisted ISAC system; wherein, the system includes a base station, K single-antenna users, sensing targets, and a stacked BD-RIS, and the base station is equipped with The base station has N transmitting antennas and a sensing and receiving array containing N transmitting antennas. The stacked BD-RIS is disposed outside the transmitting antennas of the base station, and the stacked BD-RIS contains M reflecting units.

[0009] S2, initialize the digital beamforming matrix according to the total power constraint transmitted by the base station. The digital beamforming matrix ,in, To represent a complex number, Indicates the first Digital beamforming vector for a single antenna user K represents the number of users per antenna. Indicates the number of base station transmit antennas; initializes the phase shift matrix. ,in, Indicates the first The phase shift matrix of stacked BD-RIS layers. , This indicates the total number of layers in the BD-RIS stack. express The identity matrix, This indicates the number of reflective units in each BD-RIS layer;

[0010] S3, an unconstrained optimization problem is constructed using the penalty function method;

[0011] S4. Based on the aforementioned unconstrained optimization problem, design the phase shift matrix for the transmitting end;

[0012] S5. Based on the designed phase shift matrix, design the digital beamforming matrix for the transmitter.

[0013] S6. Repeat steps S3 to S5 until the change in the system objective function value between two consecutive steps is less than a preset threshold, and obtain the optimal phase shift matrix and the corresponding digital beamforming matrix.

[0014] Furthermore, the transfer function of the stacked BD-RIS for:

[0015]

[0016] In the formula, Indicates the first layer to the first Interlayer transfer matrix of layer BD-RIS; This represents the inter-layer transmission matrix from the transmitting antenna to the first-layer BD-RIS. This represents the phase shift matrix of the first-layer BD-RIS.

[0017] Furthermore, the method of constructing an unconstrained optimization problem using a penalty function includes:

[0018] Establish the objective function for perceptual mutual information and communication constraints:

[0019] )

[0020]

[0021] in, , This represents the minimum signal-to-noise ratio that the user needs to meet. Indicates noise power. This represents the operation of finding the conjugate transpose of a matrix; the intermediate variable matrix. , , , , They are respectively expressed by the following formulas:

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] in, , This represents the steering vector for sensing the emission. The steering vectors of the receiving array are defined as follows:

[0028]

[0029]

[0030] in, Indicates the spacing between the reflective elements of the stacked BD-RIS. Indicates the spacing between the receiving array elements. Indicates the azimuth angle of the perceived target. Indicates the elevation angle of the perceived target;

[0031] make Using the penalty function method, the communication constraints are transformed into an objective function in the form of penalty terms, and the following unconstrained optimization problem is constructed:

[0032]

[0033] in, This is a penalty factor.

[0034] Furthermore, the design of the transmitter phase shift matrix based on the unconstrained optimization problem includes:

[0035] S41, let the phase shift matrix of the transmitting end group connection structure be... :

[0036]

[0037] Where G represents the number of groups of the BD-RIS reflective unit, ; express The identity matrix; This represents the transpose operation on a matrix; using Takagi decomposition to transform the first... The first layer of the BD-RIS transmitter Group phase shift matrix decomposition for ,in Represents a complex unitary matrix;

[0038] S42, according to conjugate gradient direction and To obtain the gradient direction of the unconstrained optimization problem They are respectively:

[0039]

[0040]

[0041]

[0042] Among them, the intermediate variable matrix , , , and They are respectively expressed by the following formulas:

[0043]

[0044]

[0045]

[0046]

[0047]

[0048] Among them, the intermediate variable matrix and Divided by column Group, , and Divided by row Group; , , , and They represent the corresponding first The intermediate variable matrix of the group;

[0049] S43, Update for:

[0050]

[0051] in, yes In the conjugate gradient direction of the unitary space, Indicates the update step size. ;

[0052] renew The Middle The group phase shift matrix is:

[0053]

[0054] S44, will be updated Substitute into the objective function :

[0055]

[0056] S45, repeat steps S41 to S45, and gradually increase the penalty factor. until satisfied , This represents the objective function after the last iteration update. Indicates the convergence threshold;

[0057] S46, according to Repeat steps S41 to S45 for different values, and update each group of phase shift matrices sequentially. To design the first Phase shift matrix of the BD-RIS layer transmitter ;

[0058] S47, according to Repeat steps S41 to S45 for different values ​​to design each phase shift matrix of the BD-RIS stack at the transmitting end.

[0059] Furthermore, the step of designing the digital beamforming matrix of the base station based on the pre-designed phase shift matrix includes:

[0060] S51, recalculate the transfer function based on the updated phase shift matrix. ;

[0061] S52, the objective function for perceptual mutual information and communication constraints are rewritten, and their expressions are as follows:

[0062]

[0063]

[0064] in, , , ;

[0065] S53, Based on the expression in step S52, construct the constrained optimization problem:

[0066]

[0067]

[0068]

[0069]

[0070] S54 eliminates the rank-one constraint through positive semidefinite relaxation, transforming the constrained optimization problem into a positive semidefinite programming form, which is then solved using the CVX solver. ;

[0071] S55, the solution obtained The optimal digital beamforming matrix is ​​obtained by performing rank-one recovery using the Gaussian randomization method.

[0072] Furthermore, it also includes the construction of the joint pre-encoding codeword library during the pre-configuration phase:

[0073] Based on the stacked BD-RIS deployment configuration and scenario parameters, multiple sample scenarios are established; the scenario parameters include user location distribution, target perception area, propagation environment and channel characteristics.

[0074] For each of the sample scenarios, the optimization steps described in claim 1 are performed to obtain a joint precoding matrix; wherein the joint precoding matrix includes a digital beamforming matrix and phase shift matrices of each layer of the stacked BD-RIS;

[0075] The joint precoding matrices under each of the aforementioned sample scenarios are aggregated into a joint candidate state set;

[0076] The overall transmission matrix composed of phase shift matrices of each layer in the joint candidate state set is quantized into a first number of candidate phase shift codewords; the digital beamforming matrix is ​​quantized into a second number of standard codebooks.

[0077] Furthermore, it also includes:

[0078] Based on the joint candidate state set, the base station establishes a mapping rule between standard PMI codewords, auxiliary indexes, and joint candidate states;

[0079] The base station pre-configures parameters for the terminal via RRC signaling;

[0080] The base station sends a CSI-RS, which is used to trigger the terminal to perform channel measurements.

[0081] The PMI codeword is used to indicate the active precoding direction or precoding category on the base station side; the auxiliary index is used to indicate the candidate subset associated with the selection of the stacked BD-RIS transmission matrix; the PMI codeword and the auxiliary index together determine a set of joint transmission states.

[0082] Furthermore, the terminal performs the following steps:

[0083] The terminal receives CSI-RS transmitted by the base station;

[0084] Based on the received CSI-RS, channel measurements are performed to obtain channel state information for calculating PMI codewords;

[0085] Using communication performance constraints as the calculation metric, the standard PMI codeword and the stacked BD-RIS auxiliary index were determined;

[0086] The standard PMI codeword is reported through the CSI feedback field in the CSI report, and the stacked BD-RIS auxiliary index is reported through the extended field in the CSI report.

[0087] Furthermore, the base station performs the joint precoding transmission process including:

[0088] The base station receives the PMI codewords fed back by the terminal and the stacked BD-RIS auxiliary index;

[0089] Based on the PMI codewords and the stacked BD-RIS auxiliary index, the corresponding joint precoding matrix is ​​matched from the joint candidate state set;

[0090] The base station configures the transmission parameters according to the matched joint precoding matrix and performs downlink signal transmission.

[0091] Secondly, this application provides a RIS-assisted sensing integrated joint beamforming design system, characterized in that it includes:

[0092] A building block is provided for constructing a RIS-assisted ISAC system; wherein the system includes a base station, K single-antenna users, sensing targets, and a stacked BD-RIS, and the base station is equipped with The base station has N transmitting antennas and a sensing and receiving array containing N transmitting antennas. The stacked BD-RIS is disposed outside the transmitting antennas of the base station, and the stacked BD-RIS contains M reflecting units.

[0093] The initialization module is used to initialize the digital beamforming matrix based on the total transmit power constraint of the base station. The digital beamforming matrix ,in, To represent a complex number, Indicates the first Digital beamforming vector for a single antenna user K represents the number of users per antenna. Indicates the number of base station transmit antennas; initializes the phase shift matrix. ,in, Indicates the first The phase shift matrix of stacked BD-RIS layers. , This indicates the total number of layers in the BD-RIS stack. express The identity matrix, This indicates the number of reflective units in each BD-RIS layer;

[0094] The Unconstrained Optimization Problem Construction Module is used to construct unconstrained optimization problems using the penalty function method.

[0095] The phase shift matrix design module is used to design the transmitting phase shift matrix based on the unconstrained optimization problem.

[0096] The digital beamforming design module is used to design the digital beamforming matrix for the transmitter, given a pre-designed phase shift matrix.

[0097] The iterative output module is used to repeat the steps until the change in the system objective function value between two consecutive iterations is less than a preset threshold, thereby obtaining the optimal phase shift matrix and the corresponding digital beamforming matrix.

[0098] Compared with the prior art, the beneficial effects achieved by this application are as follows:

[0099] This application discloses a RIS-assisted sensing integrated joint beamforming design method. By integrating a stacked BD-RIS with the base station transmitter, a phase shift matrix and a transmit digital beamforming matrix are jointly designed. The stacked BD-RIS enables active phase shift control of the transmitted signal and performs analog beamforming, giving the system stronger electromagnetic wave control capabilities at the transmitter. The stacked BD-RIS used in this application overcomes the limitations of diagonal control methods, enabling greater freedom in adjusting the transmitted signal. Therefore, it is more suitable for ISAC systems that simultaneously meet communication and sensing requirements, and helps improve analog beamforming efficiency. Thus, while satisfying user communication service quality constraints, it effectively improves the system's sensing mutual information, achieving a balance between communication and sensing performance. Attached Figure Description

[0100] Figure 1 This is a flowchart illustrating the RIS-assisted integrated sensing beamforming design method according to an embodiment of this application.

[0101] Figure 2 This is a schematic diagram of signaling interaction in an embodiment of this application;

[0102] Figure 3 This is a graph showing the convergence results of the iterative algorithm in this application;

[0103] Figure 4 This is a schematic diagram of the simulation results of an embodiment of this application. Detailed Implementation

[0104] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit this application or its application or use. Example 1

[0105] like Figure 1 As shown in the embodiments of this application, a RIS-assisted integrated sensing joint beamforming design method is proposed, including:

[0106] Step 1: Construct a RIS-assisted ISAC system; wherein the system includes a base station, K single-antenna users, sensing targets, and a stacked BD-RIS, and the base station is equipped with The base station has N transmitting antennas and a sensing and receiving array containing N transmitting antennas. The stacked BD-RIS is disposed outside the transmitting antennas of the base station, and the stacked BD-RIS contains M reflecting units.

[0107] Step 2: Initialize the digital beamforming matrix according to the total power constraint transmitted by the base station. The digital beamforming matrix ,in, To represent a complex number, Indicates the first Digital beamforming vector for a single antenna user K represents the number of users per antenna. Indicates the number of base station transmit antennas; initializes the phase shift matrix. ,in, Indicates the first The phase shift matrix of stacked BD-RIS layers. , This indicates the total number of layers in the BD-RIS stack. express The identity matrix, This indicates the number of reflective units in each BD-RIS layer;

[0108] Step 3: Construct an unconstrained optimization problem using the penalty function method;

[0109] In this embodiment, the transfer function of the stacked BD-RIS is defined first. for:

[0110]

[0111] In the formula, Indicates the first layer to the first Interlayer transfer matrix of layer BD-RIS; This represents the inter-layer transmission matrix from the transmitting antenna to the first-layer BD-RIS. This represents the phase shift matrix of the first-layer BD-RIS.

[0112] Establish the objective function for perceptual mutual information and communication constraints:

[0113] )

[0114]

[0115] in, , This represents the minimum signal-to-noise ratio that the user needs to meet. Indicates noise power. This represents the operation of finding the conjugate transpose of a matrix; the intermediate variable matrix. , , , , They are respectively expressed by the following formulas:

[0116]

[0117]

[0118]

[0119]

[0120]

[0121] in, , This represents the steering vector for sensing the emission. The steering vectors of the receiving array are defined as follows:

[0122]

[0123]

[0124] in, Indicates the spacing between the reflective elements of the stacked BD-RIS. Indicates the spacing between the receiving array elements. Indicates the azimuth angle of the perceived target. Indicates the elevation angle of the perceived target;

[0125] make Using the penalty function method, the communication constraints are transformed into an objective function in the form of penalty terms, and the following unconstrained optimization problem is constructed:

[0126]

[0127] in, This is a penalty factor.

[0128] Step 4: Based on the unconstrained optimization problem, design the phase shift matrix for the transmitting end;

[0129] In this embodiment, the steps for designing the phase shift matrix at the transmitting end include:

[0130] Step 4.1, set the phase shift matrix of the transmitting end group connection structure. :

[0131]

[0132] Where G represents the number of groups of the BD-RIS reflective unit, ; express The identity matrix; This represents the transpose operation on a matrix; using Takagi decomposition to transform the first... The first layer of the BD-RIS transmitter Group phase shift matrix decomposition for ,in Represents a complex unitary matrix;

[0133] Step 4.2, according to conjugate gradient direction and To obtain the gradient direction of the unconstrained optimization problem They are respectively:

[0134]

[0135]

[0136]

[0137] Among them, the intermediate variable matrix , , , and They are respectively expressed by the following formulas:

[0138]

[0139]

[0140]

[0141]

[0142]

[0143] Among them, the intermediate variable matrix and Divided by column Group, , and Divided by row Group; , , , and They represent the corresponding first The intermediate variable matrix of the group;

[0144] Step 4.3, Update for:

[0145]

[0146] in, yes In the conjugate gradient direction of the unitary space, Indicates the update step size. ;

[0147] renew The Middle The group phase shift matrix is:

[0148]

[0149] Step 4.4, update the Substitute into the objective function :

[0150]

[0151] Step 4.5: Repeat steps 4.1 to 4.5, gradually increasing the penalty factor. until satisfied , This represents the objective function after the last iteration update. Indicates the convergence threshold;

[0152] Step 4.6, according to Repeat steps 4.1 to 4.5 for different values ​​to update each set of phase shift matrices sequentially. To design the first Phase shift matrix of the BD-RIS layer transmitter ;

[0153] Step 4.7, according to Repeat steps 4.1 to 4.5 for different values ​​to design each phase shift matrix of the BD-RIS stack at the transmitting end.

[0154] Step 5: Based on the phase shift matrix, design the digital beamforming matrix for the transmitting end;

[0155] In this embodiment, the steps for designing the digital beamforming matrix at the transmitting end are as follows:

[0156] Step 5.1: Recalculate the transfer function based on the updated phase shift matrix. ;

[0157] Step 5.2: Based on the updated transfer function and phase shift matrix, rewrite the sensing mutual information objective function and communication constraints to obtain the updated expressions for the sensing mutual information objective function and communication constraints:

[0158]

[0159]

[0160] in, , , ;

[0161] Step 5.3, based on the expression in Step 5.2, construct the constrained optimization problem:

[0162]

[0163]

[0164]

[0165]

[0166] Step 5.4: Eliminate the rank-one constraint through positive semidefinite relaxation, transforming the constrained optimization problem into a positive semidefinite programming form. Solve the reconstructed optimization problem using the CVX solver to obtain the desired solution. ;

[0167] Step 5.5, the solution obtained The optimal digital beamforming matrix is ​​obtained by performing rank-one recovery using the Gaussian randomization method.

[0168] Step 6: Repeat steps 3 to 5 until the change in the system objective function value between two consecutive steps is less than a preset threshold, and obtain the optimal phase shift matrix and the corresponding digital beamforming matrix.

[0169] In this embodiment, step 6 mainly includes:

[0170] Step 6.1: Repeat steps 3 and 5. In each iteration, the phase shift matrix and digital beamforming matrix obtained are substituted into the sensing mutual information objective function until the overall gain of the system objective function is less than the set threshold. Output the optimal phase shift matrix and the optimal digital beamforming matrix;

[0171] Step 6.2: Based on the optimal phase shift matrix and the optimal digital beamforming matrix, the sensing mutual information objective function is re-introduced to calculate the final system objective function value.

[0172] In a preferred embodiment, the method further includes performing a pre-configuration phase to construct a joint pre-encoded codeword library:

[0173] Based on the stacked BD-RIS deployment configuration and scenario parameters, multiple sample scenarios are established; the scenario parameters include user location distribution, target perception area, propagation environment and channel characteristics.

[0174] For each of the sample scenarios, the optimization steps described in claim 1 are performed to obtain a joint precoding matrix; wherein the joint precoding matrix includes a digital beamforming matrix and phase shift matrices of each layer of the stacked BD-RIS;

[0175] The joint precoding matrices under each of the aforementioned sample scenarios are aggregated into a joint candidate state set;

[0176] The overall transmission matrix composed of phase shift matrices of each layer in the joint candidate state set is quantized into a first number of candidate phase shift codewords; the digital beamforming matrix is ​​quantized into a second number of standard codebooks.

[0177] Furthermore, each joint candidate state includes at least one set of base station digital beamforming matrices and one set of phase shift matrices for each layer of the stacked BD-RIS. The overall transmission matrix of the stacked BD-RIS is then statistically analyzed as follows: One candidate phase-shift codeword, using Each bit is used for indexing; the digital precoding matrix is ​​statistically analyzed as follows: A standard codebook, using Each bit is used for indexing.

[0178] Furthermore, the base station establishes a mapping rule between standard PMI codewords, auxiliary indexes, and joint candidate states based on the joint candidate state set;

[0179] The base station pre-configures parameters for the terminal via RRC signaling;

[0180] The base station sends a CSI-RS, which is used to trigger the terminal to perform channel measurements.

[0181] The PMI codeword is used to indicate the active precoding direction or precoding category on the base station side; the auxiliary index is used to indicate the candidate subset associated with the selection of the stacked BD-RIS transmission matrix; the PMI codeword and the auxiliary index together determine a set of joint transmission states.

[0182] The PMI codeword is used to indicate the active precoding direction or precoding category on the base station side; the auxiliary index is used to indicate the candidate subset associated with the selection of the stacked BD-RIS transmission matrix; the PMI codeword and the auxiliary index together determine a set of joint transmission states.

[0183] The pre-configured parameters for the terminal specifically include:

[0184] Stacked BD-RIS layer number indicator: BD-SIM_Layer_indi, 3 bits;

[0185] Stacked BD-RIS reflective element indicator: BD-SIM_Meta_indi, 3 bits;

[0186] Stacked BD-RIS structure indicator: BD-SIM_Struct_indi, 4 bits

[0187] Auxiliary index of the overall transfer matrix of stacked BD-RIS: BD-SIM_Matrix bit

[0188] Precoding Matrix Indicator (PMI): bit.

[0189] Figure 2 This is a schematic diagram of signaling interaction according to an embodiment of this application. The terminal performs the following steps:

[0190] The terminal receives CSI-RS transmitted by the base station;

[0191] Based on the received CSI-RS, channel measurements are performed to obtain channel state information for calculating PMI codewords;

[0192] Using communication performance constraints as the calculation metric, the standard PMI codeword and the stacked BD-RIS auxiliary index were determined;

[0193] The standard PMI codeword is reported through the CSI feedback field in the CSI report, and the stacked BD-RIS auxiliary index is reported through the extended field in the CSI report.

[0194] The base station performs the joint precoding transmission process including:

[0195] The base station receives the PMI codewords fed back by the terminal and the stacked BD-RIS auxiliary index;

[0196] Based on the PMI codewords and the stacked BD-RIS auxiliary index, the corresponding joint precoding matrix is ​​matched from the joint candidate state set;

[0197] The base station configures the transmission parameters according to the matched joint precoding matrix and performs downlink signal transmission.

[0198] In a preferred embodiment, Figure 3 This is a convergence result diagram of the iterative algorithm of this application, where the parameters are set as follows: there are 3 antennas at the transmitting end, 36 passive components on each stacked BD-RIS layer, 3 stacked BD-RIS layers integrated on the outside of the transmitting antenna, 16 antennas in the antenna array used to receive the sensing echo, and the minimum rate that the user needs to meet is set to 1 bit / s / hz. Figure 3 The horizontal axis represents the number of iterations, and the vertical axis represents the perceived mutual information, measured in bits per second (CPI). This means the number of bits transmitted per second by the base station within the radar coherent processing interval. The two curves in the figure: FC represents the fully connected BD-RIS structure. The figure indicates that all components on the surface of each stacked element are interconnected; GC represents a grouped BD-RIS structure, where the components on the surface of each stacked element are divided into 4 groups, with 9 components in each group interconnected. As can be seen from the figure, the algorithm proposed in this invention achieves convergence in approximately 20 iterations, demonstrating excellent convergence performance. Furthermore, the perceptual mutual information increases with the number of connections between components. This phenomenon clearly demonstrates that introducing connections between components can significantly improve the signal processing capability of stacked BD-RIS in the ISAC scenario, thus providing strong support for optimizing system performance.

[0199] Figure 4 The results shown are obtained from the simulation verification of this application, with the following parameter settings: the transmitting end has 3 antennas, each layer of stacked BD-RIS has 64 passive components, the antenna array used to receive sensing echoes has 16 antennas, and the minimum rate that the user needs to meet is set to 1 bit / s / hz. Figure 4 The horizontal axis represents the number of stacking layers, and the vertical axis represents the perceptual mutual information, measured in bits per criterion (CPI). FC indicates a fully connected stacked BD-RIS architecture. In this structure, all components on the surface of each stacked element are interconnected; the three curves in the figure represent the group-connected stacked BD-RIS structure: GC represents the group-connected stacked BD-RIS structure. The components on the surface of each stacked element were divided into four groups, with nine components in each group interconnected. The performance of a traditional stacked RIS was also compared. It can be seen that as the number of stacked layers increases, the stacked BD-RIS exhibits a significant advantage in ISAC beam processing performance compared to the traditional stacked RIS. This advantage directly translates into improved perceptual mutual information, indicating that BD-RIS can utilize wave domain resources more efficiently in a multi-layer stacked structure, thus bringing significant gains to the performance of the ISAC system. Example 2

[0200] This embodiment provides a RIS-assisted integrated sensing beamforming design system, including:

[0201] A building block is provided for constructing a RIS-assisted ISAC system; wherein the system includes a base station, K single-antenna users, sensing targets, and a stacked BD-RIS, and the base station is equipped with The base station has N transmitting antennas and a sensing and receiving array containing N transmitting antennas. The stacked BD-RIS is disposed outside the transmitting antennas of the base station, and the stacked BD-RIS contains M reflecting units.

[0202] The initialization module is used to initialize the digital beamforming matrix based on the total transmit power constraint of the base station. The digital beamforming matrix ,in, To represent a complex number, Indicates the first Digital beamforming vector for a single antenna user K represents the number of users per antenna. Indicates the number of base station transmit antennas; initializes the phase shift matrix. ,in, Indicates the first The phase shift matrix of stacked BD-RIS layers. , This indicates the total number of layers in the BD-RIS stack. express The identity matrix, This indicates the number of reflective units in each BD-RIS layer;

[0203] The Unconstrained Optimization Problem Construction Module is used to construct unconstrained optimization problems using the penalty function method.

[0204] The phase shift matrix design module is used to design the transmitting phase shift matrix based on the unconstrained optimization problem.

[0205] The digital beamforming design module is used to design the digital beamforming matrix for the transmitter, given a pre-designed phase shift matrix.

[0206] The iterative output module is used to repeat the steps until the change in the system objective function value between two consecutive iterations is less than a preset threshold, thereby obtaining the optimal phase shift matrix and the corresponding digital beamforming matrix.

[0207] The specific implementation process of each module function in this embodiment can be found in Embodiment 1, which has the same technical effect as the method provided in Embodiment 1, and will not be described in detail here.

[0208] Those skilled in the art will understand that the embodiments of this application can be provided as methods or systems. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects.

[0209] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems) according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 A system that specifies functions in one or more boxes.

[0210] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including an instruction set implemented in a process. Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0211] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0212] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims. All of these forms are within the protection scope of this application.

Claims

1. A RIS-assisted integrated sensing beamforming design method, characterized in that, include: S1, Construct a RIS-assisted ISAC system; wherein, the system includes a base station, K single-antenna users, sensing targets, and a stacked BD-RIS, and the base station is equipped with The base station has N transmitting antennas and a sensing and receiving array containing N transmitting antennas. The stacked BD-RIS is disposed outside the transmitting antennas of the base station, and the stacked BD-RIS contains M reflecting units. S2, initialize the digital beamforming matrix according to the total power constraint transmitted by the base station. The digital beamforming matrix ,in, To represent a complex number, Indicates the first Digital beamforming vector for a single antenna user K represents the number of users per antenna. Indicates the number of base station transmit antennas; initializes the phase shift matrix. ,in, Indicates the first The phase shift matrix of stacked BD-RIS layers. , This indicates the total number of layers in the BD-RIS stack. express The identity matrix, This indicates the number of reflective units in each BD-RIS layer; S3, an unconstrained optimization problem is constructed using the penalty function method; S4. Based on the aforementioned unconstrained optimization problem, design the phase shift matrix for the transmitting end; S5. Based on the designed phase shift matrix, design the digital beamforming matrix for the transmitter. S6. Repeat steps S3 to S5 until the change in the system objective function value between two consecutive steps is less than a preset threshold, and obtain the optimal phase shift matrix and the corresponding digital beamforming matrix.

2. The RIS-assisted integrated sensing beamforming design method according to claim 1, characterized in that, The transfer function of the stacked BD-RIS for: In the formula, Indicates the first layer to the first Interlayer transfer matrix of layer BD-RIS; This represents the inter-layer transmission matrix from the transmitting antenna to the first-layer BD-RIS. This represents the phase shift matrix of the first-layer BD-RIS.

3. The RIS-assisted integrated sensing beamforming design method according to claim 2, characterized in that, The method of constructing unconstrained optimization problems using the penalty function method includes: Establish the objective function for perceptual mutual information and communication constraints: ) in, , This represents the minimum signal-to-noise ratio that the user needs to meet. Indicates noise power. This represents the operation of finding the conjugate transpose of a matrix; the intermediate variable matrix. , , , , They are represented by the following formulas respectively: in, , This represents the steering vector for sensing the emission. The steering vectors of the receiving array are defined as follows: in, Indicates the spacing between the reflective elements of the stacked BD-RIS. Indicates the spacing between the receiving array elements. Indicates the azimuth angle of the perceived target. Indicates the elevation angle of the perceived target; make Using the penalty function method, the communication constraints are transformed into an objective function in the form of penalty terms, and the following unconstrained optimization problem is constructed: in, This is a penalty factor.

4. The RIS-assisted integrated sensing beamforming design method according to claim 3, characterized in that, The design of the transmitter phase shift matrix based on the unconstrained optimization problem includes: S41, let the phase shift matrix of the transmitting end group connection structure be... : Where G represents the number of groups of the BD-RIS reflective unit, ; express The identity matrix; This represents the transpose operation on a matrix; using Takagi decomposition to transform the first... The first layer of the BD-RIS transmitter Group phase shift matrix decomposition for ,in Represents a complex unitary matrix; S42, according to conjugate gradient direction and To obtain the gradient direction of the unconstrained optimization problem They are respectively: Among them, the intermediate variable matrix , , , and They are represented by the following formulas respectively: Among them, the intermediate variable matrix and Divided by column Group, , and Divided by row Group; , , , and They represent the corresponding first The intermediate variable matrix of the group; S43, Update for: in, yes In the conjugate gradient direction of the unitary space, Indicates the update step size. ; renew The Middle The group phase shift matrix is: S44, will be updated Substitute into the objective function : S45, repeat steps S41 to S45, and gradually increase the penalty factor. until satisfied , This represents the objective function after the last iteration update. Indicates the convergence threshold; S46, according to Repeat steps S41 to S45 for different values, and update each group of phase shift matrices sequentially. To design the first Phase shift matrix of the BD-RIS layer transmitter ; S47, according to Repeat steps S41 to S45 for different values ​​to design each phase shift matrix of the BD-RIS stack at the transmitting end.

5. The RIS-assisted integrated sensing beamforming design method according to claim 4, characterized in that, The step of designing the digital beamforming matrix of the base station based on the pre-designed phase shift matrix includes: S51, recalculate the transfer function based on the updated phase shift matrix. ; S52, the objective function for perceptual mutual information and communication constraints are rewritten, and their expressions are as follows: in, , , ; S53, Based on the expression in step S52, construct the constrained optimization problem: S54 eliminates the rank-one constraint through positive semidefinite relaxation, transforming the constrained optimization problem into a positive semidefinite programming form, which is then solved using the CVX solver. ; S55, the solution obtained The optimal digital beamforming matrix is ​​obtained by performing rank-one recovery using the Gaussian randomization method. .

6. The RIS-assisted integrated sensing beamforming design method according to claim 1, characterized in that, This also includes the construction of the joint pre-encoding codeword library during the pre-configuration phase: Based on the stacked BD-RIS deployment configuration and scenario parameters, multiple sample scenarios are established; the scenario parameters include user location distribution, target perception area, propagation environment and channel characteristics. For each of the sample scenarios, the optimization steps described in claim 1 are performed to obtain a joint precoding matrix; wherein the joint precoding matrix includes a digital beamforming matrix and phase shift matrices of each layer of the stacked BD-RIS; The joint precoding matrices under each of the aforementioned sample scenarios are aggregated into a joint candidate state set; The overall transmission matrix composed of phase shift matrices of each layer in the joint candidate state set is quantized into a first number of candidate phase shift codewords; the digital beamforming matrix is ​​quantized into a second number of standard codebooks.

7. The RIS-assisted integrated sensing beamforming design method according to claim 6, characterized in that, Also includes: Based on the joint candidate state set, the base station establishes a mapping rule between standard PMI codewords, auxiliary indexes, and joint candidate states; The base station pre-configures parameters for the terminal via RRC signaling; The base station sends a CSI-RS, which is used to trigger the terminal to perform channel measurements. The PMI codeword is used to indicate the active precoding direction or precoding category on the base station side; the auxiliary index is used to indicate the candidate subset associated with the selection of the stacked BD-RIS transmission matrix; the PMI codeword and the auxiliary index together determine a set of joint transmission states.

8. The RIS-assisted integrated sensing beamforming design method according to claim 7, characterized in that, The terminal performs the following steps: The terminal receives CSI-RS transmitted by the base station; Based on the received CSI-RS, channel measurements are performed to obtain channel state information for calculating PMI codewords; Using communication performance constraints as the calculation metric, the standard PMI codeword and the stacked BD-RIS auxiliary index were determined; The standard PMI codeword is reported through the CSI feedback field in the CSI report, and the stacked BD-RIS auxiliary index is reported through the extended field in the CSI report.

9. The RIS-assisted integrated sensing beamforming design method according to claim 8, characterized in that, The base station performs the joint precoding transmission process including: The base station receives the PMI codewords fed back by the terminal and the stacked BD-RIS auxiliary index; Based on the PMI codewords and the stacked BD-RIS auxiliary index, the corresponding joint precoding matrix is ​​matched from the joint candidate state set; The base station configures the transmission parameters according to the matched joint precoding matrix and performs downlink signal transmission.

10. A RIS-assisted integrated sensing beamforming design system, characterized in that, include: A building block is provided for constructing a RIS-assisted ISAC system; wherein the system includes a base station, K single-antenna users, sensing targets, and a stacked BD-RIS, and the base station is equipped with The base station has N transmitting antennas and a sensing and receiving array containing N transmitting antennas. The stacked BD-RIS is disposed outside the transmitting antennas of the base station, and the stacked BD-RIS contains M reflecting units. The initialization module is used to initialize the digital beamforming matrix based on the total transmit power constraint of the base station. The digital beamforming matrix ,in, To represent a complex number, Indicates the first Digital beamforming vector for a single antenna user K represents the number of users per antenna. Indicates the number of base station transmit antennas; initializes the phase shift matrix. ,in, Indicates the first The phase shift matrix of stacked BD-RIS layers. , This indicates the total number of layers in the BD-RIS stack. express The identity matrix, This indicates the number of reflective units in each BD-RIS layer; The module for constructing unconstrained optimization problems is used to construct unconstrained optimization problems using the penalty function method. The phase shift matrix design module is used to design the transmitting phase shift matrix based on the unconstrained optimization problem. The digital beamforming design module is used to design the digital beamforming matrix for the transmitter, given a pre-designed phase shift matrix. The iterative output module is used to repeat the steps until the change in the system objective function value between two consecutive iterations is less than a preset threshold, thereby obtaining the optimal phase shift matrix and the corresponding digital beamforming matrix.

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