A communication and positioning integrated method and system based on BD-RIS

Abstract

The present invention discloses a communication positioning integrated method and system based on BD-RIS, and relates to the field of communication technology. The method comprises: constructing a BD-RIS-assisted ISAC network model, and determining a CRB for DoA estimation; according to the BD-RIS-assisted ISAC network model, establishing an optimization problem P1 with constraints on base station transmission power, BD-RIS structure and SINR of communication users, and minimizing CRB as the goal, and transforming and decoupling it into an optimization sub-problem P2.1 focusing on the design of a transmission precoding matrix of a dual-function base station and an optimization sub-problem P2.2 focusing on the design of an optimal reflection coefficient matrix of BD-RIS, respectively solving them by using a semi-positive definite relaxation method and a penalty dual decomposition method, and finally obtaining an optimal transmission precoding matrix and an optimal reflection coefficient matrix by an alternating iteration method. The present invention realizes the minimization of CRB for DoA estimation by jointly considering the transmission precoding matrix design of the dual-function base station and the reflection coefficient matrix design of BD-RIS, while meeting the signal-to-interference-to-noise ratio requirements of the communication users.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to a communication and positioning integrated method and system based on BD-RIS. Background Art

[0002] In the current wireless communication and radar perception fusion (ISAC) network, with the continuous advancement of technology, the demand for improving system performance is increasing. ISAC networks are designed to achieve efficient wireless communication and accurate radar perception functions at the same time, thus showing great application potential in future communication systems. However, existing ISAC networks face many challenges in achieving this dual function.

[0003] On the one hand, the traditional ISAC network may be limited by the complexity of the environment and the diversity of targets in terms of radar perception, resulting in unsatisfactory performance of radar parameter estimation (such as target arrival angle Direction of Arrival, DoA estimation). On the other hand, how to effectively improve radar perception performance while ensuring the quality of multi-user communication is a key issue in the current ISAC network design.

[0004] In recent years, the Reconfigurable Intelligent Surface (RIS) technology has attracted much attention due to its ability to dynamically control the propagation path of electromagnetic waves. The traditional RIS architecture uses a single connection mode, and each reflective element is independent of each other and generates a diagonal phase shift matrix, which to a certain extent limits the flexibility and functional expansion of RIS. In order to further enhance the potential of RIS in the ISAC system, the Beyond Diagonal RIS (BD-RIS) architecture provides a new idea for improving the performance of the ISAC network.

[0005] Although there have been studies that attempt to introduce RIS into ISAC networks, most of these studies focus on theoretical analysis or simulation verification, lacking a systematic approach. In particular, in BD-RIS-assisted ISAC networks, there is no clear solution for related research on perception performance improvement and communication quality assurance, and the performance evaluation criteria for DoA estimation of perceived targets are still insufficient. Summary of the invention

[0006] In view of the defects in the prior art, the present invention proposes a communication and positioning integrated method and system based on BD-RIS, aiming to ensure the quality of multi-user communication while significantly improving the radar parameter estimation performance; by jointly designing the transmit precoding of the dual-function base station and the reflection beamforming of BD-RIS, the CRB (Cramér-Rao Bound) of the DoA estimation of the perceived target in the BD-RIS-assisted ISAC network is deeply studied, and this is used as the evaluation standard of the perception performance, while ensuring the quality of service (QoS) of the communication users. The present invention provides a new solution for achieving comprehensive optimization of the ISAC network performance.

[0007] On the one hand, the present invention provides a communication and positioning integrated method based on BD-RIS, the method comprising the following steps:

[0008] S1, based on the network scenario including dual-function base stations, BD-RIS, communication users and sensing targets, a BD-RIS-assisted ISAC network model is constructed, and the CRB for DoA estimation is determined;

[0009] S2, according to the BD-RIS assisted ISAC network model, establish an optimization problem P1 with base station transmission power, BD-RIS structure and SINR of communication users as constraints and minimizing CRB as the goal;

[0010] S3, transform and decouple the optimization problem P1 into an optimization subproblem P2.1 focusing on the design of the transmit precoding matrix of the dual-function base station and an optimization subproblem P2.2 focusing on the design of the optimal reflection coefficient matrix of the BD-RIS, and solve them respectively using the semi-positive definite relaxation method and the penalty dual decomposition method, and finally obtain the optimal transmit precoding matrix and the optimal reflection coefficient matrix through alternating iteration.

[0011] Preferably, S1 comprises the following steps:

[0012] S101, built with a dual-function base station, a BD-RIS, A BD-RIS-assisted ISAC network model with a communication user and a sensing target, wherein the dual-function base station is configured with Antenna, ; The BD-RIS is configured with A reflective element, ;

[0013] S102, constructing a radar signal model and a communication signal model based on the BD-RIS assisted ISAC network model, vectorizing the radar signal model, and determining a CRB for DoA estimation according to the vectorized radar signal model.

[0014] Preferably, the radar signal model is:

[0015]

[0016]

[0017] S ≜ [ s [ 1 ] , … , s [ L ] ]

[0018] N r ≜ [ n r [ 1 ] , … , n r [ L ] ]

[0019] in, Indicates the dual-function base station receives the target from the sensing Group echo signal, Indicates the radar cross-sectional area of ​​the perceived target, , represents a complex Gaussian distribution, for The variance of the corresponding complex Gaussian distribution; is the intermediate variable, Indicates the channel between the dual-function base station and BD-RIS, , represents the reflection coefficient matrix of BD-RIS, , represents the line-of-sight link between BD-RIS and the perceived target, , represents the path loss, represents the steering vector, a M ( i ) = [ 1 , e j π s i n i , … , e j ( M − 1 ) π s i n i ] T , represents the direction of arrival of the perceived target relative to BD-RIS, is an imaginary unit, represents the transmit precoding matrix, , s [ 1 ] Indicates the signal transmitted by the dual-function base station in the first time slot. s [ L ] Indicates The signal transmitted by the dual-function base station in the time slot is n r [ 1 ] represents the additive white Gaussian noise at the dual-function base station in the first time slot, n r [ L ] Indicates Additive white Gaussian noise at the dual-function base station in time slots, n r [ L ] ~ C N ( 0 , s r 2 I N ) ,in for n r [ L ] The variance matrix corresponding to the complex Gaussian distribution, is the N-order identity matrix.

[0020] Preferably, the CRB used for DoA estimation is:

[0021]

[0022] Preferably, in S2, the optimization problem P1 is:

[0023]

[0024] in, represents the square of the F norm of the dual-function base station transmit precoding matrix, Indicates the maximum transmit power, Indicates The signal-to-interference-to-noise ratio of each communication user is represents the minimum signal-to-interference-noise ratio, is the M-order identity matrix.

[0025] Preferably, in S3, the optimization problem P1 is first converted into an equivalent optimization problem P2, and the equivalent optimization problem P2 is:

[0026]

[0027] The equivalent optimization problem P2 is decoupled into the optimization sub-problem P2.1 focusing on the design of the transmit precoding matrix of the dual-function base station and the optimization sub-problem P2.2 focusing on the design of the optimal reflection coefficient matrix of BD-RIS:

[0028] The optimization sub-problem P2.1 is:

[0029]

[0030] The optimization sub-problem P2.2 is:

[0031] .

[0032] Preferably, the optimization subproblem P2.1 and the optimization subproblem P2.2 are solved by using an alternating iterative method to obtain an optimal transmit precoding matrix and an optimal reflection coefficient matrix, including the following steps:

[0033] S301, in the first iteration, according to Given a constraint that satisfies the constraint In the remaining iterations, based on the local approximate solution of the BD-RIS reflection coefficient matrix obtained in the previous iteration, the Schur complement combined with semi-positive definite relaxation method and the CVX toolbox are used to solve the optimization subproblem P2.1 and obtain the approximate optimal solution of the transmit precoding matrix;

[0034] S302, according to the approximate optimal solution of the transmit precoding matrix obtained in this iteration, the penalty dual decomposition method is used to solve the optimization subproblem P2.2 to obtain a local approximate solution of the BD-RIS reflection coefficient matrix;

[0035] S303, alternately iteratively executing S301 and S302 until global convergence, and obtaining the optimal transmit precoding matrix of the dual-function base station and the optimal reflection coefficient matrix of the BD-RIS.

[0036] On the other hand, the present invention provides a communication and positioning integrated system based on BD-RIS, the system comprising:

[0037] An initialization module, used to construct a BD-RIS-assisted ISAC network model according to a network scenario including a dual-function base station, BD-RIS, communication users, and sensing targets, and determine a CRB for DoA estimation;

[0038] A construction module is used to establish an optimization problem P1 based on the BD-RIS assisted ISAC network model, with the base station transmission power, BD-RIS structure and SINR of the communication user as constraints and the goal of minimizing CRB;

[0039] The calculation module is used to transform and decouple the optimization problem P1 into an optimization subproblem P2.1 focusing on the design of the transmit precoding matrix of the dual-function base station and an optimization subproblem P2.2 focusing on the design of the optimal reflection coefficient matrix of the BD-RIS, and solve them using an alternating iterative method to obtain the optimal transmit precoding matrix and the optimal reflection coefficient matrix.

[0040] The beneficial effects of the present invention are as follows: by jointly considering the transmit precoding matrix design of the dual-function base station and the reflection coefficient matrix design of the BD-RIS, the present invention achieves CRB minimization of DoA estimation while meeting the signal-to-interference-noise ratio requirements of communication users, thereby significantly improving the overall performance of the ISAC system. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for the specific embodiments or the description of the prior art. In all the 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.

[0042] Figure 1 A flow chart of a communication and positioning integration method based on BD-RIS provided in Example 1 of the present invention;

[0043] Figure 2A diagram of the BD-RIS-assisted ISAC network model provided in Example 1 of the present invention;

[0044] Figure 3 A system block diagram of a communication and positioning integrated system based on BD-RIS provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0045] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only 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 should fall within the scope of protection of the present invention.

[0046] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0047] The present invention is further described in detail below with reference to the accompanying drawings.

[0048] Example 1

[0049] like Figure 1 As shown, Figure 1 An integrated communication positioning method based on BD-RIS is provided in an embodiment of the present invention, which jointly considers the transmission precoding design of the dual-function base station and the reflection beamforming design of BD-RIS, while meeting the signal-to-interference-to-noise ratio requirements of the communication users, and realizes the minimization of the CRB of DoA estimation. Compared with the traditional diagonal RIS, BD-RIS has higher configuration flexibility and stronger beam control capability. This embodiment adopts a fully connected BD-RIS architecture, and the traditional diagonal RIS is only a simplified special case thereof, thereby significantly improving the performance of the ISAC system.

[0050] The method comprises the following steps:

[0051] The present invention provides a communication and positioning integrated method based on BD-RIS, the method comprising the following steps:

[0052] S1, based on the network scenario including dual-function base stations, BD-RIS, communication users and sensing targets, build a BD-RIS-assisted ISAC network model and determine the CRB for DoA estimation.

[0053] In this embodiment, S1 includes the following steps:

[0054] S101, built with a dual-function base station, a BD-RIS, A BD-RIS-assisted ISAC network model with a communication user and a sensing target, wherein the dual-function base station is configured with Antenna, ; The BD-RIS is configured with A reflective element, In this network, dual-function base stations are connected by BD-RIS with a reflective element Each communication user communicates and detects the sensing target at the same time; Figure 2 shown. Figure 2 In the figure, the communication tower represents a dual-function base station, the car represents a sensing target, the trees in the middle represent an obstruction, the building represents a BD-RIS, and the person represents a communication user.

[0055] S102, constructing a radar signal model and a communication signal model based on the BD-RIS assisted ISAC network model, vectorizing the radar signal model, and determining a CRB for DoA estimation according to the vectorized radar signal model.

[0056] Since the direct link between the dual-function base station and the sensing target is blocked by obstacles, the transmission signal of the dual-function base station reaches the sensing target through the auxiliary reflection link of BD-RIS and returns through the same path.

[0057] The radar signal model is:

[0058]

[0059]

[0060] S = [ s [ 1 ] , … , s [ L ] ]

[0061] N r = [ n r [ 1 ] , … , n r [ L ] ]

[0062] in, Indicates the dual-function base station receives the target from the sensing Group echo signal, Indicates the radar cross-sectional area of ​​the perceived target, , represents a complex Gaussian distribution, for The variance of the corresponding complex Gaussian distribution; is the intermediate variable, Indicates the channel between the dual-function base station and BD-RIS, , represents the reflection coefficient matrix of BD-RIS, , represents the line-of-sight link between BD-RIS and the perceived target, , represents the path loss, represents the steering vector, a M ( i ) = [ 1 , e j π s i n i , … , e j ( M − 1 ) π s i n i ] T , represents the direction of arrival of the perceived target relative to BD-RIS, is an imaginary unit, represents the transmit precoding matrix, , s [ 1 ] Indicates the signal transmitted by the dual-function base station in the first time slot. s [ L ] Indicates The signal transmitted by the dual-function base station in the time slot is n r [ 1 ] represents the additive white Gaussian noise at the dual-function base station in the first time slot, n r [ L ] Indicates Additive white Gaussian noise at the dual-function base station in time slots, n r [ L ] ~ C N ( 0 , s r 2 I N ) ,in for n r [ L ] The variance matrix corresponding to the complex Gaussian distribution, is the N-order identity matrix.

[0063] It should be noted that the present invention constructs a communication signal model while constructing a radar signal model; specifically, assuming that the equivalent baseband transmission signal of the dual-function base station is x [ l ] ∈ ℂ N × 1 , modeled as follows:

[0064]

[0065] in, s c [ l ] ∈ ℂ K × 1 Express satisfaction  { s c [ l ] s c [ l ] H } = I K Communication symbols, Express expectations, is the K-order identity matrix, s r [ l ] ∈ ℂ N × 1 Express satisfaction  { s r [ l ] s r [ l ] H } = I N and  { s c [ l ] s r [ l ] H } = 0 The radar signal, is the N-order identity matrix. and They represent the communication beamforming matrix and the radar beamforming matrix respectively. represents the equivalent dual-function communication and radar beamforming matrix, i.e., the transmit precoding matrix.

[0066] The dual-function base station sends a signal to the communication user. The received signal of a communication user is:

[0067] y k [ l ] = ( h d , k H + h r , k H F G ) x [ l ] + n k [ l ]

[0068] in, They represent the dual-function base station and the channels between users, BD-RIS and the The channels between users and the channels between the dual-function base station and BD-RIS are estimated by using the channel estimation method known in the prior art, assuming that the channels in this system are completely known; Represents the reflection coefficient matrix of BD-RIS. Due to its fully connected impedance network architecture, the reflection coefficient matrix of BD-RIS satisfy and ; n k [ l ] ∼   ( 0 , s k 2 ) is Gaussian white noise, for n k [ l ] Variance of the complex Gaussian distribution.

[0069] The first The SINR (Signal-to-interference-plus-noise ratio) of a communication user can be modeled as:

[0070]

[0071] in, , for No. List, for No. List.

[0072] The communication signal model and radar signal model were constructed through the above method, providing a data basis for the subsequent CRB derivation and research of DoA estimation.

[0073] In order to facilitate processing and analysis, the radar signal model needs to be vectorized, which can be further expressed as follows:

[0074]

[0075] in is a vectorized function.

[0076] Then, the elements of the Fisher information matrix are calculated based on the vectorized model; let x ≜ [ i , α T ] T Indicates to use α ≜ [ ℜ { α t } , ℑ { α t } ] T The estimated target parameters, where represents the real part operation, represents the operation of finding the imaginary part; then the Fisher information matrix can be expressed as:

[0077] F x = [ F i i F i α F i α T F α α ]

[0078] in,

[0079]

[0080] represents matrix trace operation, express about The partial guide, is the 2nd-order identity matrix, for The conjugate matrix of Is an imaginary unit.

[0081] Then calculate the (1, 1)th element of the inverse matrix of the Fisher information matrix to obtain the CRB for DoA estimation, which is:

[0082]

[0083] S2, based on the BD-RIS assisted ISAC network model, establish an optimization problem P1 with dual-function base station transmission power, BD-RIS structure and SINR of communication users as constraints and minimizing CRB as the goal.

[0084] Specifically, considering factors such as the dual-function base station transmission power, BD-RIS structure, and SINR, the optimization problem P1 is constructed as follows:

[0085]

[0086] in, represents the square of the F norm of the dual-function base station transmit precoding matrix, Indicates the maximum transmit power, Indicates The signal-to-interference-to-noise ratio of each communication user is represents the minimum signal-to-interference-noise ratio, constraint and All are constraints of BD-RIS. is the M-order identity matrix.

[0087] constraint Used to limit the maximum transmit power of a dual-function base station to ,constraint Used to ensure that the signal-to-interference-to-noise ratio of the communication user in the worst case is not less than Since BD-RIS is a fully connected impedance network architecture, its reflection coefficient matrix Should meet and .

[0088] S3, transform and decouple the optimization problem P1 into an optimization subproblem P2.1 focusing on the design of the transmit precoding matrix of the dual-function base station and an optimization subproblem P2.2 focusing on the design of the optimal reflection coefficient matrix of the BD-RIS, and solve them respectively using the semi-positive definite relaxation method and the penalty dual decomposition method, and finally obtain the optimal transmit precoding matrix and the optimal reflection coefficient matrix through alternating iteration.

[0089] Specifically, according to The expression of This is equivalent to maximizing its denominator, so the optimization problem P1 can be transformed into an equivalent problem P2:

[0090]

[0091] Furthermore, considering the joint optimization design of the transmit precoding matrix of the dual-function base station and the reflection coefficient matrix of BD-RIS, the optimization problem P2 is further decoupled into the optimization sub-problem P2.1 focusing on the design of the transmit precoding matrix of the dual-function base station and the optimization sub-problem P2.2 focusing on the design of the optimal reflection coefficient matrix of BD-RIS, as shown below:

[0092] a) Only retain the dual-function base station transmit precoding matrix The relevant constraints are expressed as follows for the optimization subproblem P2.1:

[0093]

[0094] b) Only keep the BD-RIS reflection coefficient matrix The relevant constraints, the optimization sub-problem P2.2 is expressed as follows:

[0095]

[0096] The present invention decouples the original optimization problem P1 into two independent sub-problems P2.1 and P2.2, focusing on the design of the transmit precoding matrix of the dual-function base station and the reflection coefficient matrix of BD-RIS, respectively, providing greater flexibility, and can select the most suitable optimization algorithm for solving the specific properties of each sub-problem. In addition, by optimizing the transmit precoding matrix of the dual-function base station and the reflection coefficient matrix of BD-RIS respectively, the overall performance of the ISAC system can be more effectively improved.

[0097] In the embodiment of the present invention, in S3, using an alternating iterative method to solve and obtain an optimal transmit precoding matrix and an optimal reflection coefficient matrix includes the following steps:

[0098] S301, in the first iteration, according to Given a constraint that satisfies the constraint In the remaining iterations, based on the local approximate solution of the BD-RIS reflection coefficient matrix obtained in the previous iteration, the Schur complement combined with semi-positive definite relaxation method and the CVX toolbox are used to solve the optimization subproblem P2.1 and obtain the approximate optimal solution of the transmit precoding matrix;

[0099] S302, according to the approximate optimal solution of the transmit precoding matrix obtained in this iteration, the penalty dual decomposition method is used to solve the optimization subproblem P2.2 to obtain a local approximate solution of the BD-RIS reflection coefficient matrix;

[0100] S303, alternately iteratively executing S301 and S302 until global convergence, and obtaining the optimal transmit precoding matrix of the dual-function base station and the optimal reflection coefficient matrix of the BD-RIS.

[0101] For the optimization subproblem P2.1, which contains The fractional and high-order terms of posed a challenge to the solution. To overcome this difficulty, the present invention introduces an appropriate lower bound To simplify the problem structure, the Schur complement combined with semi-positive definite relaxation method is cleverly used to transform the non-convex problem into a convex optimization problem. The professional convex optimization solver CVX is selected to solve the transformed convex optimization problem, thereby obtaining an approximate optimal solution to the optimization subproblem P2.1.

[0102] Specifically, the optimization subproblem P2.1 can be reformulated as:

[0103]

[0104] in , , is an auxiliary variable.

[0105] To optimize subproblem P2.2, a decomposition strategy and the method of introducing replicas were adopted.

[0106] First introduce A copy of Decompose the optimization subproblem P2.2 into and The quadratic term of The orthogonality condition of is easy to handle, introducing another replica variable , thereby decoupling the orthogonality constraint from other constraints.

[0107] Specifically, the optimization subproblem P2.2 can be reformulated as:

[0108]

[0109] Then, on this basis, the problem is further transformed into an augmented Lagrangian optimization problem as follows:

[0110]

[0111] in, is with The associated Lagrangian dual variables, is the penalty parameter, and the first-order Taylor expansion and second-order Taylor expansion are used for the non-convex terms that still exist, and a series of convex and easy-to-handle approximate functions are found. Finally, the penalty dual decomposition framework is used for solution. This method includes a two-layer iterative process: in the inner iteration, the variables are updated alternately. , and ; In the outer iteration, the penalty parameter and Lagrange dual variable are selectively adjusted to approach the optimal solution. The whole process continues until the variable and and The difference between them is small enough.

[0112] For the alternating iterations of the optimization subproblems P2.1 and P2.2, in the iterative process, reasonable initial values ​​are first set for each variable, and these initial values ​​are substituted to solve the approximate optimal solution of the dual-function base station transmit precoding matrix in the i-th iteration. Then, the approximate solution of the transmit precoding matrix obtained in the i-th iteration and other initial values ​​are substituted into the BD-RIS reflection coefficient matrix design subproblem to solve the local approximate solution of the BD-RIS reflection coefficient matrix in the i-th iteration. By continuously increasing the number of iterations and gradually approaching the optimal solution, until the difference in the value of the objective function P1 in two consecutive iterations falls within the preset threshold range, the optimal solution of the radar CRB minimization problem that meets the communication QoS constraints can be obtained.

[0113] The original optimization problem is decomposed into two independent sub-problems through the above method, and the Schur complement combined semi-positive relaxation method and penalty dual decomposition method are used to solve them respectively. By alternating these two sub-problems, we finally obtain the optimal transmit precoding matrix of the dual-function base station and the optimal reflection coefficient matrix of BD-RIS, achieving the goal of minimizing the CRB of DoA estimation while meeting the signal-to-interference-to-noise ratio requirements of communication users.

[0114] In summary, embodiment 1 of the present invention provides an integrated communication positioning method based on BD-RIS. The method constructs a BD-RIS-assisted ISAC network model according to a network scenario including a dual-function base station, BD-RIS, a communication user and a perception target, and determines the CRB used for DoA estimation; according to the BD-RIS-assisted ISAC network model, an optimization problem P1 is established with the dual-function base station transmission power, BD-RIS structure and SINR of the communication user as constraints and the goal of minimizing CRB; the optimization problem P1 is transformed and decoupled into an optimization sub-problem P2.1 focusing on the design of the transmit precoding matrix of the dual-function base station and an optimization sub-problem P2.2 focusing on the design of the optimal reflection coefficient matrix of BD-RIS, and is solved using an alternating iterative method to obtain the optimal transmit precoding matrix and the optimal reflection coefficient matrix.

[0115] The present invention combines the transmit precoding matrix design of the dual-function base station and the reflection coefficient matrix design of the BD-RIS to achieve CRB minimization of DoA estimation while meeting the signal-to-interference-noise ratio requirements of communication users, thereby significantly improving the overall performance of the ISAC system.

[0116] Example 2

[0117] like Figure 3 As shown, the present invention provides a communication and positioning integrated system based on BD-RIS, the system comprising:

[0118] An initialization module, used to construct a BD-RIS-assisted ISAC network model according to a network scenario including a dual-function base station, BD-RIS, communication users, and sensing targets, and determine a CRB for DoA estimation;

[0119] A construction module is used to establish an optimization problem P1 based on the BD-RIS assisted ISAC network model, with the base station transmission power, BD-RIS structure and SINR of the communication user as constraints and the goal of minimizing CRB;

[0120] The calculation module is used to transform and decouple the optimization problem P1 into an optimization subproblem P2.1 focusing on the design of the transmit precoding matrix of the dual-function base station and an optimization subproblem P2.2 focusing on the design of the optimal reflection coefficient matrix of the BD-RIS, and solve them using an alternating iterative method to obtain the optimal transmit precoding matrix and the optimal reflection coefficient matrix.

[0121] It should be understood that the integrated communication and positioning system based on BD-RIS provided in the embodiment of the present invention and the integrated communication and positioning method based on BD-RIS provided in the above embodiment are based on the same inventive concept. For more specific working principles of each module in the embodiment of the present invention, please refer to the above embodiment and will not be repeated in the embodiment of the present invention.

[0122] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A communication and positioning integrated method based on BD-RIS, characterized in that: The following steps are involved: S1, based on the network scenario including dual-function base stations, BD-RIS, communication users and sensing targets, a BD-RIS-assisted ISAC network model is constructed, and the CRB for DoA estimation is determined; S2, based on the BD-RIS assisted ISAC network model, establish an optimization problem P1 with base station transmission power, BD-RIS structure and SINR of communication users as constraints and minimizing CRB as the goal; the optimization problem P1 is: in, represents the square of the F-norm of the dual-function base station transmit precoding matrix W, P BS Indicates the maximum transmit power, SINR k represents the signal-to-interference-noise ratio of the kth communication user, γ k represents the minimum signal-to-interference-noise ratio, I M is the M-order unit matrix, Φ represents the reflection coefficient matrix of BD-RIS, and θ represents the direction of arrival of the perceived target relative to BD-RIS; S3, transforming the optimization problem P1 into an equivalent optimization problem P2, wherein the equivalent optimization problem P2 is: Where Tr{·} represents matrix trace operation, Represents the intermediate variable Q t Partial derivatives with respect to θ; The equivalent optimization problem P2 is decoupled into the optimization sub-problem P2.1 focusing on the design of the transmit precoding matrix of the dual-function base station and the optimization sub-problem P2.2 focusing on the design of the optimal reflection coefficient matrix of BD-RIS: The optimization sub-problem P2.1 is: The optimization sub-problem P2.2 is: The optimization subproblem P2.1 and the optimization subproblem P2.2 are solved by using an alternating iterative method to obtain an optimal transmit precoding matrix and an optimal reflection coefficient matrix, including the following steps: S301, in the first iteration, according to the constraint conditions of Φ, a Φ that meets the constraint conditions is given. In the remaining iterations, according to the local approximate solution of the BD-RIS reflection coefficient matrix obtained in the previous iteration, the Schur complement combined with semi-positive definite relaxation method and the CVX toolbox are used to solve the optimization subproblem P2.1 to obtain the approximate optimal solution of the transmit precoding matrix; S302, according to the approximate optimal solution of the transmit precoding matrix obtained in this iteration, the penalty dual decomposition method is used to solve the optimization subproblem P2.2 to obtain a local approximate solution of the BD-RIS reflection coefficient matrix; The specific process is: First, a copy of Φ Φ1 is introduced to decompose the optimization subproblem P2.2 into quadratic terms of Φ and Φ1; at the same time, another copy variable Φ2 is introduced to decouple the orthogonality constraint from other constraints; the optimization subproblem P2.2 is re-expressed as: Then the optimization subproblem P2.2 is further transformed into an augmented Lagrangian optimization problem as follows: in, is the Lagrange dual variable, ρ is the penalty parameter; the first-order Taylor expansion and the second-order Taylor expansion are used for the non-convex terms that still exist to find a series of convex and easy-to-handle approximate functions; Finally, the penalty dual decomposition framework is used to solve the problem. This method includes a two-layer iterative process: in the inner iteration, the variables Φ, Φ1 and Φ2 are updated alternately; in the outer iteration, the penalty parameter and the Lagrangian dual variable are selectively adjusted to approach the optimal solution until the difference between the variable Φ and Φ1 and Φ2 is small enough; S303, alternately iteratively executing S301 and S302 until global convergence, and obtaining the optimal transmit precoding matrix of the dual-function base station and the optimal reflection coefficient matrix of the BD-RIS.

2. The communication and positioning integrated method based on BD-RIS according to claim 1, characterized in that: The S1 comprises the following steps: S101, constructing a BD-RIS-assisted ISAC network model including a dual-function base station, a BD-RIS, K communication users and a sensing target, wherein the dual-function base station is configured with N antennas, N>1; the BD-RIS is configured with M reflective elements, M>1; S102, constructing a radar signal model and a communication signal model based on the BD-RIS assisted ISAC network model, vectorizing the radar signal model, and determining a CRB for DoA estimation according to the vectorized radar signal model.

3. The communication and positioning integrated method based on BD-RIS according to claim 2 is characterized in that: The radar signal model is: Y r =α t Q t WS+N r S=[s[1],...,s[L]] N r =[n r [1],...,n r [L]] Among them, Y r represents the L groups of echo signals received by the dual-function base station from the sensing target, α t Indicates the radar cross-sectional area of ​​the perceived target, represents a complex Gaussian distribution, is α t The variance of the corresponding complex Gaussian distribution; Q t is an intermediate variable, G represents the channel between the dual-function base station and BD-RIS, Φ represents the reflection coefficient matrix of BD-RIS, h r,t represents the line-of-sight link between BD-RIS and the perceived target, h r,t =α r,t a M (θ), α r,t represents the path loss, a M (θ) represents the steering vector, a M (θ)=[1,e jπsinθ ,...,e j(M-1)πsinθ ] T , θ represents the direction of arrival of the perceived target relative to BD-RIS, j is an imaginary unit, W represents the transmit precoding matrix, s[1] represents the signal transmitted by the dual-function base station in the first time slot, s[L] represents the signal transmitted by the dual-function base station in the Lth time slot, and n r [1] represents the additive white Gaussian noise at the dual-function base station in the first time slot, n r [L] represents the additive white Gaussian noise at the dual-function base station in the Lth time slot, in n r [L] corresponds to the variance matrix of the complex Gaussian distribution, I N is the N-order identity matrix.

4. The communication and positioning integrated method based on BD-RIS according to claim 3 is characterized in that: The CRB used for DoA estimation is: Where Tr{·} represents matrix trace operation, Indicates Q t Partial derivative with respect to θ.

5. A communication and positioning integrated system based on BD-RIS using the method of claim 1, characterized in that: include: An initialization module, used to construct a BD-RIS-assisted ISAC network model according to a network scenario including a dual-function base station, BD-RIS, communication users, and sensing targets, and determine a CRB for DoA estimation; A construction module is used to establish an optimization problem P1 based on the BD-RIS assisted ISAC network model, with the base station transmission power, BD-RIS structure and SINR of the communication user as constraints and the goal of minimizing CRB; The calculation module is used to transform and decouple the optimization problem P1 into an optimization subproblem P2.1 focusing on the design of the transmit precoding matrix of the dual-function base station and an optimization subproblem P2.2 focusing on the design of the optimal reflection coefficient matrix of the BD-RIS, and solve them using an alternating iterative method to obtain the optimal transmit precoding matrix and the optimal reflection coefficient matrix.

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