Beam generation method of BD-RIS-assisted dual-function radar communication system

Abstract

The invention provides beam generation of a BD-RIS-assisted dual-function radar communication system, and particularly relates to the technical field of wireless communication, and the scheme comprises the following steps: constructing the BD-RIS-assisted dual-function radar communication system, and constructing a user weighting and rate optimization problem under communication and perception constraints; decomposing a user weighting and rate optimization problem into a base station transmitting precoding matrix optimization problem and a BD-RIS matrix optimization problem; alternately and iteratively executing the step of solving the base station transmitting precoding matrix optimization problem and the BD-RIS matrix optimization problem to obtain an optimal precoding matrix and an optimal BD-RIS matrix; and based on the optimal precoding matrix and the optimal BD-RIS matrix, converting an initial beam pointing to the BD-RIS and the target area into a target beam. According to the scheme, the joint optimization problem is solved, the sensing performance is guaranteed, the communication rate of the communication user is remarkably improved, and the user communication and target detection requirements are met at the same time.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to beam forming of a BD-RIS-assisted dual-function radar communication system. Background Art

[0002] In order to alleviate the growing pressure on spectrum resources, communication systems tend to share spectrum with radar systems. The dual-function radar-communication (DFRC) system integrates communication and radar systems to enable them to share spectrum resources. This integration enables the simultaneous execution of communication and sensing tasks, thereby achieving high integration and reducing hardware costs. The signals transmitted by the base station of the DFRC system can be used for both user communication and target detection. At the same time, the reconfigurable intelligent surface (RIS) intelligently controls the wireless propagation environment by creating a virtual non-line-of-sight path, so it has attracted much attention in the field of auxiliary wireless communications. RIS is composed of a large number of reflection units, and the direction of the incident signal is changed by adjusting the phase of each unit. It has significant advantages in improving system capacity, spectrum efficiency and energy efficiency.

[0003] However, most of the beam design methods of RIS-based DFRC systems are aimed at traditional diagonal RIS, while traditional RIS uses diagonal matrices and can only control elements on the diagonal, with limited design freedom. It can be seen that the existing RIS-based DFRC system has limited beam design freedom, resulting in limited communication and perception performance and reduced spectrum resource utilization efficiency. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the object of the present invention is to provide a beamforming method for a BD-RIS-assisted dual-function radar communication system, aiming to solve the problem that the beam design freedom of the existing RIS-based DFRC system is limited, resulting in limited communication and perception performance and reduced spectrum resource utilization efficiency.

[0005] In order to achieve the above object, the first aspect of the present invention provides a beamforming method for a dual-function radar communication system assisted by BD-RIS, comprising:

[0006] Construct a BD-RIS-assisted dual-function radar communication system and formulate a user weighted sum rate optimization problem under communication and perception constraints;

[0007] Decomposing the user weighted and rate optimization problem into a base station transmit precoding matrix optimization problem and a BD-RIS matrix optimization problem;

[0008] Alternately and iteratively executing the steps of solving the base station transmit precoding matrix optimization problem and the BD-RIS matrix optimization problem to obtain an optimal precoding matrix and an optimal BD-RIS matrix;

[0009] Based on the optimal precoding matrix and the optimal BD-RIS matrix, an initial beam directed to the BD-RIS and the target area is converted into a target beam.

[0010] Optionally, the construction process of the BD-RIS-assisted dual-function radar communication system includes:

[0011] The system includes a DFRC base station, a BD-RIS, a sensing target and a communication user. The DFRC base station is equipped with an N t antenna, used for sensing T sensing targets while providing communication services to K communication users, wherein the communication users include K communication users located on the same side as the DFRC base station r reflection zone users, and K users located on different sides of the DFRC base station t Transmission zone users;

[0012] The BD-RIS contains N s units, each of which includes a group of unidirectional radiating antennas placed back to back, each group of unidirectional radiating antennas placed back to back covers half of the radiation space, and the ports of the two are connected by a reconfigurable impedance element, and the unit is used to change the propagation direction of the incident signal.

[0013] Optionally, if the BD-RIS operates in a hybrid mode and adopts a CW-GC connection structure, the process of constructing the communication and perception constraints includes:

[0014] The BD-RIS consists of a transmission matrix and the reflection matrix It indicates that, represents the complex field, N s ×N s Indicates that the matrix dimension is N s Row and N s Column; N s The units are divided into G groups, and the size of each group is M = N s / G,N s is an integer multiple of G, the units in each group are connected to each other through a reconfigurable impedance element, and there is no connection between the units between groups;

[0015] The transmission matrix Θ t and the reflection matrix Θ r The expression is:

[0016]

[0017] in, It is represented as a set of G unit groups, and BlkDiag(·) represents a block diagonal matrix formed by arranging multiple matrices along the diagonal line;

[0018] The transmission matrix Θ t and the reflection matrix Θ r The constraints that are satisfied are:

[0019]

[0020] Here, H represents the conjugate transpose.

[0021] Optionally, constructing a user weighting and rate optimization problem under communication and perception constraints includes:

[0022] definition is a channel between the BD-RIS and the DFRC base station, is the downlink channel between the BD-RIS and the communication user k, and the expression of the signal received by the communication user k is:

[0023]

[0024] in, is the precoding vector of the communication user k in the DFRC base station, W = [w1, ..., w k ,…,w K ] is the overall transmit precoding matrix, n k is the additive Gaussian white noise when the communication user k receives the signal, with a mean of 0 and a covariance of The complex Gaussian random process, (·) H represents conjugate transpose;

[0025] The signal to interference noise ratio corresponding to the signal received by the communication user k is:

[0026]

[0027] in, is the equivalent channel between the DFRC base station and the communication user k, |·| represents the absolute value, then the weighted sum rate expression of the communication users in the system is:

[0028]

[0029] Among them, μ k is the weight of the communication user k;

[0030] Then the user weighted sum rate optimization problem can be expressed as:

[0031]

[0032] Among them, the constraint It is used to ensure that the designed beam pattern closely matches the ideal radar beam pattern, ∈ is the threshold used to evaluate the similarity; the constraint formula is a constant modulus constraint, which is used to ensure that the radar signal distortion is minimal. t is the total power budget of the system, φ l is the azimuth of the position of the lth sampling angle, and the beam pattern with an azimuth angle of φ can be expressed as:

[0033] P bp =a H (φ)WW H a(φ),

[0034] in, is the array emission steering vector, λ is the wavelength, and d is the array element spacing.

[0035] Optionally, the alternately iteratively performing the steps of solving the base station transmit precoding matrix optimization problem and the BD-RIS matrix optimization problem to obtain an optimal precoding matrix and an optimal phase BD-RIS matrix includes:

[0036] Using a weighted minimum mean square error framework, the base station transmit precoding matrix optimization problem is converted into a semi-positive definite relaxation problem to obtain a precoding matrix;

[0037] By using fractional programming and manifold optimization strategy, the BD-RIS matrix optimization problem is converted into an unconstrained optimization problem to obtain a BD-RIS matrix;

[0038] The steps of solving the precoding matrix and the BD-RIS matrix are performed alternately and iteratively to obtain an optimal precoding matrix and an optimal BD-RIS matrix.

[0039] Optionally, the using a weighted minimum mean square error framework to convert the base station transmit precoding matrix optimization problem into a semi-positive definite relaxation problem to obtain a precoding matrix includes:

[0040] Under the condition of a fixed BD-RIS matrix, the optimization objective function of the base station transmit precoding matrix optimization problem can be expressed as:

[0041]

[0042] A linear receiver v is introduced at the communication user k. k , using the received signal yk Estimated communication symbol x k , then the estimated symbol v k y k With the real symbol x k The mean square error between k It can be expressed as:

[0043]

[0044] Among them, ||·|| 2 is the square operation of the two-norm.

[0045] When the mean square error e k When the partial derivative of the linear receiver is zero, the minimum mean square error is obtained, and based on the minimum mean square error, the base station transmit precoding matrix optimization problem is converted into a weighted mean square error minimization problem, that is:

[0046]

[0047] in, α represents the proportional factor, and the optimal proportional factor α is determined by using the preset first-order optimality condition ＊ ; Introduce auxiliary variable t of unit power k , convert the constraint into:

[0048]

[0049] After simplification, the mean square error e k The equivalent form of can be expressed as:

[0050]

[0051] in, (·) * represents conjugation, and 0 represents dimension N t A column vector with all zeros in row 1 and column 2;

[0052] make By using the property of the trace, the base station transmit precoding matrix optimization problem is converted into a semi-positive definite relaxation problem, which can be expressed as:

[0053]

[0054] Where Tr(·) represents the trace of the matrix;

[0055] The semi-positive definite relaxation problem is solved by using rank-one decomposition to obtain a precoding matrix.

[0056] Optionally, the using of fractional programming and manifold optimization strategy to convert the BD-RIS matrix optimization problem into an unconstrained optimization problem to obtain the BD-RIS matrix includes:

[0057] Under the condition that the base station transmits the precoding matrix, the optimization objective function of the BD-RIS matrix optimization problem can be expressed as:

[0058]

[0059] Θ t =BlkDiag(Θ t，1 , ..., Θ t，g , ..., Θ t，G ),

[0060] Θ r =BlkDiag(Θ r，1 , ..., Θ r，g , ..., Θ r，G ),

[0061]

[0062] Using Lagrange dual transformation and introducing auxiliary variables ξ=[ξ1,...,ξ K ] t , the equivalent form of the BD-RIS matrix optimization problem can be expressed as:

[0063]

[0064] Among them, γ k The fractional term in the logarithmic function log(·) contained in the optimization objective function of the BD-RIS matrix optimization problem is represented by the introduction of an auxiliary vector ζ = [ζ1, ..., ζ K ] T To decouple the fractional form in the optimization objective function of the BD-RIS matrix optimization problem, the equivalent form of the BD-RIS matrix optimization problem can be expressed as:

[0065]

[0066] The transmission matrix of the g-th group and the reflection matrix of the g-th group are combined as the optimization variables of the g-th group. The objective function can be equivalently expressed as:

[0067]

[0068] in,

[0069] Define a manifold space based on the constraints, namely:

[0070]

[0071] Based on the manifold space, iteratively update the transmission matrix Θ of the gth group t，g and the reflection matrix Θ of the gth group r，g , obtain the BD-RIS matrix.

[0072] A second aspect of the present invention provides a beam forming system for a dual-function radar communication system assisted by a BD-RIS, the system comprising:

[0073] The initial optimization problem building module is used to build a BD-RIS-assisted dual-function radar communication system, which constructs the user weighted sum rate optimization problem under communication and perception constraints;

[0074] An optimization problem decomposition module, used for decomposing the user weighted and rate optimization problem into a base station transmit precoding matrix optimization problem and a BD-RIS matrix optimization problem;

[0075] An optimization problem solving module, used for alternately and iteratively executing the steps of solving the base station transmit precoding matrix optimization problem and the BD-RIS matrix optimization problem to obtain an optimal precoding matrix and an optimal BD-RIS matrix;

[0076] The target beam forming module is used to convert the initial beam pointing to the BD-RIS and the target area into a target beam based on the optimal precoding matrix and the optimal BD-RIS matrix.

[0077] A third aspect of the present invention provides an intelligent terminal, which includes a memory for storing executable instructions; and a processor for calling and running the executable instructions in the memory to execute any step of the beamforming method of the above-mentioned BD-RIS-assisted dual-function radar communication system.

[0078] A fourth aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores program instructions. When the program instructions are executed by a processor, the steps of any one of the above-mentioned BD-RIS-assisted beamforming methods for a dual-function radar communication system are implemented.

[0079] Compared with the prior art, the beneficial effects of this solution are as follows:

[0080] The present invention constructs a BD-RIS-assisted DFRC system, considers different modes and different BD-RIS structures, and constructs the original optimization problem of maximizing the user weighted sum rate under the conditions of satisfying the base station beam pattern requirements, the transmission power budget and the BD-RIS constraints under different structures; in order to simplify the complexity of the solution, the original optimization problem is decomposed into two sub-problems of optimizing the base station transmit precoding matrix and optimizing the BD-RIS matrix; using the weighted minimum mean square error framework, the base station transmit precoding matrix optimization sub-problem is converted into a semi-positive definite relaxation form to solve the precoding matrix; through fractional programming and manifold optimization, the BD-RIS matrix optimization problem is converted into an unconstrained optimization problem to solve the optimal value of the BD-RIS matrix; and the two sub-problems are solved by alternating iterations to obtain the optimal solution of the original optimization problem. It can be seen that the present invention can effectively solve the joint optimization problem, significantly improve the communication rate of the communication user while ensuring the perception performance, so as to simultaneously meet the user communication and target detection requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0082] Figure 1 A simplified flow chart of a beam forming method of a dual-function radar communication system assisted by BD-RIS of the present invention;

[0083] Figure 2 A detailed diagram of a beam forming method of a dual-function radar communication system assisted by BD-RIS of the present invention;

[0084] Figure 3 A beam forming system model diagram of a dual-function radar communication system assisted by BD-RIS of the present invention;

[0085] Figure 4 A relationship diagram between the user weight and rate and the number of algorithm iterations of the present invention;

[0086] Figure 5 A diagram showing the relationship between the user weighted sum rate and the number of BD-RIS units of the present invention;

[0087] Figure 6 A diagram showing the relationship between the beam patterns of base stations of BD-RIS-assisted DFRC systems with different structures and the ideal beam patterns when the present invention works in a hybrid mode;

[0088] Figure 7It is a schematic diagram of the beam forming system module of the BD-RIS-assisted dual-function radar communication system of the present invention;

[0089] Figure 8 It is a schematic diagram of the structure of the intelligent terminal of the present invention. DETAILED DESCRIPTION

[0090] In the following description, for the purpose of illustration rather than limitation, specific details such as specific system structures, technologies, etc. are proposed so as to thoroughly understand the embodiments of the present invention. However, it should be clear to those skilled in the art that the present invention can also be implemented in other embodiments without these specific details. It should be understood that when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, wholes, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or their collections. It should also 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.

[0091] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings of 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 are within the scope of protection of the present invention.

[0092] In a Multiple-Input Multiple-Output (MIMO) radar system, each waveform transmitted to the radar antenna is usually required to have the same power to ensure that the power amplifier in the RF chain operates in the saturation region to avoid signal distortion. Therefore, in a DFRC system, the constant modulus constraint of the radar system needs to be considered, but this constraint is not considered in most DFRC system designs. Most of the existing beam design methods for RIS-assisted DFRC systems are aimed at traditional diagonal RIS. Since the structure of the Beyond Diagonal Reconfigurable Intelligent Surface (BD-RIS) is different from that of the traditional diagonal RIS, it can control the units in the diagonal and non-diagonal positions, thereby providing higher design freedom.

[0093] In order to improve the communication and perception performance of the DFRC system, it is possible to consider deploying BD-RIS near the base station of the DFRC system to provide additional non-line-of-sight paths to enhance the received signal strength of communication users and target echoes. However, in the DFRC system, the radar and communication systems share waveforms, so the base station transmit precoding matrix and the BD-RIS matrix need to be carefully designed to meet the needs of user communication and target detection at the same time.

[0094] Based on the above analysis, this embodiment provides a beamforming method for a dual-function radar communication system assisted by BD-RIS, which is deployed on electronic devices such as computers and servers and applied to the scenario of joint optimization of the DFRC base station transmit precoding matrix and the BD-RIS matrix, and is aimed at the dual-function radar communication system assisted by BD-RIS. Specifically, Figure 1 and Figure 2 As shown, the steps of the method in this embodiment include:

[0095] Step S100: constructing a BD-RIS-assisted dual-function radar communication system, and constructing a user weighted sum rate optimization problem under communication and perception constraints;

[0096] Specifically, the BD-RIS-assisted dual-function radar communication system constructed in this embodiment includes a dual-function radar communication base station (i.e., a DFRC base station), a BD-RIS, a sensing target, and a communication user with a single antenna, such as Figure 3 As shown, the DFRC base station is equipped with N t antenna, used for sensing T sensing targets while providing communication services to K communication users, wherein the communication users include K communication users located on the same side as the DFRC base station r The K reflection zone communication users and the K DFRC base station located on different sides t For the convenience of description, the set of communication users in the reflection area is defined as The set of communication users in the transmission zone is defined as The total communication user set is defined as

[0097] The BD-RIS contains N s A unit is provided, and the propagation direction of the incident signal is changed by adjusting the phase and amplitude on the unit. Each of the units includes a group of unidirectional radiating antennas placed back to back, and each group of unidirectional radiating antennas placed back to back each covers half of the radiation space, and the ports of the two are connected by a reconfigurable impedance element. The unit is used to change the propagation direction of the incident signal.

[0098] Assume that BD-RIS is far from the target, so BD-RIS only serves the communication users and does not affect the target perception. For the convenience of analysis, the line-of-sight path between the DFRC base station and the communication user is blocked by obstacles, the line-of-sight path does not exist, and the base station provides communication services to the communication user through the reflection / transmission path provided by BD-RIS.

[0099] Then, this embodiment designs general constraints for BD-RIS with different modes and different structures. Since BD-RIS can support three different modes, namely transmission mode, reflection mode and hybrid mode. When BD-RIS is in transmission mode / reflection mode, it can only provide services to communication users located in the transmission area / reflection area. Since the hybrid mode can provide services to both transmission and reflection areas at the same time, the transmission mode and reflection mode can be regarded as special cases of the hybrid mode. While maintaining generality, this embodiment considers BD-RIS working in hybrid mode. Mathematically, the hybrid mode is represented by two matrices of BD-RIS, namely the transmission matrix and the reflection mode. and the reflection matrix Where C represents the complex field, N s ×N s Indicates that the matrix dimension is N s Row and N s List.

[0100] This embodiment considers three different connection structures of BD-RIS, namely, cell-wise single connected (CW-SC), cell-wise group connected (CW-GC / ), and cell-wise fully connected (CW-FC). Among these three structures, CW-GC can be regarded as a universal structure. s The units are evenly divided into G groups, each group size is M = N s / G, the cells in each group are connected to each other through the reconfigurable impedance element, while the cells between groups are not connected to each other. Therefore, the transmission matrix Θ t and the reflection matrix Θ r It can be considered as a block diagonal matrix and is expressed as:

[0101]

[0102] in, It is represented as a set of 1-G groups, and BlkDiag(·) means that multiple matrices are arranged diagonally to form a block diagonal matrix. Since the impedance network of BD-RIS is purely reactive, the BD-RIS matrix satisfies the following constraints:

[0103]

[0104] The CW-FC and CW-SC structures can be considered as two special cases of the CW-GC structure. In the CW-FC structure, the entire BD-RIS can be considered as a whole, in which all units are interconnected through reconfigurable impedance elements. This structure provides the highest beam design freedom among the three types, but also has the highest circuit complexity among the three structures. The BD-RIS matrix must satisfy the constraints In the CW-SC structure, each unit of BD-RIS is regarded as an independent group, and there is no connection between the units. Therefore, the BD-RIS matrix degenerates into a regular diagonal matrix, satisfying the following constraints: where θ t，g and θ r，g is Θ t and θ r The g-th BD-RIS coefficient in .

[0105] Therefore, in order to meet the base station beam pattern requirements, transmit power budget and BD-RIS constraint requirements under different structures, this embodiment adopts the constraint conditions of the CW-GC structure in the hybrid mode as the general constraint of the BD-RIS matrix, constructs the optimization problem of maximizing the user weighted sum rate (Weighted Sum-Rate, WSR), and realizes WSR maximization by jointly optimizing the DFRC base station transmit precoding matrix and the BD-RIS matrix.

[0106] Specifically, the definition It is the channel between BD-RIS and DFRC base station. is the channel between BD-RIS and the communication users located in the reflection area, is the channel between BD-RIS and the communication user located in the transmission area, where (·) H represents the conjugate transpose. To simplify the representation, define is the downlink channel between BD-RIS and communication user k. The DFRC base station transmits the symbol vector for dual functions in, The representation is defined as, [·] T represents transposition. After being precoded by the base station and passing through the BD-RIS assisted channel (i.e., base station-BD-RIS-communication user), the signal is interfered by additive white Gaussian noise. Therefore, the signal received by communication user k can be expressed as:

[0107]

[0108] in, is the precoding vector of the DFRC base station of communication user k, W = [w1, ..., w k ,…,w K ] is the overall transmit precoding matrix, n k is the additive Gaussian white noise when communication user k receives the signal, with a mean of 0 and a covariance of The complex Gaussian random process, (·) H represents the conjugate transpose.

[0109] According to the signal model shown in equation (3), the signal-to-interference-noise ratio (SINR) received by communication user k is expressed as:

[0110]

[0111] in, is the equivalent channel between the DFRC base station and the communication user k, |·| represents the absolute value, then the weighted sum rate of the communication users in the system can be expressed as:

[0112]

[0113] Among them, μ k is the weight of communication user k.

[0114] In the DFRC system, the design of the beam pattern is crucial. The beam pattern with an azimuth angle of φ can be expressed as:

[0115] P bp =a H (φ)WW H a(φ), (6)

[0116] in, is the array transmission steering vector, λ represents the wavelength, and d is the array element spacing. Without loss of generality, the antenna spacing is assumed to be half the wavelength. In order to ensure the perception performance, the similarity between the ideal beam pattern and the designed beam pattern in the radar system is calculated, and the expression is:

[0117]

[0118] Among them, α is the scale factor, L is the number of sampling points, φ l represents the lth sampling angle in the range of [-π / 2, π / 2], with a resolution of 1° and an ideal beam pattern P d (φ l ) is defined as:

[0119]

[0120] in, is the azimuth of the location of the tth target, and Δφ is the beam width in the target area.

[0121] In this embodiment, the base station transmit precoding matrix and the BD-RIS matrix are jointly designed to maximize the system user WSR. The constructed joint optimization problem is expressed as:

[0122]

[0123] Θ t =BlkDiag(Θ t，1 , ..., Θ t，g , ..., Θ t，G ), (9d)

[0124] Θ r =BlkDiag(Θ r，1 , ..., Θ r，g , ..., Θ r，G ), (9e)

[0125]

[0126] Wherein, Equation (9b) represents the constraint used to ensure that the designed beam pattern closely matches the radar ideal beam pattern to achieve effective radar operation; ∈ represents the threshold used to evaluate the similarity; Equation (9c) represents the constant modulus constraint to ensure the minimum distortion of the radar signal, P t is the total power budget of the system; Equations (9d) to (9f) represent the constraints on the BD-RIS matrix.

[0127] Step S200: decomposing the user weighted and rate optimization problem into a base station transmit precoding matrix optimization problem and a BD-RIS matrix optimization problem;

[0128] Specifically, since the user weighted sum rate optimization problem (Equation (9a)-Equation (9f)) has optimization variable coupling, is highly non-convex, difficult to solve, and has high complexity, the optimization variables are decoupled and the original optimization problem is decomposed into two sub-problems: optimizing the base station transmit precoding matrix and optimizing the BD-RIS matrix. The complex problem is simplified to improve the calculation accuracy and efficiency. When the BD-RIS matrix is ​​fixed, the base station transmit precoding matrix is ​​optimized.

[0129] After determining the optimal precoding matrix of the base station, it is necessary to design the optimal BD-RIS matrix according to the direction and shape of the target beam. Each unit of the BD-RIS matrix represents the phase difference of each unit in the array antenna relative to the reference unit. In the case of a fixed base station transmit precoding matrix, the BD-RIS matrix is ​​optimized. That is, the user weighted and rate optimization problem is decomposed into the base station transmit precoding matrix optimization problem and the BD-RIS matrix optimization problem. The specific solution process of the base station transmit precoding matrix optimization problem and the BD-RIS matrix optimization problem is detailed in step S300.

[0130] Step S300: alternately and iteratively executing the steps of solving the base station transmit precoding matrix optimization problem and the BD-RIS matrix optimization problem to obtain an optimal precoding matrix and an optimal BD-RIS matrix;

[0131] Under the condition of fixed BD-RIS matrix, the base station transmit precoding matrix is ​​optimized, and the optimization objective function of the base station transmit precoding matrix optimization problem is obtained, namely:

[0132]

[0133] In order to simplify the difficulty of solving the optimization objective function, this embodiment uses the weighted minimum mean square error framework to convert the base station transmit precoding matrix optimization problem into a semi-positive definite relaxation problem to obtain the precoding matrix. Specifically, a linear receiver v is introduced at the communication user k. k , using the received signal y k Estimated communication symbol x k , and estimate the symbol v k y k With the real symbol x k Mean Square Error (MSE) between k , which is expressed as follows:

[0134]

[0135] Among them, ||·|| 2 is the square operation of the two norm. The minimum mean square error (MMSE) receiver can be obtained by setting the partial derivative of the mean square error with respect to the linear receiver to zero, that is, by solving the expression To get, among them, represents the partial derivative of the function f(x) with respect to the variable x. At this time, the MMSE receiver The expression is:

[0136]

[0137] The MMSE receiver is used to receive the signal. The mean square error is The expression is:

[0138]

[0139] Using the existing WMMSE framework, the WSR maximization problem is converted into a weighted mean square error minimization problem. The equivalent optimization problem can be expressed as:

[0140]

[0141] in, Observing the above optimization problem, it can be found that the proportional factor α only exists in constraint (14b). The optimal value of α can be determined by the first-order optimality condition, expressed as:

[0142]

[0143] By solving the above equation, we can get the optimal proportional factor α ＊ for:

[0144]

[0145] in,(·) ★ Expressed as the optimal value of the variable. The optimal proportional factor α ★ Substituting into constraint (14b) it can be expressed as:

[0146]

[0147] Similarly, constraint (14c) can be expressed as:

[0148]

[0149] In order to effectively solve the optimization problem, this embodiment introduces an auxiliary variable t of unit power. k , and let Then constraint equations (17) and (18) are expressed as:

[0150]

[0151] By treating the target similarly and ignoring the constant in the objective function, the mean square error e can be obtained. k The equivalent objective function is:

[0152]

[0153] in, (·) * Indicates conjugation, 0 indicates dimension is Nt A column vector with all zeros in row 1 and column 2.

[0154] In order to solve this optimization problem, And by applying the properties of the trace, the optimization problem is transformed into a semi-definite relaxation (SDR) problem, which can be expressed as:

[0155]

[0156] Here, Tr(·) is the trace of the matrix. This semi-positive definite relaxation optimization problem is a convex optimization problem. It can be solved directly using the Convex Optimization Toolbox (CVX) by omitting the rank-one constraint in the above optimization problem. However, the E k The rank-one constraint may not be satisfied. In this case, a rank-one decomposition is performed to obtain the optimal precoding vector w k ★ , thus obtaining the optimal precoding matrix W ★ .

[0157] It can be seen that in this embodiment, when the BD-RIS matrix is ​​fixed, the iterative solution process of the base station transmit precoding matrix optimization problem mainly includes: according to formula (11), the estimated symbol v is calculated k y k and the real symbol x k The mean square error between k According to the formula Calculating MMSE Receiver and the mean square error under this receiver According to the formula Calculate the weight vector According to formula (16), the optimal proportional factor α is calculated ★ ; Introduce auxiliary variable t of unit power k , and use the properties of the trace to organize the objective function and constraints; by considering the rank-one constraint, use the rank-one decomposition to obtain the optimal precoding vector w k ★ And the optimal precoding matrix W ★ , which greatly simplifies the complexity of solving optimization problems and can significantly improve the effectiveness and accuracy of solutions.

[0158] In the case of a fixed base station transmit precoding matrix, the BD-RIS matrix is ​​optimized, and the optimization objective function of the BD-RIS matrix optimization problem is obtained, namely:

[0159]

[0160] Θ t =BlkDiag(Θ t，1, ..., Θ t，g , ..., Θ t，G ), (23b)

[0161] Θ r =BlkDiag(Θ r，1 , ..., Θ r，g , ..., Θ r，G ), (23c)

[0162]

[0163] Since the fractional term γ in the logarithmic function log(·) contained in the objective function (23a) k , this optimization problem is difficult to solve in the current form, so this embodiment uses fractional programming and manifold optimization strategy to convert the BD-RIS matrix optimization problem into an unconstrained optimization problem to obtain the BD-RIS matrix. Specifically, the Lagrange dual transformation is applied and the auxiliary variable ξ=[ξ1,...,ξ K ] T , convert the target into an equivalent form as follows:

[0164]

[0165] By alternating the optimization of the transmission matrix Θ t , the reflection matrix Θ r and auxiliary variables ξ to solve the problem. First, fix the transmission matrix Θ t and the reflection matrix Θ r In the case of To obtain the best value Right now:

[0166]

[0167] Given ξ, the objective function takes the form of a fraction that is difficult to handle. This embodiment introduces another auxiliary vector ζ=[ζ1, ..., ζ K ] T To decouple the fractional form, the objective function can be expressed as:

[0168]

[0169] Next, the auxiliary variable ζ and the transmission matrix Θ are optimized alternately t and the reflection matrix Θ r To solve. and They represent two different auxiliary variables. represents the decoupled logarithmic and form, Represents decoupled fractional form.

[0170] Given a transmission matrix Θ t and the reflection matrix Θ r In the case of To obtain the best value The expression is:

[0171]

[0172] In order to obtain the optimal auxiliary variable and After that, the objective function can be simplified to:

[0173]

[0174] in, In the above formula, Re{·} represents the real part operation. Substitute into the objective function (28) to explicitly express the transmission matrix Θ t and the reflection matrix Θ r , using the properties of the trace, the BD-RIS matrix optimization problem can be reformulated as:

[0175]

[0176] stΘ t =BlkDiag(Θ t，1 , ..., Θ t，g , ...Θ t，G ), (29b)

[0177] Θ r =BlkDiag(Θ r，1 , ..., Θ r，g , ..., Θ r，G ), (29c)

[0178]

[0179] Among them, the definition is,

[0180]

[0181] In order to solve the problem effectively, we first transform the BD-RIS matrix Θ in the objective function (29a) into r and θ t , the transmission matrix and reflection matrix of the gth group are represented as Θ t，g and θ r，g . Then, the objective function can be equivalently expressed as:

[0182]

[0183] For simplicity, construct the matrix U g，q =f(U, g, q), which means extracting a submatrix with row index g and column index q from matrix U, where Then, while keeping the transmission matrix and reflection matrix pairs of other groups unchanged, optimize the transmission matrix Θ of the gth group t，g and the reflection matrix Θ r，g , so the corresponding optimization objective function of the g-th group can be expressed as:

[0184]

[0185] in Consider the transmission matrix Θ of the gth group t，g and the reflection matrix Θ of the gth group r，g At the same time, optimizing and combining the transmission matrix and reflection matrix of group g, we can get:

[0186]

[0187] Therefore, the optimization objective function of the g-th group can be equivalently expressed as:

[0188]

[0189] Due to the non-convex unitary constraint (38b), the above optimization problem is still difficult to solve. It can be observed that constraint (38b) is a typical manifold space, and manifold optimization can be used to solve the optimal value. Therefore, this embodiment defines a manifold space according to the constraint, that is:

[0190]

[0191] Every point in the manifold space satisfies the constraint (38b). At this time, the optimization problem is an unconstrained optimization problem. The minimum value of the objective function can be found on this manifold space. At this time, the point corresponding to the minimum value of the objective function is the optimal BD-RIS. At every point on the manifold that satisfies the unitary constraint, there exists a tangent space, which can be regarded as a Euclidean space with tangent vectors. Mathematically, the manifold is at point Θ. g The tangent space at can be expressed as:

[0192]

[0193] Among them, X g Represents Θ g The tangent vector of θ. The tangent space contains the Riemann gradient, which indicates the direction in which the objective function decays fastest. The Riemann gradient is the orthogonal projection of the Euclidean gradient on the Riemann manifold. g At The expression is:

[0194]

[0195] in, represents the Euclidean gradient, and chdiag(·) represents selecting all diagonal cells of a matrix to construct a diagonal matrix. In the pth iteration, the search direction expression is as follows:

[0196]

[0197] in, It is represented as the parameter of the pth iteration of the conjugate gradient method. After obtaining the search direction, the solution still stays in the tangent space In order to obtain the optimal BD-RIS solution, BD-RIS is cut from the space Mapping back to the manifold Then, the BD-RIS of the p+1th iteration on the manifold is mapped back to the manifold by backtracking method:

[0198]

[0199] in, is the step size obtained by the backtracking method. By setting the appropriate BD-RIS initial value, the optimal matrix of the gth group is obtained In getting After that, the optimal values ​​of the g-th group of transmission matrix and reflection matrix can be separated and expressed as:

[0200]

[0201] It can be seen that in this embodiment, when the base station transmits the precoding matrix, the iterative solution process of the BD-RIS matrix optimization problem mainly includes: using the properties of the trace to simplify the objective function of the BD-RIS matrix optimization problem, and introducing auxiliary variables ξ and ζ, by setting the matrix initial point and defining the manifold space of the g-th group, projecting the tangent space search BD-RIS to the manifold space, and updating the matrix Θ of the g-th group g ; Calculate the matrix Θ g The Riemann gradient at , we get the transmission matrix Θ of each group in G group t，g and the reflection matrix Θ r，g ; Arrange the matrices of group G diagonally to obtain the optimal transmission matrix Θ t and the reflection matrix Θ r .

[0202] In order to obtain the optimal solution to the optimization problem, this embodiment alternately iterates and executes the steps of solving the precoding matrix and the BD-RIS matrix to obtain the optimal precoding matrix and the optimal BD-RIS matrix. Specifically, the base station transmit precoding matrix, the transmission matrix and the reflection matrix are initialized; in the case of a fixed BD-RIS matrix, the above process of solving the optimization problem of the base station transmit precoding matrix is ​​iteratively executed to obtain the optimal solution of the base station transmit precoding matrix, which refers to the base station precoding matrix that can maximize the system performance (such as transmission rate, signal-to-noise ratio, etc.); search on the manifold space, in the case of a fixed base station transmit precoding matrix, according to the iterative solution process of the above BD-RIS matrix optimization problem, iteratively update the transmission matrix Θ of BD-RIS. t，g and the reflection matrix Θ r，g When the Riemann gradient converges, the minimum value of the g-th group of objective functions is searched in the manifold space, the search is stopped, an iteration is completed, and the optimal value of the g-th group of matrices is obtained. Get the corresponding g-th group transmission matrix Θ t，g and the reflection matrix Θ r，g The termination condition for the g-th group matrix search is that the Frobenius norm of the difference between the transmission matrix and reflection matrix of the g-th group in the previous iteration and the transmission matrix and reflection matrix of the next iteration is less than a certain threshold, or the preset number of iterations is reached. When the termination condition for the g-th group matrix search is reached, the optimal matrix corresponding to the g-th group can be obtained, and the transmission matrix and reflection matrix of the g-th group can be obtained; otherwise, the iterative update steps are repeated; according to this principle, the transmission matrix and reflection matrix of each group are solved until the G-th group iteration is completed; the matrices of the G-th group are arranged diagonally to obtain the optimal transmission matrix Θ t and the reflection matrix Θ r , thus obtaining the optimal BD-RIS matrix, which can accurately generate the matrix of the target beam.

[0203] In addition, the two connection structures of CW-FC and CW-SC can be regarded as a special case of CW-GC, and the above method is also used to solve them. For the CW-FC connection structure, all units can be regarded as a group, that is, the entire BD-RIS is regarded as a group, so the optimization problem can be simplified by equations (29a) to (29d) as follows:

[0204]

[0205] in, Then, the solution can be obtained by manifold optimization according to equations (39)-(45). For the CW-SC connection structure, each unit can be regarded as a group and the solution is also obtained by the above method, which will not be repeated here.

[0206] Step S400: Based on the optimal precoding matrix and the optimal BD-RIS matrix, convert the initial beam pointing to the BD-RIS and the target area into a target beam.

[0207] In wireless communications, the base station uses the optimal precoding matrix to preprocess the transmitted signal to match the characteristics of the channel, reduce interference between signals, and improve transmission performance (such as transmission rate, signal-to-noise ratio, etc.); in beamforming, the signal can be focused and transmitted in a directional manner by adjusting the phase of each unit in the array antenna. Therefore, the optimal BD-RIS matrix is ​​used to adjust the phase of the signal to generate the shape and direction of the target beam.

[0208] Specifically, during the target beamforming process, the base station generates an initial beam pointing to the BD-RIS and the target area through an optimized precoding matrix. Then, the initial beam is transmitted through the array antenna, and the optimal BD-RIS matrix is ​​applied to each antenna unit to control the incident signal, forming a reflected beam that accurately points to the user, and then the target beam is formed through constructive and destructive interference of the signals of each unit in the array antenna. The shape and direction of the target beam are jointly determined by the optimal base station transmit precoding matrix and the optimal BD-RIS matrix, which can accurately point to the communication user and the perception target area, realize efficient transmission and precise orientation of the signal, and provide strong support for fields such as wireless communication and radar detection.

[0209] In order to prove the effectiveness of the proposed algorithm for the BD-RIS assisted DFRC system, the present invention conducted the following simulation experiments, and the main simulation parameters used were: the number of DFRC antennas N t =16, the number of BD-RIS units N s =64, for the unit-group connection structure of BD-RIS, the number of groups G is set to 8. The total power of the system P t =10dBm, there are K = 6 communication users in the system, of which K t = 3 communication users are located in the transmission area, and the remaining K r = 3 communication users are located in the reflection area. The receiving noise power of each communication user is σ 2 = -80dBm. The channel G between the DFRC base station and the RIS and the channel h between the RIS and the communication user k The Rice channel model is adopted, that is:

[0210]

[0211] Among them, k1 and k2 are Rice factors, G LOS and is the deterministic component of the line of sight, G NLOS and is the non-line-of-sight Rayleigh fading component, βG and β r is the corresponding path loss parameter. Set the Rice factor k1=k2=5dB. For the path loss β of the two channels G and β r , using a distance-dependent path loss model Where ζ0 = -30 dB represents the signal attenuation at the reference distance d0 = 1 m, d BR and d RU The distances from the DFRC base station to the BD-RIS and from the BD-RIS to the communication user are respectively represented. BR The communication users are randomly distributed in a circle with a radius of 2.5 m and centered at BD-RIS. The path loss index ε of these two channels is BR and ε RU Both are set to 2.2.

[0212] The BD-RIS working in reflection mode is used as a benchmark scheme to compare it with the existing dual diagonal RIS in hybrid mode. This comparison scheme is essentially a special case of the unit-single connection structure in BD-RIS. The reflection matrix and transmission matrix expressions of the dual diagonal RIS are: Θ r =Diag(β r )Θ r，CW-SC , Θ t =Diag(β t )Θ t，CW-SC , Among them, Θ r，CW-SC is the reflection matrix of the unit-single-connected structure, Θ t，CW-SC is the transmission matrix of the unit-single-connected structure, Diag(β r ) / Diag(β t ) represents the column vector β r / β t A diagonal matrix formed as the diagonal elements of a diagonal matrix.

[0213] In order to test the effect of the present invention, a convergence test experiment was carried out on the proposed method, considering the influence of the number of iterations on the system weighted sum rate. Figure 4It is the relationship curve between the user weighted sum rate (WSR) and the number of algorithm iterations. In this experiment, all scenarios are set to the same hybrid mode. It can be seen from the test results that after a certain number of iterations, all curves converge to a stable point, indicating that the method proposed in the present invention can achieve the convergence of different BD-RIS structures, which is consistent with the theoretical analysis. The performance of the pure communication system assisted by BD-RIS under the unit-fully connected structure is better than that of the BD-RIS assisted DFRC system under the unit-fully connected structure. This is because in the BD-RIS assisted DFRC system scenario under the unit-fully connected structure, part of the power is used to form a beam pointing to the target for perception. In contrast, under the same system power budget, all power is used for communication in BD-RIS assisted communication. In addition, in the beamforming design, BD-RIS under the unit-fully connected structure has the best performance, while the dual diagonal RIS assisted DFRC system has the worst performance due to its limited degrees of freedom.

[0214] The present invention also studies the influence of the number of BD-RIS units on the system weighted sum rate in BD-RIS assisted DFRC systems with different structures. Figure 5 As shown in the figure, as the number of BD-RIS units increases, the weighted sum rate and all curves will also increase. Under the same structure of BD-RIS, the hybrid mode performs better than the reflection mode. This is because the hybrid mode can provide full-space services to all communication users, while the reflection mode can only serve communication users within the reflection area. In contrast, under the same mode, BD-RIS under the unit-fully connected structure shows better performance than other structures and dual diagonal RIS. This is because under the unit-fully connected structure, the transmission matrix and the reflection matrix have more non-zero positions, which has higher beam design flexibility and brings the greatest performance gain.

[0215] The present invention also studies the beam patterns of DFRC base stations with different BD-RIS structures in the hybrid mode, such as Figure 6 As shown. Set the total power to P t =10dBm. The three targets are set at -30°, 0° and 30° of the DFRC base station, and the BD-RIS is located at 45° of the DFRC base station. The beam width of the target area is Δφ=10°. The designed base station beam pattern has high power in the target area and low power in other directions, which is close to the ideal beam pattern. In the three structures of BD-RIS, namely the beam pattern under the unit-fully connected structure, the beam pattern under the unit-group connected structure, and the beam pattern under the unit-single connected structure, there is a peak pointing to BD-RIS, which shows the effectiveness of BD-RIS in enhancing WSR while maintaining perception performance.

[0216] In summary, the above simulation results verify the effectiveness of the proposed method and the superiority of using BD-RIS in the DFRC system to enhance the communication and radar performance.

[0217] like Figure 7 As shown, corresponding to the beam forming method of the dual-function radar communication system assisted by BD-RIS, an embodiment of the present invention further provides a beam forming system of the dual-function radar communication system assisted by BD-RIS, and the beam forming system of the dual-function radar communication system assisted by BD-RIS includes:

[0218] The initial optimization problem construction module 710 is used to construct a BD-RIS-assisted dual-function radar communication system, and construct a user weighted sum rate optimization problem under communication and perception constraints;

[0219] An optimization problem decomposition module 720, configured to decompose the user weighted and rate optimization problem into a base station transmit precoding matrix optimization problem and a BD-RIS matrix optimization problem;

[0220] The optimization problem solving module 730 is used to alternately and iteratively perform the steps of solving the base station transmit precoding matrix optimization problem and the BD-RIS matrix optimization problem to obtain an optimal precoding matrix and an optimal BD-RIS matrix;

[0221] The target beam forming module 740 is configured to convert an initial beam directed to the BD-RIS and the target area into a target beam based on the optimal precoding matrix and the optimal BD-RIS matrix.

[0222] Specifically, in this embodiment, the specific functions of the beamforming system of the above-mentioned BD-RIS-assisted dual-function radar communication system can also refer to the corresponding description in the beamforming method of the above-mentioned BD-RIS-assisted dual-function radar communication system, which will not be repeated here.

[0223] Based on the above embodiments, the present invention further provides an intelligent terminal, whose principle block diagram can be shown as follows: Figure 8 As shown. The intelligent terminal can be used to execute the beamforming method of the BD-RIS-assisted dual-function radar communication system provided in the above embodiment. For the sake of brevity, it is not repeated here. The intelligent terminal includes: a processor, the processor is coupled to a memory, the memory is used to store computer programs or instructions, and the processor is used to execute the computer programs or instructions stored in the memory, so that the method in the above method embodiment is executed.

[0224] The present invention also provides a computer-readable storage medium on which computer instructions for implementing the method in the above method embodiment are stored. When the computer program is executed by a computer, the computer can implement the method in the above method embodiment.

[0225] The embodiment of the present application also provides a computer program product including instructions, which, when executed by a computer, enables the computer to implement the method in the above method embodiment.

[0226] Those of ordinary skill in the art can appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working process of the above-described system, device and unit can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

Claims

1. A beam forming method for a BD-RIS-assisted dual-function radar communication system, characterized in that: The following steps are involved: Construct a BD-RIS-assisted dual-function radar communication system and formulate a user weighted sum rate optimization problem under communication and perception constraints; Decomposing the user weighted and rate optimization problem into a base station transmit precoding matrix optimization problem and a BD-RIS matrix optimization problem; Alternately and iteratively executing the steps of solving the base station transmit precoding matrix optimization problem and the BD-RIS matrix optimization problem to obtain an optimal precoding matrix and an optimal BD-RIS matrix; Based on the optimal precoding matrix and the optimal BD-RIS matrix, an initial beam directed to the BD-RIS and the target area is converted into a target beam.

2. The beam forming method of the BD-RIS-assisted dual-function radar communication system according to claim 1, characterized in that: The construction process of the BD-RIS-assisted dual-function radar communication system includes: The system includes a DFRC base station, a BD-RIS, a sensing target and a communication user. The DFRC base station is equipped with an N t antenna, used for sensing T sensing targets while providing communication services to K communication users, wherein the communication users include K communication users located on the same side as the DFRC base station r reflection zone users, and K users located on different sides of the DFRC base station t Transmission zone users; The BD-RIS contains N s units, each of which includes a group of unidirectional radiating antennas placed back to back, each group of unidirectional radiating antennas placed back to back covers half of the radiation space, and the ports of the two are connected by a reconfigurable impedance element, and the unit is used to change the propagation direction of the incident signal.

3. The beam forming method of the BD-RIS-assisted dual-function radar communication system according to claim 2, characterized in that: If the BD-RIS operates in hybrid mode and adopts a CW-GC connection structure, the process of constructing the communication and perception constraints includes: The BD-RIS consists of a transmission matrix and the reflection matrix It indicates that, represents the complex field, N s ×N s Indicates that the matrix dimension is N s Row and N s Column; N s The units are divided into G groups, and the size of each group is M = N s / G,N s is an integer multiple of G, the units in each group are connected to each other through a reconfigurable impedance element, and there is no connection between the units between groups; The transmission matrix Θ t and the reflection matrix Θ r The expression is: in, It is represented as a set of G unit groups, and BlkDiag(·) represents a block diagonal matrix formed by arranging multiple matrices along the diagonal line; The transmission matrix Θ t and the reflection matrix Θ r The constraints that are satisfied are: in,(·) H represents the conjugate transpose.

4. The beam forming method of the BD-RIS-assisted dual-function radar communication system according to claim 3, characterized in that: The user weighting and rate optimization problem is constructed under the communication and perception constraints, including: definition is a channel between the BD-RIS and the DFRC base station, is the downlink channel between the BD-RIS and the communication user k, and the expression of the signal received by the communication user k is: in, is the precoding vector of the communication user k in the DFRC base station, W = [w1, ..., w k ,…,w K ] is the overall transmit precoding matrix, n k is the additive Gaussian white noise when the communication user k receives the signal, with a mean of 0 and a covariance of The complex Gaussian random process, (·) H represents conjugate transpose; The signal to interference noise ratio corresponding to the signal received by the communication user k is: in, is the equivalent channel between the DFRC base station and the communication user k, |·| represents the absolute value, then the weighted sum rate expression of the communication users in the system is: Among them, μ k is the weight of the communication user k; Then the user weighted sum rate optimization problem can be expressed as: Among them, the constraint It is used to ensure that the designed beam pattern closely matches the ideal radar beam pattern, ∈ is the threshold used to evaluate the similarity; the constraint formula is a constant modulus constraint, which is used to ensure that the radar signal distortion is minimal. t is the total power budget of the system, φ l is the azimuth of the position of the lth sampling angle, and the beam pattern with an azimuth angle of φ can be expressed as: P bp =a H (f)WW H a(φ), in, is the array emission steering vector, λ is the wavelength, and d is the array element spacing.

5. The beam forming method of the BD-RIS-assisted dual-function radar communication system according to claim 4, characterized in that: The alternately iteratively executing the steps of solving the base station transmit precoding matrix optimization problem and the BD-RIS matrix optimization problem to obtain an optimal precoding matrix and an optimal BD-RIS matrix includes: Using a weighted minimum mean square error framework, the base station transmit precoding matrix optimization problem is converted into a semi-positive definite relaxation problem to obtain a precoding matrix; By using fractional programming and manifold optimization strategy, the BD-RIS matrix optimization problem is converted into an unconstrained optimization problem to obtain a BD-RIS matrix; The steps of solving the precoding matrix and the BD-RIS matrix are performed alternately and iteratively to obtain an optimal precoding matrix and an optimal BD-RIS matrix.

6. The beam forming method of the BD-RIS-assisted dual-function radar communication system according to claim 5, characterized in that: The method of converting the base station transmit precoding matrix optimization problem into a semi-positive definite relaxation problem by using a weighted minimum mean square error framework to obtain a precoding matrix includes: Under the condition of a fixed BD-RIS matrix, the optimization objective function of the base station transmit precoding matrix optimization problem can be expressed as: A linear receiver υ is introduced at the communication user k k , using the received signal y k Estimated communication symbol x k , then the estimated symbol υ k y k With the real symbol x k The mean square error between k It can be expressed as: Among them, ||·|| 2 is the square operation of the two-norm. When the mean square error e k When the partial derivative of the linear receiver is zero, the minimum mean square error is obtained, and based on the minimum mean square error, the base station transmit precoding matrix optimization problem is converted into a weighted mean square error minimization problem, that is: in, α represents the proportional factor, and the optimal proportional factor α is determined by using the preset first-order optimality condition ＊ ; Introduce auxiliary variable t of unit power k , convert the constraint into: After simplification, the mean square error e k The equivalent form of can be expressed as: in, (·) * Indicates conjugation, 0 indicates dimension is N t A column vector with all zeros in row 1 and column 2; make By using the property of the trace, the base station transmit precoding matrix optimization problem is converted into a semi-positive definite relaxation problem, which can be expressed as: Where Tr(·) represents the trace of the matrix; The semi-positive definite relaxation problem is solved by using rank-one decomposition to obtain a precoding matrix.

7. The beam forming method of the BD-RIS-assisted dual-function radar communication system according to claim 6, characterized in that: The BD-RIS matrix optimization problem is converted into an unconstrained optimization problem by using fractional programming and manifold optimization strategy to obtain a BD-RIS matrix, including: Under the condition that the base station transmits the precoding matrix, the optimization objective function of the BD-RIS matrix optimization problem can be expressed as: Using Lagrange dual transformation and introducing auxiliary variables ξ=[ξ1,…,ξ K ] T , the equivalent form of the BD-RIS matrix optimization problem is expressed as: Among them, γ k The fractional term in the logarithmic function log(·) contained in the optimization objective function of the BD-RIS matrix optimization problem is introduced by introducing the auxiliary vector ζ=[ζ1,…,ζ k ] T To decouple the fractional form in the optimization objective function of the BD-RIS matrix optimization problem, the equivalent form of the BD-RIS matrix optimization problem can be expressed as: The transmission matrix of the g-th group and the reflection matrix of the g-th group are combined as the optimization variables of the g-th group. The objective function can be equivalently expressed as: in, Define a manifold space based on the constraints, namely: Based on the manifold space, iteratively update the transmission matrix Θ of the gth group t,g and the reflection matrix Θ of the gth group r,g , obtain the BD-RIS matrix.

8. A beam forming system for a BD-RIS-assisted dual-function radar communication system, characterized in that: The system comprises: The initial optimization problem building module is used to build a BD-RIS-assisted dual-function radar communication system, which constructs the user weighted sum rate optimization problem under communication and perception constraints; An optimization problem decomposition module, used for decomposing the user weighted and rate optimization problem into a base station transmit precoding matrix optimization problem and a BD-RIS matrix optimization problem; An optimization problem solving module, used for alternately and iteratively executing the steps of solving the base station transmit precoding matrix optimization problem and the BD-RIS matrix optimization problem to obtain an optimal precoding matrix and an optimal BD-RIS matrix; The target beam forming module is used to convert the initial beam pointing to the BD-RIS and the target area into a target beam based on the optimal precoding matrix and the optimal BD-RIS matrix.

9. An intelligent terminal, characterized in that: include: A memory for storing executable instructions; A processor, configured to call and run the executable instructions in the memory to execute the steps of the beamforming method of the BD-RIS-assisted dual-function radar communication system as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores program instructions, and when the program instructions are executed by the processor, the beam forming method of the BD-RIS-assisted dual-function radar communication system as claimed in any one of claims 1 to 7 is implemented.

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