A bayesian cramér-rao bound beamforming optimization method integrating near field communication

Abstract

The present invention discloses a Bayesian-Cramer-Rao bounded beamforming optimization method for near-field synaesthesia integration. The method aims to minimize the Bayesian-Cramer-Rao bound of the extended target response matrix, with constraints including the maximum transmit power of the base station, the minimum signal-to-interference-and-noise ratio requirement of the communication user, and the minimum energy efficiency of the system. Auxiliary variables are introduced to transform the original optimization problem into an equivalent all-digital beamforming matrix optimization problem, and a sequential convex approximation method is used to iterate until convergence to obtain a local optimal solution. For the local optimal solution, a hybrid beamforming matrix is ​​used to approximate the equivalent all-digital beamforming matrix to construct an optimization problem. An alternating optimization method is used to obtain an analog beamforming matrix and a digital beamforming matrix. The present invention studies the Bayesian-Cramer-Rao bounded minimization transmit beam design problem for a near-field synaesthesia integration system, and can achieve perception of the extended target while satisfying the system's communication energy efficiency.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of transmitting beam optimization in near-field communication and sensing integrated system, and particularly relates to a near-field communication and sensing integrated Bayesian Cramer-Rao bound beamforming optimization method. BACKGROUND

[0002] Real-time location awareness and ubiquitous communication are the main features of the upcoming 6G network. In order to achieve both functions, academia and industry are actively exploring new communication technologies, among which the communication and sensing integrated system has become one of the research directions in recent years. The communication and sensing integrated technology aims to integrate the functions of communication and sensing through the same hardware platform, providing high-quality communication while accurately sensing the environment, greatly improving the resource utilization efficiency of the system. However, the communication and sensing integrated technology also brings many challenges, including the trade-off between communication and sensing performance, spectrum resource sharing, waveform design, and system hardware implementation. The main difficulty lies in how to balance the performance of communication and sensing at the same time and in the same spectrum. In traditional communication systems, in order to improve the communication rate, the system needs to optimize the beamforming and power allocation of the signal; while in the sensing system, in order to achieve high-precision target positioning and tracking, the signal is required to have good autocorrelation and cross-correlation characteristics. This contradiction makes the communication and sensing integrated system need to balance multiple demands in signal design and beam design, and find the optimal solution that takes into account both communication and sensing.

[0003] With the continuous development of the communication and sensing system, the frequency of the signal is gradually increased, and the base station is deployed with more and more super-large-scale antennas, resulting in a fundamental change in electromagnetic propagation characteristics, from the far-field region to the near-field region. At the same time, due to the deployment of super-large-scale antennas, the overall system energy consumption is growing at an extremely fast rate. As an effective method to reduce system energy consumption, the hybrid architecture will become an inevitable choice for future large-scale antennas. However, the hybrid architecture will also cause the problem of missing degrees of freedom, bringing a series of challenges. Therefore, under the hybrid architecture, achieving efficient transmission and sensing will become an important concern of the communication and sensing integrated waveform design. SUMMARY

[0004] The purpose of the application is to provide a near-field communication and sensing integrated Bayesian Cramer-Rao bound beamforming optimization method that meets the communication requirements and energy efficiency of the system under the hybrid architecture while achieving the sensing function.

[0005] Technical solution: To solve the above technical problems, the specific technical solution of the application is as follows:

[0006] The application provides a near-field communication and sensing integrated Bayesian Cramer-Rao bound beamforming optimization method, comprising the following steps:

[0007] Step S1, establishing a near-field steering vector model, a near-field channel model and an extended target response matrix model;

[0008] Step S2, based on the near-field channel model and the extended target response matrix model, an initial optimization model is built, in which the optimization target is to minimize the Bayesian Cramer-Rao bound for the extended target, the constraint conditions include the limitation of base station transmitting power, the minimum signal-to-noise ratio requirement of communication and the minimum energy efficiency of the system, and the optimization variable is the downlink transmitting digital beamforming matrix T of the base station D and the analog beamforming matrix T A .

[0009] Step S3, introducing the equivalent full-digital beamforming matrix T, the initial optimization problem is converted into an optimization problem about variable T;

[0010] Step S4, according to the problem converted in step S3, auxiliary variables t and are introduced, and a rank-one constraint is added, wherein (·) H denotes the conjugate transpose, t k is the downlink beamforming vector of the base station for the kth user, that is, the kth column of the matrix T, and K is the total number of users in the system;

[0011] Step S5, the matrix is converted into an equivalent constraint form, and is added as a penalty term to the objective function;

[0012] Step S6, for the non-convex penalty term and the non-convex energy efficiency constraint in the problem converted in step S5, a sequential convex approximation method is used for iterative solution to obtain a locally optimal equivalent full-digital matrix;

[0013] Step S7, for the locally optimal solution obtained in step S6, an optimization problem of approximating the equivalent full-digital beamforming matrix by the hybrid beamforming matrix is established;

[0014] Step S8, for the optimization problem established in step S7, a locally optimal digital beamforming matrix and an analog beamforming matrix are obtained by iterative solution through an alternating optimization method.

[0015] Further, in the step S1, the transmitting array steering vector at the base station is modeled as follows:

[0016]

[0017] wherein denotes the distance between the nth array element and the target, d denotes the distance between the array elements, denotes the angle between the target and the array center, and r denotes the distance between the antenna center and the target, N t denotes the number of transmit array antennas, and λ denotes the wavelength of electromagnetic wave. T denotes the transpose;

[0018] The receive array steering vector at the base station is modeled as follows:

[0019]

[0020] where N r denotes the number of receive array antennas.

[0021] The near-field channel of the kth single-antenna user is modeled as follows:

[0022]

[0023] where ζ denotes the large-scale fading, and r c,k , denote the distance and angle of the LoS path between the kth user and the base station, respectively, and r c,i , denote the distance and angle of the non-line-of-sight (NLoS) path between the kth user and the base station, respectively, and I denotes the total number of NLoS paths, and β i denotes the small-scale fading.

[0024] The extended target-aware response matrix can be expressed as follows:

[0025]

[0026] where N denotes the number of scattering points of the extended target, μ denotes the reflection coefficient of the target, and r s,i and denote the distance and angle between the extended target and the base station.

[0027] Further, in the step S2, the initial optimization model is built as follows:

[0028] The optimization objective is to minimize

[0029] The constraint conditions are:

[0030]

[0031] where denotes the N t dimensional identity matrix, ‖·‖ F denotes the F-norm, and log2(·) denotes the logarithmic function with base 2, |·| p,q denotes the modulus value of the pth row and qth column element of the matrix, and (·) -1denotes the matrix inverse operation, Tr(·) denotes the trace of a matrix, denotes the noise power at the base station receiver, denotes the noise power of the kth user, denotes the variance of the matrix B, denotes the covariance matrix, h k denotes the near-field channel vector from the base station to the kth user, t k = T A t D,k denotes the beamforming vector of the kth user, t D,k denotes the kth column of the matrix T D , Γ th denotes the minimum signal-to-noise ratio required by each user, η th denotes the minimum energy efficiency of the system, ρ ∈ (0, 1] denotes the base station amplifier operating efficiency, P0 denotes the entire system circuit power, P denotes the maximum base station transmit power, e is the natural base, j is the imaginary unit, and L denotes the base station transmit frame length.

[0032] Further, according to the problem transformed in step S2, in the step S3, an equivalent full-digital beamforming matrix T is introduced, and the optimization problem is equivalent to the following problem:

[0033] The optimization objective is to minimize

[0034] The constraint condition is:

[0035]

[0036] Further, according to the problem transformed in step S3, in the step S4, auxiliary variables t and are introduced, and a rank-one constraint is added, and the optimization problem is equivalent to the following problem:

[0037] The optimization objective is:

[0038] The constraint condition is:

[0039]

[0040] wherein, T k ≥ 0 indicates that T k is a positive semi-definite matrix.

[0041] Further, according to the problem transformed in step S4, in the step S5, the rank-one constraint is transformed into an equivalent form, and is added to part of the optimization objective as a penalty term, and the specific form is as follows:

[0042] The optimization objective is to minimize

[0043] The constraint condition is

[0044]

[0045] where γ represents a penalty factor, and ||·|| * represents a kernel norm, and ||·||2 represents a 2-norm.

[0046] Further, according to the problem converted in step S5, in step S6, a sequential convex approximation method is used to iteratively solve the non-convex penalty term and the non-convex energy efficiency constraint; the optimization problem in the nth iteration is expressed as follows:

[0047] The optimization objective is to minimize

[0048] The constraint condition is

[0049]

[0050]

[0051] where

[0052] is the eigenvector corresponding to the maximum eigenvalue of the matrix .

[0053] Further, in each iteration of step S6, the problem is a convex optimization problem, and an interior point method is used to solve.

[0054] Further, according to the equivalent digital beamformer T finally obtained in step S7, an optimization problem of approximating the equivalent full-digital beamformer matrix by a hybrid beamforming matrix is established, and the optimization problem is as follows:

[0055] The optimization objective is to minimize

[0056] The constraint condition is

[0057]

[0058] |T A | p,q = 1.

[0059] Further, according to the optimization problem established in step S7, an alternating iterative optimization algorithm is used to iteratively solve, and the optimization problem in the mth iteration is respectively expressed as follows:

[0060] (1) Fixed analog beamforming matrix

[0061] Optimization goal: Minimize

[0062] Constraint condition is:

[0063]

[0064] The closed-form expression of the mth iteration [T D ] is wherein the is expressed as the number of radio frequency (RF) links under the hybrid architecture.

[0065] (2) Fixed digital beamforming matrix

[0066] Optimization goal: Minimize

[0067] Constraint condition is:

[0068] θ p,q ∈(0, 2π],

[0069] The closed-form expression of the mth iteration [T A ] p,q ] is t p is expressed as the pth row of the matrix T, is expressed as the qth column of the matrix .

[0070] The application also provides a computer program product comprising computer programs / instructions, which, when executed by a processor, implement the steps of the near-field sensing-integrated Bayesian Cramer-Rao bound beamforming optimization method.

[0071] Advantages: The near-field sensing-integrated Bayesian Cramer-Rao bound beamforming optimization method has the following advantages:

[0072] 1. The application provides a near-field sensing-integrated Bayesian Cramer-Rao bound beamforming optimization method. Step S1 constructs a near-field channel model and an extended target response matrix model, and step S2 establishes a Bayesian Cramer-Rao bound minimum transmission beam design problem. Then, steps S3 to S8 solve the problem, and the optimal solution obtained realizes the sensing of the extended target under the premise of meeting the user communication demand and system energy efficiency.

[0073] 2, The sequential convex approximation algorithm adopted by the application is a high-efficiency general method, which aims to indirectly solve non-convex optimization problems. Through a series of iterations, the algorithm gradually solves approximate convex problems, thereby monotonically approaching the original non-convex problem, and within a reasonable time complexity, the algorithm can obtain a local optimal solution of the original non-convex problem. BRIEF DESCRIPTION OF DRAWINGS

[0074] Figure 1 A flowchart of the Bayesian Cramer-Rao bound beamforming optimization method for near-field communication and sensing integration of the application is shown in the figure.

[0075] Figure 2 A simulation experiment result graph of the Bayesian Cramer-Rao bound beamforming optimization method for near-field communication and sensing integration of the application is shown in the figure. DETAILED DESCRIPTION

[0076] In order to better understand the purpose, structure and function of the application, the technical solutions of the application will be further described in detail below in combination with the drawings and specific embodiments.

[0077] The embodiment provides a Bayesian Cramer-Rao bound beamforming optimization method for near-field communication and sensing integration, which is applicable in a near-field communication and sensing integration scene, and a base station sends a signal represented as The transmitting beam of the base station end is optimized s k The base station sends a symbol to the kth user, and K is the total number of system users. The method maximizes the sensing performance of the system under the premise of meeting the transmission power limit, the minimum signal-to-noise ratio of communication, and the minimum energy efficiency requirement of the system.

[0078] Specifically, the flow of the Bayesian Cramer-Rao bound beamforming optimization method for near-field communication and sensing integration in the embodiment is as shown in the figure, and specifically includes the following steps: Figure 1

[0079] Step S1, a near-field guide vector model, a near-field channel and a sensing response matrix model are established. Specifically as follows:

[0080] Due to the spherical wave nature of the near field, the guide vector modeling of the transmitting array at the base station is as follows:

[0081]

[0082] Wherein represents the distance between the nth array element and the target, d represents the distance between the array elements, represents the angle between the target and the array center, r represents the distance between the antenna center and the target, N t represents the number of transmitting array antennas, λ represents the wavelength of electromagnetic waves, (·)​represents transpose;

[0083] The array reception steering vector at the base station is modeled as follows:

[0084]

[0085] where N r represents the number of receive array antennas;

[0086] The near-field channel of the kth single-antenna user is modeled as follows:

[0087]

[0088] where ζ represents large-scale fading, r c,k , and r c,i , respectively represent the distance and angle of the LoS path between the kth user and the base station, and r i and r respectively represent the distance and angle of the non-line-of-sight (NLoS) path between the kth user and the base station, I represents the total number of NLoS paths, and β s,i represents small-scale fading;

[0089] The extended target sensing response matrix can be modeled as follows:

[0090]

[0091] where N represents the number of scattering points of the extended target, μ represents the reflection coefficient of the target, r D and r represent the distance and angle between the extended target and the base station.

[0092] In step S2, based on the near-field channel model and the extended target response matrix model, an initial optimization model is established, in which the optimization objective is to minimize the Bayesian Cramer-Rao bound for the extended target, the constraint conditions include the limitation of the base station transmit power, the minimum signal-to-noise ratio requirement of communication, and the minimum energy efficiency of the system, and the optimization variables are the base station downlink transmit digital beamforming matrix T A and the analog beamforming matrix T r . Specifically as follows:

[0093] The array reception sensing signal is represented as Y = BX + N, where X represents the signal matrix transmitted by the base station, and N represents the noise matrix of the base station. The receive signal matrix is vectorized as y = vec(Y) = υ + n, where n is a noise vector, represents the Kronecker product, is an N r dimensional identity matrix, and Nr denotes the number of days of reception. Let the vector of parameters to be estimated be where β R denotes the real part of β, β I denotes the imaginary part of β. The Bayesian Cramer-Rao bound of the extended target response matrix is defined as:

[0094] BCRB(B) = Tr((J1+ J2) -1 )

[0095] where δ i and δ j denote the i-th and j-th element of the vector of parameters to be estimated δ, respectively, p(δ) denotes the prior probability density function of the parameters to be estimated, the extended target response matrix is subject to a normal distribution according to the Central Limit Theorem, i.e. p(δ) is the probability density function of a normal distribution, and thus where R δ is the covariance matrix of δ, is the covariance of δ, is a 2N t N r dimensional identity matrix. According to the properties of δ, the partial derivatives of β R and β I with respect to v are and the J1 matrix is divided into block matrices as follows:

[0096]

[0097] where each block matrix is represented as:

[0098]

[0099] Therefore, the Bayesian Cramer-Rao bound of the extended target is represented as:

[0100]

[0101] Next, the initial optimization problem built can be represented as:

[0102] The optimization objective is to minimize

[0103] The constraint conditions are:

[0104]

[0105] where denotes a N t dimensional identity matrix, ‖·‖ F denotes the F-norm, and log2(·) denotes the logarithmic function with base 2, |·| p,qThe pth row, qth column element of the table matrix modulo value, (·) -1 Denotes matrix inversion, Tr(·) denotes the trace of the matrix, Denotes the noise power at the base station receiving end, Denotes the noise power of the kth user, Denotes the variance of matrix B, Denotes the covariance matrix, h k Denotes the near-field channel vector from the base station to the kth user, t k = T A t D,k Denotes the beamforming vector of the kth user, t D,k Denotes the kth column of matrix T D , Γ th Denotes the minimum signal-to-noise ratio required by each user, η th Denotes the minimum energy efficiency of the system, ρ ∈ (0, 1] denotes the base station amplifier operating efficiency, P0 denotes the circuit power of the entire system, P denotes the maximum transmit power of the base station, e is the natural base, j is the imaginary unit, and L denotes the base station transmission frame length.

[0106] Step S3, introduce the equivalent full-digital beamforming matrix T, and optimize the problem to the following problem:

[0107] The optimization goal is to minimize

[0108] The constraint condition is:

[0109]

[0110] Step S4, according to the problem obtained in step S3, introduce auxiliary variables t and And add a rank-one constraint, where (·) H Denotes the conjugate transpose, and the optimization problem is equivalent to the following problem:

[0111] The optimization goal is:

[0112] The constraint condition is:

[0113]

[0114] Where, T k ≥ 0 indicates that T k is a positive semi-definite matrix.

[0115] S5, according to the problem obtained in step S4, transform the rank-one constraint into an equivalent form, and add it as a penalty term to part of the optimization goal, the specific form is as follows:

[0116] Objective: Minimize

[0117] Constraints:

[0118]

[0119] where γ denotes a penalty factor, ||·|| * denotes the nuclear norm, and ||·||2 denotes the 2-norm.

[0120] Step S6, according to the problem obtained by the step S5, a sequential convex approximation method is used to iteratively solve the non-convex penalty term and the non-convex energy efficiency constraint; the optimization problem in the nth iteration is expressed as follows:

[0121] Objective: Minimize

[0122] Constraints:

[0123]

[0124]

[0125] where

[0126] is the eigenvector corresponding to the maximum eigenvalue of the matrix .

[0127] S7, according to the equivalent digital beamformer T finally obtained by the step S6, an optimization problem of approximating the equivalent fully digital beamforming matrix by the hybrid beamforming matrix is established, and the optimization problem is as follows:

[0128] Objective: Minimize

[0129] Constraints:

[0130]

[0131] |T A | p,q = 1.

[0132] S8, according to the optimization problem established by the step S7, an alternating iterative optimization algorithm is used to iteratively solve the optimization problem, and the optimization problem in the mth iteration is respectively expressed as follows:

[0133] (1) Fixing the analog beamforming matrix

[0134] Objective: Minimize

[0135] The constraint condition is:

[0136]

[0137] The closed-form expression of the mth iteration T D is wherein denotes the number of RF chains.

[0138] (2) Fixed digital beamforming matrix

[0139] The optimization objective is to minimize

[0140] The constraint condition is:

[0141] θ p,q ∈(0, 2π],

[0142] The closed-form expression of the mth iteration [T A ] p,q is t p denotes the pth row of the matrix T, denotes the qth column of the matrix .

[0143] In order to verify the effect of the near-field sensing system provided by the embodiment, a simulation experiment is performed. The parameters involved in the simulation experiment are shown in the following table:

[0144] Table 1 Simulation experiment parameter table

[0145]

[0146] Figure 2 For the comparison results of the simulation experiment, the BCRB of the traditional beam gain design scheme and the BCRB of the present design scheme in 4 RF chains, 8 RF chains, 16 RF chains and full digital are given. The simulation results show that the transmission beam optimization method provided by the present application has better estimation accuracy than the scheme with the maximum beam pointing gain.

[0147] The embodiments of the present application also disclose a computer program product comprising computer programs / instructions which, when executed by a processor, implement the steps of the near-field sensing integrated Bayesian Cramer-Rao bound beamforming optimization method. The program / instruction code for implementing the method of the present application can be written in any combination of one or more programming languages. The program / instruction code can be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing apparatus, such that the program / instruction code, when executed by the processor or controller, cause the steps of the method of the present application to be implemented. The program / instruction code can be executed entirely on a machine, partially on a machine, partially on a machine as a stand-alone software package, partially on a machine and partially on a remote machine, or entirely on a remote machine or server. The present application is not limited in this regard.

[0148] It is to be understood that the present application is described by way of example only, and that modifications and alterations can be made to the features and embodiments described without departing from the spirit and scope of the application. In addition, modifications can be made to the features and embodiments described to adapt them to particular situations and materials without departing from the spirit and scope of the present application. Accordingly, the present application is not limited to the specific embodiments disclosed herein, but rather includes all embodiments falling within the scope of the claims.

Claims

1. A Bayesian Cramé-Rao bounded beamforming optimization method for near-field synaesthesia integration, characterized by: The following steps are involved: Step S1: establishing a near-field steering vector model, a near-field channel model, and an extended target response matrix model; Step S2: Based on the near-field channel model and the extended target response matrix model, an initial optimization model is constructed. In the optimization model, the optimization objective is to minimize the Bayesian Cramer-Rao bound of the extended target. The constraints include the limited base station transmit power, the minimum signal-to-interference-and-noise ratio requirement of the communication, and the minimum energy efficiency of the system. The optimization variable is the base station's downlink transmit digital beamforming matrix T. D and the simulated beamforming matrix T A ; Step S3: introducing an equivalent all-digital beamforming matrix T, and converting the initial optimization problem into an optimization problem about the variable T; Step S4: Based on the problem obtained in step S3, introduce auxiliary variables t and And add rank-one constraint, where (·) H represents the conjugate transpose, t k is the downlink beamforming vector of the base station for the kth user, that is, the kth column of the matrix T, where K is the total number of users in the system; Step S5: The rank-one constraint is converted into an equivalent constraint form and added to the objective function as a penalty term; Step S6: for the non-convex penalty term and non-convex energy efficiency constraint in the problem obtained by step S5, a sequential convex approximation method is used to iteratively solve the problem to obtain a local optimal equivalent full digital matrix; Step S7: for the local optimal solution obtained in step S6, establish a hybrid beamforming matrix to approximate the equivalent full digital beamforming matrix optimization problem; Step S8: For the optimization problem established in step S7, an alternating optimization method is used to iteratively solve the problem to obtain a locally optimal digital beamforming matrix and an analog beamforming matrix.

2. The Bayesian Cramér-Rao bounded beamforming optimization method for near-field synaesthesia integration according to claim 1, characterized in that: In step S1, the transmitting array steering vector at the base station is modeled as follows: in n∈[1,N t ] represents the distance between the nth array element and the target, d represents the spacing between array elements, represents the angle between the target and the center of the array, r represents the distance between the center of the antenna and the target, N t represents the number of transmitting array antennas, λ represents the wavelength of the electromagnetic wave, (·) T represents transpose; The receiving array steering vector at the base station is modeled as follows: in n∈[1,N r ], N r Indicates the number of receiving array antennas; The near-field channel model of the kth single-antenna user is as follows: Among them, ζ represents large-scale fading, r c,k , They represent the distance and angle of the Los path between the kth user and the base station, r c,i , denote the distance and angle of the non-line-of-sight (NLoS) path between the kth user and the base station, I denotes the total number of NLoS paths, and β i Indicates small-scale fading; The extended target perception response matrix is ​​modeled as follows: Where N represents the number of scattering points of the extended target, μ represents the reflection coefficient of the target, and r s,i and Indicates the distance and angle between the extended target and the base station.

3. The Bayesian Cramé-Rao bounded beamforming optimization method for near-field synaesthesia integration according to claim 2, characterized in that: In step S2, the initial optimization problem is constructed as follows: The optimization goal is to minimize The constraints are: |T A | p,q ＝1, in Indicated as N t The identity matrix of dimension ‖·‖ F represents the F norm, log2(·) represents the logarithmic function with base 2, |·| p,q The modulus value of the element in the pth row and qth column of the table matrix, (·) -1 represents the matrix inverse operation, Tr(·) represents the trace of the matrix, Expressed as the noise power at the base station receiver, Expressed as the noise power of the kth user, Expressed as the variance of matrix B, Expressed as a covariance matrix, h k Denote the near-field channel vector from the base station to the kth user, t k =T A t D,k Denote the beamforming vector of the kth user, t D,k Represented as matrix T D The kth column of Γ th Denotes the minimum signal to interference and noise ratio required for each user, η th It represents the minimum energy efficiency of the system, ρ∈(0,1] represents the working efficiency of the base station amplifier, P0 represents the circuit power of the entire system, P represents the maximum transmission power of the base station, e is the natural base, j is the imaginary unit, and L represents the base station transmission frame length.

4. The Bayesian Cramér-Rao bounded beamforming optimization method for near-field synaesthesia integration according to claim 3, characterized in that: Based on the problem obtained in step S2, in step S3, an equivalent all-digital beamforming matrix T is introduced, and the optimization problem is equivalently transformed into the following problem: The optimization goal is to minimize The constraints are:

5. The Bayesian Cramér-Rao bounded beamforming optimization method for near-field synaesthesia integration according to claim 4, characterized in that: Based on the problem obtained in step S3, in step S4, auxiliary variables t and And add the rank-one constraint, the optimization problem is equivalently transformed into the following problem: The optimization goal is: The constraints are: rank(T k )≤1,k=1,…,K, in, Indicates T k is a positive semidefinite matrix.

6. The Bayesian Cramér-Rao bounded beamforming optimization method for near-field synaesthesia integration according to claim 5, characterized in that: Based on the problem obtained by the transformation in step S4, in step S5, the rank-one constraint is transformed into an equivalent form and added to the optimization objective as a penalty term. The specific form is as follows: The optimization goal is to minimize The constraints are: Where γ is the penalty factor, ∥·∥ * represents the nuclear norm, and ∥·∥2 represents the 2-norm.

7. The Bayesian Cramér-Rao bounded beamforming optimization method for near-field synaesthesia integration according to claim 6, characterized in that: Based on the problem obtained by the transformation in step S5, in step S6, a sequential convex approximation method is used to iteratively solve the non-convex penalty term and the non-convex energy efficiency constraint; the optimization problem in the nth iteration is expressed as follows: The optimization goal is to minimize The constraints are: in is a matrix The eigenvector corresponding to the largest eigenvalue of .

8. The Bayesian Cramér-Rao bounded beamforming optimization method for near-field synaesthesia integration according to claim 7, characterized in that: In each iteration of step S6, the problem is a convex optimization problem and is solved using an interior point method.

9. The Bayesian Cramér-Rao bounded beamforming optimization method for near-field synaesthesia integration according to claim 8, characterized in that: Based on the equivalent digital beamformer T obtained by iteration in step S7, a hybrid beamforming matrix is ​​established to approximate the optimization problem of the equivalent full digital beamforming matrix. The optimization problem is expressed as follows: The optimization goal is to minimize The constraints are: |T A | p,q ＝1； According to the optimization problem established in step S7, the alternating iterative optimization algorithm is used to iteratively solve the optimization problem in the mth iteration. The optimization problem in the mth iteration is expressed as follows: (1) Fixed analog beamforming matrix Optimization goal: minimize The constraints are: The mth iteration T D The closed-form expression is Among them Expressed as the number of radio frequency links; (2) Fixed digital beamforming matrix The optimization goal is to minimize The constraints are: i p,q ∈(0,2π], The mth iteration [T A ] p,q The closed-form expression is t p Represented as the p-th row of matrix T, Represented as a matrix The qth column of .

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the Bayesian Clamer-Rao bound beamforming optimization method for near-field synaesthesia integration according to any one of claims 1 to 9 are implemented.

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