Bayesian Cramer-Rao bound beamforming optimization method for near-field flux and inductance integration

Abstract

The invention discloses a near-field flux-sensing integrated Bayesian Cramer-Rao bound beamforming optimization method, which aims at minimizing the Bayesian Cramer-Rao bound of an extended target response matrix, and constraint conditions comprise the maximum transmitting power of a base station, the minimum signal to interference plus noise ratio requirement of a communication user and the minimum energy efficiency of a system. Auxiliary variables are introduced, an original optimization problem is converted into an equivalent full-digital beam forming matrix optimization problem, and iteration is carried out by adopting a sequential convex approximation method until convergence is carried out to obtain a local optimal solution; aiming at the local optimal solution, constructing an optimization problem by using a method of approaching an equivalent full-digital beam forming matrix by using a hybrid beam forming matrix; and an analog beam forming matrix and a digital beam forming matrix are obtained through an alternate optimization method. According to the method, the Bayesian Cramer-Rao bound minimum transmitting beam design problem of the near-field communication and sensing integrated system is researched, and sensing of an extended target can be realized under the condition that the communication energy efficiency of the system is met.

Description

Technical Field

[0001] The invention belongs to the technical field of transmission beam optimization in a near-field synaesthesia integration system, and in particular relates to a Bayesian Cramé-Rao bound beamforming optimization method for near-field synaesthesia integration. Background Art

[0002] Real-time location awareness and ubiquitous communication are the main features of the upcoming 6G network. In order to achieve both functions at the same time, academia and industry are actively exploring new communication technologies, among which the synaesthesia integrated system has become one of the research directions that has attracted much attention in recent years. Synaesthesia integrated technology aims to integrate the functions of communication and perception through the same hardware platform, provide high-quality communication and accurately perceive the environment, and greatly improve the resource utilization efficiency of the system. However, synaesthesia integrated technology also brings many challenges, including the trade-off between communication and perception performance, spectrum resource sharing, waveform design, and hardware implementation of the system. The main difficulty lies in how to balance the performance of communication and perception at the same time and on the same spectrum. In traditional communication systems, in order to increase the communication rate, the system needs to optimize the beamforming and power allocation of the signal; while in the perception 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 requires the synaesthesia integrated system to balance multiple requirements in signal design and beam design to find the optimal solution that takes into account both communication and perception.

[0003] With the continuous development of the synaesthesia system, the frequency of the signal has gradually increased, and more and more ultra-large-scale antennas have been deployed in base stations, resulting in a fundamental change in the electromagnetic propagation characteristics, from the far-field area to the near-field area. At the same time, due to the deployment of ultra-large-scale antennas, the energy consumption of the overall system has increased rapidly. As an effective way to reduce system energy consumption, hybrid architecture will become an inevitable choice for large-scale antennas in the future. However, hybrid architecture will also cause the problem of lack of degrees of freedom and bring a series of challenges. Therefore, achieving efficient transmission and perception under the hybrid architecture will become an important focus of synaesthesia integrated waveform design. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a near-field synaesthesia integrated Bayesian Cramé-Rao bound beamforming optimization method to achieve perception functions while meeting the communication requirements under a hybrid architecture and the energy efficiency of the system.

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

[0006] The present invention provides a near-field synaesthesia integrated Bayesian Cramé-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 constructed. In this model, the optimization target 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-to-noise ratio requirement of the communication, and the minimum energy efficiency of the system. The optimization variable is the downlink transmit digital beamforming matrix T of the base station. D and the simulated beamforming matrix T A .

[0009] Step S3: introducing an equivalent all-digital beamforming matrix T, and converting the initial optimization problem into an optimization problem about the variable T;

[0010] Step S4: According to the problem obtained in step S3, introduce auxiliary variables t and And add a rank-one constraint, where (·) H represents the conjugate transpose, t k is the downlink beamforming vector of the base station for the k-th user, that is, the k-th column of the matrix T, and K is the total number of users in the system;

[0011] Step S5: The rank-one constraint is converted into an equivalent constraint form and added to the objective function as a penalty term;

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

[0013] Step S7, for the local optimal solution obtained in step S6, establishing a hybrid beamforming matrix to approximate an equivalent full digital beamforming matrix optimization problem;

[0014] Step S8: for the optimization problem established in step S7, an alternating optimization method is used to iteratively solve the problem to obtain a local optimal digital beamforming matrix and an analog beamforming matrix.

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

[0016]

[0017] in 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;

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

[0019]

[0020] in N r Indicates the number of receiving array antennas;

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

[0022]

[0023] Among them, ζ represents large-scale fading, r c,k , Respectively 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;

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

[0025]

[0026] 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.

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

[0028] The optimization goal is to minimize

[0029] The constraints are:

[0030]

[0031] 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 p-th row and q-th column element of the table matrix, (·) -1represents 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 It is represented as 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-noise ratio required for each user, η th It is represented as the minimum energy efficiency of the system, ρ∈(0,1] is represented as the working efficiency of the base station amplifier, P0 is represented as the circuit power of the entire system, P is represented as the maximum transmission power of the base station, e is the natural base, j is the imaginary unit, and L is the transmission frame length of the base station.

[0032] Further, according to the problem obtained by transformation 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:

[0033] The optimization goal is to minimize

[0034] The constraints are:

[0035]

[0036] Further, according to the problem obtained in step S3, in step S4, auxiliary variables t and And add the rank-one constraint, the optimization problem is equivalent to the following problem:

[0037] The optimization goal is:

[0038] The constraints are:

[0039]

[0040] in, T k ≥0 means T k is a positive semidefinite matrix.

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

[0042] The optimization goal is to minimize

[0043] The constraints are:

[0044]

[0045] Where γ is the penalty factor, ∥·∥ * represents the nuclear norm, and ∥·∥2 represents the 2-norm.

[0046] Further, according to 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:

[0047] The optimization goal is to minimize

[0048] The constraints are:

[0049]

[0050]

[0051] in

[0052] is a matrix The eigenvector corresponding to the largest eigenvalue of .

[0053] Furthermore, in each iteration of step S6, the problem is a convex optimization problem and is solved using an interior point method.

[0054] Further, according to the equivalent digital beamformer T finally obtained 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 as follows:

[0055] The optimization goal is to minimize

[0056] The constraints are:

[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 the optimization problem in the mth iteration. The optimization problem in the mth iteration is expressed as follows:

[0060] (1) Fixed analog beamforming matrix

[0061] Optimization goal: Minimize

[0062] The constraints are:

[0063]

[0064] The mth iteration T D The closed form expression for Among them It is expressed as the number of Radio Frequency (RF) links in the hybrid architecture.

[0065] (2) Fixed digital beamforming matrix

[0066] The optimization goal is to minimize

[0067] The constraints are:

[0068] θ p,q ∈(0,2π],

[0069] The mth iteration [T A ] p,q The closed form expression for t p Represented as the p-th row of matrix T, Represented as a matrix The qth column of .

[0070] The present invention also provides a computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the steps of the Bayesian-Cramer-Rao bound beamforming optimization method for near-field synaesthesia integration.

[0071] Beneficial effects: The Bayesian Cramé-Rao bound beamforming optimization method based on near-field synaesthesia integration has the following advantages:

[0072] 1. The present invention provides a near-field synaesthesia 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 minimization transmit beam design problem. Subsequently, steps S3 to S8 solve the problem, and the optimal solution obtained realizes the perception of the extended target under the premise of meeting the user's communication needs and system energy efficiency.

[0073] 2. The sequential convex approximation algorithm used in the present invention is an efficient and universal method for indirectly solving non-convex optimization problems. The algorithm gradually solves the approximate convex problem through a series of iterations, thereby monotonically approximating the original non-convex problem. Within a reasonable time complexity, the algorithm can obtain the local optimal solution of the original non-convex problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 It is a schematic flow chart of the Bayesian Cramé-Rao bound beamforming optimization method for near-field synaesthesia integration of the present invention;

[0075] Figure 2 This is a simulation experiment result diagram of the Bayesian Cramé-Rao bound beamforming optimization method for near-field synaesthesia integration of the present invention. DETAILED DESCRIPTION

[0076] In order to better understand the purpose, structure and function of the present invention, the technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0077] This embodiment provides a Bayesian Cramé-Rao bound beamforming optimization method for near-field synaesthesia integration. The method is applicable to near-field synaesthesia integration scenarios. The base station sends a signal represented by By optimizing the design of the base station's transmission beam s k is the symbol sent by the base station to the kth user, K is the total number of users in the system, and the method maximizes the system's perceived performance while meeting the transmission power limit, the minimum communication signal-to-noise ratio, and the system's minimum energy efficiency requirements.

[0078] Specifically, the process of a near-field synaesthesia integrated Bayesian Cramé-Rao bound beamforming optimization method in this embodiment is as follows: Figure 1 As shown, the specific steps include:

[0079] Step S1: Establish a near-field steering vector model, a near-field channel, and a perception response matrix model. The details are as follows:

[0080] Due to the spherical wave properties of the near field, the transmitting array steering vector at the base station is modeled as follows:

[0081]

[0082] in 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;

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

[0084]

[0085] in N r Indicates the number of receiving array antennas;

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

[0087]

[0088] Among them, ζ represents large-scale fading, r c,k , Respectively 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;

[0089] The extended target perception 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, and r s,i and Indicates the distance and angle between the extended target and the base station.

[0092] 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 target 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-to-noise ratio requirement of the communication, and the minimum energy efficiency of the system. The optimization variable is the downlink transmit digital beamforming matrix T of the base station. D and the simulated beamforming matrix T A The details are as follows:

[0093] The array receives the sensed signal and expresses it as Y=BX+N, where X represents the signal matrix transmitted by the base station and N represents the base station noise matrix. The received signal matrix column vector is expressed as y=vec(Y)=υ+n, where n is the noise vector, represents the Kronecker product, N r The identity matrix of dimension Nr represents the number of receiving days. Let the parameter vector to be estimated be where β R Expressed as the real part of β, β I It is expressed as the imaginary part of β. The Bayesian Cramé-Rao bound of the extended target response matrix is ​​defined as:

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

[0095] in δ i and δ j They represent the i-th and j-th elements of the estimated parameter vector δ, respectively. p(δ) represents the prior probability density function of the estimated parameter. According to the central limit theorem, the extended target response matrix obeys the normal distribution, that is, p(δ) is the probability density function of the normal distribution. Therefore Where R δ is the covariance matrix of δ, is the covariance of δ, 2N t N r According to the characteristics of δ, we use v to calculate β R and β I Finding partial derivatives And divide the J1 matrix into block matrices:

[0096]

[0097] Each block matrix is ​​represented as:

[0098]

[0099] Therefore, the Bayesian Cramérale bound for the extended objective is expressed as:

[0100]

[0101] Next, the initial optimization problem constructed can be expressed as:

[0102] The optimization goal is to minimize

[0103] The constraints are:

[0104]

[0105] in Indicated as N t The identity matrix of dimension ‖·‖ F represents the F norm, log2(·) represents the logarithmic function with base 2, |·| p,qThe modulus value of the p-th row and q-th column element 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 It is represented as 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-noise ratio required for each user, η th It is represented as the minimum energy efficiency of the system, ρ∈(0,1] is represented as the working efficiency of the base station amplifier, P0 is represented as the circuit power of the entire system, P is represented as the maximum transmission power of the base station, e is the natural base, j is the imaginary unit, and L is the transmission frame length of the base station.

[0106] Step S3: introducing the equivalent all-digital beamforming matrix T, the optimization problem is equivalently transformed into the following problem:

[0107] The optimization goal is to minimize

[0108] The constraints are:

[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 Represents the conjugate transpose, and the optimization problem is equivalent to the following problem:

[0111] The optimization goal is:

[0112] The constraints are:

[0113]

[0114] in, T k ≥0 means T k is a positive semidefinite matrix.

[0115] S5. According to the problem obtained in step S4, the rank-one constraint is converted into an equivalent form and added as a penalty term to the optimization objective. The specific form is as follows:

[0116] The optimization goal is to minimize

[0117] The constraints are:

[0118]

[0119] Where γ is the penalty factor, ∥·∥ * represents the nuclear norm, and ∥·∥2 represents the 2-norm.

[0120] Step S6: According to the problem obtained by the transformation in 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] The optimization goal is to minimize

[0122] The constraints are:

[0123]

[0124]

[0125] in

[0126] is a matrix The eigenvector corresponding to the largest eigenvalue of .

[0127] S7. According to the equivalent digital beamformer T finally obtained in step S6, a hybrid beamforming matrix is ​​established to approximate the optimization problem of the equivalent full digital beamforming matrix. The optimization problem is as follows:

[0128] The optimization goal is to minimize

[0129] The constraints are:

[0130]

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

[0132] S8. According to the optimization problem established in step S7, an alternating iterative optimization algorithm is used to iteratively solve the optimization problem. The optimization problem in the mth iteration is expressed as follows:

[0133] (1) Fixed analog beamforming matrix

[0134] Optimization goal: Minimize

[0135] The constraints are:

[0136]

[0137] The mth iteration T D The closed form expression for in Expressed as the number of RF chains.

[0138] (2) Fixed digital beamforming matrix

[0139] The optimization goal is to minimize

[0140] The constraints are:

[0141] θ p,q ∈(0,2π],

[0142] The mth iteration [T A ] p,q The closed form expression for t p Represented as the p-th row of matrix T, Represented as a matrix The qth column of .

[0143] In order to verify the effect of the Cramé-Rao bound minimization transmission beam optimization method for the near-field synaesthesia system provided in this embodiment, a simulation experiment was conducted. The parameters involved in the simulation experiment are shown in the following table:

[0144] Table 1 Simulation experiment parameters

[0145]

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

[0147] The embodiment of the present invention also discloses a computer program product, including a computer program / instruction, which implements the steps of the Bayesian-Cramer-Rao bound beamforming optimization method for near-field synaesthesia integration when executed by a processor. The program / instruction code for implementing the method of the present invention can be written in any combination of one or more programming languages. These program / instruction codes can be provided to a processor or controller of a general-purpose computer, a special-purpose computer or other programmable data processing device, so that the program / instruction code implements the steps of the method of the present invention when executed by the processor or controller. The program / instruction code can be executed entirely on the machine, partially on the machine, partially on the machine as an independent software package, or entirely on a remote machine or server. The parts not described in detail in the present invention are all well-known technologies of those skilled in the art.

[0148] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A near-field synaesthesia integrated Bayesian Cramé-Rao bound beamforming optimization method, characterized in that: 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 target 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-to-noise ratio requirement of the communication, and the minimum energy efficiency of the system. The optimization variable is the downlink transmit digital beamforming matrix T of the base station. 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: According to the problem obtained by step S3, introduce auxiliary variables t and And add a rank-one constraint, where (·) H represents the conjugate transpose, t k is the downlink beamforming vector of the base station for the k-th user, that is, the k-th column of the matrix T, and 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 converted in step S5, a sequential convex approximation method is used to iteratively solve and obtain a local optimal equivalent full digital matrix; Step S7, for the local optimal solution obtained in step S6, establishing a hybrid beamforming matrix to approximate an 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 local optimal digital beamforming matrix and an analog beamforming matrix.

2. The Bayesian Cramé-Rao bound beamforming optimization method for near-field synaesthesia integration according to claim 1 is 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 , Respectively 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 bound beamforming optimization method for near-field synaesthesia integration according to claim 2 is 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 p-th row and q-th column element 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 It is represented as 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-noise ratio required for each user, η th It is represented as the minimum energy efficiency of the system, ρ∈(0,1] is represented as the working efficiency of the base station amplifier, P0 is represented as the circuit power of the entire system, P is represented as the maximum transmission power of the base station, e is the natural base, j is the imaginary unit, and L is the transmission frame length of the base station.

4. The Bayesian Cramé-Rao bound beamforming optimization method for near-field synaesthesia integration according to claim 3 is characterized in that: Based on the problem obtained by transformation 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 Cramé-Rao bound 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 equivalent to 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 Cramé-Rao bound beamforming optimization method for near-field synaesthesia integration according to claim 5, characterized in that: Based on the problem obtained by 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, and 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 Cramé-Rao bound beamforming optimization method for near-field synaesthesia integration according to claim 6, characterized in that: Based on 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: The optimization goal is to minimize The constraints are: in is a matrix The eigenvector corresponding to the largest eigenvalue of .

8. The Bayesian Cramé-Rao bound 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 Cramé-Rao bound beamforming optimization method for near-field synaesthesia integration according to claim 8, characterized in that: According to 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 for Among them It is 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 for 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 Cramé-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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