Method and system for optimal multicast robust transmit beamforming in a miso system

Abstract

This invention relates to the field of signal processing technology and discloses an optimal multicast robust transmit beamforming method and system in a MISO system, comprising the following steps: S1. Obtaining channel state information of a multiple-input single-output (MISO) system, and establishing a signal-to-noise ratio (SNR) model based on the channel state information; the MISO system is referred to as an MISO system; S2. Establishing a beamforming communication model based on the SNR model, and establishing an optimization objective function with minimizing transmission power as the optimization index; S3. Analyzing the uncertainty of channel state information and the uncertainty of transmission power in a specific direction, establishing an uncertainty model, and obtaining an uncertainty set; S4. Substituting the modeled uncertainty set into the optimization objective function for robustness optimization; obtaining the optimal multicast robust transmit beam through an iterative algorithm. This invention solves the problem that existing technologies cannot fully consider channel state information, and has the characteristics of high robustness and close applicability to practical applications.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and more specifically, to an optimal multicast robust transmit beamforming method and system in a MISO system. Background Technology

[0002] MISO, or Multiple-Input Single-Output, is an antenna technology used in wireless communication. In this technology, the source (transmitter) uses multiple antennas, which are combined to achieve minimal error and optimal data transmission speed. The destination (receiver) uses only one antenna. MISO is one of several forms of smart antenna technology; the others are MIMO (Multiple-Input Multiple-Output) and SIMO (Single-Input Multiple-Output).

[0003] In MISO downlink communication systems, linear beamforming technology plays a crucial role in improving spectral efficiency and reducing mutual interference. In many existing beamforming optimization designs, the Quality of Service (QoS) design problem typically aims to minimize base station power consumption under receiver signal-to-noise ratio (SNR) constraints. In this design, the receiver must be able to obtain channel state information (CSO) at the transmitter and determine the SNR. However, in practical applications, only estimated and imperfect CSO information is typically available, leading to inaccurate SNR calculations. To address this inaccuracy, the uncertainties inherent in these estimates must be considered. A particularly effective approach is to design beamforming vectors that are robust to uncertainties in channel state information.

[0004] In recent years, robust beamforming optimization based on worst-case scenarios has been widely studied and developed in various communication systems. For the uncertainty set of real-world channels, it is often modeled as a sphere or ellipsoid, and the traditional S-lemma is frequently used to solve the optimization problem. Recently, an extended S-lemma has been developed to address the robust beamforming problem in frequency division duplex systems. This paper models the uncertainty of channel state information as two homogeneous inequalities and one non-homogeneous equality, incorporating the uncertainty into user service constraints and adding the uncertainty of the ellipsoid set to power constraints in a specific direction, considering the problem of minimizing transmission power under this condition. This problem considers imperfect channel state information to improve the overall system robustness, and proposes an effective method for solving this problem.

[0005] A two-dimensional robust beamforming method based on interruption probability constraints for MISO eavesdropping channels is proposed. This method proposes a robust beamforming scheme for MISO eavesdropping channels. In the case of single-group multicast, the non-convex problem with interruption probability constraints is transformed into a series of semidefinite programming problems using the bisection method, semidefinite relaxation, and Bernstein-type inequalities. The optimal robust beamforming design is obtained with the help of Gaussian variables, which effectively improves the confidentiality rate of the communication system, reduces the eavesdropping ability of the eavesdropping user, and improves the security of the communication system.

[0006] However, existing technologies cannot fully consider channel state information. Therefore, how to invent an optimal multicast robust transmit beamforming method in a MISO system is an urgent problem to be solved in this technical field. Summary of the Invention

[0007] To address the problem that existing technologies cannot fully consider channel state information, this invention provides an optimal multicast robust transmit beamforming method and system in a MISO system, which features high robustness and close applicability to practical applications.

[0008] To achieve the above-mentioned objectives of this invention, the technical solution adopted is as follows:

[0009] An optimal multicast robust transmit beamforming method in a MISO system includes the following steps:

[0010] S1. Obtain the channel state information of the multiple-input single-output system, and establish a signal-to-noise ratio model based on the channel state information; the multiple-input single-output system is called a MISO system;

[0011] S2. Establish a beamforming communication model based on the signal-to-noise ratio model, and establish an optimization objective function with minimizing transmission power as the optimization index;

[0012] S3. Analyze the uncertainty of channel state information and the uncertainty of transmission power in a specific direction, establish an uncertainty model, and obtain the uncertainty set;

[0013] S4. Substitute the modeled uncertainty set into the optimization objective function for robustness optimization; obtain the optimal multicast robust transmission beam through an iterative algorithm.

[0014] Preferably, in step S1, establishing a signal-to-noise ratio model based on channel state information specifically involves representing the channel state information as follows: Where e k It is the channel direction error, u k It is the channel estimation error and the outdated channel benefit, α k To quantize the multipliers, Here are the codebook elements describing the channel direction:

[0015]

[0016] Where k represents the k-th user, and SNR k Let w be the signal-to-noise ratio of the k-th user, and w be the beamforming vector. This represents the channel information between the base station and the k-th user, where Let N be the set of complex numbers. t The number of antennas, It is the variance of additivity zero-mean circular complex Gaussian noise.

[0017] 11. Further, in step S2, the communication model has two constraints: a communication service quality constraint satisfying a given signal-to-noise ratio and a transmission power constraint in a specific direction. The communication service quality constraint is replaced by the signal-to-noise ratio constraint, and considering uncertainties, the optimization objective function of step S2 is expressed as:

[0018]

[0019]

[0020]

[0021] Where L represents the maximum number of transmission directions, and K represents the maximum number of users. η l For each of the l preset power thresholds, g l σ represents the l-th specific transmission direction. k and γ k It is a given power threshold. Represents the set of real numbers. Let denote any , and let ‖˙‖ denote the 2-norm of the matrix.

[0022] Furthermore, in step S3, the uncertainty of the channel state information is analyzed, an uncertainty model is established, and an uncertainty set is obtained. The specific steps are as follows:

[0023] S301. According to e k and u k The property of ε′ modeles the uncertainty of channel state information as ε′ k :

[0024]

[0025] Where, β k To represent the channel estimation error and the outdated channel benefit u k The disturbance radius;

[0026] S302. Set parameters The uncertainty set εk Represented as:

[0027]

[0028] Where, N t The number of antennas, For N t A set of complex numbers of dimension express Belongs to N t ×N t The set of complex numbers;

[0029] S303. Model the mismatch error in the transmission direction to obtain the uncertainty set ε in the transmission direction. l :

[0030]

[0031] Where, ∈ l The radius of the perturbation set is given in advance.

[0032] Furthermore, robustness optimization can be expressed as:

[0033]

[0034] st

[0035] Robust optimization constraint 1:

[0036]

[0037] Robust optimization constraint 2:

[0038]

[0039] Wherein, Δ l Uncertain set ε belonging to the transmission direction l .

[0040] Furthermore, in step S4, the modeled uncertainty set is substituted into the optimization objective function for robustness optimization; the specific steps to obtain the optimal multicast robust transmission beam through an iterative algorithm are as follows:

[0041] S401. By using phase rotation, semi-definite relaxation, and the strong duality theorem, the problem of robust optimization constraint 1 is replaced by its dual problem, resulting in the first convex constraint:

[0042]

[0043]

[0044] x k1 ≥0, x k3 ≤0

[0045] Among them Indicates positive semidefinite; x k1 x k2 x k3 A is the dual variable; ki , i = 1, 2, 3, represent the transformed matrix;

[0046] S402. Using the S-lemma to process the problem of robust optimization constraint 2, we obtain the second convex constraint:

[0047]

[0048] Among them, dual variables

[0049] S403. Replace robust optimization constraint 1 and robust optimization constraint 2 with the first convex constraint and the second convex constraint to obtain the updated robust optimization expression;

[0050] S404. Perform semidefinite relaxation on the updated robust optimization expression, and add a penalty term to the objective function of the robust optimization after semidefinite relaxation to make the objective problem a convex problem;

[0051] S405. Iterative solution: Using a semi-definite relaxation method, the objective function with added penalty terms is obtained, resulting in the optimal multicast robust transmission beam.

[0052] Furthermore, in step S403, the first convex constraint can also be expressed as:

[0053]

[0054]

[0055]

[0056] Where I represents the identity matrix.

[0057] Furthermore, the updated robustness optimization expression in step S404 is as follows:

[0058] minw H w

[0059]

[0060]

[0061]

[0062]

[0063] Furthermore, the objective function obtained in step S405 is specifically:

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] Where tr(˙) represents the trace of the matrix, W0 is the starting point, and ρ is the penalty term; (‖˙‖ F ) is the F-norm of the matrix.

[0070] An optimal multicast robust transmit beamforming system in a MISO system includes a signal acquisition module, a signal-to-noise ratio model module, a communication model module, an uncertainty model module, and an iterative optimization module.

[0071] The signal acquisition module is used to acquire channel state information of a multiple-input single-output system, i.e., a MISO system.

[0072] The signal-to-noise ratio (SNR) model module is used to establish a SNR model based on channel state information.

[0073] The communication model module is used to establish a beamforming communication model based on the signal-to-noise ratio model, and to establish an optimization objective function with minimizing transmission power as the optimization index.

[0074] The uncertainty model module is used to analyze the uncertainty of channel state information and the uncertainty of transmission power in a specific direction, establish an uncertainty model, and obtain an uncertainty set;

[0075] The iterative optimization module is used to substitute the modeled uncertainty set into the optimization objective function for robust optimization; through iterative algorithms, the optimal multicast robust transmission beam is obtained.

[0076] The beneficial effects of this invention are as follows:

[0077] This invention proposes a robust optimization method for minimizing transmission power in a frequency division duplex (FDM) MISO system. Based on channel state information, this invention establishes a signal-to-noise ratio (SNR) model, taking into account the signal SNR. A beamforming communication model is then established based on this SNR model, and the minimization of transmission power is used as the optimization objective function. Furthermore, the uncertainty of channel state information and the uncertainty of transmission power in a specific direction are analyzed to establish an uncertainty model, obtaining an uncertainty set. This modeled uncertainty set is then substituted into the optimization objective function for robustness optimization. An iterative algorithm is used to obtain the optimal multicast robust transmit beam. Therefore, this invention solves the problem that existing technologies cannot fully consider channel state information and features high robustness and practical applicability. Attached Figure Description

[0078] Figure 1 This is a flowchart of an optimal multicast robust transmit beamforming method in a MISO system according to the present invention.

[0079] Figure 2 This is a schematic diagram of the MISO system.

[0080] Figure 3 This is a schematic diagram of the simulation results of an optimal multicast robust transmit beamforming method in a MISO system according to the present invention.

[0081] Figure 4 This is a schematic diagram illustrating the optimized process of an optimal multicast robust transmit beamforming method in a MISO system according to the present invention. Detailed Implementation

[0082] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0083] Example 1

[0084] like Figure 1 As shown, an optimal multicast robust transmit beamforming method in a MISO system includes the following steps:

[0085] S1. Obtain the channel state information of the multiple-input single-output system, and establish a signal-to-noise ratio model based on the channel state information; the multiple-input single-output system is called a MISO system;

[0086] S2. Establish a beamforming communication model based on the signal-to-noise ratio model, and establish an optimization objective function with minimizing transmission power as the optimization index;

[0087] S3. Analyze the uncertainty of channel state information and the uncertainty of transmission power in a specific direction, establish an uncertainty model, and obtain the uncertainty set;

[0088] S4. Substitute the modeled uncertainty set into the optimization objective function for robustness optimization; obtain the optimal multicast robust transmission beam through an iterative algorithm.

[0089] Example 2

[0090] An optimal multicast robust transmit beamforming method in a MISO system includes the following steps:

[0091] S1. Obtain the channel state information of the multiple-input single-output system, and establish a signal-to-noise ratio model based on the channel state information; the multiple-input single-output system is called a MISO system;

[0092] S2. Establish a beamforming communication model based on the signal-to-noise ratio model, and establish an optimization objective function with minimizing transmission power as the optimization index;

[0093] S3. Analyze the uncertainty of channel state information and the uncertainty of transmission power in a specific direction, establish an uncertainty model, and obtain the uncertainty set;

[0094] S4. Substitute the modeled uncertainty set into the optimization objective function for robustness optimization; obtain the optimal multicast robust transmission beam through an iterative algorithm.

[0095] like Figure 2 As shown, in this embodiment, the MISO system is a MISO system with a uniform linear array, and the base station uses linear beamforming to construct the transmission signal for each channel.

[0096] In this embodiment, let s k It is a normalized information symbol for user k, and This is the corresponding beamforming vector. The signal received by the k-th user is... in This represents the channel between the base station and the k-th user, and This indicates that the user's additivity is zero-mean circular complex Gaussian noise.

[0097] In one specific embodiment, in step S1, a signal-to-noise ratio (SNR) model is established based on the channel state information. Specifically, the channel state information is represented as... Where e k It is the channel direction error, u k It is the channel estimation error and the outdated channel benefit, α k To quantize the multipliers, Here are the codebook elements describing the channel direction:

[0098]

[0099] Where k represents the k-th user, and SNR k Let w be the signal-to-noise ratio of the k-th user, and w be the beamforming vector. This represents the channel information between the base station and the k-th user, where Let N be the set of complex numbers. t The number of antennas, It is the variance of additivity zero-mean circular complex Gaussian noise.

[0100] In this embodiment, the quality of service constraint is transformed into a signal-to-noise ratio (SNR) constraint. The transmitter seeks a set of beamformers to achieve a specific SNR for each user. and specific directions The required transmit power for the power-constrained target is minimized. Let γ k Let represent the target signal-to-noise ratio for the k-th user. The optimization problem is: min w w H w.

[0101] 12. In a specific embodiment, in step S2, the communication model has two constraints: a communication service quality constraint satisfying a given signal-to-noise ratio and a transmission power constraint in a specific direction. The communication service quality constraint is replaced by a signal-to-noise ratio constraint, and considering uncertainties, the optimization objective function of step S2 is expressed as:

[0102]

[0103]

[0104]

[0105] Where L represents the maximum number of transmission directions, and K represents the maximum number of users. η l For each of the l preset power thresholds, g l σ represents the l-th specific transmission direction. k and γ k It is a given power threshold. Represents the set of real numbers. Let denote any , and let ‖˙‖ denote the 2-norm of the matrix.

[0106] In this embodiment, it is assumed that the downlink in the frequency division duplex system is a quasi-static channel, utilizing structured vector quantization. The receiver estimates the channel based on the training signal transmitted by the base station, and then quantizes the channel gain and direction separately before sending them back to the base station. This represents the receiver's estimate, which uses a scalar quantizer. Perform quantization and use memoryless vector quantization from the Grassman codebook. If the codebook Indicates in M of user k k A Grassman codebook with unit norm elements, the codebook elements describing the channel direction can be represented as follows:

[0107] In this embodiment, let It can be accurately estimated and α k This is quantization at high resolution. The transmitter's estimate of the channel. Related to the actual channel, the actual estimated channel state information h k for:

[0108]

[0109] Where e k It is the channel direction error and u k These are channel estimation error and outdated channel benefits.

[0110] In one specific embodiment, step S3 involves analyzing the uncertainty of channel state information, establishing an uncertainty model, and obtaining an uncertainty set. The specific steps are as follows:

[0111] S301. According to e k and u k The property of ε′ modeles the uncertainty of channel state information as ε′ k :

[0112]

[0113] Where, β k To represent the channel estimation error and the outdated channel benefit u k The disturbance radius;

[0114] S302. Set parameters The uncertainty set ε k Represented as:

[0115]

[0116] Where, N t The number of antennas, For N t维 The set of complex numbers of degree, express Belongs to N t ×N t The set of complex numbers;

[0117] S303. Model the mismatch error in the transmission direction to obtain the uncertainty set ε in the transmission direction. l :

[0118]

[0119] Where, ∈ l The radius of the perturbation set is given in advance.

[0120] In one specific embodiment, robustness optimization can be expressed as:

[0121]

[0122] st

[0123] Robust optimization constraint 1:

[0124]

[0125] Robust optimization constraint 2:

[0126]

[0127] Wherein, Δ l Uncertain set ε belonging to the transmission direction l .

[0128] In this embodiment, robustness optimization constraint 1 can be written as Equation 2:

[0129]

[0130]

[0131]

[0132]

[0133] in

[0134] In this embodiment, robustness optimization constraint 1 is expanded because... and Modulus 1, it is redescribed as in This represents taking the real part and performing a phase rotation. The problem can be rewritten as Equation 3:

[0135]

[0136]

[0137]

[0138]

[0139] Since Equation 3 is homogeneous, we can write it in matrix inequality form:

[0140]

[0141]

[0142]

[0143]

[0144] in and:

[0145]

[0146]

[0147] The above is optimized using semidefinite relaxation:

[0148]

[0149]

[0150] tr(A K2 Y k ) = 1

[0151]

[0152] like Figure 4 As shown, in a specific embodiment, in step S4, the modeled uncertainty set is substituted into the optimization objective function for robustness optimization; the specific steps to obtain the optimal multicast robust transmission beam through an iterative algorithm are as follows:

[0153] S401. By using phase rotation, semi-definite relaxation, and the strong duality theorem, the problem of robust optimization constraint 1 is replaced by its dual problem, resulting in the first convex constraint:

[0154]

[0155]

[0156] x k1 ≥0, x k3 ≤0

[0157] Among them Indicates positive semidefinite; x k1 x k2 x k3 A is the dual variable; ki , i = 1, 2, 3, represent the transformed matrix;

[0158] In this embodiment, according to the strong duality theorem of linear cone programming, the duality gap between the semidefinite problem and its dual problem is zero. This can be achieved by replacing the minimization problem constraint of robust optimization constraint 1 with the dual problem.

[0159] S402. Using the S-lemma to process the problem of robust optimization constraint 2, we obtain the second convex constraint:

[0160]

[0161] Among them, dual variables

[0162] In this embodiment, robustness optimization constraint 2 is rewritten as Equation 4:

[0163]

[0164] ||Δ l ||≤∈ l

[0165] Expand the objective function and constraints as follows: and Using the S-lemma, it can be written as a quadratic matrix inequality as follows:

[0166]

[0167] in,

[0168] S403. Replace robust optimization constraint 1 and robust optimization constraint 2 with the first convex constraint and the second convex constraint to obtain the updated robust optimization expression;

[0169] S404. Perform semidefinite relaxation on the updated robust optimization expression, and add a penalty term to the objective function of the robust optimization after semidefinite relaxation to make the objective problem a convex problem;

[0170] In this embodiment, the semidefinite relaxation optimization and the quadratic matrix inequality are substituted back into the robust optimization problem, resulting in the updated robust optimization:

[0171] In this embodiment, optimization problem 3 is relaxed to a positive semidefinite degree, resulting in the following convex problem:

[0172] Mintr(W)

[0173]

[0174]

[0175]

[0176]

[0177] S405. Iterative solution: Using a semi-definite relaxation method, the objective function with added penalty terms is obtained, resulting in the optimal multicast robust transmission beam.

[0178] In this embodiment, since the convex problem discards the constraints related to rank, the optimal solution of the convex problem is the optimal solution of the updated robustness optimization when the rank is one. Therefore, when the optimal solution of the convex problem is a high-rank solution, it is necessary to perform the operation of seeking the rank-one solution.

[0179] When W is a positive semi-definite matrix and W is not a zero matrix, if tr(W) = ||W|| F When the relation is defined, the matrix W is rank-one. Where |˙| F Let F represent the F-norm of the matrix. Therefore, the above relationship can be equivalently rewritten as Equation 5:

[0180]

[0181] When the above relationships are satisfied, the rank of the optimal solution is one. Multiplying the convex problem by a penalty factor ρ as a penalty term and substituting this penalty term into the objective function, the new objective function can be written as:

[0182]

[0183] The new objective function is transformed and expressed as follows:

[0184]

[0185] W0 is the starting point.

[0186] In one specific embodiment, in step S403, the first convex constraint can also be expressed as:

[0187]

[0188]

[0189]

[0190] Where I represents the identity matrix.

[0191] In one specific embodiment, the updated robustness optimization expression in step S404 is as follows:

[0192] minw H w

[0193]

[0194]

[0195]

[0196]

[0197] In one specific embodiment, substituting the new objective function into Equation 5 yields the objective function obtained in step S405, specifically:

[0198]

[0199]

[0200]

[0201]

[0202]

[0203] Where tr(˙) represents the trace of the matrix, W0 is the starting point, and ρ is the penalty term; (‖˙‖ F ) is the F-norm of the matrix.

[0204] like Figure 3 As shown, G represents the number of specific power directions, K represents the number of users, and the sample size is 200. Observing the simulation results, it can be seen that compared with other beamforming design methods, the optimal multicast robust transmit beamforming method in the MISO system adopted in this invention is closer to reality and has better performance. Therefore, the robust transmit beamforming design in this multi-input single-output system achieves good results.

[0205] This invention proposes a robust optimization method for minimizing transmission power in a frequency division duplex (FDM) MISO system. Based on channel state information, this invention establishes a signal-to-noise ratio (SNR) model, taking into account the signal SNR. A beamforming communication model is then established based on this SNR model, and the minimization of transmission power is used as the optimization objective function. Furthermore, the uncertainty of channel state information and the uncertainty of transmission power in a specific direction are analyzed to establish an uncertainty model, obtaining an uncertainty set. This modeled uncertainty set is then substituted into the optimization objective function for robustness optimization. An iterative algorithm is used to obtain the optimal multicast robust transmit beam. Therefore, this invention solves the problem that existing technologies cannot fully consider channel state information and features high robustness and practical applicability.

[0206] In this embodiment, the invention considers uncertainties in the estimated channel state information fed back from the receiver and provides constraints on robust user service quality and transmission power in a specific direction. First, a transmission power minimization problem is established, with robust user service quality constraints and transmission power constraints in a specific direction given. Then, phase rotation, semi-definite relaxation, and the strong duality theorem are applied to transform the robust user service quality constraints, and the S-lemma is used to transform the transmission power constraints in the specific direction, transforming the optimization problem into a convex problem. A rank-one penalty term is added to reduce the rank of the problem. Finally, the CVX toolkit is used to solve this convex problem. This approach improves the system's robustness and makes the system more practical for real-world applications.

[0207] Example 3

[0208] An optimal multicast robust transmit beamforming system in a MISO system includes a signal acquisition module, a signal-to-noise ratio model module, a communication model module, an uncertainty model module, and an iterative optimization module.

[0209] The signal acquisition module is used to acquire channel state information of a multiple-input single-output system, i.e., a MISO system.

[0210] The signal-to-noise ratio (SNR) model module is used to establish a SNR model based on channel state information.

[0211] The communication model module is used to establish a beamforming communication model based on the signal-to-noise ratio model, and to establish an optimization objective function with minimizing transmission power as the optimization index.

[0212] The uncertainty model module is used to analyze the uncertainty of channel state information and the uncertainty of transmission power in a specific direction, establish an uncertainty model, and obtain an uncertainty set;

[0213] The iterative optimization module is used to substitute the modeled uncertainty set into the optimization objective function for robust optimization; through iterative algorithms, the optimal multicast robust transmission beam is obtained.

[0214] In practice, it is difficult to obtain perfect channel state information.

[0215] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. An optimal multicast robust transmit beamforming method in a MISO system, characterized in that: Includes the following steps: S1. Obtain the channel state information of the multiple-input single-output system, and establish a signal-to-noise ratio model based on the channel state information; the multiple-input single-output system is referred to as a MISO system; S2. Establish a beamforming communication model based on the signal-to-noise ratio (SNR) model, and establish an optimization objective function with minimizing transmission power as the optimization index. In step S2, the communication model has two constraints: a communication service quality constraint satisfying a given SNR and a transmission power constraint in a specific direction. Replacing the communication service quality constraint with the SNR constraint and considering uncertainties, the optimization objective function of step S2 is expressed as follows: s.t in k Indicates the first k One user, w For beamforming vector, For channel state information, Indicates base station and the k Channel information between users L The maximum number of transmission directions, K For the maximum number of users, , for Preset power threshold values ​​for each direction, Indicates the first l A specific transmission direction, and It is a given power threshold. Represents the set of real numbers. To represent any one, Denotes the 2-norm of a matrix; S3. Analyze the uncertainty of channel state information and the uncertainty of transmission power in a specific direction, establish an uncertainty model, and obtain the uncertainty set; S4. Substitute the modeled uncertainty set into the optimization objective function for robustness optimization; obtain the optimal multicast robust transmission beam through an iterative algorithm.

2. The optimal multicast robust transmit beamforming method in the MISO system according to claim 1, characterized in that: In step S1, a signal-to-noise ratio (SNR) model is established based on the channel state information. Specifically, the channel state information is represented as... ,in It is the channel direction error. These are channel estimation error and outdated channel benefits. To quantize the multipliers, Codebook elements describing the channel direction; in, For the first k The signal-to-noise ratio of each user, of which For the set of complex numbers, The number of antennas. It is the variance of additivity zero-mean circular complex Gaussian noise.

3. The optimal multicast robust transmit beamforming method in the MISO system according to claim 2, characterized in that: In step S3, the uncertainty of channel state information is analyzed, an uncertainty model is established, and an uncertainty set is obtained. The specific steps are as follows: S301. According to and The properties of channel state information are modeled as... : in, Indicates channel estimation error and outdated channel benefits The disturbance radius; S302. Set parameters , will the uncertain set Represented as: ； in, The number of antennas, for A set of complex numbers of dimension express belong The set of complex numbers; S303. Model the mismatch error in the transmission direction to obtain the uncertainty set in the transmission direction. : in, The radius of the perturbation set is given in advance.

4. The optimal multicast robust transmit beamforming method in the MISO system according to claim 3, characterized in that: Robustness optimization can be expressed as: st Robust optimization constraint 1: Robust optimization constraint 2: in, Uncertain set belonging to the direction of transmission .

5. The optimal multicast robust transmit beamforming method in the MISO system according to claim 4, characterized in that: In step S4, the modeled uncertainty set is substituted into the objective function for robustness optimization; the specific steps to obtain the optimal multicast robust transmission beam through an iterative algorithm are as follows: S401. By using phase rotation, semi-definite relaxation, and the strong duality theorem, the problem of robust optimization constraint 1 is replaced by its dual problem, resulting in the first convex constraint: max s.t Among them Indicates positive semidefinite; , , As dual variables; , i=1,2,3, represent the transformed matrix; S402. Using the S-lemma to process the problem with robust optimization constraint 2, we obtain the second convex constraint: Among them, dual variables , ; S403. Replace robust optimization constraint 1 and robust optimization constraint 2 with the first convex constraint and the second convex constraint to obtain the updated robust optimization expression; S404. Perform semidefinite relaxation on the updated robust optimization expression, and add a penalty term to the objective function of the robust optimization after semidefinite relaxation to make the objective problem a convex problem; S405. Iterative solution: Using a semi-positive definite relaxation method, the objective function with a penalty term is obtained, resulting in the optimal multicast robust transmission beam.

6. The optimal multicast robust transmit beamforming method in the MISO system according to claim 5, characterized in that: In step S403, the first convex constraint can also be expressed as: max s.t , , , , in Represents the identity matrix.

7. The optimal multicast robust transmit beamforming method in the MISO system according to claim 6, characterized in that: The updated robustness optimization expression in step S404 is as follows: min s.t , , , , , , 。 8. The optimal multicast robust transmit beamforming method in the MISO system according to claim 7, characterized in that: The objective function obtained in step S405 is specifically as follows: min + s.t , , , , , , in, Represents the trace of a matrix. Starting point This is a penalty item; ) is the F-norm of the matrix.

9. An optimal multicast robust transmit beamforming system in a MISO system, characterized in that: The method for performing the method as described in any one of claims 1 to 8 includes a signal acquisition module, a signal-to-noise ratio model module, a communication model module, an uncertainty model module, and an iterative optimization module; The signal acquisition module is used to acquire channel state information of a multiple-input single-output system, i.e., a MISO system. The signal-to-noise ratio (SNR) model module is used to establish a SNR model based on channel state information. The communication model module is used to establish a beamforming communication model based on the signal-to-noise ratio model, and to establish an optimization objective function with minimizing transmission power as the optimization index. The uncertainty model module is used to analyze the uncertainty of channel state information and the uncertainty of transmission power in a specific direction, establish an uncertainty model, and obtain an uncertainty set; The iterative optimization module is used to substitute the modeled uncertainty set into the optimization objective function for robust optimization; through iterative algorithms, the optimal multicast robust transmission beam is obtained.

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