A continuous aperture antenna system multi-group multicast energy efficiency maximization precoding method

Abstract

This invention discloses a precoding method for maximizing the energy efficiency of multicast groups in a continuous aperture antenna array (CAPA) system. First, an integral-based energy efficiency maximization problem model for the multicast system is constructed, where each user group must satisfy a minimum multicast rate requirement and a total transmit power constraint. Then, the Dinkelbach method is used to transform the problem, and a quadratic transformation is used to equivalently transform the minimum multicast rate constraint. Based on this, the block coordinate descent (BCD) method is further used to alternately optimize the optimization variables. The variational method (CoV) and Lagrange duality theory are used to directly solve related subproblems, obtaining a CAPA precoder in continuous space. To further reduce complexity, a CAPA-ZF precoder is designed based on the zero-forcing (ZF) precoding principle, simplifying the original problem into a directly solvable power allocation problem. Compared to traditional spatial discrete antenna arrays (SPDA), CAPA can significantly improve the energy efficiency of multicast systems.

Description

Technical Field

[0001] This invention relates to the field of continuous aperture array (CAPA) wireless communication, and in particular to CAPA multi-user downlink communication methods and systems. Background Technology

[0002] In the rapid development of wireless communication, Multiple-Input Multiple-Output (MIMO) technology has become one of the most critical technologies. Compared to fifth-generation (5G) wireless networks, next-generation wireless systems—especially sixth-generation (6G) and post-6G (B6G) eras—pose more stringent performance requirements, including ultra-high speeds, massive connectivity, and high-precision sensing capabilities. To address these challenges, current mainstream technologies are evolving MIMO technology from traditional architectures to massive MIMO (mMIMO) and even ultra-massive MIMO (XL-MIMO) systems by increasing the number of antenna elements and expanding the array aperture size. It should be noted that these MIMO implementations essentially rely on Spatial Discrete Antenna Array (SPDA) configurations, i.e., deploying a large number of discrete antenna elements within a fixed physical aperture. However, such methods are inherently constrained by degrees of freedom. Given the boundless growth in connectivity demands in the B6G era, infinitely expanding the MIMO dimension would lead to a dramatic increase in hardware costs and energy consumption. Therefore, groundbreaking technological innovation is imperative.

[0003] In recent years, a novel concept called Continuous Aperture Array (CAPA) has attracted widespread research attention. Compared with traditional SPDA, the core feature of CAPA lies in gradually reducing the spacing between antenna elements to an infinitesimal size, thereby forming a continuous electromagnetic radiation surface within a given array aperture. Generally speaking, CAPA can be regarded as a spatially continuous structure with an antenna number approaching infinity. Therefore, CAPA can achieve flexible control of the signal amplitude and phase at any point on the radiation surface through a continuous current source distribution pattern; this process is called CAPA Beamformer. Compared with SPDA, CAPA can significantly improve the degrees of freedom and array gain of communication systems, thereby effectively enhancing communication performance, and is therefore considered one of the promising key technologies for the B6G era.

[0004] Current research has focused solely on the performance gains of CAPA beamforming in unicast scenarios, where CAPA transmits an independent data stream to each user. In such scenarios, the enhanced spatial degrees of freedom provided by CAPA can be effectively used to suppress inter-user interference, thereby improving system performance. However, research on CAPA-based multicast communication has not been widely conducted. Unlike unicast, multicast transmits the same data stream to a group of users simultaneously, making it valuable for applications such as video streaming and online conferencing. Furthermore, compared to unicast, multicast requires fewer RF links, resulting in higher energy efficiency and cost-effectiveness. Despite these potential advantages, multicast beamforming design differs significantly from unicast and presents greater complexity. In multicast communication with multiple groups, beamforming for each group not only needs to suppress inter-group interference but also improve the worst-case performance of users within the group. Therefore, research on CAPA-based multicast communication is of great significance. Summary of the Invention

[0005] Purpose of the Invention: In view of the above-mentioned research status, the purpose of this invention is to study multicast communication in CAPA systems and provide a precoding method for maximizing the energy efficiency of multicast communication in CAPA systems. This method aims to maximize the energy efficiency (EE) of the system. After constructing a model of the problem of maximizing the energy efficiency of multicast communication in CAPA systems, a CAPA precoder in a continuous space is directly designed. Based on this, and based on the ZF precoding principle, a low-complexity CAPA precoder is designed.

[0006] Technical solution: To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] A precoding method for maximizing energy efficiency in a continuous aperture antenna system using multiple sets of multicast signals, comprising the following steps:

[0008] An integral-based energy efficiency maximization optimization model is established with the ratio of spectral efficiency to transmit power of a multicast system as the objective function, and minimum multicast rate constraints and transmit power constraints are set.

[0009] A pre-encoder is constructed based on the current density distribution of a continuous aperture array antenna; the pre-encoder is a current density function in continuous space.

[0010] The objective function of the optimization problem is transformed using the Dinkelbach method;

[0011] The minimum multicast rate constraint is transformed using a quadratic transformation, and auxiliary variables are introduced to convert the fractional structure of the signal-to-interference-plus-noise ratio into a linear function of the optimization variables.

[0012] The Block Coordinate Descent (BCD) algorithm based on Variational Method (CoV) is used to alternately optimize the relevant optimization variables to obtain the final solution. The optimal CAPA precoder is obtained using CoV and is in the form of a linear combination of user channels in the system. Alternatively, using the channel information of each group of representative users, based on the Zero Forcing (ZF) principle, the optimal CAPA-ZF precoder is expressed as a low-complexity linear combination of representative user channels. The optimal CAPA-ZF precoder is obtained by directly solving the power allocation problem.

[0013] In one implementation, the optimization objective is expressed as: in, The CAPA is located on a continuous surface on which a continuous current is distributed; this is the CAPA pre-encoder that needs to be designed. Subscript G represents the user's group, and G is the total number of groups; J g (s) represents the current density function of the CAPA surface, used to carry the data sent to the g-th group of users; s is the coordinate of a point at any location on the CAPA surface; For the spectral efficiency of multicast systems, γ g,k (J) represents the signal-to-interference-plus-noise ratio (SIR) of the k-th user in the g-th group. h g,k (s) represents the channel function between CAPA and the k-th user in the g-th group, with the subscript... K g Let g be the number of users in the g-th group; This represents the noise power at the user's receiver.

[0014] The minimum multicast rate constraint is expressed as: in, The minimum multicast rate constraint that the g-th group of users needs to satisfy;

[0015] The transmit power constraint is expressed as: Among them, P t This represents the total transmission power.

[0016] In one implementation, within the Dinkelbach framework, let No. The subproblem is reconstructed under the next Dinkelbach iteration as follows:

[0017]

[0018] in, The Dinkelbach auxiliary variable is introduced.

[0019] In one implementation, the multicast rate constraint is equivalently transformed using a quadratic transformation as follows:

[0020]

[0021] in, These are the auxiliary variables introduced.

[0022] No. The subproblem under the Dinkelbach iteration is transformed into the following problem with optimization variables J, r, and μ:

[0023]

[0024] Construct the dual problem of the J,r related subproblems using Lagrange duality theory, where the optimal solution for r is:

[0025]

[0026] The optimal CAPA precoder J was obtained using CoV:

[0027]

[0028] in, And ξ≥0 is the introduced Lagrange dual multiplier. Subscript i = (g-1)K g +k, c j,i The proportion coefficients of each channel are denoted by <·,·>, which represent inner product operations. After obtaining the optimal structure of the CAPA precoder, the optimal Lagrange multipliers are obtained by further solving the ellipsoid method, thereby obtaining the optimization result of the CAPA precoder.

[0029] In solving the r and μ related subproblems, the optimal μ is obtained according to the following formula:

[0030]

[0031] The best Substitute y(μ) g,k The optimal r can be obtained by considering J).

[0032]

[0033] In one implementation, the optimal CAPA-ZF precoder is found based on the ZF principle.

[0034]

[0035] in, ρg h represents the power sent to the g-th group of users. j (s) represents the channel representing the user in the j-th group; yes The g-th column, H ot The (g,j)th element is defined as follows:

[0036] [H ot ] g,j = <h g ,h j >,

[0037] Among them, the CAPA-ZF precoder is based on the optimal structure of the CAPA precoder, while utilizing ZF to eliminate inter-user interference, transforming the optimization variable into the power ρ allocated to each user. g .

[0038] Based on the ZF principle, solve the following power allocation problem:

[0039]

[0040] ρ g ≥0,

[0041] in,

[0042] The present invention also provides a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, it implements the multi-group multicast energy efficiency maximization precoding method for the continuous aperture antenna system.

[0043] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0044] 1. This invention studies the problem of maximizing the energy efficiency of multicast in CAPA systems, filling the gap in the existing research on precoding design for multicast communication systems;

[0045] 2. This invention uses the variational method to directly process and design the CAPA precoder in continuous space, and the optimization results obtained are more accurate than those approximated by discrete Fourier series expansion.

[0046] 3. This invention proposes a block coordinate descent algorithm based on variational methods. First, a quadratic transformation is used to convert the non-convex minimum multicast rate constraint into a tractable linear constraint. Then, the BCD algorithm is used to iteratively solve the reconstructed problem. The CAPA precoder design subproblem obtains its optimal solution through variational theory and the Lagrange duality method. Numerical results show that the optimized CAPA precoder achieves higher energy efficiency compared to the SPDA precoder.

[0047] 4. This invention further proposes a CAPA-ZF precoder based on representative users, transforming the original optimization problem into a power allocation problem, which can be directly solved using convex optimization tools. Numerical results show that the CAPA-ZF precoder has lower complexity compared to the original CAPA precoder. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of CAPA multicast downlink transmission in an embodiment of the present invention.

[0049] Figure 2 This is a comparison chart of the system energy efficiency of the CAPA pre-encoder, CAPA-ZF pre-encoder, and traditional SPDA pre-encoder proposed in the embodiments of the present invention. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0051] This invention discloses a precoding method for maximizing the energy efficiency of multiple groups of multicast antennas in a continuous aperture antenna system. The base station is equipped with a CAPA, on which the current density distribution can be arbitrarily designed. Therefore, the functions involved in the design of the CAPA precoder are all continuous functions in space.

[0052] like Figure 1 As shown, the base station is equipped with a CAPA to send the same multicast data to multiple users in each group. Each user is equipped with an omnidirectional polarized single antenna, and each user must meet the minimum multicast rate requirement.

[0053] The method of this embodiment will be explained in more detail below with a specific scenario.

[0054] Part 1: CAPA Multicast System Model and Problem Construction

[0055] The base station is equipped with a CAPA, and the continuous surface on which it is located is denoted as . Arbitrary current density J is distributed on it. g (s), Serving G groups of users, i.e., the CAPA pre-encoder that needs to be designed. Subscript G represents the user's group, and G is the total number of groups; J g (s) represents the current density function of the CAPA surface, used to carry the data sent to the g-th group of users; s is the coordinate of a point at any location on the CAPA surface. In this embodiment, within the same group, users receive the same data signal, and the same user can only belong to one group, that is, there is no user overlap between different groups. To simplify the analysis of the problem, the current density function only considers the y-axis polarization, i.e. Let be the unit vector in the y-direction. The expression for the transmitted signal is:

[0056]

[0057] in, For the data sent to the g-th group of users, satisfy ε{xx H} = I G x = [x1, x2, ..., x G ] T , Let J denote the set of complex numbers, and ε denote the expectation operation. g,y (s) represents the current density function for y-direction polarization. Each user is equipped with an omnidirectional polarized single antenna with polarization direction as follows: Therefore, the expression for the received signal is:

[0058]

[0059] in, Let r be the equivalent channel function for the k-th user in the g-th group of CAPA, where r g,k Let (g,k) be the spatial coordinates of the user. Let λ be the Green's function in free space, η be the wavelength, and n be the free space wave impedance. g,k Let be the noise at user (g,k), and ‖·‖ be the vector 2-norm operation.

[0060] The expression for the spectral efficiency of the CAPA multicast system is:

[0061]

[0062] in, This is the signal-to-interference-plus-noise ratio (SIR) expression at user (g,k). Subscript K g Let g be the number of users in the g-th group; This represents the noise power at the user's receiver.

[0063] The expression for the transmit power at the base station is:

[0064]

[0065] The system energy efficiency expression is:

[0066]

[0067] Therefore, the model for maximizing the energy efficiency of a continuous aperture system with multiple sets of multicast is as follows:

[0068]

[0069] in, For the minimum multicast rate constraint that the g-th group of users needs to satisfy, P t This represents the total transmission power.

[0070] Part 2: CoV-based BCD Algorithm Design

[0071] After transformation using the Dinkelbach method, the first The subproblems in the next Dinkelbach iteration are as follows:

[0072]

[0073] in, The introduced Dinkelbach auxiliary variable is updated using the following formula:

[0074]

[0075] in, For the first The optimization result obtained from the Dinkelbach iteration.

[0076] Within the Dinkelbach framework, let Thus, the first The subproblem under the next Dinkelbach iteration is further reconstructed as follows:

[0077]

[0078] in,

[0079] The multicast rate constraint is equivalently transformed using a quadratic transformation as follows:

[0080]

[0081] in, These are the auxiliary variables introduced.

[0082] Therefore, the first The subproblem under the Dinkelbach iteration is transformed into the following problem with optimization variables J, r, and μ:

[0083]

[0084] Therefore, the original optimization problem is transformed into iterative solutions to the J,r-related subproblems and the r,μ-related subproblems, with the specific steps as follows:

[0085] 1) Solving J,r-related subproblems:

[0086] a) Using Lagrange duality theory, the dual problem of this subproblem is constructed as follows:

[0087]

[0088] in, And ξ≥0 is the introduced Lagrange dual multiplier. In this dual problem, the optimal solution for r is:

[0089]

[0090] The optimal CAPA precoder J can be obtained using CoV:

[0091]

[0092] in, Subscript i = (g-1)K g +k, c j,i The proportion of each channel is defined as follows: P oth =diag{p1,...,p i ,...,}, [Q] i,j = <g i ,g j >, <·,·> represent inner product operations, specifically...<f(x),g(x)> =∫f(x)g * (x)dx;

[0093] b) The optimal Lagrange multipliers {λ} are obtained by iterative solution using the ellipsoid method. opt In each iteration of the ellipsoidal method, {λ,ξ} is updated via the following subgradient:

[0094]

[0095] The optimal {λ} is obtained by using the above subgradient update. opt ,ξ opt}

[0096] c) {λ opt ,ξ opt Substitute as well as The expression yields the optimal solution to the atomic problem {r}. opt J opt};

[0097] 2) Solving the r and μ related subproblems:

[0098] The optimal μ is obtained according to the following formula:

[0099]

[0100] The best Substitute y(μ) g,k The optimal r can be obtained by considering J).

[0101]

[0102] Part 3: Design of a Low-Complexity BCD Algorithm Based on ZF

[0103] First, based on the channel correlation coefficient, representative users for each group are selected. The following selection criteria can be adopted: First, consider the channel correlation among users in the group, and select the user with the largest sum of correlation coefficients with all users in the group as the representative user of the group; Second, when the sum of correlation coefficients in the group is the same, consider the sum of channel correlation coefficients between users in the group and representative users in other groups, and select the user with the smallest sum of channel correlation coefficients with users outside the group as the representative user of the group.

[0104] Each group of representative users is denoted as a set. Its representative user channel set is denoted as

[0105] Then, using the channel information representing the user, and based on the ZF principle, the optimal CAPA-ZF precoder is designed.

[0106]

[0107] in, ρ g h represents the power sent to the g-th group of users; j (s) represents the channel representing the user in the j-th group; yes The g-th column, H ot The (g,j)th element is defined as follows:

[0108] [H ot ] g,j = <h g ,h j >,

[0109] The original optimization problem simplifies to the following power allocation problem:

[0110]

[0111] ρ g ≥0,

[0112] This problem can be solved directly using Matlab's convex optimization tools.

[0113] To satisfy the minimum multicast rate constraint that the g-th group of users needs to meet, the total system transmit power is: The transmit power limit must be met, i.e.

[0114] The system EE implemented by the CAPA precoder proposed in this invention, as well as the CAPA-ZF precoder and the traditional SPDA precoder, is compared to, for example... Figure 2 As shown. Compared to the SPDA precoder, the CAPA-ZF precoder proposed in this invention achieves higher system EE in both multicast and unicast systems.

[0115] In summary, this invention discloses a precoding method for maximizing the energy efficiency of a multicast system with multiple groups of antennas (CAPAs). The base station is equipped with a CAPA, and each user is equipped with an omnidirectional polarized single antenna. First, an integral-based energy efficiency maximization problem model is constructed for this multicast system. In this problem, each user group must satisfy a minimum multicast rate requirement and a total transmit power constraint. Considering the fractional structure of this problem, the Dinkelbach method is chosen to transform the problem. Within this framework, a quadratic transformation is used to further transform the minimum multicast rate constraint for each user group. Based on the above, the block coordinate descent (BCD) method is further used to alternately optimize the optimization variables. Specifically, the variational method (CoV) and Lagrange duality theory are used to directly solve related subproblems, obtaining a CAPA precoder in continuous space. To further reduce the algorithm complexity, a CAPA-ZF precoder is designed based on the zero-forcing (ZF) precoding principle, simplifying the original problem into a directly solvable power allocation problem. Compared to traditional spatial discrete antenna arrays (SPDA), CAPA can significantly improve the energy efficiency of multicast systems.

[0116] Based on the same inventive concept, an embodiment of the present invention discloses a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the steps of the multi-group multicast energy efficiency maximization precoding method for the continuous aperture antenna system.

[0117] All aspects of this invention not described in detail are well-known to those skilled in the art. The preferred embodiments of this invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of this invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of this invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A precoding method for maximizing energy efficiency in a continuous aperture antenna system using multiple groups of multicast signals, characterized in that, Includes the following steps: An integral-based energy efficiency maximization optimization model is established with the ratio of spectral efficiency to transmit power of a multicast system as the objective function, and minimum multicast rate constraints and transmit power constraints are set. A pre-encoder is constructed based on the current density distribution of a continuous aperture array antenna; the pre-encoder is a current density function in continuous space. The objective function of the optimization problem is transformed using the Dinkelbach method; The minimum multicast rate constraint is transformed using a quadratic transformation, and auxiliary variables are introduced to convert the fractional structure of the signal-to-interference-plus-noise ratio into a linear function of the optimization variables. Using the CoV-based BCD algorithm, the optimization variables involved are alternately optimized to obtain the final solution. The optimal CAPA precoder is obtained using CoV and is in the form of a linear combination of user channels in the system. Alternatively, using the channel information of each group of representative users, based on the ZF principle, the optimal CAPA-ZF precoder is expressed as a low-complexity linear combination of representative user channels. The optimal CAPA-ZF precoder is obtained by directly solving the power allocation problem. The optimization objective is expressed as ,in, The CAPA is located on a continuous surface on which a continuous current is distributed; this is the CAPA pre-encoder that needs to be designed. subscript Represents the user's group. This represents the total number of groups; The current density function representing the CAPA surface is used to carry the data sent to the first... Group user data; Let be the coordinates of a point at any location on the CAPA surface; For the spectral efficiency of multicast systems, ; For the first Group 1 Signal-to-interference-plus-noise ratio for each user , For CAPA to the Group 1 Channel function between users, subscript , For the first Number of users in the group; This represents the noise power at the user's receiver.

2. The precoding method for maximizing energy efficiency in a continuous aperture antenna system using multiple groups of multicast signals according to claim 1, characterized in that, The minimum multicast rate constraint is expressed as: ,in, For the first The minimum multicast rate constraint that a group of users needs to satisfy; The transmit power constraint is expressed as: ,in, This represents the total transmission power.

3. The precoding method for maximizing energy efficiency of a continuous aperture antenna system using multiple groups of multicast signals according to claim 2, characterized in that: Within the Dinkelbach framework, let , No. The subproblem is reconstructed under the next Dinkelbach iteration as follows: ； in, The Dinkelbach auxiliary variable is introduced. .

4. The precoding method for maximizing energy efficiency in a continuous aperture antenna system using multiple groups of multicast signals according to claim 1, characterized in that, The multicast rate constraint is equivalently transformed using a quadratic transformation as follows: ， in, , These are the auxiliary variables introduced.

5. The precoding method for maximizing energy efficiency in a continuous aperture antenna system using multiple groups of multicast signals according to claim 4, characterized in that, No. The subproblem under the Dinkelbach iteration is transformed into the following optimization variables: Question: ； in, The Dinkelbach auxiliary variable is introduced. , , For the first The minimum multicast rate constraint that a group of users needs to satisfy. This represents the total transmission power.

6. The precoding method for maximizing energy efficiency in a continuous aperture antenna system using multiple groups of multicast signals according to claim 5, characterized in that, Constructing using Lagrange duality theory The dual problem of the related subproblems, where, The optimal solution is: ； Optimal CAPA precoder Obtained using CoV: ， in, as well as For the introduced Lagrange dual multipliers, , subscript , This represents the proportion of each channel. The inner product operation is represented. After obtaining the optimal structure of the CAPA precoder, the optimal Lagrange multipliers are obtained by further solving the ellipsoid method, thereby obtaining the optimization result of the CAPA precoder. In solving related subproblems, the optimal It is obtained from the following formula: ， The best Substitution Optimal results can be obtained : 。 7. The precoding method for maximizing energy efficiency in a continuous aperture antenna system using multiple groups of multicast signals according to claim 1, characterized in that, Solving for the optimal CAPA-ZF precoder based on the ZF principle. : in, , The representative sent to the The power of the group of users, For the selected representative user set, The channel representing the user in group j; yes The List, The Each element is defined as follows: ； in, This represents the inner product operation; the CAPA-ZF precoder is based on the optimal structure of the CAPA precoder, while utilizing ZF to eliminate inter-user interference, transforming the optimization variable into the power allocated to each user. .

8. The precoding method for maximizing energy efficiency in a continuous aperture antenna system using multiple groups of multicast signals according to claim 7, characterized in that, Based on the ZF principle, solve the following power allocation problem: ； in, The Dinkelbach auxiliary variable is introduced. , , , , ,in, , .

9. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is loaded into the processor, it implements the multi-group multicast energy efficiency maximization precoding method for continuous aperture antenna systems according to any one of claims 1-8.

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