High-orbit satellite beam forming method and system based on DVB-S2X multicast frame structure

Abstract

The invention relates to the technical field of wireless communication, in particular to a high-orbit satellite beam forming method and system based on a DVB-S2X multicast frame structure. The method comprises the following steps: establishing a high-orbit satellite multi-group multicast beam forming transmission system; wherein the transmission system adopts a DVB-S2X multi-group multicast frame structure, and each group of users need to meet QoS constraints; a beam forming optimization model is constructed, and a system total spectrum efficiency maximization problem under user QoS and satellite transmitting power constraints is established; a beam forming problem is decoupled; solving an optimal beam pointing vector; determining a user with the worst signal to interference plus noise ratio in each multicast group, calculating a channel coefficient of each multicast group, and solving to obtain an optimal power distribution coefficient; and multiplying the power allocation factor by the normalized beam pointing vector to obtain a multicast beam forming vector. According to the invention, the spectrum efficiency of the high-orbit multicast communication system and the user service quality can be improved on the premise of satisfying the QoS constraint and the power constraint, the complexity is reduced, and hardware implementation is facilitated.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular, to a high-orbit satellite beamforming method and system based on a DVB-S2X multicast frame structure. Background Art

[0002] The next-generation mobile communication system will achieve the integration of satellite communication systems and terrestrial mobile communication systems, meeting the vision of global seamless coverage of mobile broadband services. Among them, high-throughput satellites (usually high-orbit satellites) are an important part of the space-based nodes of future mobile communication networks.

[0003] However, since high-orbit satellites usually adopt a multicast frame structure based on DVB-S2X, implementing GEO satellite beamforming requires considering multicast beamforming, and at the same time, the minimum demodulation threshold in each user group needs to be satisfied. Few existing satellite multicast beamforming methods have closed-form or semi-closed-form solutions, but mostly rely on the serial convex approximation framework and optimization toolkits. These general optimization toolkits do not optimize the hardware, and the internal execution algorithms are invisible, making it difficult to run on the hardware platforms of actual systems.

[0004] That is to say, most existing spectral efficiency maximization satellite multicast beamforming algorithms use serial convex approximation and optimization toolkits for solution, with high computational complexity. At the same time, the impact of the same modulation and coding scheme required by users in the multicast group on spectral efficiency is not considered, and the system performance cannot be fully optimized. Summary of the Invention

[0005] To solve the problems existing in the prior art, the present invention provides a high-orbit satellite beamforming method and system based on a DVB-S2X multicast frame structure. By decoupling the beam pointing vector and power allocation coefficient and respectively solving the first-order optimality conditions, the spectral efficiency can be maximized while ensuring the QoS constraints of each user group. This solution is based on an iterative semi-closed-form solution method, without the need to rely on a convex optimization solution toolkit, with low complexity and is beneficial to hardware execution in actual systems.

[0006] In a first aspect, a high-orbit satellite beamforming method based on a DVB-S2X multicast frame structure provided in an embodiment of the present invention includes the following steps:

[0007] S1. Establish a multi-group multicast beamforming transmission system for high-orbit satellites. The multi-group multicast beamforming system includes a GEO satellite and M terrestrial multicast groups. Each multicast group contains K single-antenna user terminals. The users adopt a DVB-S2X multicast frame structure and a modulation and coding scheme, and the users in the same multicast group demodulate the same multicast frame;

[0008] S2. Construct a beamforming optimization model, establish a problem of maximizing the total system spectral efficiency under the constraints of user QoS and satellite transmit power, use the total system spectral efficiency function as the objective function, the beamforming weights as the optimization variables, and the transmit power inequality and user QoS inequality as the constraint conditions for optimization; the total system spectral efficiency takes into account the impact brought by the modulation and coding of the DVB-S2X protocol and is determined by the user with the lowest signal-to-interference-plus-noise ratio (SINR) in each user group; the user QoS constraint means that the spectral efficiency or SINR needs to exceed a preset threshold to ensure successful signal demodulation; the satellite transmit power constraint means that the total power consumed by the high-earth orbit satellite beamforming shall not exceed the upper limit of the satellite's transmit power resources.

[0009] S3. Decouple the beamforming problem, decompose the problem of maximizing the total system spectral efficiency into an unconstrained normalized beam pointing vector optimization sub-problem and a power allocation sub-problem that satisfies the user QoS constraint and the satellite transmit power constraint.

[0010] S4. Solve the optimal beam pointing vector. For the equivalent beam pointing vector optimization sub-problem, represent its first-order optimality condition as a non-linear eigenvalue problem, and obtain the optimal solution of the equivalent beam pointing vector optimization sub-problem by solving the principal eigenvector.

[0011] S5. After completing the optimization of the beam pointing vector, combine the normalized beam vector with the original channel, determine the user with the worst SINR in each multicast group, and calculate the channel coefficient of each multicast group.

[0012] S6. Optimize by replacing the channels of other users in the group with the channel of the worst user in each multicast group, and equivalently transform the power allocation sub-problem into a unicast power allocation problem.

[0013] S7. For the transformed unicast power allocation problem, first obtain an equivalent two-dimensional optimization form of the unicast power allocation problem through Lagrangian dual transformation; then alternately optimize the SINR auxiliary variable and the power coefficient introduced in the transformation process until convergence to the optimal solution, and further obtain the optimal power allocation coefficient.

[0014] S8. Multiply the power allocation factor by the normalized beam pointing vector to obtain the multicast beamforming vector.

[0015] In the second aspect, an embodiment of the present invention provides a high-earth orbit satellite beamforming system based on the DVB-S2X multicast frame structure, which is implemented based on the above beamforming method and specifically includes the following modules:

[0016] A high-earth orbit satellite multicast beamforming system establishment module, used to establish a high-earth orbit satellite multicast beamforming system, including a high-earth orbit satellite and a user group divided into multiple multicast groups in the coverage area; and use the modulation and coding scheme and multicast frame structure in the DVB-S2X protocol for transmission.

[0017] The multicast beamforming optimization model construction module is used to construct a beamforming optimization model and establish a spectral efficiency maximization model under satellite transmit power constraints and user QoS constraints;

[0018] The beamforming problem decoupling module is used to decompose the system total spectral efficiency maximization problem into an unconstrained normalized beam steering vector optimization sub-problem and a power allocation sub-problem that satisfies user QoS constraints and satellite transmit power constraints;

[0019] The beam steering vector optimization module represents the first-order optimality condition of the equivalent beam steering vector optimization sub-problem as a non-linear eigenvalue problem and obtains the optimal solution of the equivalent beam steering vector optimization sub-problem by solving the principal eigenvector;

[0020] The multicast group worst channel acquisition module is used to solve the equivalent user channels, combine the normalized beam vector with the original channels, determine the user with the worst signal-to-interference-plus-noise ratio (SINR) in each multicast group, and calculate the channel coefficients of each multicast group;

[0021] The power allocation optimization module optimizes by replacing the channels of other users in each multicast group with the channels of the worst users in the group, and equivalently converts the power allocation sub-problem into a unicast power allocation problem; for the converted unicast power allocation problem, first obtain the equivalent two-dimensional optimization form of the unicast power allocation problem through Lagrangian dual transformation; then alternately optimize the SINR auxiliary variable and power coefficient introduced in the transformation process until convergence to the optimal solution, and further obtain the optimal power allocation coefficient;

[0022] The beamforming weight calculation module is used to multiply the power allocation factor by the normalized beam steering vector to obtain the multicast beamforming vector.

[0023] The geostationary satellite multicast beamforming system establishment module is used to establish a geostationary satellite multicast beamforming system, including a geostationary satellite and a user group divided into multiple multicast groups in the coverage area; and adopt the modulation and coding scheme and multicast frame structure in the DVB-S2X protocol for transmission;

[0024] The multicast beamforming optimization model construction module is used to construct a beamforming optimization model and establish a spectral efficiency maximization model under transmit power constraints and QoS constraints; the transmit power constraint means that the transmit power of the GEO satellite shall not exceed a given threshold; the spectral efficiency is the maximum transmission rate after considering the DVB-S2X modulation and coding scheme and multicast frame structure;

[0025] The beam steering vector optimization module is used to solve the normalized beam steering vector. According to the beam steering optimization sub-problem decoupled from the original beamforming problem, a non-linear eigenvalue decomposition method is adopted to obtain the optimal beam steering;

[0026] The worst channel acquisition module for multicast groups is used to solve the equivalent user channels and select the channels with the worst signal-to-interference-plus-noise ratio (SINR) from each multicast group for optimization;

[0027] The power allocation optimization module is used to solve the optimal power allocation coefficients for each beam. Based on the worst equivalent channels of each multicast group, a power allocation optimization sub-problem is established, and a multi-ratio summation fractional programming quadratic transformation framework is combined with the Lagrangian dual decomposition algorithm to solve the optimal power allocation coefficients;

[0028] The beamforming weight calculation module is used to solve the beamforming weights. According to the beam steering vectors obtained from the two decoupled sub-problems and the power allocation results, the two are multiplied to obtain the final multicast beamforming matrix, thereby realizing the solution of the original problem.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] By decoupling the original multicast beamforming problem, the present invention first optimizes the beam steering vector based on the non-linear eigenvalue decomposition method, and secondly adopts a multi-ratio summation fractional programming quadratic transformation framework, combined with the Lagrangian dual decomposition algorithm, to realize the optimization of the power allocation coefficients. The present invention has an iterative semi-closed form solution. Compared with the traditional spectral efficiency optimization algorithm for multicast systems, it greatly reduces the algorithm complexity without losing optimality and does not rely on an optimization toolkit, which is beneficial to the hardware implementation of the actual system. Description of the Drawings

[0031] Figure 1 It is a schematic flowchart of the high-orbit satellite beamforming method based on the DVB-S2X multicast frame structure provided in the embodiment of the present invention;

[0032] Figure 2 It is a schematic structural diagram of the high-orbit satellite multi-group multicast beamforming transmission system established in the embodiment of the present invention;

[0033] Figure 3 It is a comparison schematic diagram of the total spectral efficiency at different signal-to-noise ratios with and without using an optimization toolkit when the high-orbit satellite beamforming method provided in the embodiment of the present invention is adopted;

[0034] Figure 4 It is a schematic diagram of the change of the total spectral efficiency with the number of algorithm iterations under different system layouts when the high-orbit satellite beamforming method provided in the embodiment of the present invention is adopted;

[0035] Figure 5Schematic diagram of comparison of the minimum spectral efficiency of multicast groups and QoS constraints under different methods after adopting the high-orbit satellite beamforming method provided by the embodiments of the present invention. Detailed implementation manners

[0036] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention; obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0037] It should be noted that the step numbers in the text are only for the convenience of explaining specific embodiments and do not serve as a limitation on the execution order of steps. The method provided in this embodiment can be executed by a related server, and hereinafter, an edge server is taken as an example of the execution entity for illustration.

[0038] Embodiment 1

[0039] As Figure 1 shown, this embodiment provides a high-orbit satellite beamforming method based on the DVB-S2X multicast frame structure, which specifically includes the following steps:

[0040] S1. Establish a high-orbit satellite multi-group multicast beamforming transmission system; the multi-group multicast beamforming system includes a GEO satellite and M ground multicast groups, and each multicast group contains K single-antenna user terminals. The users in the multi-group multicast beamforming system adopt the DVB-S2X multicast frame structure and modulation and coding scheme, and the users in the same multicast group demodulate the same multicast frame and extract their corresponding information. The GEO satellite adopts N t multi-feed reflector antennas, and each antenna generates a beam and serves one multicast group; the users (which can be simply referred to as ground users) in the multi-group multicast beamforming system adopt omnidirectional receiving antennas.

[0041] As Figure 2 shown, in this embodiment, the high-orbit satellite multi-group multicast beamforming transmission system includes a GEO satellite and 7 ground multicast groups, and each multicast group contains 5 users; the satellite transmitter adopts a multi-feed reflector antenna and can generate 7 beams, and the user terminal adopts a single-antenna receiver. The users in each multicast group will receive the same DVB-S2X data frame.

[0042] Specifically, in the high-orbit satellite multi-group multicast beamforming transmission system of this step, the mth multicast group is denoted as the kth user in the mth multicast group is denoted as the channel vector between the GEO satellite and the user is denoted as gm,k ; represents the system transmission symbol, where s m represents the transmission symbol of the m-th multicast group (also called the m-th user group); represents the precoding vector set by the GEO satellite for the m-th multicast group.

[0043] S2. Construct a beamforming optimization model, establish the problem of maximizing the total system spectral efficiency under the constraints of user QoS and satellite transmit power, use the total system spectral efficiency function as the objective function, the beamforming weight as the optimization variable, and the transmit power inequality and user QoS inequality as the constraint conditions for optimization.

[0044] Among them, the user QoS constraint means that the spectral efficiency or signal-to-interference-plus-noise ratio needs to exceed a certain preset threshold to ensure that the signal can be successfully demodulated; the satellite transmit power constraint means that the total power consumed by the high-orbit satellite beamforming shall not exceed the upper limit of the satellite transmit power resource. The total system spectral efficiency takes into account the impact brought by the DVB-S2X protocol modulation and coding, and is determined by the user with the lowest signal-to-interference-plus-noise ratio in each multicast group.

[0045] In the beamforming optimization model constructed in this step, the problem of maximizing the total system spectral efficiency is optimized with the total system spectral efficiency function as the objective function, the beamforming weight as the optimization variable, and the transmit power inequality and user QoS inequality as the constraint conditions. The specific description is as follows:

[0046] S21. The total system spectral efficiency function is defined as the sum of the total spectral efficiencies of each multicast group; the total spectral efficiency of the multicast group is equal to the minimum value of the achievable spectral efficiencies of the users in the multicast group multiplied by the number of users. At the same time, the achievable spectral efficiency of the user needs to consider the performance loss brought by the DVB-S2X protocol modulation and coding. The mathematical model expression of the performance loss R is:

[0047]

[0048] where R m represents the spectral efficiency of the m-th multicast group, γ m,k is the signal-to-interference-plus-noise ratio of the user , represents the channel from the GEO satellite to the user , w i represents the precoding vector set by the GEO satellite for the multicast group i, b represents the multicast group subscript, B represents the number of beams generated by the satellite (corresponding to the number of multicast groups, that is, B = M), σ 2 represents the noise variance; the fitting parameter ξ fit characterizes the loss of modulation and coding compared to the Shannon limit, and usually takes ξ fit = 1.473.

[0049] The mathematical model of the system total spectral efficiency maximization problem can be specifically expressed as the following optimization problem:

[0050]

[0051] The meanings of the parameters in formulas (1a) to (1c) are described as follows:

[0052] The optimization variable in the objective function (1a) is the precoding vector for all multicast groups, and the specific expression of the function R m (w) can be seen in the mathematical model of the performance loss in step S21.

[0053] Formula (1b) represents the user QoS constraint, and the lowest user rate in each multicast group is not lower than the QoS rate threshold η.

[0054] Formula (1c) represents that the total power consumed by the beamformer cannot exceed the power resource upper limit P T .

[0055] S3. Decouple the beamforming problem and decompose the optimization problem in step S22 into an unconstrained normalized beam pointing vector optimization sub-problem and a power allocation sub-problem that satisfies the user QoS constraint and the satellite transmission power constraint.

[0056] In this step, the optimization problem is decoupled. The first sub-problem above does not consider the user QoS constraint and the satellite transmission power constraint, and only considers the normalized beam pointing vector optimization with the goal of maximizing the system total spectral efficiency; the second sub-problem considers the power allocation problem under the condition that the beam pointing vector is determined to satisfy the user QoS constraint and the satellite transmission power constraint.

[0057] Specifically, the decoupling steps of the system total spectral efficiency maximization beamforming problem in this step are as follows:

[0058] S31. Consider the system total spectral efficiency maximization problem under the normalized power constraint:

[0059]

[0060] Among them, represents the normalized beam pointing vectors of all multicast groups, represents the normalized beam pointing vector of the m-th multicast group, represents the spectral efficiency of the m-th multicast group, and its definition and expression are shown in step 21 and restated as follows:

[0061]

[0062] Among them Among them pm represents the power allocation coefficient of the m-th multicast group, p i represents the power allocation coefficient of the i-th multicast group.

[0063] Furthermore, for the min(·) function in the function, the LogSumExp function is used for approximation; meanwhile, for the signal-to-interference-plus-noise ratio γ m,k , it is equivalently represented in the form of a Rayleigh quotient, then the problem can be equivalently transformed into:

[0064]

[0065] where represents the conjugate transpose of the normalized beam steering vector , A m,k represents the equivalent matrix for calculating the numerator part, B m,k represents the equivalent matrix for calculating the denominator part, τ represents the fitting parameter of the LogSumExp function for the min(·) function, and there is:

[0066]

[0067] In the formula, I M represents the identity matrix, represents the standard basis vector with the m-th element being 1 and the remaining elements being 0; G m,k is the channel vector correlation matrix, I M×M represents the identity matrix of dimension M×M, where the dimension corresponds to the total number of multicast groups, and is represented by the letter M in this embodiment.

[0068] S32. Equivalently represent the signal-to-interference-plus-noise ratio γ in step S21 m,k as where p m represents the power allocation coefficient of the m-th multicast group, p i represents the power allocation coefficient of the i-th multicast group, represents the normalized precoding vector of the i-th multicast group. Considering the power allocation problem under the condition of determining the beam steering vector as:

[0069]

[0070] where p = [p 1 , p 2 , … p m …, p M T is the power allocation vector.

[0071] ​S4. Solve the optimal beam steering vector. For the equivalent beam steering vector optimization sub-problem (abbreviated as the equivalent problem, i.e., the normalized beam steering vector optimization problem in step S31), express its first-order optimality condition as a non-linear eigenvalue problem, and obtain the optimal solution of the above equivalent problem by solving the principal eigenvector.

[0072] In this embodiment, the specific steps to solve the optimal solution of the equivalent beam steering vector optimization sub-problem are as follows:

[0073] S41. Define the first first-order optimality condition auxiliary calculation function for the normalized beam steering vector :

[0074]

[0075] where represents the spectral efficiency of the k-th user in the m-th multicast group;

[0076] S42. Define the second first-order optimality condition auxiliary calculation function for :

[0077]

[0078] S43. Define the optimal value of the objective function:

[0079]

[0080] S44. Define the third first-order optimality condition auxiliary calculation function for :

[0081]

[0082] S45. Construct the equivalent first-order optimality condition of the problem where δ represents the maximum eigenvalue and is also the optimal value of the objective function. where δ represents the maximum eigenvalue and is also the optimal value of the objective function.

[0083] S46. Randomly initialize the normalized beam steering vector Set the iteration superscript t = 0.

[0084] S47. Calculate

[0085] S48. Normalize the power of the beam steering vector

[0086] S49. Calculate If the calculation result is less than the threshold ∈ or the iteration number t reaches the upper limit, output the optimal solution Otherwise, let the iteration superscript t = t + 1, and jump to step S47 to continue execution in sequence.

[0087] S5. After optimizing the beam steering vector and assuming normalized power allocation for each multicast group, determine the user with the worst signal-to-interference-plus-noise ratio (SINR) in each multicast group and calculate the channel coefficient of each multicast group.

[0088] Since the beam steering optimization process can effectively suppress inter-beam interference, the relative SINR of each user can be determined according to the gain of the equivalent channel. In the case of multicast, if the allocated power can meet the QoS constraint of the worst user, the QoS constraints of other users in the group will also be satisfied naturally.

[0089] In a preferred embodiment, the process of calculating the channel coefficient of the multicast group in this step S5 includes the following steps:

[0090] S51. For the multicast group to According to the optimization result of step S4, determine the user with the lowest SINR through the following formula:

[0091]

[0092] where represents the normalized beam steering vector of the i-th multicast group;

[0093] S52. Denote the channel of the worst user in the m-th multicast group as Then the channel coefficient of the m-th multicast group is

[0094] S6. Optimize by replacing the channels of other users in each group with the channels of the worst users in each multicast group obtained in step S52, and equivalently transform the original multicast power allocation sub-problem (i.e., the second sub-problem decoupled in step S3) into a unicast power allocation problem.

[0095] In this embodiment, the unicast power allocation problem obtained by equivalent transformation is specifically expressed as:

[0096]

[0097] In the formula, h m,m represents the equivalent channel from the m-th reflecting surface antenna to the worst user in the m-th multicast group.

[0098] S7. For the unicast power allocation problem obtained by transformation in step S6, first obtain the equivalent two-dimensional optimization form of the unicast power allocation problem through Lagrangian dual transformation; then alternately optimize the SINR auxiliary variable and power coefficient introduced in the transformation process until convergence to the optimal solution, and further obtain the optimal power allocation coefficient.

[0099] In this step, for the alternating optimization process of the SINR auxiliary variable and the power coefficient, specifically:

[0100] Optimize the power coefficient on the premise that the SINR auxiliary variable is fixed. When the power coefficient is fixed, regard the part related to the power coefficient in the equivalent two-dimensional optimization problem as a constant, and obtain a one-dimensional sub-problem about the SINR auxiliary variable;

[0101] Obtain the first-order optimality condition of the one-dimensional sub-problem about the SINR auxiliary variable through the Lagrangian function, and obtain the optimal solution of the SINR auxiliary variable based on the first-order optimality condition.

[0102] Furthermore, optimize the power coefficient on the premise that the SINR auxiliary variable is fixed, specifically:

[0103] Regard the part related to the auxiliary variable in the equivalent two-dimensional optimization problem as a constant, and obtain a one-dimensional sub-problem about the power coefficient;

[0104] For the one-dimensional sub-problem about the power coefficient, based on the quadratic transformation framework of the multi-fractional programming, determine the update formula of the fractional programming auxiliary variable and the outer iteration form, and determine the inner update form about the power coefficient;

[0105] Alternately update the fractional programming auxiliary variable and the power coefficient until the power coefficient converges to the optimal solution, so as to obtain the optimal power coefficient under the condition that the SINR auxiliary variable is fixed.

[0106] In this embodiment, alternately update the SINR auxiliary variable, the fractional programming auxiliary variable and the power coefficient optimization variable. The specific solution steps of step S7 are as follows:

[0107] S71. Define the SINR auxiliary variable γ = [γ 1 , …, γ M T ; Replace the original user QoS rate threshold η with the signal-to-interference-plus-noise ratio threshold γ th = 2 η - 1; Initialize the power coefficient p (0) ; Initialize the Lagrange multiplier λ (0) = 0, ν (0) = 0; Initialize the iteration number t = 0.

[0108] S72. When the power coefficient p is fixed, update γ according to the following update formula according to the first-order optimality condition of the auxiliary variable γ:

[0109]

[0110] Among them, represents the power allocation coefficient of the m-th multicast group after the t-th iteration update,​ denotes the power allocation coefficient of the \(i\)-th multicast group after the \(t\)-th iterative update, \(h\) m,i denotes the equivalent channel from the \(m\)-th reflecting surface antenna to the worst user in the \(i\)-th multicast group;

[0111] S73. When the auxiliary variable \(\gamma\) is fixed, the optimization problem in step S71 becomes a multi-ratio summation fractional programming problem with respect to the power coefficient \(p\). According to the quadratic transformation framework, an auxiliary variable \(t\) is introduced, and the update formula for \(t\) is:

[0112]

[0113] S74. For each multicast group \(m\), verify the condition whether it is less than 0, and divide the multicast group subscripts into the set and the set ; for let the Lagrange multiplier \(\lambda\) j = 0; meanwhile, let \(v = 0\).

[0114] S75. For all solve the equation \(|h\) m,m |\) 2 \(p\) m \((\lambda\) m ) - \(\gamma\) th \(\xi\) fit \((\sum\) i≠m \(|h\) m,i |\) 2 \(p\) i + \(\sigma\) 2 ) = 0 with respect to \(\lambda\) m and update \(\lambda\) m ; where the function \(p\) m \((\lambda\) m ) is given according to the expression of \(p\) m in step S76, and \(\lambda\) m denotes the \(m\)-th Lagrange multiplier.

[0115] S76. For the multicast group, the update formula for \(p\) m is:

[0116]

[0117] where denotes the \((t + 1)\)-th iteration result of the \(j\)-th Lagrange multiplier \(\lambda\) j , and \(h\) j,m denotes the equivalent channel from the \(j\)-th reflecting surface antenna to the worst user in the \(m\)-th multicast group.

[0118] For the multicast group, \(p\) mThe update formula is as follows:

[0119]

[0120] If S77 Solve the equation for the root of v by the bisection method and update v.

[0121] S78. According to step S76, update p of again. m

[0122] S79. Calculate ∥∥y (t+1) -y (t) ∥∥. If it is less than the threshold ∈ or the iteration number t reaches the upper limit, output the optimal solution p * ; otherwise, let the iteration index t = t + 1 and jump to step S72 to update the variables in sequence.

[0123] S8. Multiply the power allocation factor by the normalized beam steering vector to obtain the desired multicast beamforming vector. Specifically:

[0124]

[0125] In this embodiment, Matlab 2023a is used to perform mathematical modeling and simulation on the system. Numerical simulation of the proposed beamforming method is carried out based on the ITU-R P.618 channel model defined in the 3GPP standard, as shown in Figures 3 - 5 shown.

[0126] From the comparison of Figure 3 it can be seen that the spectral efficiency of the multicast beamforming method proposed in this embodiment can reach or exceed the solution accuracy of the convex optimization toolbox.

[0127] From the comparison of Figure 4 it can be seen that under the condition that the system contains 8 to 16 multicast groups, the algorithm converges within 10 iterations; and as the number of multicast groups (beams) increases, the convergence speed slows down and the overall spectral efficiency performance of the system improves.

[0128] From the comparison of Figure 5 it can be seen that the multicast beamforming method proposed in this embodiment obtains similar solution results to the convex optimization toolbox method, and at the same time, this algorithm can well meet the QoS constraints.

[0129] Embodiment 2

[0130] This embodiment is based on the same inventive concept as Embodiment 1 and provides a high-orbit satellite beamforming system based on the DVB-S2X multicast frame structure, including:

[0131] The high-orbit satellite multicast beamforming system establishment module is used to establish a high-orbit satellite multicast beamforming system, including high-orbit satellites and a user group divided into multiple multicast groups in the coverage area; and the modulation and coding scheme and multicast frame structure in the DVB-S2X protocol are used for transmission;

[0132] The multicast beamforming optimization model construction module is used to construct a beamforming optimization model and establish a spectral efficiency maximization model under satellite transmit power constraints and user QoS constraints;

[0133] The beamforming problem decoupling module is used to decompose the system total spectral efficiency maximization problem into an unconstrained normalized beam pointing vector optimization sub-problem and a power allocation sub-problem that satisfies user QoS constraints and satellite transmit power constraints;

[0134] The beam pointing vector optimization module, for the equivalent beam pointing vector optimization sub-problem, represents its first-order optimality condition as a non-linear eigenvalue problem, and obtains the optimal solution of the equivalent beam pointing vector optimization sub-problem by solving the principal eigenvector;

[0135] The multicast group worst channel acquisition module is used to solve the equivalent user channels, combine the normalized beam vector with the original channels, determine the user with the worst signal-to-interference-plus-noise ratio in each multicast group, and calculate the channel coefficients of each multicast group;

[0136] The power allocation optimization module optimizes by replacing the channels of other users in each group with the channels of the worst user in each multicast group, and equivalently converts the power allocation sub-problem into a unicast power allocation problem; for the converted unicast power allocation problem, first obtain the equivalent two-dimensional optimization form of the unicast power allocation problem through Lagrangian dual transformation; then alternately optimize the SINR auxiliary variable and power coefficient introduced in the transformation process until convergence to the optimal solution, and further obtain the optimal power allocation coefficient;

[0137] The beamforming weight calculation module is used to multiply the power allocation factor by the normalized beam pointing vector to obtain the multicast beamforming vector.

[0138] Each module in this embodiment is respectively used to implement the steps in Embodiment 1. For the detailed implementation process, please refer to Embodiment 1 and will not be elaborated here.

[0139] As can be seen from the detailed technical solutions described in the above embodiments, the technical solution of the present invention has the following beneficial effects:

[0140] The high-orbit beamforming method and system based on the DVB-S2X multicast frame structure of the present invention can obtain a semi-closed solution to the problem of maximizing the spectral efficiency of multicast beamforming, and has made adaptations and optimizations for the link communication link in the DVB standard, further improving the spectral efficiency of the high-orbit satellite multicast transmission system. Most of the existing satellite multicast beamforming algorithms use serial convex approximation and optimization toolkits to solve the problem of maximizing the spectral efficiency of multicast beamforming, without considering the impact of the modulation and coding scheme and the complexity of algorithm deployment, which is not conducive to the hardware implementation of the actual system. The present invention greatly reduces the algorithm complexity through the decoupling of the beam pointing and the power coefficient, and the scheme based on the iterative semi-closed solution is conducive to the hardware deployment of the actual system, so as to achieve efficient satellite multicast beamforming.

[0141] The above is the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements are also regarded as the protection scope of the present invention.

Claims

1. A high-orbit satellite beamforming method based on a DVB-S2X multicast frame structure, characterized in that: The following steps are involved: S1. Establish a high-orbit satellite multi-group multicast beamforming transmission system, wherein the multi-group multicast beamforming system includes a GEO satellite and M ground multicast groups, each multicast group includes K single-antenna user terminals, and the users adopt a DVB-S2X multicast frame structure and modulation and coding scheme, and users in the same multicast group demodulate the same multicast frame; S2. Construct a beamforming optimization model to maximize the total spectrum efficiency of the system under the constraints of user QoS and satellite transmission power. The total spectrum efficiency function of the system is used as the objective function, the beamforming weight is used as the optimization variable, and the transmission power inequality and user QoS inequality are used as constraints for optimization. The total spectrum efficiency of the system takes into account the impact of DVB-S2X protocol modulation and coding, and is determined by the user with the lowest signal-to-interference-noise ratio in each user group. User QoS constraints indicate that the spectrum efficiency or signal-to-interference-noise ratio must exceed a preset threshold to ensure successful signal demodulation; The satellite transmission power constraint means that the total power consumed by high-orbit satellite beamforming must not exceed the upper limit of the satellite's transmission power resources; S3, decouple the beamforming problem and decompose the system total spectrum efficiency maximization problem into an unconstrained normalized beam pointing vector optimization sub-problem and a power allocation sub-problem that satisfies user QoS constraints and satellite transmit power constraints; S4. Solve the optimal beam pointing vector. For the equivalent beam pointing vector optimization subproblem, express its first-order optimality condition as a nonlinear eigenvalue problem, and obtain the optimal solution of the equivalent beam pointing vector optimization subproblem by solving the main eigenvector. S5. After the optimization of the beam pointing vector is completed, the normalized beam vector is combined with the original channel to determine the user with the worst signal to interference and noise ratio in each multicast group, and the channel coefficient of each multicast group is calculated; S6, using the channel of the worst user in each multicast group to replace the channels of other users in the group for optimization, and converting the power allocation sub-problem into a unicast power allocation problem; S7, for the converted unicast power allocation problem, firstly obtain an equivalent two-dimensional optimization form of the unicast power allocation problem through Lagrange dual transformation; then alternately optimize the SINR auxiliary variable and the power coefficient introduced in the transformation process until convergence to the optimal solution, thereby obtaining the optimal power allocation coefficient; S8. Multiply the power allocation factor by the normalized beam steering vector to obtain a multicast beamforming vector.

2. The high-orbit satellite beamforming method according to claim 1, characterized in that: In the high-orbit satellite multi-group multicast beamforming transmission system in step S1, the mth multicast group is denoted as The kth user in the mth multicast group is denoted by GEO Satellites and Users The channel vector between m,k ; Represents the system transmission symbol, where s m represents the transmission symbol of the mth multicast group; Represents the precoding vector set by the GEO satellite for the mth multicast group.

3. The high-orbit satellite beamforming method according to claim 2, characterized in that: Step S2 includes: S21. The total spectrum efficiency function of the system is defined as the sum of the total spectrum efficiency of each multicast group. The total spectrum efficiency of a multicast group is equal to the minimum achievable spectrum efficiency of users in the multicast group multiplied by the number of users. The achievable spectrum efficiency of users needs to take into account the performance loss caused by the modulation and coding of the DVB-S2X protocol. The mathematical model of the performance loss R is expressed as: Where R m represents the spectrum efficiency of the mth multicast group, γ m,k For users The signal-to-interference-noise ratio, Indicates GEO satellite to user The channel, w i represents the precoding vector set by the GEO satellite for multicast group i, b represents the multicast group subscript, B represents the number of beams generated by the satellite, σ 2 represents the noise variance; the fitting parameter ξ fit Characterizes the loss of modulation coding compared to the Shannon limit; S22. The mathematical model of the system total spectrum efficiency maximization problem is expressed as the following optimization problem: Optimization variables in the objective function (1a) is the precoding vector for all multicast groups, function R m (w) is the mathematical model of performance loss in step S21; Formula (1b) represents the user QoS constraint, the lowest user rate in each multicast group is not less than the QoS rate threshold η; Formula (1c) indicates that the total power consumed by the beamformer cannot exceed the power resource upper limit P T .

4. The high-orbit satellite beamforming method according to claim 3, characterized in that: Step S3 decouples the beamforming problem of maximizing the total spectrum efficiency of the system, including: S31. Consider the problem of maximizing the total spectrum efficiency of the system under the normalized power constraint: in, represents the normalized beam pointing vector for all multicast groups, represents the normalized beam pointing vector of the m-th multicast group, represents the spectrum efficiency of the mth multicast group; right The min(·) function in the function is approximated by the LogSumExp function; the signal-to-interference-noise ratio γ m,k , which is equivalent to the Rayleigh quotient form, then the problem The equivalent conversion is: in represents the normalized beam pointing vector The conjugate transpose of A m,k Represents auxiliary calculation The equivalent matrix of the molecular part, B m,k Represents auxiliary calculation The equivalent matrix of the denominator, τ represents the fitting parameter of the LogSumExp function to the min(·) function, and has: Where I M represents the identity matrix, represents a standard basis vector whose mth element is 1 and the rest are 0; G m,k is the channel vector correlation matrix, I M×M represents the identity matrix of dimension M×M, where the dimension corresponds to the total number of multicast groups; S32: The signal to interference noise ratio γ in step S21 is m,k The equivalent expression is where p m represents the power allocation coefficient of the mth multicast group, p i represents the power allocation coefficient of the i-th multicast group, represents the normalized precoding vector of the i-th multicast group. Considering the power allocation problem when the beam pointing vector is determined, it is: where p=[p1,p2,…p m …,p M ] T is the power allocation vector.

5. The high-orbit satellite beamforming method according to claim 4, characterized in that: Step S4 includes: S41. Definition of normalized beam pointing vector The first-order optimal condition auxiliary calculation function: in represents the spectral efficiency of the kth user in the mth multicast group; S42. Definition of The second first-order optimal condition auxiliary calculation function: S43. Define the optimal value of the objective function: S44. Definition of The third first-order optimal condition auxiliary calculation function: S45. Construction issues The equivalent first-order optimal condition of S46, Randomly initialize the normalized beam pointing vector Set iteration superscript t = 0; S47, calculation S48, Normalized beam pointing vector power S49, calculation If the calculated result is less than the threshold ∈ or the number of iterations t reaches the upper limit, output the optimal solution Otherwise, set the iteration superscript t=t+1 and jump to step S47 to continue execution in sequence.

6. The high-orbit satellite beamforming method according to claim 3, characterized in that: Step S5 is a process of calculating the multicast group channel coefficient, comprising the following steps: S51. For multicast groups arrive According to the optimization result of step S4, the user with the lowest signal to interference noise ratio is determined by the following formula: in, represents the normalized beam pointing vector of the m-th multicast group, represents the normalized beam pointing vector of the i-th multicast group; S52: The channel of the worst user in the m-th multicast group is Then the channel coefficient of the mth multicast group is 7. The high-orbit satellite beamforming method according to claim 1, characterized in that: The alternating optimization process of the SINR auxiliary variable and the power coefficient in step S7 includes: The power coefficient is optimized under the premise that the SINR auxiliary variable is fixed. When the power coefficient is fixed, the part about the power coefficient in the equivalent two-dimensional optimization problem is regarded as a constant, and a one-dimensional sub-problem about the SINR auxiliary variable is obtained; The first-order optimality condition is obtained through the Lagrangian function of the one-dimensional sub-problem about the SINR auxiliary variable, and the optimal solution of the SINR auxiliary variable is obtained based on the first-order optimality condition; The optimization of the power coefficient under the premise of fixing the SINR auxiliary variable is specifically as follows: The part about auxiliary variables in the equivalent two-dimensional optimization problem is regarded as a constant, and a one-dimensional sub-problem about power coefficient is obtained; For the one-dimensional subproblem about power coefficient, based on the quadratic transformation framework of multi-fractional programming, the update form and outer iteration form of fractional programming auxiliary variables are determined, and the inner update form about power coefficient is determined; The fractional programming auxiliary variables and the power coefficient are updated alternately until the power coefficient converges to the optimal solution, thereby obtaining the optimal power coefficient when the SINR auxiliary variables are fixed.

8. The high-orbit satellite beamforming method according to claim 7, characterized in that: The SINR auxiliary variable, the fractional programming auxiliary variable and the power coefficient optimization variable are updated alternately. The solution step of step S7 includes: S71, define SINR auxiliary variable γ=[γ1,…,γ M ] T ; Replace the original user QoS rate threshold η with the signal-to-interference-noise ratio threshold γ th =2 η -1; Initialize power coefficient p (0) ; Initialize the Lagrange multiplier λ (0) =0, ν (0) =0; Initialize the number of iterations t = 0; S72. When the power coefficient p is fixed, according to the first-order optimality condition of the auxiliary variable γ, γ is updated according to the following update formula: Among them, h m,m represents the equivalent channel from the mth reflector antenna to the worst user in the mth multicast group, represents the power allocation coefficient of the m-th multicast group after the t-th iteration update, represents the power allocation coefficient of the ith multicast group after the tth iteration update, h m,i represents the equivalent channel from the mth reflector antenna to the worst user in the i-th multicast group, ξ fit represents the fitting parameter, σ 2 represents the noise variance; S73, when the auxiliary variable γ is fixed, the optimization problem in step S71 becomes a multi-ratio sum fraction programming problem about the power coefficient p; according to the quadratic transformation framework, the auxiliary variable y is introduced, and the update formula of y is: S74. For each multicast group m, verify the condition f(p m )=|h m,m | 2 p m -γ th ξ fit (∑ i≠m |h m,i | 2 p i +σ 2 ) is less than 0, and divide the multicast group index into sets and collection in; for Let the Lagrange multiplier λ j =0; at the same time, let ν = 0; S75, for all Solve the equation by bisection method |h m,m | 2 p m (λ m )-γ th ξ fit (∑ i≠m |h m,i | 2 p i +σ 2 )=0 about λ m The root of λ m ; where the function p m (λ m ) According to step S76 m The expression of λ is given by m represents the mth Lagrange multiplier; p m represents the power allocation coefficient of the mth multicast group, p i represents the power allocation coefficient of the i-th multicast group; S76, for The power allocation coefficient p for a multicast group m The update formula is: In the formula represents the jth Lagrange multiplier λ j The t+1th iteration result, h j,m represents the equivalent channel from the jth reflector antenna to the worst user in the mth multicast group; for The power allocation coefficient p for a multicast group m The update formula is: S77 Solving equations by bisection about the root of ν, and update ν; S78. According to step S76, p m Re-update; S79, calculate ∥∥y (t+1) -y (t) ∥∥, if it is less than the threshold ∈ or the number of iterations t reaches the upper limit, output the optimal solution p * ; Otherwise, set the iteration index t=t+1 and jump to step S72 to update the variables in sequence.

9. A high-orbit satellite beamforming system based on a DVB-S2X multicast frame structure, characterized in that: The beamforming system is implemented based on the beamforming method according to any one of claims 1 to 8, and the beamforming system comprises the following modules: A high-orbit satellite multicast beamforming system establishment module is used to establish a high-orbit satellite multicast beamforming system, including a high-orbit satellite and a user group divided into multiple multicast groups under the coverage area; The modulation and coding scheme and multicast frame structure in the DVB-S2X protocol are used for transmission; Multicast beamforming optimization model building module, used to build a beamforming optimization model and establish a spectrum efficiency maximization model under satellite transmission power constraints and user QoS constraints; The beamforming problem decoupling module is used to decompose the system total spectrum efficiency maximization problem into an unconstrained normalized beam pointing vector optimization subproblem and a power allocation subproblem that satisfies user QoS constraints and satellite transmit power constraints; The beam pointing vector optimization module expresses the first-order optimality condition of the equivalent beam pointing vector optimization subproblem as a nonlinear eigenvalue problem, and obtains the optimal solution of the equivalent beam pointing vector optimization subproblem by solving the main eigenvector; The worst channel acquisition module of the multicast group is used to solve the equivalent user channel, combine the normalized beam vector with the original channel, determine the user with the worst signal-to-interference-noise ratio in each multicast group, and calculate the channel coefficient of each multicast group; A power allocation optimization module, which optimizes the channels of the worst user in each multicast group instead of the channels of other users in the group, and converts the power allocation sub-problem into a unicast power allocation problem; For the converted unicast power allocation problem, the equivalent two-dimensional optimization form of the unicast power allocation problem is first obtained through Lagrange dual transformation; then the SINR auxiliary variable and the power coefficient introduced in the transformation process are alternately optimized until they converge to the optimal solution, thereby obtaining the optimal power allocation coefficient; The beamforming weight calculation module is used to multiply the power allocation factor and the normalized beam pointing vector to obtain the multicast beamforming vector.

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