WO2023071142A1 - 一种分布式多卫星联合波束赋形方法 - Google Patents

一种分布式多卫星联合波束赋形方法 Download PDF

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WO2023071142A1
WO2023071142A1 PCT/CN2022/092303 CN2022092303W WO2023071142A1 WO 2023071142 A1 WO2023071142 A1 WO 2023071142A1 CN 2022092303 W CN2022092303 W CN 2022092303W WO 2023071142 A1 WO2023071142 A1 WO 2023071142A1
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satellite
matrix
user
formula
calculate
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French (fr)
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郑重
王英杰
费泽松
张蕾
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北京理工大学
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0408—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas using two or more beams, i.e. beam diversity
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • H04B7/043—Power distribution using best eigenmode, e.g. beam forming or beam steering
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/14—Relay systems
    • H04B7/15—Active relay systems
    • H04B7/185—Space-based or airborne stations; Stations for satellite systems
    • H04B7/1853—Satellite systems for providing telephony service to a mobile station, i.e. mobile satellite service
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Definitions

  • the invention relates to a distributed multi-satellite joint beamforming method, belonging to the technical field of multi-satellite multi-beam cooperative transmission under the satellite network architecture.
  • Next-generation high-throughput satellite (HTS) systems need to provide ultra-high data rate services to meet the needs of high-bandwidth multimedia applications in remote areas and integrate with next-generation terrestrial communication systems such as 5G technology and beyond.
  • Next-generation terrestrial communication systems such as 5G technology and beyond.
  • multi-beam satellite communication (SatCom) systems have emerged as a powerful solution, and some multi-beam HTS systems currently in operation, such as Wildblue-1 and Anik F2, can cover parts of the United States with 66 spot beams. Due to the influence of the side lobe of the radiation pattern of the multi-beam antenna, this technology will generate strong inter-beam interference (IBI).
  • IBI inter-beam interference
  • Currently operating multi-beam satellite communication systems usually use four-color or higher frequency multiplexing to reduce IBI.
  • next-generation HTS systems in order to achieve high spectral efficiency and throughput, full frequency reuse (FFR) needs to be adopted so that each beam can fully utilize the entire available bandwidth.
  • FFR full frequency reuse
  • Ishtiaq Ahmad et al. analyzed the average and rate performance with zero-forcing (ZF) precoding, D. Christopoulos Then the performance of the minimum mean square error (MMSE) receiver in the Ricean channel is studied.
  • ZF zero-forcing
  • Multi-satellite cooperative transmission technology as a new technology to improve satellite transmission rate, has important application prospects.
  • Traditional satellite communications generally use a single satellite to serve one user, which imposes certain restrictions on the data transmission rate and capacity of the user, and the utilization efficiency of satellite resources cannot be fully utilized.
  • one terminal can be connected to multiple satellites in formation at the same time. These satellites cooperate to realize joint data transmission and obtain diversity gain or multiplexing gain.
  • Maik Röper et al. designed a distributed MMSE beamforming algorithm in which multiple satellites cooperate to transmit user data. The research results show that the algorithm can significantly improve the speed and performance, but it requires a lot of signaling interactions between satellites, and each satellite obtains instantaneous channel information multiple times in iterative calculations, which is a challenge for the current satellite system. huge challenge.
  • the purpose of the present invention is to provide a distributed multi-satellite
  • the joint beamforming method approximates the iterative process of the traditional weighted minimum mean square error WMMSE by applying the deterministic equivalent DE theorem.
  • the satellites replace the large-dimensional instantaneous channel with an auxiliary variable in the form of an interactive scalar Matrix, which significantly reduces the amount of information interacted between satellites; after iterative convergence, the precoding matrix is calculated through the receiving filter matrix, user weights and a set of instantaneous channel information, and the distributed multi-satellite joint beamforming is realized according to the precoding matrix.
  • multi-satellite joint beamforming effectively reduces inter-beam interference and improves overall system throughput.
  • a distributed multi-satellite joint beamforming method disclosed by the present invention comprises the following steps:
  • Step 1 Initialize the composition structure and input conditions of the multi-satellite cooperative transmission system
  • Step 1.1 Initialize the composition structure of the multi-satellite cooperative transmission system
  • composition structure of the multi-satellite cooperative transmission system is the communication system model, including the instantaneous channel matrix from the satellite to the ground user, the signal transmitted by the satellite, the signal received by the ground user, the precoding matrix of the ground user served by the satellite, and the noise at the user.
  • Formula (1) expresses:
  • M is the number of satellite transmitting antennas
  • g c,k represents the precoding matrix from satellite c to user k in cell c
  • sc c,k represents the transmitted signal from satellite c to user k in cell c
  • n c , k is the noise at user k in cell c
  • [ ⁇ ] H represents the conjugate transpose of matrix [ ⁇ ];
  • Step 1.2 Initialize the input conditions of the multi-satellite cooperative transmission system
  • the input conditions include the limitation of satellite transmission power, denoted as P c ; and the instantaneous channel matrix of n groups of satellites to ground users Expressed by formula (2);
  • ⁇ c, c, k represent the path loss from satellite c to user k in cell c
  • ⁇ represents the Rice factor
  • I 1 ⁇ M represents a unit matrix with 1 row and M columns
  • Z c, c, k represent the mean value of 0 , a Gaussian vector with variance 1;
  • Step 2 Initialize the statistical information of the channel according to multiple sets of instantaneous channel information
  • Step 2.1 According to multiple sets of instantaneous channel information, initialize the mean value matrix of the channel by formula (3):
  • Step 2.2 According to multiple sets of instantaneous channel information and the mean matrix of the channel obtained in step 2.1 The covariance matrix of the channel is initialized by formula (4):
  • ⁇ c, c, k is the channel transmission covariance matrix of satellite c to user k in cell c;
  • Step 3 all satellites use the statistical information of the channel obtained in step 2 to calculate the signal power, interference signal power and signal-to-interference-noise ratio SINR of the serving user through matched filtering MF;
  • Step 3.1 The mean matrix obtained from step 2 Covariance matrix ⁇ c,c,k , through the formula (5), calculate the power normalization factor;
  • Step 3.2 According to the mean matrix obtained in step 2 Covariance matrix ⁇ c, c, k and the normalization factor obtained in step 3.1 Calculate the signal power of the user by formula (6);
  • Step 3.3 The mean matrix obtained from step 2 Covariance matrix ⁇ c, c, k and the normalization factor obtained in step 3.1 Calculate the interference signal power of the user by formula (7);
  • Step 3.4 According to the signal power obtained in step 3.2 Get the interfering signal power with step 3.3 Calculate the user's SINR by formula (8);
  • Step 4 initialize the convergence accuracy threshold and the maximum number of iterations
  • the convergence accuracy threshold is denoted as ⁇
  • the maximum number of iterations is denoted as ⁇ ;
  • Step 5 Apply the deterministic equivalent DE theorem to approximate the iterative process of the traditional weighted minimum mean square error WMMSE. After each round of iteration, the satellites replace the large-dimensional instantaneous channel matrix with auxiliary variables in the form of interactive scalars, which significantly reduces The amount of information exchanged between small stars;
  • Step 5.1 According to the signal power obtained in step 3 SINR All satellites independently calculate the receiving filter matrix, weights and values of variables that need to interact with other satellites for their service users;
  • Step 5.1.1 According to the signal power obtained in step 3 SINR Calculate the receiving filter matrix of the user by formula (9);
  • Step 5.1.2 According to the SINR obtained in step 3 Calculate the user's weight by formula (10);
  • Step 5.1.3 receive filter matrix obtained according to 5.1.1 and the user weight obtained in 5.1.2 Calculate the value of the auxiliary variable by formula (11);
  • Step 5.2 All satellites iterate through three sets of fixed-point equations until the results converge, so as to solve the values of auxiliary variables;
  • Step 5.2.1 given auxiliary variable E( ⁇ 2 ) and After the initial value, Equation (12) and Equation (13) are iteratively updated until the two converge, and the converged auxiliary variable T( ⁇ 2 ) and Finally substitute into formula (14) and formula (15), (16) to calculate auxiliary variable m c, c, k , n c, c, k and n m, c, k, m, l ;
  • I M is a unit matrix with M rows and M columns, It is a diagonal matrix of KC rows and KC columns, and its diagonal elements are in order in in diag[ ] represents a diagonal matrix composed of elements in matrix [ ], and [ ] -1 represents the inverse matrix of matrix [ ];
  • Step 5.2.2 Given auxiliary variable E'( ⁇ 2 ) and After the initial value, Equation (17) and Equation (18) are iteratively updated until the two converge, and the converged auxiliary variable T'( ⁇ 2 ) is calculated, and finally substituted into Equation (19) and Equation (20) to calculate the auxiliary variable m' c, c, k and n' c, c, k ;
  • Step 5.2.3 given auxiliary variable E'(Z) and After the initial value, Equation (21) and Equation (22) are iteratively updated until the two converge, and the converged auxiliary variable T'(Z) is calculated, and finally substituted into the formula (23) to calculate the auxiliary variable m' m,c, k,m,l ;
  • Step 5.3 Each satellite updates the power normalization factor, signal power, interference signal power, and SINR of its serving users according to the auxiliary variable obtained in step 5.2;
  • Step 5.3.1 according to the auxiliary variable obtained in step 5.2, calculate the user's power normalization factor by formula (24);
  • Step 5.3.2 According to the auxiliary variable obtained in step 5.2 and the power normalization factor obtained in step 5.3.1, calculate the signal power of the user by formula (25);
  • Step 5.3.3 according to the auxiliary variable obtained in step 5.2, calculate the interference signal power of the user by formula (26);
  • Step 5.3.4 According to the signal power obtained in step 5.3.2 Get the interfering signal power with step 5.3.3 Calculate the user's SINR by formula (28);
  • Step 5.4 Auxiliary variables in the form of interactive scalars between satellites Instead of large-dimensional instantaneous channel matrix, receiving filter matrix and user weight On the basis of significantly reducing the amount of information exchanged between satellites, complete the information exchange between satellites;
  • Step 6 Determine whether the SINR in formula (28) is convergent, that is, whether the difference between the optimized SINR value and the SINR value before updating is less than the convergence accuracy threshold ⁇ or reaches the maximum number of iterations ⁇ , and if so, output the converged receiving filter If the device matrix and user weights are used, proceed to step 7; otherwise, return to step 5;
  • Step 7 Calculate the precoding matrix according to the converged receiving filter matrix and user weights output in step 6 and the current set of instantaneous channel information, and realize distributed multi-satellite joint beamforming according to the precoding matrix;
  • Step 7.1 According to the converged auxiliary variables output from step 6 With the current set of instantaneous channel information, the auxiliary variable ⁇ c is calculated by formula (29);
  • H c [h c,1,1 ,...,h c,1,K ,h c,2,1 ,...,h c,2,K ,...,h c,C, K ]
  • H ,h c,i,j is the instantaneous channel matrix from satellite c to user j in cell i
  • Step 7.2 Converged auxiliary variables according to the output of step 6 With the auxiliary variable ⁇ c obtained in step 7.1, the precoding matrix is calculated by formula (30);
  • Step 7.3 Realize distributed multi-satellite joint beamforming according to the precoding matrix obtained in step 7.2;
  • Step 8 According to the above steps, the distributed multi-satellite joint beamforming under the multi-satellite system is realized, which effectively reduces inter-beam interference and improves the throughput of the overall system.
  • a distributed multi-satellite joint beamforming method disclosed in the present invention uses the deterministic equivalent DE theorem to The traditional weighted minimum mean square error (WMMSE) iterative process is approximated.
  • WMMSE weighted minimum mean square error
  • the satellites After each round of iteration, the satellites replace the large-dimensional instantaneous channel matrix with auxiliary variables in the form of interactive scalars, which significantly reduces the amount of inter-satellite interaction information; according to
  • the receiving filter matrix and user weights and the current set of instantaneous channel information can calculate the precoding matrix without multiple sets of instantaneous channel information, effectively solving the problem of obtaining instantaneous channel information, thereby saving the time and cost of obtaining instantaneous channel information cost.
  • a distributed multi-satellite joint beamforming method disclosed in the present invention performs distributed multi-satellite joint beamforming according to the precoding matrix obtained in beneficial effect 1 shape, which can significantly reduce the inter-beam interference suffered by users in a multi-satellite system, thereby obtaining higher communication throughput.
  • FIG. 1 is a flow chart of a distributed multi-satellite joint beamforming method and the DE approximate overall method proposed in Embodiment 1 of the present invention
  • Fig. 2 is a comparison diagram of the amount of information that needs to be interacted after each round of iterations using the WMMSE optimal method and the DE approximation method proposed in Embodiment 1;
  • FIG. 3 is a CDF comparison diagram of the system transmission rate under 500 groups of channels using the DE approximation method proposed in Embodiment 1, the WMMSE optimal method, and the non-cooperative method.
  • This embodiment describes in detail the steps in the specific implementation of a distributed multi-satellite joint beamforming method described in the present invention.
  • FIG. 1 is a flow chart of a distributed multi-satellite joint beamforming method and the overall method of Embodiment 1 according to the present invention
  • Step 1 Initialize the composition structure and input conditions of the multi-satellite cooperative transmission system
  • Step 1.1 Initialize the composition structure of the multi-satellite cooperative transmission system
  • composition structure of the multi-satellite cooperative transmission system is the communication system model, including the instantaneous channel matrix from the satellite to the ground user, the signal transmitted by the satellite, the signal received by the ground user, the precoding matrix of the ground user served by the satellite, and the noise at the user.
  • the communication system model including the instantaneous channel matrix from the satellite to the ground user, the signal transmitted by the satellite, the signal received by the ground user, the precoding matrix of the ground user served by the satellite, and the noise at the user.
  • Step 1.2 Initialize the input conditions of the multi-satellite cooperative transmission system
  • Step 2 Initialize the statistical information of the channel
  • Step 2.1 According to multiple sets of instantaneous channel information, initialize the mean value matrix of the channel by formula (3):
  • M 30, that is, 30 ⁇ 1
  • M 30, that is, 30 ⁇ 1
  • n 500 groups of instantaneous channels
  • Step 2.2 According to multiple sets of instantaneous channel information and the mean matrix of the channel obtained in step 2.1 The covariance matrix of the channel is initialized by formula (4):
  • Step 3 All satellites use the statistical information of the channel obtained in step 2 to calculate the signal power, interference signal power and signal-to-interference-noise ratio SINR of the serving user through matched filtering MF;
  • Step 3.1 The mean matrix obtained from step 2 Covariance matrix ⁇ c,c,k , through the formula (5), calculate the power normalization factor;
  • Step 3.2 According to the mean matrix obtained in step 2 Covariance matrix ⁇ c, c, k and the normalization factor obtained in step 3.1 Calculate the signal power of the user by formula (6);
  • Step 3.3 The mean matrix obtained from step 2
  • the covariance matrix ⁇ c,c,k calculates the interference signal power of the user through the formula (7);
  • Step 3.4 According to the signal power obtained in step 3.2 Get the interfering signal power with step 3.3 Calculate the user's SINR by formula (8);
  • Step 5 Apply the deterministic equivalent DE theorem to approximate the iterative process of the traditional weighted minimum mean square error WMMSE. After each iteration, the satellites replace the large-dimensional instantaneous channel matrix with auxiliary variables in the form of interactive scalars, which significantly reduces The amount of information exchanged between small stars;
  • Step 5.1.1 According to the signal power obtained in step 3 SINR Calculate the receiving filter matrix of the user by formula (9);
  • Step 5.1.2 According to the SINR obtained in step 3 Calculate the user's weight by formula (10);
  • Step 5.1.3 receive filter matrix obtained according to 5.1.1 and the user weight obtained in 5.1.2 Calculate the value of the auxiliary variable by formula (11);
  • Step 5.2 All satellites iterate through three sets of fixed-point equations until the results converge, so as to solve the values of auxiliary variables.
  • Step 5.2.1 Set the auxiliary variable E( ⁇ 2 ) and initial value of Equation (12) and equation (13) are iteratively updated until the two converge, and the converged auxiliary variable T( ⁇ 2 ) and Finally substitute into formula (14) and formula (15), (16) to calculate auxiliary variable m c, c, k , n c, c, k and n m, c, k, m, l ;
  • Step 5.3 Each satellite updates the power normalization factor, signal power, interference signal power, and SINR of its serving users according to the auxiliary variables obtained in step 5.2;
  • Step 5.3.1 according to the auxiliary variable obtained in step 5.2, calculate the power normalization factor by formula (24);
  • Step 5.3.2 Calculate the signal power of the user by formula (25) according to the auxiliary variable obtained in step 5.2;
  • Step 5.3.3 according to the auxiliary variable obtained in step 5.2, calculate the interference signal power of the user by formula (26);
  • Step 5.3.4 calculate the user's SINR by formula (28);
  • Step 5.4 Auxiliary variables in the form of interactive scalars between satellites Instead of large-dimensional instantaneous channel matrix, receiving filter matrix and user weight On the basis of significantly reducing the amount of information exchanged between satellites, complete the information exchange between satellites;
  • Step 6 Determine whether the SINR in formula (28) is convergent, that is, whether the difference between the optimized SINR value and the SINR value before updating is less than the convergence accuracy threshold ⁇ or reaches the maximum number of iterations ⁇ , and if so, output the converged receiving filter If the user matrix and user weights are used, proceed to step 7, otherwise skip to step 5;
  • Step 7 Converged auxiliary variables according to the output of step 6 And the current set of instantaneous channel information calculates the precoding matrix, and realizes distributed multi-satellite joint beamforming according to the precoding matrix;
  • Step 7.1 According to the converged receiving filter matrix output in step 6 user weight With the current set of instantaneous channel information, the auxiliary variable ⁇ c is calculated by formula (29);
  • H c [h c,1,1 ,...,h c,1,K ,h c,2,1 ,...,h c,2,K ,...,h c,C, K ] H
  • h c, i, j are the instantaneous channel matrix from satellite c to user j in cell i
  • Step 7.2 According to the converged receiving filter matrix output in step 6 user weight With the auxiliary variable ⁇ c obtained in step 7.1, the precoding matrix is calculated by formula (30);
  • Step 7.3 Realize distributed multi-satellite joint beamforming according to the precoding matrix obtained in step 7.2;
  • Step 8 According to the above steps, the distributed multi-satellite joint beamforming under the multi-satellite system is realized, which effectively reduces inter-beam interference and improves the throughput of the overall system.
  • Fig. 2 shows the comparison result of the amount of information that needs to be exchanged after each round of iterations using the WMMSE optimal method and the DE approximation method proposed in Example 1;
  • satellite c in Figure 2 needs to Send receive filter matrix a c,k (k ⁇ K c ), weights w c,k (k ⁇ K c ), and instantaneous channel matrix h c,c,k (k ⁇ K c ) to satellite m, where a c, k and w c, k are scalars, h c, c, k are a 1 ⁇ M complex matrix,
  • FIG. 3 is a CDF comparison diagram of the system transmission rate under 500 groups of channels using the DE approximation method proposed in Embodiment 1, the WMMSE optimal method, and the non-cooperative method.
  • the non-cooperative method means that there is no cooperative transmission between multiple satellites.
  • the abscissa of the image is the transmission rate, and the ordinate is the cumulative distribution probability.
  • the transmission rate of the DE approximation method is concentrated at 13.2 nats/s/ Near Hz
  • adopt the transmission rate of non-cooperative method to concentrate on the vicinity of 3.9nats/s/Hz
  • adopt the transmission rate of WMMSE optimum method to concentrate on the vicinity of 13.8nats/s/Hz therefore can draw a conclusion: 1) adopt the method of the present invention Compared with the non-cooperative method, the transmission rate can be increased by about 3 times, and the throughput is significantly improved; 2) Compared with the optimal MMSE method, the method of the present invention only sacrifices about 5% of the performance, but can significantly reduce the interaction between satellites amount of information.
  • a distributed multi-satellite joint beamforming method of the present invention can effectively reduce inter-beam interference through multi-satellite joint beamforming, improve the throughput of the overall system, and can solve the problem of large inter-beam interference existing in multi-satellite systems, and In the traditional multi-satellite cooperative transmission technology, the signaling interaction burden is too large and the technical problems of obtaining instantaneous channel information are difficult. It has a wide range of applications and has good industrial practicability.

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Abstract

本发明公开的一种分布式多卫星联合波束赋形方法，属于卫星网络架构下多星多波束协作传输技术领域。本发明实现方法为：通过应用确定性等价DE定理对传统的加权最小均方误差WMMSE的迭代过程进行近似，在每轮迭代后，卫星间通过交互标量形式的辅助变量代替大维的瞬时信道矩阵，显著减小星间交互的信息量；迭代收敛后，通过接收滤波器矩阵和用户权值以及一组瞬时信道信息计算预编码矩阵，根据预编码矩阵实现分布式多卫星联合波束赋形。此外，通过多星间联合波束赋形有效减少波束间干扰，提高整体系统的吞吐量。本发明能够解决多星系统中存在的波束间干扰较大，以及传统的多星协作传输技术中信令交互负担过大、获取瞬时信道信息困难的技术问题。

Description

一种分布式多卫星联合波束赋形方法 技术领域
本发明涉及一种分布式多卫星联合波束赋形方法，属于卫星网络架构下多星多波束协作传输技术领域。
背景技术
下一代高吞吐量卫星(HTS)系统需要提供超高数据速率服务，以满足偏远地区高带宽多媒体应用的需求，并与下一代地面通信系统(如5G技术及更高技术)集成。为此，多波束卫星通信(SatCom)系统已成为一个强有力的解决方案，一些目前正在运行的多波束HTS系统例如Wildblue-1和Anik F2，可以覆盖美国部分地区66个点波束。由于多波束天线辐射方向图旁瓣的影响，该技术会产生较强的波束间干扰(IBI)，目前运行的多波束卫星通信系统通常采用四色或更高频率的复用来降低IBI。然而，在下一代HTS系统中，为了实现高频谱效率和吞吐量，需要采取全频率复用(FFR)，以便每个波束充分利用整个可用带宽。目前，已有许多工作研究了HTS系统中用于抑制IBI的各种多用户检测和波束赋形技术，Ishtiaq Ahmad等人分析了采用迫零(ZF)预编码的平均和速率性能，D.Christopoulos则研究了在莱斯信道下采用最小均方误差(MMSE)接收机的性能。上述研究表明，对于单星系统而言，这些方法可以有效降低IBI，但对于存在两颗及以上的多星系统而言，如何降低不同卫星波束间的干扰，提高整体系统的吞吐量仍是一个待解决的难题。
多星协作传输技术作为提升卫星传输速率的一种新型技术，有着重要的应用前景。传统的卫星通信一般采用单星服务一个用户，这对用户的数据传输速率和容量带来一定的限制，卫星资源的使用效率也未能充分利用。为了进一步利用卫星的空间传输特性，可以让一个终端同时连接在编队多颗卫星上。这些卫星通过协作实现联合数据传输，获得分集增益或者复用增益。Maik R per等人设计了一种分布式MMSE波束赋形算法，其中多个卫星协同传输用户数据。研究结果表明该算法可以显著提升和速率性能，但它需要卫星间进行大量的信令交互，以及各卫星在迭代计算中多次获取瞬时的信道信息，这对于当前的卫星系统而言是一项巨大的挑战。
发明内容
针对多星系统中存在的波束间干扰较大，以及传统的多星协作传输技术中信令交互负担过大、获取瞬时信道信息困难的技术缺陷，本发明的目的在于提供一种分布式多卫星联合波束赋形方法，通过应用确定性等价DE定理对传统的加权最小均方误差WMMSE的迭代过程进行近似，在每轮迭代后，卫星间通过交互标量形式的辅助变量代替大维的瞬时信道矩阵，显著减小星间交互的信息量；迭代收敛后，通过接收滤波器矩阵和用户权值以及一组瞬时信道信息计算预编码矩阵，根据预编码矩阵实现分布式多卫星联合波束赋形。此外，通过多星间联合波束赋形有效减少波束间干扰，提高整体系统的吞吐量。
本发明的目的是通过下述技术方案实现的。
本发明公开的一种分布式多卫星联合波束赋形方法，包括以下步 骤：
步骤1、初始化多星协作传输系统的组成架构及输入条件；
步骤1.1：初始化多星协作传输系统的组成架构；
多星协作传输系统的组成架构即通信系统模型，包括卫星到地面用户的瞬时信道矩阵、卫星发射信号、地面用户接收信号、卫星对其服务的地面用户的预编码矩阵以及用户处的噪声，通过公式(1)表示：
Figure PCTCN2022092303-appb-000001
卫星集合为Λ＝{1,2,...C}，其中卫星c服务的用户集合为K c＝{1,2,...K}，y c,k为卫星c服务的小区c中用户k的接收信号，M为卫星发射天线数，g c,k表示卫星c到小区c中用户k的预编码矩阵，s c,k表示卫星c向小区c中用户k的发射信号，n c,k为小区c中用户k处的噪声，[·] H表示矩阵[·]的共轭转置；
步骤1.2：初始化多星协作传输系统的输入条件；
其中，输入条件包括卫星发射功率限制，记为P c；以及n组卫星到地面用户的瞬时信道矩阵
Figure PCTCN2022092303-appb-000002
由公式(2)表示；
Figure PCTCN2022092303-appb-000003
其中Ξ c,c,k表示卫星c到小区c中用户k的路径损耗，τ表示莱斯因子，I 1×M表示1行M列的单位阵，Z c,c,k表示服从均值为0，方差为1的高斯向量；
步骤2、根据多组瞬时信道信息初始化信道的统计信息；
步骤2.1：根据多组瞬时信道信息，通过公式(3)初始化信道的均值矩阵：
Figure PCTCN2022092303-appb-000004
其中
Figure PCTCN2022092303-appb-000005
表示卫星c到小区c中用户k的信道均值矩阵，
Figure PCTCN2022092303-appb-000006
表示第i组瞬时信道信息；
步骤2.2：根据多组瞬时信道信息以及步骤2.1得到的信道的均值矩阵
Figure PCTCN2022092303-appb-000007
通过公式(4)初始化信道的协方差矩阵：
Figure PCTCN2022092303-appb-000008
其中Θ c,c,k为卫星c到小区c中用户k的信道发射协方差矩阵；
步骤3、所有卫星各自利用步骤2得到的信道的统计信息，通过匹配滤波MF计算服务用户的信号功率、干扰信号功率和信干噪比SINR；
步骤3.1：根据步骤2得到的均值矩阵
Figure PCTCN2022092303-appb-000009
协方差矩阵Θ c,c,k，通过公式(5)，计算功率归一化因子；
Figure PCTCN2022092303-appb-000010
其中
Figure PCTCN2022092303-appb-000011
为卫星c的功率归一化因子，P c为卫星发射功率，trace[·]表示矩阵[·]的迹；
步骤3.2：根据步骤2得到的均值矩阵
Figure PCTCN2022092303-appb-000012
协方差矩阵Θ c,c,k与步骤3.1得到的归一化因子
Figure PCTCN2022092303-appb-000013
通过公式(6)，计算用户的信号功率；
Figure PCTCN2022092303-appb-000014
其中
Figure PCTCN2022092303-appb-000015
为c小区中用户k的信号功率；
步骤3.3：根据步骤2得到的均值矩阵
Figure PCTCN2022092303-appb-000016
协方差矩阵Θ c,c,k与步骤3.1得到的归一化因子
Figure PCTCN2022092303-appb-000017
通过公式(7)计算用户的干扰信号功率；
Figure PCTCN2022092303-appb-000018
其中，
Figure PCTCN2022092303-appb-000019
为c小区中用户k的干扰信号功率；
步骤3.4：根据步骤3.2得到的信号功率
Figure PCTCN2022092303-appb-000020
与步骤3.3得到干扰信号功率
Figure PCTCN2022092303-appb-000021
通过公式(8)，计算用户的SINR；
Figure PCTCN2022092303-appb-000022
其中，
Figure PCTCN2022092303-appb-000023
表示c小区中用户k的SINR，σ 2为噪声功率；
步骤4、初始化收敛精度阈值以及最大迭代次数；
其中，收敛精度阈值，记为ε,最大迭代次数，记为γ；
步骤5、应用确定性等价DE定理对传统的加权最小均方误差WMMSE的迭代过程进行近似，在每轮迭代后，卫星间通过交互标量形式的辅助变量代替大维的瞬时信道矩阵，显著减小星间交互的信息量；
步骤5.1：根据步骤3得到的信号功率
Figure PCTCN2022092303-appb-000024
与信干噪比
Figure PCTCN2022092303-appb-000025
所有卫星各自计算其服务用户的接收滤波器矩阵、权值及需要与其他卫星交互的变量的值；
步骤5.1.1:根据步骤3得到的信号功率
Figure PCTCN2022092303-appb-000026
与信干噪比
Figure PCTCN2022092303-appb-000027
通过公式(9)计算用户的接收滤波器矩阵；
Figure PCTCN2022092303-appb-000028
其中，
Figure PCTCN2022092303-appb-000029
表示c小区中用户k的接收滤波器矩阵；
步骤5.1.2:根据步骤3得到的信干噪比
Figure PCTCN2022092303-appb-000030
通过公式(10)计算用户的权值；
Figure PCTCN2022092303-appb-000031
其中
Figure PCTCN2022092303-appb-000032
表示卫星c服务的用户k的权值；
步骤5.1.3:根据5.1.1得到的接收滤波器矩阵
Figure PCTCN2022092303-appb-000033
与5.1.2得到的用户权值
Figure PCTCN2022092303-appb-000034
通过公式(11)计算辅助变量的值；
Figure PCTCN2022092303-appb-000035
其中
Figure PCTCN2022092303-appb-000036
表示卫星c服务的用户k的辅助变量。
步骤5.2：所有卫星各自通过三组固定点方程进行迭代，直至结果收敛，从而求解辅助变量的值；
步骤5.2.1:给定辅助变量E(σ 2)与
Figure PCTCN2022092303-appb-000037
初始值后，通过方程(12)与方程(13)进行迭代更新，直至二者收敛，计算收敛后的辅助变量T(σ 2)与
Figure PCTCN2022092303-appb-000038
最后代入公式(14)与公式(15)、(16)计算辅助变量m c,c,k、n c,c,k与n m,c,k,m,l；
Figure PCTCN2022092303-appb-000039
Figure PCTCN2022092303-appb-000040
m c,c,k＝trace(Θ c,c,kT(σ 2))        (14)
Figure PCTCN2022092303-appb-000041
Figure PCTCN2022092303-appb-000042
其中，
Figure PCTCN2022092303-appb-000043
D＝I M，I M为一个M行M列的单位阵，
Figure PCTCN2022092303-appb-000044
为一KC行KC列的对角阵，且其对角元素依次为
Figure PCTCN2022092303-appb-000045
其中
Figure PCTCN2022092303-appb-000046
其中
Figure PCTCN2022092303-appb-000047
Figure PCTCN2022092303-appb-000048
diag[·]表示由矩阵[·]中的元素组成的对角矩阵，[·] -1表示矩阵[·]的逆矩阵；
步骤5.2.2:给定辅助变量E'(σ 2)与
Figure PCTCN2022092303-appb-000049
初始值后，通过方程(17)与方程(18)进行迭代更新，直至二者收敛，计算收敛后的辅助变量T'(σ 2)，最后代入公式(19)与公式(20)计算辅助变量m' c,c,k与n′ c,c,k；
Figure PCTCN2022092303-appb-000050
Figure PCTCN2022092303-appb-000051
m' c,c,k＝trace(Θ c,c,kT'(σ 2))         (19)
Figure PCTCN2022092303-appb-000052
其中辅助变量E(σ 2)、
Figure PCTCN2022092303-appb-000053
T(σ 2)、
Figure PCTCN2022092303-appb-000054
均为步骤5.2.1中固定点方程经过迭代收敛后的结果；
步骤5.2.3:给定辅助变量E'(Z)与
Figure PCTCN2022092303-appb-000055
初始值后，通过方程(21)与方程(22)进行迭代更新，直至二者收敛，计算收敛后的辅助变量T'(Z)，最后代入公式(23)计算辅助变量m' m,c,k,m,l；
Figure PCTCN2022092303-appb-000056
Figure PCTCN2022092303-appb-000057
Figure PCTCN2022092303-appb-000058
其中辅助变量E(Z)、
Figure PCTCN2022092303-appb-000059
T(Z)、
Figure PCTCN2022092303-appb-000060
均为步骤5.2.1中固定点方程经过迭代收敛后的结果；
步骤5.3：各卫星根据步骤5.2得到的辅助变量更新其服务用户 的功率归一化因子、信号功率、干扰信号功率、以及SINR；
步骤5.3.1:根据步骤5.2得到的辅助变量，通过公式(24)计算用户的功率归一化因子；
Figure PCTCN2022092303-appb-000061
步骤5.3.2:根据步骤5.2得到的辅助变量以及步骤5.3.1得到的功率归一化因子，通过公式(25)计算用户的信号功率；
Figure PCTCN2022092303-appb-000062
步骤5.3.3:根据步骤5.2得到的辅助变量，通过公式(26)计算用户的干扰信号功率；
Figure PCTCN2022092303-appb-000063
其中，L m,c,k,m,l通过公式(27)计算：
Figure PCTCN2022092303-appb-000064
步骤5.3.4:根据步骤5.3.2得到的信号功率
Figure PCTCN2022092303-appb-000065
与步骤5.3.3得到干扰信号功率
Figure PCTCN2022092303-appb-000066
通过公式(28)计算用户的SINR；
Figure PCTCN2022092303-appb-000067
步骤5.4：卫星间通过交互标量形式的辅助变量
Figure PCTCN2022092303-appb-000068
代替大维的 瞬时信道矩阵、接收滤波器矩阵
Figure PCTCN2022092303-appb-000069
和用户权值
Figure PCTCN2022092303-appb-000070
在显著减小星间交互的信息量基础上，完成卫星间信息交互；
步骤6、判断公式(28)中的SINR是否收敛，即优化后的SINR值与更新前的SINR值的差是否小于收敛精度阈值ε或达到最大迭代次数γ，若是，则输出收敛后的接收滤波器矩阵和用户权值，进行步骤7；否则返回至步骤5；
步骤7、根据步骤6输出的收敛后的接收滤波器矩阵和用户权值以及当前的一组瞬时信道信息计算预编码矩阵，根据预编码矩阵实现分布式多卫星联合波束赋形；
步骤7.1：根据步骤6输出的收敛后的辅助变量
Figure PCTCN2022092303-appb-000071
与当前一组瞬时信道信息，通过公式(29)计算辅助变量Γ c；
Figure PCTCN2022092303-appb-000072
其中H c＝[h c,1,1,...,h c,1,K,h c,2,1,...,h c,2,K,...,h c,C,K] H,h c,i,j为卫星c到小区i中的用户j的瞬时信道矩阵，
Figure PCTCN2022092303-appb-000073
Figure PCTCN2022092303-appb-000074
步骤7.2：根据步骤6输出的收敛后的辅助变量
Figure PCTCN2022092303-appb-000075
与步骤7.1得到的辅助变量Γ c，通过公式(30)计算预编码矩阵；
Figure PCTCN2022092303-appb-000076
其中，
Figure PCTCN2022092303-appb-000077
为卫星c对它服务用户k的预编码矩阵，ξ c为功率归一化因子，
Figure PCTCN2022092303-appb-000078
步骤7.3：根据步骤7.2得到的预编码矩阵实现分布式多卫星联合波束赋形；
步骤8、根据上述步骤实现了多星系统下的分布式多卫星联合波束赋形，有效减少波束间干扰，提高整体系统的吞吐量。
有益效果：
1、针对多星协作传输技术中信令交互负担过大、获取瞬时信道信息困难的技术缺陷，本发明公开的一种分布式多卫星联合波束赋形方法，通过应用确定性等价DE定理对传统的加权最小均方误差WMMSE的迭代过程进行近似，在每轮迭代后，卫星间通过交互标量形式的辅助变量代替大维的瞬时信道矩阵，显著减小星间交互的信息量；根据收敛后的接收滤波器矩阵和用户权值以及当前一组瞬时信道信息，无需多组瞬时信道信息，即能够计算预编码矩阵，有效解决获取瞬时信道信息困难的问题，进而节约获取瞬时信道信息的时间与成本。
2、针对多星系统中存在的波束间干扰较大的问题，本发明公开的一种分布式多卫星联合波束赋形方法，按照有益效果1获得的预编码矩阵进行分布式多卫星联合波束赋形，能够使多星系统中用户受到的波束间干扰显著减少，从而获得更高的通信吞吐量。
附图说明
图1为本发明一种分布式多卫星联合波束赋形方法及实施例1中提出的DE近似整体方法流程图；
图2为采用WMMSE最优方法与实施例1中提出的DE近似方法在每轮迭代后需要交互的信息量的对比图；
图3为采用实施例1中提出的DE近似方法、WMMSE最优方法、以及非协作方法在500组信道下的系统传输速率CDF对比图。
具体实施方式
下面结合附图和具体实施例对本发明所述的一种分布式多卫星联合波束赋形方法进行详细说明。
实施例1
本实施例详细阐述了本发明所述的一种分布式多卫星联合波束赋形方法具体实施时的步骤。
本实例考虑一个多星协作传输系统，设置该系统中共三颗卫星进行协同传输，即C＝3，每颗卫星向地面小区中发射十路波束，并且假设该小区中共十名用户分别接收该十路波束，即K＝10，卫星天线数设置为M＝30，通过对WMMSE迭代过程进行近似，不仅使得系统整体的吞吐量提高，并且保证了较小的信令交互负担；
图1为本发明所述的一种分布式多卫星联合波束赋形方法及实施例1整体方法流程图；
如图1所示，本实施例公开的一种分布式多卫星联合波束赋形方法，具体实现步骤如下：
步骤1：初始化多星协作传输系统的组成架构及输入条件；
步骤1.1：初始化多星协作传输系统的组成架构；
其中多星协作传输系统的组成架构即通信系统模型，包括卫星到地面用户的瞬时信道矩阵、卫星发射信号、地面用户接收信号、卫星对其服务的地面用户的预编码矩阵以及用户处的噪声，通过公式(1) 表示：
Figure PCTCN2022092303-appb-000079
设置该系统中卫星数C＝3，即卫星集合Λ＝{1,2,3}，单颗卫星服务的地面用户数K＝10，即用户集合K c＝{1,2,...10}，y c,k为标量，表示卫星c服务的小区c中用户k的接收信号，设置卫星发射天线数M＝30，g c,k为一M×1(M＝30,即30×1)的复数矩阵，表示卫星c到小区c中用户k的预编码矩阵，s c,k为标量，表示卫星c向小区c中的用户k的发射信号，n c,k为标量，表示小区c中的用户k处的噪声，
Figure PCTCN2022092303-appb-000080
为一1×M(M＝30,即1×30)的复数矩阵，表示卫星c到小区c中的用户k的信道矩阵；
步骤1.2：初始化多星协作传输系统的输入条件；
初始化卫星发射功率P c＝10W；以及n＝500组卫星到地面用户的瞬时信道矩阵
Figure PCTCN2022092303-appb-000081
其中Ξ c,c,k表示卫星c到小区c中用户k的路径损耗，由STK仿真平台提供，τ表示莱斯因子，并设置τ＝1，I 1×M表示1行M列的单位阵(M＝30)，Z c,c,k为一1×M(M＝30,即1×30)的复数矩阵，其中每个元素为服从均值为0，方差为1的高斯向量；
步骤2：初始化信道的统计信息；
步骤2.1：根据多组瞬时信道信息，通过公式(3)初始化信道的均值矩阵：
Figure PCTCN2022092303-appb-000082
其中
Figure PCTCN2022092303-appb-000083
为一M×1(M＝30,即30×1)的复数矩阵，表示卫星c到小区c中用户k的信道均值矩阵，
Figure PCTCN2022092303-appb-000084
表示第i组瞬时信道信息，共n＝500组瞬时信道；
步骤2.2：根据多组瞬时信道信息以及步骤2.1得到的信道的均值矩阵
Figure PCTCN2022092303-appb-000085
通过公式(4)初始化信道的协方差矩阵:
Figure PCTCN2022092303-appb-000086
其中Θ c,c,k为一M×M(M＝30,即30×30)的复数矩阵，表示卫星c到小区c中的用户k的信道发射协方差矩阵；
步骤3：所有卫星各自利用步骤2得到的信道的统计信息，通过匹配滤波MF计算服务用户的信号功率、干扰信号功率和信干噪比SINR；
步骤3.1：根据步骤2得到的均值矩阵
Figure PCTCN2022092303-appb-000087
协方差矩阵Θ c,c,k，通过公式(5)，计算功率归一化因子；
Figure PCTCN2022092303-appb-000088
其中
Figure PCTCN2022092303-appb-000089
为卫星c的功率归一化因子；
步骤3.2：根据步骤2得到的均值矩阵
Figure PCTCN2022092303-appb-000090
协方差矩阵Θ c,c,k与步骤3.1得到的归一化因子
Figure PCTCN2022092303-appb-000091
通过公式(6)，计算用户的信号功率；
Figure PCTCN2022092303-appb-000092
其中
Figure PCTCN2022092303-appb-000093
为小区c中的用户k的信号功率；
步骤3.3：根据步骤2得到的均值矩阵
Figure PCTCN2022092303-appb-000094
协方差矩阵Θ c,c,k，通过公式(7)，计算用户的干扰信号功率；
Figure PCTCN2022092303-appb-000095
其中，
Figure PCTCN2022092303-appb-000096
为c小区中的用户k的干扰信号功率；
步骤3.4：根据步骤3.2得到的信号功率
Figure PCTCN2022092303-appb-000097
与步骤3.3得到干扰信号功率
Figure PCTCN2022092303-appb-000098
通过公式(8)，计算用户的SINR；
Figure PCTCN2022092303-appb-000099
其中，
Figure PCTCN2022092303-appb-000100
表示c小区中用户k的SINR，σ 2表示噪声功率，设置σ 2＝1.1943×10 -13W；
步骤4：初始化收敛精度阈值ε＝0.1以及最大迭代次数γ＝20；
步骤5：应用确定性等价DE定理对传统的加权最小均方误差WMMSE的迭代过程进行近似，在每轮迭代后，卫星间通过交互标量形式的辅助变量代替大维的瞬时信道矩阵，显著减小星间交互的信息量；
步骤5.1.1:根据步骤3得到的信号功率
Figure PCTCN2022092303-appb-000101
与信干噪比
Figure PCTCN2022092303-appb-000102
通过公式(9)计算用户的接收滤波器矩阵；
Figure PCTCN2022092303-appb-000103
其中，
Figure PCTCN2022092303-appb-000104
表示c小区中用户k的接收滤波器矩阵；
步骤5.1.2:根据步骤3得到的信干噪比
Figure PCTCN2022092303-appb-000105
通过公式(10)计算用户的权值；
Figure PCTCN2022092303-appb-000106
步骤5.1.3:根据5.1.1得到的接收滤波器矩阵
Figure PCTCN2022092303-appb-000107
与5.1.2得到的用户权值
Figure PCTCN2022092303-appb-000108
通过公式(11)计算辅助变量的值；
Figure PCTCN2022092303-appb-000109
其中
Figure PCTCN2022092303-appb-000110
表示卫星c服务的用户k的辅助变量；
步骤5.2：所有卫星各自通过三组固定点方程进行迭代，直至结果收敛，从而求解辅助变量的值。
步骤5.2.1:设置辅助变量E(σ 2)与
Figure PCTCN2022092303-appb-000111
的初始值
Figure PCTCN2022092303-appb-000112
通过方程(12)与方程(13)进行迭代更新，直至二者收敛，计算收敛后的辅助变量T(σ 2)与
Figure PCTCN2022092303-appb-000113
最后代入公式(14)与公式(15)、(16)计算辅助变量m c,c,k、n c,c,k与n m,c,k,m,l；
(12)
Figure PCTCN2022092303-appb-000114
m c,c,k＝trace(Θ c,c,kT(σ 2))       (14)
Figure PCTCN2022092303-appb-000115
Figure PCTCN2022092303-appb-000116
其中，
Figure PCTCN2022092303-appb-000117
为一 M×CK(M＝30,C＝3,K＝10,即30×30)的复数矩阵，D＝I M，I M为一M×M(M＝30,即30×30)的单位阵，
Figure PCTCN2022092303-appb-000118
为一KC×KC(KC＝30,即30×30)的对角阵，且其对角元素依次为
Figure PCTCN2022092303-appb-000119
其中
Figure PCTCN2022092303-appb-000120
其中
Figure PCTCN2022092303-appb-000121
Figure PCTCN2022092303-appb-000122
A c与W c均为K×K(K＝10,即10×10)的对角矩阵；
步骤5.2.2:设置辅助变量E'(σ 2)与
Figure PCTCN2022092303-appb-000123
初始值E'(σ 2)＝1,
Figure PCTCN2022092303-appb-000124
后，通过方程(17)与方程(18)进行迭代更新，直至二者收敛，计算收敛后的辅助变量T'(σ 2)，最后代入公式(19)与公式(20)计算辅助变量m' c,c,k与n' c,c,k；
Figure PCTCN2022092303-appb-000125
Figure PCTCN2022092303-appb-000126
m' c,c,k＝trace(Θ c,c,kT'(σ 2))       (19)
Figure PCTCN2022092303-appb-000127
其中辅助变量E(σ 2)、
Figure PCTCN2022092303-appb-000128
T(σ 2)、
Figure PCTCN2022092303-appb-000129
均为步骤5.2.1中固 定点方程经过迭代收敛后的结果；
步骤5.2.3：设置辅助变量E'(Z)与
Figure PCTCN2022092303-appb-000130
初始值E'(Z)＝1,
Figure PCTCN2022092303-appb-000131
后，通过方程(21)与方程(22)进行迭代更新，直至二者收敛，计算收敛后的辅助变量T'(Z)，最后代入公式(23)计算辅助变量m' m,c,k,m,l；
Figure PCTCN2022092303-appb-000132
Figure PCTCN2022092303-appb-000133
Figure PCTCN2022092303-appb-000134
其中辅助变量E(Z)、
Figure PCTCN2022092303-appb-000135
T(Z)、
Figure PCTCN2022092303-appb-000136
均为步骤5.2.1中固定点方程经过迭代收敛后的结果；
步骤5.3：各卫星根据步骤5.2得到的辅助变量更新其服务用户的功率归一化因子、信号功率、干扰信号功率、以及SINR；
步骤5.3.1:根据步骤5.2得到的辅助变量，通过公式(24)计算功率归一化因子；
Figure PCTCN2022092303-appb-000137
步骤5.3.2：根据步骤5.2得到的辅助变量，通过公式(25)计算用户的信号功率；
Figure PCTCN2022092303-appb-000138
步骤5.3.3:根据步骤5.2得到的辅助变量，通过公式(26)计算用户的干扰信号功率；
Figure PCTCN2022092303-appb-000139
其中，L m,c,k,m,l通过公式(27)计算：
Figure PCTCN2022092303-appb-000140
步骤5.3.4:通过公式(28)计算用户的SINR；
Figure PCTCN2022092303-appb-000141
步骤5.4：卫星间通过交互标量形式的辅助变量
Figure PCTCN2022092303-appb-000142
代替大维的瞬时信道矩阵、接收滤波器矩阵
Figure PCTCN2022092303-appb-000143
和用户权值
Figure PCTCN2022092303-appb-000144
在显著减小星间交互的信息量基础上，完成卫星间信息交互；
步骤6：判断公式(28)中的SINR是否收敛，即优化后的SINR值与更新前的SINR值的差是否小于收敛精度阈值ε或达到最大迭代次数γ，若是，则输出收敛后的接收滤波器矩阵和用户权值，进行步骤7，否则跳至步骤5；
步骤7：根据步骤6输出的收敛后的辅助变量
Figure PCTCN2022092303-appb-000145
以及当前一组瞬时信道信息计算预编码矩阵，根据预编码矩阵实现分布式多卫星联合波束赋形；
步骤7.1：根据步骤6输出的收敛后的接收滤波器矩阵
Figure PCTCN2022092303-appb-000146
用户权值
Figure PCTCN2022092303-appb-000147
与当前一组瞬时信道信息，通过公式(29)计算辅助变量Γ c；
Figure PCTCN2022092303-appb-000148
其中H c＝[h c,1,1,...,h c,1,K,h c,2,1,...,h c,2,K,...,h c,C,K] H,H c为一KC×M(KC＝30,M＝30即30×30)的复数矩阵,h c,i,j为卫星c到小区i中的用户j的瞬时信道矩阵，
Figure PCTCN2022092303-appb-000149
Figure PCTCN2022092303-appb-000150
步骤7.2：根据步骤6输出的收敛后的接收滤波器矩阵
Figure PCTCN2022092303-appb-000151
用户权值
Figure PCTCN2022092303-appb-000152
与步骤7.1得到的辅助变量Γ c，通过公式(30)计算预编码矩阵；
Figure PCTCN2022092303-appb-000153
其中，
Figure PCTCN2022092303-appb-000154
为卫星c对它服务用户k的预编码矩阵，ξ c为功率归一化因子，
Figure PCTCN2022092303-appb-000155
步骤7.3：根据步骤7.2得到的预编码矩阵实现分布式多卫星联合波束赋形；
步骤8、根据上述步骤实现了多星系统下的分布式多卫星联合波 束赋形，有效减少波束间干扰，提高整体系统的吞吐量。
图2展示了采用WMMSE最优方法与实施例1中提出的DE近似方法在每轮迭代后需要交互的信息量的对比结果；
其中，若采用WMMSE最优方法，则在每轮迭代后，卫星间需要交互其服务用户的接收滤波器矩阵、权值、以及瞬时信道矩阵，例如图2中卫星c在每轮迭代后，需要向卫星m发送接收滤波器矩阵a c,k(k∈K c)、权值w c,k(k∈K c)、以及瞬时信道矩阵h c,c,k(k∈K c)，其中a c,k与w c,k均为标量，h c,c,k为一1×M的复数矩阵，
而采用DE近似方法时，卫星间只需交互一个辅助变量，如图2中卫星c在每轮迭代后只需要向卫星m发送辅助变量
Figure PCTCN2022092303-appb-000156
为一标量，因此，从该对比图中可看出：采用本发明提出的DE近似方法相较于WMMSE最优方法，能够显著减小卫星间的交互信息量。
图3为采用实施例1中提出的DE近似方法、WMMSE最优方法、以及非协作方法在500组信道下的系统传输速率CDF对比图。
其中非协作方法为多星间不进行协作传输，该图像的横坐标为传输速率，纵坐标为累积分布概率，由图中结果可看出采用DE近似方法的传输速率集中在13.2nats/s/Hz附近，采用非协作方法的传输速率集中在3.9nats/s/Hz附近，采用WMMSE最优方法的传输速率集中在13.8nats/s/Hz附近，因此可得出结论：1)采用本发明方法相较于非协作方法可提升传输速率3倍左右，吞吐量提升显著；2)采用本发明方法相较于最优MMSE方法只牺牲了5％左右的性能，却能够显著减小卫星间的交互信息量。
以上所述的具体描述，对发明的目的、技术方案和有益效果进行了进一步详细说明，所应理解的是，以上所述仅为本发明的具体实施例而已，并不用于限定本发明的保护范围，凡在本发明的精神和原则之内，所做的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。
工业实用性
本发明一种分布式多卫星联合波束赋形方法，通过多星间联合波束赋形有效减少波束间干扰，提高整体系统的吞吐量，能够解决多星系统中存在的波束间干扰较大，以及传统的多星协作传输技术中信令交互负担过大、获取瞬时信道信息困难的技术问题，适用范围广，具有良好的工业实用性。

Claims (7)

  1. 一种分布式多卫星联合波束赋形方法，其特征在于：包括以下步骤，
    步骤1、初始化多星协作传输系统的组成架构及输入条件；
    步骤2、根据多组瞬时信道信息初始化信道的统计信息；
    步骤3、所有卫星各自利用步骤2得到的信道的统计信息，通过匹配滤波MF计算服务用户的信号功率、干扰信号功率和信干噪比SINR；
    步骤4、初始化收敛精度阈值以及最大迭代次数；
    其中，收敛精度阈值，记为ε,最大迭代次数，记为γ；
    步骤5、应用确定性等价DE定理对传统的加权最小均方误差WMMSE的迭代过程进行近似，在每轮迭代后，卫星间通过交互标量形式的辅助变量代替大维的瞬时信道矩阵，显著减小星间交互的信息量；
    步骤6、判断SINR是否收敛，即优化后的SINR值与更新前的SINR值的差是否小于收敛精度阈值ε或达到最大迭代次数γ，若是，则输出收敛后的接收滤波器矩阵和用户权值，进行步骤7；否则返回至步骤5；
    步骤7、根据步骤6输出的收敛后的接收滤波器矩阵和用户权值以及当前的一组瞬时信道信息计算预编码矩阵，根据所述预编码矩阵实现分布式多卫星联合波束赋形。
  2. 如权利要求1所述的一种分布式多卫星联合波束赋形方法， 其特征在于：还包括步骤8、根据上述步骤实现多星系统下的分布式多卫星联合波束赋形，有效减少波束间干扰，提高整体系统的吞吐量。
  3. 如权利要求1或2所述的一种分布式多卫星联合波束赋形方法，其特征在于：步骤1实现方法为，
    步骤1.1：初始化多星协作传输系统的组成架构；
    多星协作传输系统的组成架构即通信系统模型，包括卫星到地面用户的瞬时信道矩阵、卫星发射信号、地面用户接收信号、卫星对其服务的地面用户的预编码矩阵以及用户处的噪声，通过公式(1)表示：
    Figure PCTCN2022092303-appb-100001
    卫星集合为Λ＝{1,2,...C}，其中卫星c服务的用户集合为K c＝{1,2,...K}，y c,k为卫星c服务的小区c中用户k的接收信号，M为卫星发射天线数，g c,k表示卫星c到小区c中用户k的预编码矩阵，s c,k表示卫星c向小区c中用户k的发射信号，n c,k为小区c中用户k处的噪声，[·] H表示矩阵[·]的共轭转置；
    步骤1.2：初始化多星协作传输系统的输入条件；
    其中，输入条件包括卫星发射功率限制，记为P c；以及n组卫星到地面用户的瞬时信道矩阵
    Figure PCTCN2022092303-appb-100002
    由公式(2)表示；
    Figure PCTCN2022092303-appb-100003
    其中Ξ c,c,k表示卫星c到小区c中用户k的路径损耗，τ表示莱斯因子，I 1×M表示1行M列的单位阵，Z c,c,k表示服从均值为0，方差为1 的高斯向量。
  4. 如权利要求3所述的一种分布式多卫星联合波束赋形方法，其特征在于：步骤2实现方法为，
    步骤2.1：根据多组瞬时信道信息，通过公式(3)初始化信道的均值矩阵：
    Figure PCTCN2022092303-appb-100004
    其中
    Figure PCTCN2022092303-appb-100005
    表示卫星c到小区c中用户k的信道均值矩阵，
    Figure PCTCN2022092303-appb-100006
    表示第i组瞬时信道信息；
    步骤2.2：根据多组瞬时信道信息以及步骤2.1得到的信道的均值矩阵
    Figure PCTCN2022092303-appb-100007
    通过公式(4)初始化信道的协方差矩阵：
    Figure PCTCN2022092303-appb-100008
    其中Θ c,c,k为卫星c到小区c中用户k的信道发射协方差矩阵。
  5. 如权利要求3所述的一种分布式多卫星联合波束赋形方法，其特征在于：步骤3实现方法为，
    步骤3.1：根据步骤2得到的均值矩阵
    Figure PCTCN2022092303-appb-100009
    协方差矩阵Θ c,c,k，通过公式(5)，计算功率归一化因子；
    Figure PCTCN2022092303-appb-100010
    其中
    Figure PCTCN2022092303-appb-100011
    为卫星c的功率归一化因子，P c为卫星发射功率，trace[·]表示矩阵[·]的迹；
    步骤3.2：根据步骤2得到的均值矩阵
    Figure PCTCN2022092303-appb-100012
    协方差矩阵Θ c,c,k与步骤3.1得到的归一化因子
    Figure PCTCN2022092303-appb-100013
    通过公式(6)，计算用户的信号功率；
    Figure PCTCN2022092303-appb-100014
    其中
    Figure PCTCN2022092303-appb-100015
    为c小区中用户k的信号功率；
    步骤3.3：根据步骤2得到的均值矩阵
    Figure PCTCN2022092303-appb-100016
    协方差矩阵Θ c,c,k与步骤3.1得到的归一化因子
    Figure PCTCN2022092303-appb-100017
    通过公式(7)计算用户的干扰信号功率；
    Figure PCTCN2022092303-appb-100018
    其中，
    Figure PCTCN2022092303-appb-100019
    为c小区中用户k的干扰信号功率；
    步骤3.4：根据步骤3.2得到的信号功率
    Figure PCTCN2022092303-appb-100020
    与步骤3.3得到干扰信号功率
    Figure PCTCN2022092303-appb-100021
    通过公式(8)，计算用户的SINR；
    Figure PCTCN2022092303-appb-100022
    其中，
    Figure PCTCN2022092303-appb-100023
    表示c小区中用户k的SINR，σ 2为噪声功率。
  6. 如权利要求4所述的一种分布式多卫星联合波束赋形方法，其特征在于：步骤5实现方法为，
    步骤5.1：根据步骤3得到的信号功率
    Figure PCTCN2022092303-appb-100024
    与信干噪比
    Figure PCTCN2022092303-appb-100025
    所有卫星各自计算其服务用户的接收滤波器矩阵、权值及需要与其他卫星交互的变量的值；
    步骤5.1.1:根据步骤3得到的信号功率
    Figure PCTCN2022092303-appb-100026
    与信干噪比
    Figure PCTCN2022092303-appb-100027
    通过公式(9)计算用户的接收滤波器矩阵；
    Figure PCTCN2022092303-appb-100028
    其中，
    Figure PCTCN2022092303-appb-100029
    表示c小区中用户k的接收滤波器矩阵；
    步骤5.1.2:根据步骤3得到的信干噪比
    Figure PCTCN2022092303-appb-100030
    通过公式(10)计算用户的权值；
    Figure PCTCN2022092303-appb-100031
    其中
    Figure PCTCN2022092303-appb-100032
    表示卫星c服务的用户k的权值；
    步骤5.1.3:根据5.1.1得到的接收滤波器矩阵
    Figure PCTCN2022092303-appb-100033
    与5.1.2得到的用户权值
    Figure PCTCN2022092303-appb-100034
    通过公式(11)计算辅助变量的值；
    Figure PCTCN2022092303-appb-100035
    其中
    Figure PCTCN2022092303-appb-100036
    表示卫星c服务的用户k的辅助变量；
    步骤5.2：所有卫星各自通过三组固定点方程进行迭代，直至结果收敛，从而求解辅助变量的值；
    步骤5.2.1:给定辅助变量E(σ 2)与
    Figure PCTCN2022092303-appb-100037
    初始值后，通过方程(12)与方程(13)进行迭代更新，直至二者收敛，计算收敛后的辅助变量T(σ 2)与
    Figure PCTCN2022092303-appb-100038
    最后代入公式(14)与公式(15)、(16)计算辅助变量m c,c,k、n c,c,k与n m,c,k,m,l；
    Figure PCTCN2022092303-appb-100039
    Figure PCTCN2022092303-appb-100040
    m c,c,k＝trace(Θ c,c,kT(σ 2))  (14)
    Figure PCTCN2022092303-appb-100041
    Figure PCTCN2022092303-appb-100042
    其中，
    Figure PCTCN2022092303-appb-100043
    D＝I M，I M为一个M行M列的单位阵，
    Figure PCTCN2022092303-appb-100044
    为一KC行KC列的对角阵，且其对角元素依次为
    Figure PCTCN2022092303-appb-100045
    其中
    Figure PCTCN2022092303-appb-100046
    其中
    Figure PCTCN2022092303-appb-100047
    Figure PCTCN2022092303-appb-100048
    diag[·]表示由矩阵[·]中的元素组成的对角矩阵，[·] -1表示矩阵[·]的逆矩阵；
    步骤5.2.2:给定辅助变量E'(σ 2)与
    Figure PCTCN2022092303-appb-100049
    初始值后，通过方程(17)与方程(18)进行迭代更新，直至二者收敛，计算收敛后的辅助变量T'(σ 2)，最后代入公式(19)与公式(20)计算辅助变量m' c,c,k与n′ c,c,k；
    Figure PCTCN2022092303-appb-100050
    Figure PCTCN2022092303-appb-100051
    m' c,c,k＝trace(Θ c,c,kT'(σ 2))  (19)
    Figure PCTCN2022092303-appb-100052
    其中辅助变量E(σ 2)、
    Figure PCTCN2022092303-appb-100053
    T(σ 2)、
    Figure PCTCN2022092303-appb-100054
    均为步骤5.2.1中固定点方程经过迭代收敛后的结果；
    步骤5.2.3:给定辅助变量E'(Z)与
    Figure PCTCN2022092303-appb-100055
    初始值后，通过方程(21)与方程(22)进行迭代更新，直至二者收敛，计算收敛后的辅助变量T'(Z)，最后代入公式(23)计算辅助变量m' m,c,k,m,l；
    Figure PCTCN2022092303-appb-100056
    Figure PCTCN2022092303-appb-100057
    Figure PCTCN2022092303-appb-100058
    其中辅助变量E(Z)、
    Figure PCTCN2022092303-appb-100059
    T(Z)、
    Figure PCTCN2022092303-appb-100060
    均为步骤5.2.1中固定点方程经过迭代收敛后的结果；
    步骤5.3：各卫星根据步骤5.2得到的辅助变量更新其服务用户的功率归一化因子、信号功率、干扰信号功率、以及SINR；
    步骤5.3.1:根据步骤5.2得到的辅助变量，通过公式(24)计算用户的功率归一化因子；
    Figure PCTCN2022092303-appb-100061
    步骤5.3.2:根据步骤5.2得到的辅助变量以及步骤5.3.1得到的功率归一化因子，通过公式(25)计算用户的信号功率；
    Figure PCTCN2022092303-appb-100062
    步骤5.3.3:根据步骤5.2得到的辅助变量，通过公式(26)计算用户的干扰信号功率；
    Figure PCTCN2022092303-appb-100063
    其中，L m,c,k,m,l通过公式(27)计算：
    Figure PCTCN2022092303-appb-100064
    步骤5.3.4:根据步骤5.3.2得到的信号功率
    Figure PCTCN2022092303-appb-100065
    与步骤5.3.3得到干扰信号功率
    Figure PCTCN2022092303-appb-100066
    通过公式(28)计算用户的SINR；
    Figure PCTCN2022092303-appb-100067
    步骤5.4：卫星间通过交互标量形式的辅助变量
    Figure PCTCN2022092303-appb-100068
    代替大维的瞬时信道矩阵、接收滤波器矩阵
    Figure PCTCN2022092303-appb-100069
    和用户权值
    Figure PCTCN2022092303-appb-100070
    在显著减小星间交互的信息量基础上，完成卫星间信息交互。
  7. 如权利要求6所述的一种分布式多卫星联合波束赋形方法， 其特征在于：步骤7实现方法为，
    步骤7.1：根据步骤6输出的收敛后的辅助变量
    Figure PCTCN2022092303-appb-100071
    与当前一组瞬时信道信息，通过公式(29)计算辅助变量Γ c；
    Figure PCTCN2022092303-appb-100072
    其中H c＝[h c,1,1,...,h c,1,K,h c,2,1,...,h c,2,K,...,h c,C,K] H,h c,i,j为卫星c到小区i中的用户j的瞬时信道矩阵，
    Figure PCTCN2022092303-appb-100073
    Figure PCTCN2022092303-appb-100074
    步骤7.2：根据步骤6输出的收敛后的接收滤波器矩阵
    Figure PCTCN2022092303-appb-100075
    用户权值
    Figure PCTCN2022092303-appb-100076
    与步骤7.1得到的辅助变量Γ c，通过公式(30)计算预编码矩阵；
    Figure PCTCN2022092303-appb-100077
    其中，
    Figure PCTCN2022092303-appb-100078
    为卫星c对它服务用户k的预编码矩阵，ξ c为功率归一化因子，
    Figure PCTCN2022092303-appb-100079
    步骤7.3：根据步骤7.2得到的预编码矩阵实现分布式多卫星联合波束赋形。
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117858234A (zh) * 2023-12-18 2024-04-09 暨南大学 适用于高移动性场景的短包速率分割多址接入方法及系统

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104869626A (zh) * 2014-10-17 2015-08-26 东南大学 基于低复杂度接收机的上行大规模mimo系统功率控制方法
US20170149493A1 (en) * 2014-06-18 2017-05-25 European Space Agency Joint transmitter signal processing in multi-beam satellite systems
CN111835406A (zh) * 2020-06-30 2020-10-27 东南大学 适用于多波束卫星通信的能效谱效权衡的鲁棒预编码方法
CN113472425A (zh) * 2021-06-30 2021-10-01 中国电子科技集团公司第三十八研究所 一种能效优先的卫星多波束协作通信下行功率分配方法
CN114244413A (zh) * 2021-10-28 2022-03-25 北京理工大学 一种分布式多卫星联合波束赋形方法

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2965428A1 (fr) * 2010-09-24 2012-03-30 France Telecom Procede d'emission double iteratif de flux multiples par utilisateur pour un systeme mimo multi utilisateurs, emetteur, produit programme d'ordinateur et support d'information correspondants
CN106549697B (zh) * 2017-01-12 2020-12-01 重庆邮电大学 协作通信系统中联合波束赋形和天线选择的发射方法

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20170149493A1 (en) * 2014-06-18 2017-05-25 European Space Agency Joint transmitter signal processing in multi-beam satellite systems
CN104869626A (zh) * 2014-10-17 2015-08-26 东南大学 基于低复杂度接收机的上行大规模mimo系统功率控制方法
CN111835406A (zh) * 2020-06-30 2020-10-27 东南大学 适用于多波束卫星通信的能效谱效权衡的鲁棒预编码方法
CN113472425A (zh) * 2021-06-30 2021-10-01 中国电子科技集团公司第三十八研究所 一种能效优先的卫星多波束协作通信下行功率分配方法
CN114244413A (zh) * 2021-10-28 2022-03-25 北京理工大学 一种分布式多卫星联合波束赋形方法

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117858234A (zh) * 2023-12-18 2024-04-09 暨南大学 适用于高移动性场景的短包速率分割多址接入方法及系统

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