Multi-star massive MIMO precoder and receiver decoupling design method

Abstract

This invention discloses a decoupling design method for precoders and receivers in multi-satellite massive MIMO systems. This includes a decoupling design method for uplink / downlink precoders and receivers. The invention also establishes a beam-based channel model to further reduce implementation complexity. The downlink / uplink beam domain channel is the product of a random vector / spread vector and the conjugate transpose of a spread vector / random vector. Each satellite independently designs its downlink precoder and uplink receiver using only local statistical channel information, and uses the designed precoder and receiver to implement downlink precoding transmission and uplink linear reception processing. Similarly, each user independently designs its uplink precoder and downlink receiver using only local statistical channel information, and uses the designed precoder and receiver to implement uplink precoding transmission and downlink linear reception processing. This invention can significantly reduce the design and implementation complexity of precoders and receivers while ensuring the performance of the multi-satellite massive MIMO system.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, specifically relating to a decoupling design method for a multi-satellite massive MIMO precoder and receiver. Background Technology

[0002] In recent years, breakthroughs in terrestrial mobile communication technology have spurred exponential growth in emerging industries such as the mobile internet and the Internet of Things. However, with the rapid iteration of cutting-edge fields like smart cities and autonomous driving, the shortcomings in network coverage in remote areas are becoming increasingly prominent. This digital divide makes satellite communication systems, which combine wide-area coverage and flexible deployment, a core solution for bridging the gap in global communication. A multi-orbit collaborative networking system, built by leveraging the millisecond-level latency of low-Earth orbit satellites, the balanced coverage of medium-Earth orbit satellites, and the wide-area service characteristics of high-Earth orbit satellites, is reshaping the integrated "air, land, sea" communication landscape.

[0003] Massive Multiple-Input Multiple-Output (MIMO) is one of the core technologies of fifth-generation mobile communication (5G). It utilizes a large number of antennas deployed at base stations to achieve flexible dynamic beam configuration, enabling multi-user communication under the same time-frequency resources. Extending MIMO technology to satellite mobile communication can build highly efficient satellite communication systems, achieving higher spectral and power efficiency. This technological convergence can significantly improve the performance of satellite communication, particularly demonstrating significant value in meeting the needs of large-scale terminal access.

[0004] In recent years, the surge in global demand for seamless internet access has driven the development of mega-satellite constellations. By launching hundreds or thousands of low-Earth orbit satellites, mega-satellite constellations can not only cover remote areas that are difficult for traditional communication networks to reach, but also enable a single user to simultaneously receive multi-stream signals from multiple satellites through joint transmission technologies. Compared to a single satellite system, the deployment of mega-satellite constellations will further improve the spectral efficiency of satellite mobile communications, laying a solid foundation for achieving integrated air-space-ground core networking and seamless global communication coverage. In existing technologies, the precoder and receiver designs, which rely on statistical channel state information, are typically coupled and require iterative development. Therefore, decoupling the precoder and receiver designs while ensuring system rate performance is crucial. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a decoupled design method for precoders and receivers in multi-satellite massive MIMO systems, so as to overcome the shortcomings of the prior art and significantly reduce the design and implementation complexity of precoders and receivers while ensuring the performance of multi-satellite massive MIMO systems.

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

[0007] Firstly, this invention provides a decoupling design method for downlink precoders and receivers in multi-satellite massive MIMO. On the satellite side, the precoder is calculated using the Average Signal-to-Leakage-to-Noise Ratio (ASINR) criterion to generate the respective transmitted signals. The user terminal uses the ASINR criterion to calculate the received signals from each satellite and performs linear reception processing. The satellite... Relevant users The decoupling closed-form expression for the pre-encoder is: by using satellite The outer product of the satellite-side rudder vectors of all corresponding user terminals is multiplied by the maximum eigenvalue of the corresponding user-side channel correlation matrix, then summed, and finally loaded onto the satellite along its diagonal. Relevant users The inverse of the downlink transmission signal-to-noise ratio is used to inverse the resulting matrix with the satellite signal-to-noise ratio. Relevant users The vector is obtained by multiplying the satellite side rudder vectors and then scaling them using a coefficient; User corresponding satellites The decoupling closed-form expression for the receiver is: through the user The user-side channel correlation matrix for each satellite is multiplied by the corresponding downlink transmit signal-to-noise ratio, summed over each satellite, and then added to the identity matrix. The inverse of the resulting matrix is ​​then multiplied by the user... corresponding satellites The user-side channel correlation matrix is ​​obtained by performing eigenvalue decomposition on the resulting matrix, and then the eigenvector corresponding to its largest eigenvalue is obtained.

[0008] Secondly, this invention provides a decoupling design method for uplink precoders and receivers in multi-satellite massive MIMO. User terminals generate their respective transmit signals using precoders calculated by the average signal-to-leakage-noise ratio (ASINR) criterion, while the satellite side calculates the receiver's linear reception processing of each user's signal using the average signal-to-interference-plus-noise ratio (ASINR) criterion. Among these, the user... corresponding satellites The decoupling closed-form expression for the precoder is: through the user The user-side channel correlation matrices for different satellites are summed over each satellite, and the inverse of the uplink transmission signal-to-noise ratio is loaded onto the diagonal. The inverse of the resulting matrix is ​​then multiplied by the user... corresponding satellites The user-side channel correlation matrix is ​​then used to perform eigenvalue decomposition on the resulting matrix, and the eigenvector corresponding to the largest eigenvalue is obtained; satellite Relevant users The decoupling closed-form expression for the receiver is: through the satellite The outer product of the satellite-side rudder vectors of all user terminals served is multiplied by the maximum eigenvalue of the corresponding user-side channel correlation matrix, then multiplied by the corresponding uplink transmission signal-to-noise ratio, and summed. The resulting matrix is ​​then added to the identity matrix, and the inverse of the resulting matrix is ​​then multiplied by the satellite... Relevant users The vector obtained by multiplying the satellite side rudder vectors.

[0009] Thirdly, the present invention further provides a multi-satellite large-scale MIMO beam-based channel model for the decoupling design method, wherein the downlink beam-based channel model is represented as the product of the user-side beam matrix, the downlink beam domain channel, and the conjugate transpose of the satellite-side beam matrix; the uplink beam-based channel model is represented as the product of the satellite-side beam matrix, the uplink beam domain channel, and the conjugate transpose of the user-side beam matrix; the beam matrix is ​​composed of the sampling array response vectors corresponding to a selected set of scaled direction cosine sampling points, and each sampling array response vector is called a beam; the downlink beam domain channel is the product of a random vector and the conjugate transpose of a spread vector, and the uplink beam domain channel is the product of a spread vector and the conjugate transpose of a random vector; the random vector follows a Ricean distribution, and the spread vector is a real-valued vector representing the distribution of channel energy on different beams.

[0010] A decoupled design method for downlink beam structure precoders based on beam-based channel models for multi-satellite massive MIMO includes: each satellite designs its own beam structure precoder using the downlink beam-based channel model and the local (without involving other satellites) statistical channel information of each user terminal, and uses the obtained precoders for downlink precoding transmission; the beam structure precoder includes a low-dimensional beam domain precoder for each user, a beam mapping module for each user, and a beam modulation module. The low-dimensional beam domain precoder for each user is a precoder on the beam set of each user. The beam mapping module maps the low-dimensional beam domain precoded signals of each user into complete beam domain transmitted signals. The beam modulation module multiplies the beam matrix by the beam domain transmitted signal vector, which is the sum of the beam domain transmitted signal vectors of each user.

[0011] Furthermore, the beam domain precoder relies on the Average Signal-to-Noise Ratio (ASLNR) criterion, satellite Relevant users The beam domain precoder is: through satellite The spread vectors of all corresponding user terminals are left-multiplied by the beam matrix and its conjugate transpose, and the resulting vectors are then processed according to the satellite... Relevant users The beam set is extracted, and then the vector obtained by multiplying it by the square root of the largest eigenvalue of the corresponding user's side channel correlation matrix is ​​summed. The resulting matrix is ​​then combined with the conjugate transpose of the beam matrix according to the satellite... Relevant users The beam set is extracted, and the extracted matrix is ​​right-multiplied by its conjugate transpose before being compared with the satellite beam set. Relevant users Add the matrices obtained by multiplying the reciprocals of the downlink transmission signal-to-noise ratios, and then combine the inverse of the resulting matrix with the satellite signal-to-noise ratio. Relevant users The diffusion vector is multiplied by the beam matrix and its conjugate transpose, and then multiplied by the satellite. Relevant users The vector is obtained by multiplying the extracted beam sets into vectors and then scaling them with a coefficient.

[0012] A decoupling design method for uplink beamform receivers in multi-satellite massive MIMO based on beam-based channel models includes: each satellite designs its own beamform receiver using the uplink beam-based channel model and statistical channel information from each user terminal, and then uses the obtained receivers for uplink linear reception processing. The beamform receiver includes a beam transform module, a beam decimation module, and beam domain receivers for each user. The beam transform module transforms the spatial domain received signal vectors on each subcarrier into beam domain received signal vectors. The beam decimation module decimates the beam domain received signal vectors according to the beam sets of each user. Finally, the beam domain receivers for each user and the decimated beam domain received signal vectors are used to perform linear processing on the signals of each user.

[0013] Furthermore, the beam domain receiver relies on the average signal-to-interference-plus-noise ratio (ASINR) criterion, satellite Relevant users The beam domain receiver is used to detect satellites. The spread vectors of all user terminals served are left-multiplied by the beam matrix and its conjugate transpose, and the resulting vectors are then processed according to the satellite... Relevant users The beam set is extracted to obtain the desired result. Then, the product of the outer product of the vector obtained by multiplying the root of the maximum eigenvalue of the corresponding user's side channel correlation matrix and the root of the corresponding user's uplink transmission signal-to-noise ratio is calculated. The resulting matrix is ​​then summed with the conjugate transpose of the beam matrix, based on the satellite... Relevant users The beam set is extracted, and the extracted matrix is ​​right-multiplied by its conjugate transpose, and the resulting matrix is ​​added together. The inverse of the resulting matrix is ​​then used with the satellite beam set. Relevant users The diffusion vector is multiplied by the beam matrix and its conjugate transpose, and then multiplied by the satellite. Relevant users The vector obtained by multiplying the vectors extracted from the beam set.

[0014] Furthermore, the calculation of the beam domain pre-encoder or beam domain receiver relies solely on real-valued matrix operations, and the product of the conjugate transpose of the beam matrix and itself can be calculated from the first column of the matrix obtained by multiplying the conjugate transpose of the component beam matrices in both directions by themselves, and stored in advance; and the product of the conjugate transpose of the beam matrix and itself multiplied by the diffusion vector of each user can be approximated by increasing the number of sampling points of the direction cosine, and calculated and stored in advance.

[0015] Fourthly, the present invention provides a multi-satellite massive MIMO communication system, including satellites and user terminals, said satellites or gateway stations associated with them, and user terminals implementing the steps of the decoupling design method described above.

[0016] Fifthly, the present invention provides a computer program product, including a computer program / instructions, wherein the computer program / instructions, when executed by a processor, implement the steps of the decoupling design method described above.

[0017] Beneficial Effects: Compared with existing technologies, this invention fully utilizes the characteristics of satellite channels to implement a decoupled design method for multi-satellite large-scale MIMO precoders and receivers. Each satellite independently designs its downlink precoder and uplink receiver using only local statistical channel information, and implements downlink precoding transmission and uplink linear reception processing using the designed precoder and receiver. Similarly, each user independently designs its uplink precoder and downlink receiver using only local statistical channel information, and implements uplink precoding transmission and downlink linear reception processing using the designed precoder and receiver. Furthermore, the decoupled antenna-dimensional precoder and receiver design can be transformed into a beam-structured precoder and receiver design using a beam-based channel model, converting the antenna-dimensional vector design into a low-dimensional beam-domain vector design. Therefore, while ensuring system ergodic and rate performance, the design and implementation complexity of the precoder and receiver can be significantly reduced. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below only illustrate some embodiments of the present invention. For those skilled in the art, other embodiments can be obtained from these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the decoupling design method for multi-satellite massive MIMO precoder and receiver according to an embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of the satellite-side processing method in multi-satellite massive MIMO mobile communication according to an embodiment of the present invention.

[0021] Figure 3 This is a schematic diagram of the user terminal-side processing method in multi-satellite massive MIMO mobile communication according to an embodiment of the present invention.

[0022] Figure 4 This is a comparison chart of traversal and rate performance in multi-satellite massive MIMO mobile communication according to an embodiment of the present invention. Detailed Implementation

[0023] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0024] This invention discloses a decoupling design method for multi-satellite massive MIMO precoders and receivers. This method is applied to satellites or gateway stations connected to satellites and user terminals, wherein the satellites are equipped with antenna arrays and communicate with user terminals equipped with antenna arrays within their coverage area. Each satellite or gateway station and user terminal uses statistical channel information, including average channel energy and spatial angle information, to calculate the corresponding precoder for each satellite and each user terminal, and the corresponding receiver for each user terminal and each satellite. Figure 1 As shown, a decoupling design method for multi-satellite massive MIMO precoders and receivers is presented, including a decoupling design method for multi-satellite massive MIMO downlink precoders and receivers, and a decoupling design method for multi-satellite massive MIMO uplink precoders and receivers.

[0025] In one specific embodiment, in the decoupling design method of the downlink precoder and receiver for multi-satellite massive MIMO, each satellite uses a calculated precoder to generate its own transmission signal, implementing multi-satellite massive MIMO downlink transmission. The user terminal uses a calculated receiver to perform linear reception processing on the signals transmitted by each satellite. Statistical channel information is obtained from the feedback information of each user or from the uplink probing process; the feedback information of each user includes the user's geographical location information, average channel energy, or spatial angle information; during the uplink probing process, each user periodically transmits a probing signal, and the satellite estimates the average channel energy and spatial angle information of each user based on the received probing signals.

[0026] In the decoupling design method of downlink precoder and receiver for multi-satellite massive MIMO, the decoupling design of the downlink precoder relies on the average signal-to-leakage-noise ratio (ASLNR) criterion and the average signal-to-interference-plus-noise ratio (ASINR) criterion. The satellite side uses the ASLNR criterion to calculate the precoder to generate its respective transmit signal. The user terminal uses the ASINR criterion to calculate the receiver's linear reception processing of the signals transmitted by each satellite. Specifically, the satellite side uses the ASLNR criterion to calculate the precoder to generate its respective transmit signal, and the user terminal uses the ASINR criterion to calculate the receiver's linear reception processing of the signals transmitted by each satellite. Relevant users The decoupling closed-form expression for the pre-encoder is: by using satellite The outer product of the satellite-side rudder vectors of all corresponding user terminals is multiplied by the maximum eigenvalue of the corresponding user-side channel correlation matrix, then summed, and finally loaded onto the satellite along its diagonal. Relevant users The inverse of the downlink transmission signal-to-noise ratio is used to inverse the resulting matrix with the satellite signal-to-noise ratio. Relevant users The vector is obtained by multiplying the satellite side rudder vectors and then scaling them using a coefficient; User corresponding satellites The decoupling closed-form expression for the receiver is: through the user The user-side channel correlation matrix for each satellite is multiplied by the corresponding downlink transmit signal-to-noise ratio, summed over each satellite, and then added to the identity matrix. The inverse of the resulting matrix is ​​then multiplied by the user... corresponding satellites The user-side channel correlation matrix is ​​obtained by performing eigenvalue decomposition on the resulting matrix, and then the eigenvector corresponding to its largest eigenvalue is obtained.

[0027] In a multi-satellite system, ASINR is the ratio of the average power of the signal transmitted from the serving satellite to the user to the average power of the signal transmitted to other users to the sum of the average power of the signal transmitted from the non-serving satellite to the user's receiver.

[0028] In one specific embodiment, a decoupled design method for multi-satellite massive MIMO uplink precoders and receivers is employed. Each satellite or gateway station and user terminal utilizes statistical channel information, including average channel energy and spatial angle information, to calculate the corresponding receiver for each satellite and user terminal, and the corresponding precoder for each user terminal and satellite. The user terminals use the calculated precoders to generate their respective transmit signals, implementing multi-satellite massive MIMO uplink transmission. Each satellite uses its calculated receiver to perform linear reception processing on the signals from each user.

[0029] In the decoupling design method of the uplink precoder and receiver in multi-satellite massive MIMO, the decoupling design of the uplink precoder relies on the average signal-to-leakage-noise ratio (ASLNR) criterion and the average signal-to-interference-plus-noise ratio (ASINR) criterion. User terminals use the precoder calculated by the ASLNR criterion to generate their respective transmit signals, while the satellite side uses the ASINR criterion to calculate the precoder for linear reception processing of each user's signal. Among these, the user... corresponding satellites The decoupling closed-form expression for the precoder is: through the user The user-side channel correlation matrices for different satellites are summed over each satellite, and the inverse of the uplink transmission signal-to-noise ratio is loaded onto the diagonal. The inverse of the resulting matrix is ​​then multiplied by the user... corresponding satellites The user-side channel correlation matrix is ​​then used to perform eigenvalue decomposition on the resulting matrix, and the eigenvector corresponding to the largest eigenvalue is obtained; satellite Relevant users The decoupling closed-form expression for the receiver is: through the satellite The outer product of the satellite-side rudder vectors of all user terminals served is multiplied by the maximum eigenvalue of the corresponding user-side channel correlation matrix, then multiplied by the corresponding uplink transmission signal-to-noise ratio, and summed. The resulting matrix is ​​then added to the identity matrix, and the inverse of the resulting matrix is ​​then multiplied by the satellite... Relevant users The vector obtained by multiplying the satellite side rudder vectors.

[0030] In some lower-complexity embodiments, a multi-satellite massive MIMO beam-based channel model is provided. The downlink beam-based channel model is represented as the product of the user-side beam matrix, the downlink beam domain channel, and the conjugate transpose of the satellite-side beam matrix; the uplink beam-based channel model is represented as the product of the satellite-side beam matrix, the uplink beam domain channel, and the conjugate transpose of the user-side beam matrix; the beam matrix consists of the sampling array response vectors corresponding to a selected set of scaled direction cosine sampling points, and each sampling array response vector is called a beam; the downlink beam domain channel is the product of a random vector and the conjugate transpose of a spread vector, and the uplink beam domain channel is the product of a spread vector and the conjugate transpose of a random vector; the random vector follows a Ricean distribution, and the spread vector is a real-valued vector representing the distribution of channel energy on different beams.

[0031] In one specific embodiment, a decoupled design method for downlink beam structure precoders based on a beam-based channel model for multi-satellite massive MIMO is provided. Each satellite uses the downlink beam-based channel model and local (without involving other satellites) statistical channel information of each user terminal, including average channel energy and spatial angle information, to design its own user beam structure precoder, and uses the obtained precoder for downlink precoding transmission. The beam structure precoder consists of a user low-dimensional beam domain precoder, a user beam mapping module, and a beam modulation module. The user low-dimensional beam domain precoder is a precoder on the user beam set. The user beam mapping maps the user low-dimensional beam domain precoded signals into complete beam domain transmitted signals. Beam modulation is the beam matrix multiplied by the beam domain transmitted signal vector, which is the sum of the user beam domain transmitted signal vectors.

[0032] In the aforementioned decoupling design method for multi-satellite massive MIMO downlink beam structure precoder based on beam-based channel model, the beam domain precoder relies on the average signal-to-leakage-noise ratio (ASLNR) criterion. Relevant users The beam domain precoder is: through satellite The spread vectors of all corresponding user terminals are left-multiplied by the beam matrix and its conjugate transpose, and the resulting vectors are then processed according to the satellite... Relevant users The beam set is extracted, and then the vector obtained by multiplying it by the square root of the largest eigenvalue of the corresponding user's side channel correlation matrix is ​​summed. The resulting matrix is ​​then combined with the conjugate transpose of the beam matrix according to the satellite... Relevant users The beam set is extracted, and the extracted matrix is ​​right-multiplied by its conjugate transpose before being compared with the satellite beam set. Relevant users Add the matrices obtained by multiplying the reciprocals of the downlink transmission signal-to-noise ratios, and then combine the inverse of the resulting matrix with the satellite signal-to-noise ratio. Relevant users The diffusion vector is multiplied by the beam matrix and its conjugate transpose, and then multiplied by the satellite. Relevant users The vector is obtained by multiplying the extracted beam sets into vectors and then scaling them with a coefficient.

[0033] In one specific embodiment, a decoupling design method for uplink beamform receivers in multi-satellite massive MIMO based on a beam-based channel model is provided. Each satellite uses the uplink beam-based channel model and statistical channel information of each user terminal, including average channel energy and spatial angle information, to design its own user beamform receiver, and then uses the resulting receivers for uplink linear reception processing. The beamform receiver consists of a beam transform module, a beam decimation module, and user beam domain receivers. The beam transform module transforms the spatial domain received signal vectors on each subcarrier into beam domain received signal vectors. The beam decimation module decimates the beam domain received signal vectors according to the beam sets of each user. Finally, the user beam domain receivers and the decimated beam domain received signal vectors are used to perform linear processing on the signals of each user.

[0034] In the aforementioned decoupling design method for multi-satellite massive MIMO uplink beam structure receivers based on beam-based channel models, the beam domain receiver relies on the average signal-to-interference-plus-noise ratio (ASINR) criterion. Relevant users The beam domain receiver is used to detect satellites. The spread vectors of all user terminals served are left-multiplied by the beam matrix and its conjugate transpose, and the resulting vectors are then processed according to the satellite... Relevant users The beam set is extracted to obtain the desired result. Then, the product of the outer product of the vector obtained by multiplying the root of the maximum eigenvalue of the corresponding user's side channel correlation matrix and the root of the corresponding user's uplink transmission signal-to-noise ratio is calculated. The resulting matrix is ​​then summed with the conjugate transpose of the beam matrix, based on the satellite... Relevant users The beam set is extracted, and the extracted matrix is ​​right-multiplied by its conjugate transpose, and the resulting matrix is ​​added together. The inverse of the resulting matrix is ​​then used with the satellite beam set. Relevant users The diffusion vector is multiplied by the beam matrix and its conjugate transpose, and then multiplied by the satellite. Relevant users The vector obtained by multiplying the vectors extracted from the beam set.

[0035] In specific embodiments, the calculations of the beam domain pre-encoder and beam domain receiver rely solely on real-valued matrix operations. The product of the conjugate transpose of the beam matrix and itself can be calculated from the first column of the matrix obtained by multiplying the conjugate transposes of the component beam matrices in both directions by themselves, and stored in advance. Furthermore, the product of the conjugate transpose of the beam matrix and itself multiplied by the diffusion vector of each user can be approximated by increasing the number of sampling points of the direction cosine, and calculated and stored in advance.

[0036] The method of the present invention will be further described below with reference to specific implementation scenarios. The method of the present invention does not limit the specific scenario. For other implementations outside the exemplary scenario of the present invention, those skilled in the art can make adaptive adjustments based on the technical ideas of the present invention and existing knowledge according to the specific scenario.

[0037] I. System Configuration

[0038] Consider that each satellite is equipped with an antenna array (which can be one-dimensional or two-dimensional, with tens to hundreds of antennas). The most basic is a two-dimensional uniform planar array (UPA), where the antenna elements are uniformly arranged horizontally and vertically. Assume each satellite is equipped with a UPA. shaft and The number of antenna elements in the axial direction are respectively and ,but The total number of antennas equipped for the satellite. Assuming each user side is equipped with a UPA, shaft and The number of antenna elements in the axial direction are respectively and ,but The total number of antennas equipped for the satellite. ( ) represents all The set of satellites. Among them, satellites service A set of users With users communicative A collection of satellites Let the set of all users being served be denoted as . The size of the set is .

[0039] Let the number of subcarriers in Orthogonal Frequency Division Multiplexing (OFDM) be . The length of the cyclic prefix (CP) is The system sampling time interval is Then the OFDM symbol time length is CP time length is .remember .

[0040] II. Downlink / Uplink Beambase Channel Model

[0041] After time-frequency compensation is performed on the satellite signal at the user side, the satellite To users The channel matrix on a certain subcarrier can be represented as:

[0042] (1)

[0043] in , Indicates satellite To users The number of multipath paths in the channel, Indicates satellite To users Channel number Equivalent channel gain of the stripe path. and The array response vectors on the satellite side and the user side are respectively represented as...

[0044] (2)

[0045] in and They represent satellites For users Corresponding to direction and The direction cosine, and and Representing users respectively For satellite Corresponding to the Strip diameter, corresponding to direction and The direction cosine of the direction. , , ,and They respectively represent the corresponding , , and The angle of direction. Remember. ,but Defined as

[0046] (3)

[0047] and In order to make Factors that satisfy the conjugate central symmetry property, i.e. This property can be used to reduce the complexity of subsequent beam structure designs. express Number of antennas in the direction, , ,and , and They represent The antenna spacing in the direction, the downlink center frequency, and the speed of light. We call... In The direction cosine is the one after scaling.

[0048] The following section uses the direction cosine after scaling. , and , Perform uniform sampling and derive the beam-based channel model. For the maximum nadir angle of the satellite, then satisfy The corresponding scaling direction cosine. satisfy ,in .make ,in , , and They represent The number of samples and the refinement factor for each direction. (Note: The original text contains some inconsistencies and unclear formatting. A more accurate translation would require the full context.) ,in , , and They represent Number of samples and refinement factor for each direction. Definition and The beam matrix of the direction is

[0049] (4)

[0050] in and For set and The approximate scaled direction cosine in the equation, and Defined as

[0051] (5)

[0052] and We call This is the sampled array response vector. Therefore, It can be represented as

[0053] (6)

[0054] in This represents the diffusion vector, which describes how channel energy spreads between different adjacent beams. Then the satellite-side downlink array response vector can be expressed as

[0055] (7)

[0056] in , ,and . It can be represented as

[0057] (8)

[0058] in This represents the diffusion vector. Let it be... User-side downlink array response vector It can be represented as

[0059] (9)

[0060] in , ,and At this point, the downlink channel matrix can be represented as...

[0061] (10)

[0062] in , and Denotes the downlink beam domain channel, where It follows a Rice distribution with Rice factor. We call The channel in the model is represented as a downlink beam-based channel model. That is, the downlink beam-based channel model is represented as the product of the user-side beam matrix, the downlink beam domain channel, and the conjugate transpose of the satellite-side beam matrix. The downlink beam domain channel is the product of a random vector and the conjugate transpose of a spread vector, where the random vector follows a Rice distribution, and the spread vector is a real-valued vector representing the distribution of channel energy on different beams.

[0063] For the uplink, after time-frequency pre-compensation is performed on the user side, the user... To satellite The uplink channel matrix on a certain subcarrier is represented as follows:

[0064] (11)

[0065] in , Indicates user To satellite Channel number Equivalent channel gain of the stripe. Uplink array response vector. and Defined as

[0066] (12)

[0067] in

[0068] (13)

[0069] , , , This represents the uplink center frequency. (Note: The original text contains some formatting errors and inconsistencies. A more accurate translation would require the full context.) and For upward direction and The beam matrix of the direction, its definition is the same as Similarly, the uplink array response vectors on the satellite side and the user side can be re-represented as follows:

[0070] (14)

[0071] and

[0072] (15)

[0073] in , , , , , , and and Let each represent the corresponding diffusion vector. Then the uplink channel matrix can be rewritten as...

[0074] (16)

[0075] in ,and Denotes the uplink beam domain channel, where It follows a Rice distribution with Rice factor. We call The channel in the model is represented as an uplink beam-based channel model. That is, the uplink beam-based channel model is represented as the product of the satellite-side beam matrix, the uplink beam domain channel, and the conjugate transpose of the user-side beam matrix; the uplink beam domain channel is the product of the spread vector and the conjugate transpose of the random vector; where the random vector follows a Rice distribution, and the spread vector is a real-valued vector representing the distribution of channel energy on different beams.

[0076] It is worth noting that, for Beam matrix and It is independent of OFDM symbols and OFDM subcarriers, and is the same for different users. Definition , , , , , , ,as well as .So and They can be represented as follows:

[0077] (17)

[0078] and

[0079] (18)

[0080] in , , and express Point DFT matrix. Furthermore... , Its row and column index set , , and They are respectively , , and It is worth noting that although the uplink and downlink beam matrices differ between the satellite and user sides due to their different center frequencies, they can be constructed from phase-shifted partial DFT matrices. This helps reduce the complexity of the subsequently proposed downlink beamformer (BSP) design and uplink beamformer (BSR) design. Since the subsequent analysis of uplink and downlink is conducted independently, we retain the uplink and downlink superscripts of the equivalent channel gain to distinguish between the uplink and downlink channels, and omit the uplink and downlink superscripts of the remaining terms to maintain simplicity.

[0081] Due to the limited number of satellite antennas, channel energy will diffuse around adjacent beams near the beam with the highest energy. The channel energy tends to have a diamond-shaped distribution around the beam with the highest energy, and increasing the finer sampling factor can effectively suppress energy leakage. The diffusion vector is defined below. The set of beam indices corresponding to the selected elements is

[0082] (19)

[0083] in express direction and The direction has the number of additional beam indices selected near the maximum energy beam, and .So and The downlink and uplink channel matrices in the equation can be approximated as follows:

[0084] (20)

[0085] and

[0086] (twenty one)

[0087] in , , , And beam selection matrix Defined as

[0088] (twenty two)

[0089] For uplink and downlink, assuming and It follows a Rice distribution, and its average channel energy is Rice factor is The user-side channel correlation matrix can be represented as

[0090] (twenty three)

[0091] in This represents the user-side beam domain channel correlation array.

[0092] III. Downlink / Uplink Signal Model

[0093] Consider using a linear receiver on the user side to extract the target satellite's signal and perform time and frequency compensation on the extracted signal to achieve time and frequency synchronization with the target satellite. Each satellite uses linear precoding to generate the transmitted signal for each user. Specifically, the user... Satellite received on a certain subcarrier The signal can be represented as

[0094] (twenty four)

[0095] in For users For satellite downlink receiver, For satellite For users The transmission power, For satellite For users The normalized downlink precoder satisfies , For a transmitted data stream with a mean of 0 and a variance of 1, the satellite Total transmission power is . The signal is a Gaussian asynchronous interference signal with variance . ,in Represented as

[0096] (25)

[0097] and This represents the variance of Gaussian white noise on the user side. For the uplink, consider that the satellite uses a linear receiver, and the user uses linear precoding to generate signals to be transmitted to each satellite. Received user on a certain subcarrier The received signal is

[0098] (26)

[0099] in Indicates satellite For users The uplink receiver, For users For satellite The transmission power, For normalized uplink precoder, For a transmitted data stream with a mean of 0 and a variance of 1, the satellite Total transmission power is . The signal is a Gaussian asynchronous interference signal, and its covariance matrix is... , Represented as

[0100] (27)

[0101] in The variance of Gaussian white noise on the satellite side.

[0102] IV. Downlink / Uplink Decoupling Precoder and Receiver Design

[0103] For a given downlink receiver, consider designing the downlink precoder using the ASLNR maximization criterion. Specifically, for satellites... For users The ASLNR is represented as

[0104] (28)

[0105] in , Indicates the downlink signal-to-noise ratio. Make The largest downlink precoder can be represented as

[0106] (29)

[0107] in The power normalization factor makes , The following section considers downlink receiver design using the ASINR maximization criterion for a given downlink precoder. Specifically, the user... For satellite ASINR can be represented as

[0108] (30)

[0109] in .make The largest downlink receiver can be represented as

[0110] (31)

[0111] in The normalized corresponding matrix The eigenvector with the largest eigenvalue, and .pass and It can be observed that the design of each satellite's downlink precoder and each user receiver depends on information from the other, and the convergence of alternating optimization of the precoder and receiver cannot be guaranteed. We can first prove that the design of the downlink precoder and receiver can be decoupled in the following two cases: i. and ii. In both cases, the downlink precoder and downlink receiver The decoupling expression is as follows

[0112] (32)

[0113] in for The power normalization factor. ,and express The largest eigenvalue. That is, the satellite. Relevant users The decoupling closed-form expression for the pre-encoder is: by using satellite Satellite side rudder vectors corresponding to all user terminals ,in The outer product of the set of users within the system and the largest eigenvalue of the corresponding user-side channel correlation matrix represents the total number of users in the system. Then sum them up, and then launch the satellite on its diagonal. Relevant users The reciprocal of the downlink transmission signal-to-noise ratio The inverse of the resulting matrix is ​​then compared with the satellite. Relevant users Satellite side rudder vector Multiply, then pass through a coefficient The scaled vector; user corresponding satellites The decoupling closed-form expression for the receiver is: through the user Correlation arrays of user-side channels for different satellites With the corresponding downlink transmission signal-to-noise ratio Multiply the results, sum them over different satellites, add the sum to the identity matrix, and multiply the inverse of the resulting matrix by the user's... corresponding satellites The user-side channel correlation matrix is ​​obtained by performing eigenvalue decomposition on the resulting matrix, and then the eigenvector corresponding to its largest eigenvalue is obtained.

[0114] For both low and high SNR, the design of the downlink precoder and receiver can be independent of each other and depends only on the sCSI. Notably, the downlink precoder design for each satellite depends only on its local sCSI and is independent of other satellites. Similarly, the downlink receiver design for each user depends only on their local sCSI and is independent of other users. Therefore, the computational complexity of the downlink precoder and receiver, along with the complexity of inter-satellite and satellite-to-ground interactions, can be significantly reduced.

[0115] For a given uplink precoder, consider designing an uplink receiver using the ASINR maximization criterion, and the satellite... For users ASINR can be considered as about The function. Specifically, it can be represented as

[0116] (33)

[0117] in .make The largest uplink receiver can be represented as

[0118] (34)

[0119] in For a given uplink receiver, consider designing an uplink precoder using the ASLNR maximization criterion, and using... The ASLNR for the satellite is about The function can be represented as

[0120] (35)

[0121] in ,and Indicates the uplink SNR. Make The largest uplink precoder can be represented as

[0122] (36)

[0123] in .observe and It can be observed that the uplink precoder and receiver designs are coupled. For both low and high SNR cases, we can prove that the uplink precoder and receiver designs can be decoupled in the following two cases: i. and ii. In both cases, the uplink precoder and uplink receiver The decoupling expression is as follows

[0124] (37)

[0125] i.e., user corresponding satellites The decoupling closed-form expression for the precoder is: through the user Correlation arrays of user-side channels for different satellites Summing the values ​​from different satellites and loading the uplink transmission signal-to-noise ratio onto the diagonal. The reciprocal of the result, multiplied by the inverse of the resulting matrix by the user. corresponding satellites The user-side channel correlation matrix is ​​then used to perform eigenvalue decomposition on the resulting matrix, and the eigenvector corresponding to the largest eigenvalue is obtained; satellite Relevant users The decoupling closed-form expression for the receiver is: through the satellite Satellite side rudder vectors of all user terminals served The outer product multiplied by the largest eigenvalue of the corresponding user-side channel correlation matrix Then multiply by the corresponding uplink transmission signal-to-noise ratio Then sum them up, add the resulting matrix to the identity matrix, and then sum the inverse of the resulting matrix to the satellite matrix. Relevant users Satellite side rudder vector The vector obtained after multiplication.

[0126] For both low and high SNR, the design of the uplink receiver on each satellite side and the uplink precoder on each user side can be independent of each other and depend only on the local sCSI of each satellite and each user.

[0127] V. Design of Downlink Beam Structure Precoder and Uplink Beam Structure Receiver

[0128] First, it can be proven that when ,and hour, It can be represented as

[0129] (38)

[0130] in

[0131] (39)

[0132] and

[0133] (40)

[0134] as well as When the satellite antenna approaches infinity and the beam index sets for any two users do not overlap, the space domain downlink precoder... The design can be converted into a beam domain vector. The design. Due to the sparsity of the beam domain channel in satellite massive MIMO, The dimension is typically smaller than The dimension of the downlink precoder can be significantly reduced. Therefore, the complexity of designing the downlink precoder can be significantly reduced. We call this... Spatial domain precoder For beamforming pre-encoders, it is called For beam domain pre-encoders. Furthermore, In Indicates the beam index set ASLNR is implemented using a beamform pre-encoder.

[0135] As the number of users in a multi-satellite massive MIMO system increases, the beam index sets for different users may overlap. In this case, it is necessary to consider incorporating more beams into the design of the beam structure precoder to improve system performance. It can be proven that when... At that time, define a new set of beam indexes. Its definition and set in Similarly, only In Replace with At this point, we can obtain

[0136] (41)

[0137] When set elements in The inequality sign becomes equal when the following conditions are met.

[0138] (42)

[0139] In beamforming pre-encoder design, incorporating more beams can improve performance, and The beam selection criterion is given, namely, satisfying Beams should not be considered because their participation will not improve performance.

[0140] In practical systems, although the number of antennas on the satellite side is limited, the proposed beam structure precoder can still achieve near-optimal performance when a large number of antennas are deployed on the satellite side. Below, the constrained spatial domain precoder satisfies... ,in And beam selection matrix Definition and Similarly, except for the beam index set Replace with The size of the set is Therefore, ASLNR can be rewritten as

[0141] (43)

[0142] in , ,and .make The largest beam domain precoder is represented as

[0143] (44)

[0144] in Make The decoupling design of the downlink beamforming pre-encoder can be expressed as:

[0145] (45)

[0146] in Make That is, satellite. Relevant users The beam domain precoder is: through satellite Left-multiply the spread vector of all user terminals by the beam matrix and its conjugate transpose And the obtained vector is based on the satellite Relevant users The beam set is extracted and then correlated with the maximum eigenvalue of the user-side channel correlation matrix of the corresponding user. The square root product of the vectors obtained by multiplying the vectors by their square roots is summed, and the resulting matrix is... The conjugate transpose of the beam matrix is ​​based on the satellite Relevant users The beam set is extracted, and the extracted matrix is ​​right-multiplied by its conjugate transpose before being compared with the satellite beam set. Relevant users The matrix obtained by multiplying the reciprocals of the downlink transmit signal-to-noise ratio Add them together, and then add the inverse of the resulting matrix to the satellite. Relevant users The diffusion vector is multiplied by the beam matrix and its conjugate transpose, and then multiplied by the satellite. Relevant users The vector after beam set extraction The vector is obtained by multiplying and then scaling by a coefficient.

[0147] therefore, The derived spatial domain downlink precoding can be represented as

[0148] (46)

[0149] For the design of uplink beamforming receivers, it can first be proven that when ,and hour, It can be represented as

[0150] (47)

[0151] in

[0152] (48)

[0153] and

[0154] (49)

[0155] as well as When the number of satellite antennas approaches infinity, and the beam index sets of each satellite for any two users do not overlap, the space domain uplink receiver... The design can be transformed into beam domain vector The design, we call This is a beam domain receiver. Because... The dimensions are much lower than Therefore, the design complexity of the uplink receiver can be significantly reduced. We call this... In It is a beamforming receiver. Furthermore... Indicates the beam index set ASINR implemented using a beam structure receiver. As the number of users increases and the beam index sets of different users overlap, it can be proven that when... At that time, for the beam index set and You can get

[0156] (50)

[0157] When set elements in The inequality is equal when the following conditions are met.

[0158] (51)

[0159] Below, the constrained spatial domain uplink receiver satisfies the following structure. And ASINR can be rewritten as

[0160] (52)

[0161] in .make The largest beam domain receiver can be calculated as

[0162] (53)

[0163] The decoupled beam structure uplink receiver can be expressed as follows:

[0164] (54)

[0165] in .satellite Relevant users The beam domain receiver is used to detect satellites. Multiply the spread vectors of all user terminals served by the beam matrix and its conjugate transpose, and then multiply the resulting vectors by the beam matrix and its conjugate transpose. According to satellite Relevant users The beam set is extracted to obtain Then, the maximum eigenvalue of the user-side channel correlation matrix of the corresponding user. The square root and the corresponding user's uplink transmission signal-to-noise ratio The square root product of the vectors obtained by multiplying the vectors by their square roots is summed, and the resulting matrix is... The conjugate transpose of the beam matrix is ​​based on the satellite Relevant users The beam set is extracted, and the extracted matrix is ​​right-multiplied by its conjugate transpose to obtain the matrix. Add them together, and then add the inverse of the resulting matrix to the satellite. Relevant users The diffusion vector is multiplied by the beam matrix and its conjugate transpose, and then multiplied by the satellite. Relevant users The vector after beam set extraction The vector obtained by multiplication.

[0166] Its derived spatial domain uplink receiver can be represented as

[0167] (55)

[0168] VI. Low-complexity design and implementation

[0169] The design complexity of the beamforming downlink precoder and uplink receiver comes from... and First, prove and The design relies solely on real-valued matrix operations. (Note:) It is a reverse permutation matrix and satisfies .because Each column is conjugately centrally symmetric, therefore we can obtain And the matrices in (45) and (54) It can be rewritten as

[0170] (56)

[0171] This means It is a real-valued matrix. Because the rudder vector... It is also conjugately centrally symmetric, therefore we can obtain It is also a real-valued vector. Furthermore, it is easy to verify that the beam selection matrix is ​​also real-valued. Therefore, calculating... and It depends only on real-valued matrix operations.

[0172] because It is independent of specific signals and users, and therefore can be calculated and stored in advance. Specifically, It can be represented as

[0173] (57)

[0174] in This indicates rounding down, and It can be calculated directly from its first column, that is

[0175] (58)

[0176] Therefore, by calculation and Can be obtained directly Its computational and storage complexities are respectively and .

[0177] The following can be done by sampling interval Introduced in China Each sampling point, i.e. ,and This allows for a simplified expression of the satellite's side rudder vector. Let... And make Represents the direction cosine closest to scaling. The sampling points are defined as follows:

[0178] (59)

[0179] Therefore, the rudder vector It can be approximated as

[0180] (60)

[0181] Note that when hour, It can be by Obtained through cyclic shift, represented as

[0182] (61)

[0183] Real value vector It can be represented as

[0184] (62)

[0185] in Calculated as

[0186] (63)

[0187] Therefore, we can obtain the results from (58), (61), (62), and (63). Its computational complexity is The storage complexity is Downlink beam domain pre-encoder and uplink beam domain receiver The design complexity is ,in In comparison, the design complexity of the spatial domain downlink precoder and uplink receiver is... .

[0188] The complexity arising from using a designed downlink precoder to generate the transmitted signals for each user on each satellite, and from using a designed uplink receiver to recover the transmitted signals for each user on each satellite, is called implementation complexity. Using a designed beamform downlink precoder, the satellite... The downlink transmission signal can be represented as

[0189] (64)

[0190] in , Therefore, the implementation complexity of the beamform precoder is... The implementation complexity of the spatial domain precoder is... .

[0191] Using a pre-designed beamform receiver, the satellite Restore user The signal can be represented as

[0192] (65)

[0193] in ,and Therefore, the implementation complexity of the beamforming uplink receiver is... The implementation complexity of a space domain receiver is... .

[0194] We assume that the downlink precoder and uplink receiver are designed once over 100 subframes and 14 resource blocks, and used to generate the transmitted signal. Assume one subframe has 14 OFDM symbols and one resource block has 12 subcarriers. Then, the total complexity of using a downlink beamforming precoder and an uplink beamforming receiver is the sum of the design complexity and the implementation complexity, which can be expressed as follows: and ,in , The total complexity of using a spatial domain precoder and receiver can be calculated as follows: .

[0195] Figure 4 This paper presents the proposed methods (DL DPR, DL BSP, UL DPR, UL BSR), uplink / downlink traversal and rate-optimal precoder and receiver joint design methods (JPRD, JPRVD), and precoder design methods for single-satellite scenarios. Figure 4 It can be seen that the proposed method can approximate the traversal and rate-optimal design method, and has a significant improvement in traversal and rate performance compared with the single-satellite precoding design method.

[0196] This invention also discloses a multi-satellite massive MIMO communication system, including satellites and user terminals, wherein the satellites or gateway stations associated with them, and the user terminals implement any of the decoupling design methods described above.

[0197] This invention also discloses a computer program product, including a computer program / instructions, wherein the computer program / instructions, when executed by a processor, follow the steps of any of the decoupling design methods described above.

[0198] Any aspects of this invention not described in detail are well-known to those skilled in the art.

[0199] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A decoupling design method for downlink precoder and receiver in multi-satellite massive MIMO, characterized in that, The satellites use the Average Signal-to-Leakage-to-Noise Ratio (ASLNR) criterion to calculate precoders to generate their respective transmitted signals. The user terminals use the ASINR criterion to calculate the average signal-to-interference-plus-noise ratio (ASINR) for the receiver to perform linear reception processing of the signals transmitted by each satellite. Among these, the satellites... Relevant users The decoupling closed-form expression for the pre-encoder is: by using satellite The outer product of the satellite-side rudder vectors of all corresponding user terminals is multiplied by the maximum eigenvalue of the corresponding user-side channel correlation matrix, then summed, and finally loaded onto the satellite along its diagonal. Relevant users The inverse of the downlink transmission signal-to-noise ratio is used to inverse the resulting matrix with the satellite signal-to-noise ratio. Relevant users The vector is obtained by multiplying the satellite side rudder vectors and then scaling them using a coefficient; User corresponding satellites The decoupling closed-form expression for the receiver is: through the user The user-side channel correlation matrix for each satellite is multiplied by the corresponding downlink transmit signal-to-noise ratio, summed over each satellite, and then added to the identity matrix. The inverse of the resulting matrix is ​​then multiplied by the user... corresponding satellites The user-side channel correlation matrix is ​​obtained by performing eigenvalue decomposition on the resulting matrix, and then the eigenvector corresponding to its largest eigenvalue is obtained.

2. A decoupling design method for uplink precoder and receiver in multi-satellite massive MIMO, characterized in that, User terminals use precoders calculated using the Average Signal-to-Leakage-Noise Ratio (ASLNR) criterion to generate their respective transmit signals, while the satellite side uses the Average Signal-to-Interference-Noise Ratio (ASINR) criterion to calculate the receiver's linear reception processing of each user's signal; among which, user corresponding satellites The decoupling closed-form expression for the precoder is: through the user The user-side channel correlation matrices for different satellites are summed over each satellite, and the inverse of the uplink transmission signal-to-noise ratio is loaded onto the diagonal. The inverse of the resulting matrix is ​​then multiplied by the user... corresponding satellites The user-side channel correlation matrix is ​​then used to perform eigenvalue decomposition on the resulting matrix, and the eigenvector corresponding to the largest eigenvalue is obtained; satellite Relevant users The decoupling closed-form expression for the receiver is: through the satellite The outer product of the satellite-side rudder vectors of all user terminals served is multiplied by the maximum eigenvalue of the corresponding user-side channel correlation matrix, then multiplied by the corresponding uplink transmission signal-to-noise ratio, and summed. The resulting matrix is ​​then added to the identity matrix, and the inverse of the resulting matrix is ​​then multiplied by the satellite... Relevant users The vector obtained by multiplying the satellite side rudder vectors.

3. A decoupling design method for pre-encoders of multi-satellite massive MIMO downlink beam structure, characterized in that, include: Each satellite uses the downlink beambase channel model and the local statistical channel information of each user terminal to design the precoder for each user beam structure, and uses the obtained precoder for downlink precoding transmission. The downlink beam-based channel model is represented as the product of the user-side beam matrix, the downlink beam domain channel, and the conjugate transpose of the satellite-side beam matrix. The beam matrix consists of the sampling array response vectors corresponding to a selected set of scaled direction cosine sampling points. The downlink beam domain channel is the product of the conjugate transpose of a random vector and a spread vector. The random vector follows a Ricean distribution, and the spread vector is a real-valued vector representing the distribution of channel energy across different beams. The beam structure precoder includes a low-dimensional beam domain precoder for each user, a beam mapping module for each user, and a beam modulation module. The low-dimensional beam domain precoder for each user is a precoder on the user's beam set. The beam mapping module maps the low-dimensional beam domain precoded signals of each user into a complete beam domain transmitted signal. The beam modulation module multiplies the beam matrix by the beam domain transmitted signal vector, which is the sum of the transmitted signal vectors of each user's beam domain. The beam domain precoder relies on the Average Signal-to-Noise Ratio (ASLNR) criterion. Relevant users The beam domain precoder is: through satellite The spread vectors of all corresponding user terminals are left-multiplied by the beam matrix and its conjugate transpose, and the resulting vectors are then processed according to the satellite... Relevant users The beam set is extracted, and then the vector obtained by multiplying it by the square root of the largest eigenvalue of the corresponding user's side channel correlation matrix is ​​summed. The resulting matrix is ​​then combined with the conjugate transpose of the beam matrix according to the satellite... Relevant users The beam set is extracted, and the extracted matrix is ​​right-multiplied by its conjugate transpose before being compared with the satellite beam set. Relevant users Add the matrices obtained by multiplying the reciprocals of the downlink transmission signal-to-noise ratios, and then combine the inverse of the resulting matrix with the satellite signal-to-noise ratio. Relevant users The diffusion vector is multiplied by the beam matrix and its conjugate transpose, and then multiplied by the satellite. Relevant users The vector is obtained by multiplying the extracted beam sets into vectors and then scaling them with a coefficient.

4. A decoupling design method for a multi-satellite massive MIMO uplink beam structure receiver, characterized in that, include: Each satellite uses the uplink beam base channel model and the statistical channel information of each user terminal to design the receiver for each user beam structure, and uses the obtained receiver to perform uplink linear reception processing. The uplink beam-based channel model is represented as the product of the satellite-side beam matrix, the uplink beam-domain channel, and the conjugate transpose of the user-side beam matrix. The beam matrix consists of the sampling array response vectors corresponding to a selected set of scaled direction cosine sampling points. The uplink beam-domain channel is the product of the spread vector and the conjugate transpose of a random vector; the random vector follows a Ricean distribution, and the spread vector is a real-valued vector representing the distribution of channel energy across different beams. The beam structure receiver includes a beam transformation module, a beam decimation module, and user beam-domain receivers. The beam transformation module transforms the spatial domain received signal vectors on each subcarrier into beam-domain received signal vectors. The beam decimation module decimates the beam-domain received signal vectors according to the beam sets of each user. Finally, the user beam-domain receivers and the decimated beam-domain received signal vectors are used to linearly process the signals of each user. The beam-domain receivers rely on the average signal-to-interference-plus-noise ratio (ASINR) criterion. Relevant users The beam domain receiver is used to detect satellites. The spread vectors of all user terminals served are left-multiplied by the beam matrix and its conjugate transpose, and the resulting vectors are then processed according to the satellite... Relevant users The beam set is extracted, and then the outer product of the vector obtained by multiplying the square root of the maximum eigenvalue of the corresponding user's side channel correlation matrix and the square root of the corresponding user's uplink transmission signal-to-noise ratio is calculated. The resulting matrix is ​​then summed with the conjugate transpose of the beam matrix according to the satellite... Relevant users The beam set is extracted, and the extracted matrix is ​​right-multiplied by its conjugate transpose, and the resulting matrix is ​​added together. The inverse of the resulting matrix is ​​then used with the satellite beam set. Relevant users The diffusion vector is multiplied by the beam matrix and its conjugate transpose, and then multiplied by the satellite. Relevant users The vector obtained by multiplying the vectors extracted from the beam set.

5. The decoupling design method according to claim 3 or 4, characterized in that, The calculation of the beam domain precoder or beam domain receiver relies solely on real-valued matrix operations. The product of the conjugate transpose of the beam matrix and itself can be calculated from the first column of the matrix obtained by multiplying the conjugate transposes of the component beam matrices in both directions by themselves, and stored in advance. Furthermore, the product of the conjugate transpose of the beam matrix and itself multiplied by the diffusion vector of each user can be approximated by increasing the number of sampling points of the direction cosine, and calculated and stored in advance.

6. A multi-satellite massive MIMO communication system, comprising satellites and user terminals, characterized in that, The satellite and user terminal implement the steps of the decoupling design method according to any one of claims 1-5.

7. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the decoupling design method according to any one of claims 1-5.

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