Decoupling design method for multi-satellite large-scale MIMO precoder and receiver

Abstract

The invention discloses a multi-satellite large-scale MIMO precoder and receiver decoupling design method, which comprises a multi-satellite large-scale MIMO uplink / downlink precoder and receiver decoupling design method, and further establishes a beam-based channel model to further reduce the implementation complexity. And the downlink / uplink beam domain channel is a product of a random vector / diffusion vector and a diffusion vector / random vector conjugate transpose. Independently designing a downlink precoder and an uplink receiver by each satellite only by using local statistical channel information, and implementing downlink precoding transmission and uplink linear receiving processing by using the designed precoder and receiver; each user independently designs an uplink precoder and a downlink receiver only by using local statistical channel information, and performs uplink precoding transmission and downlink linear receiving processing by using the designed precoder and receiver. According to the method, the design and implementation complexity of the precoder and the receiver can be greatly reduced while the performance of the multi-satellite large-scale MIMO system is ensured.

Description

Technical Field

[0001] The present invention belongs to the field of communication technology, and in particular relates to a multi-satellite large-scale MIMO precoder and receiver decoupling design method. Background Art

[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. Amidst the rapid advancements in cutting-edge fields like smart cities and autonomous driving, network coverage shortcomings in remote areas have become increasingly prominent. This digital divide has made satellite communication systems, offering wide-area coverage and flexible deployment, a key solution for bridging global communications. A multi-orbit collaborative networking system, leveraging the millisecond-level latency advantages of low-orbit satellites, the balanced coverage capabilities of medium-orbit satellites, and the wide-area service capabilities of high-orbit satellites, is reshaping the integrated communications landscape across air, space, land, and sea.

[0003] Massive Multiple-Input Multiple-Output (MIMO) is a core technology of fifth-generation mobile communications (5G). By deploying a large number of antennas at base stations, MIMO enables flexible configuration of dynamic beams, enabling multi-user communications using the same time-frequency resources. Extending Massive MIMO technology to mobile satellite communications enables the construction of efficient satellite communication systems, achieving higher spectral and power efficiency. This technological convergence can significantly enhance satellite communication performance, particularly in meeting the needs of large-scale terminal access.

[0004] In recent years, the global demand for seamless internet access has surged, driving the development of mega-satellite constellations. By launching hundreds or even thousands of low-orbit satellites, mega-satellite constellations can not only cover remote areas that are difficult to reach with traditional communication networks, but also, through joint transmission technology, enable a single user to simultaneously receive multi-stream signals from multiple satellites. Compared to single-satellite systems, the deployment of mega-satellite constellations will further improve the spectrum 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, precoder and receiver designs that rely on statistical channel state information are typically coupled and require iteration. Therefore, while ensuring system rate performance, it is crucial to decouple the precoder and receiver designs. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a decoupling design method for multi-satellite massive MIMO precoders and receivers to overcome the shortcomings of the existing technology 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 purpose, the present invention adopts the following technical solution:

[0007] In the first aspect, the present invention provides a decoupling design method for a multi-satellite massive MIMO downlink precoder and receiver. The satellite side uses the average signal-to-leakage-to-noise ratio (ASLNR) criterion to calculate the precoder to generate each transmission signal. The user terminal uses the average signal-to-interference-to-noise ratio (ASINR) criterion to calculate the receiver to perform linear reception processing on the signals sent by each satellite. The decoupling closed-form expression of the precoder of the corresponding user k of the satellite s is as follows: the outer product of the satellite side rudder vectors of all user terminals corresponding to the satellite s is multiplied by the maximum eigenvalue of the corresponding user side channel correlation matrix, and then the sum is calculated, and then the sum is calculated on the diagonal thereof. Load the inverse of the downlink signal-to-noise ratio of user k corresponding to satellite s, multiply the inverse matrix of the resulting matrix by the satellite-side rudder vector of user k corresponding to satellite s, and then scale the resulting vector by a coefficient. The decoupling closed-form expression of the receiver for user k corresponding to satellite s is as follows: multiply the user-side channel correlation matrix of different satellites corresponding to user k by the corresponding downlink signal-to-noise ratio, sum it for different satellites, add it to the identity matrix, multiply the inverse matrix of the resulting matrix by the user-side channel correlation matrix of satellite s corresponding to user k, and then perform eigenvalue decomposition on the resulting matrix to obtain the eigenvector corresponding to the largest eigenvalue.

[0008] In the second aspect, the present invention provides a decoupling design method for multi-satellite massive MIMO uplink precoder and receiver. The user terminal uses the precoder calculated by the average signal-to-leakage-to-noise ratio (ASLNR) criterion to generate its own transmission signal, and the satellite side uses the average signal-to-interference-and-noise ratio (ASINR) criterion to calculate the receiver to perform linear reception processing on the signal of each user. The decoupling closed-form expression of the precoder of user k corresponding to satellite s is as follows: by summing the user-side channel correlation matrix of different satellites corresponding to user k for different satellites, and loading the inverse of the uplink transmission signal-to-noise ratio on the diagonal, the obtained The inverse matrix of the matrix is multiplied by the user side channel correlation matrix of satellite s corresponding to user k, and then the obtained matrix is eigenvalue decomposed, and the eigenvector corresponding to its maximum eigenvalue is obtained; the decoupling closed-form expression of the receiver corresponding to user k by satellite s is: the outer product of the satellite side steering vectors of all user terminals served by satellite s is multiplied by the maximum eigenvalue of the corresponding user side channel correlation matrix, multiplied by the corresponding uplink transmission signal-to-noise ratio, and then summed, and then the obtained matrix is added to the unit matrix, and the inverse matrix of the obtained matrix is multiplied by the satellite side steering vector of user k corresponding to satellite s to obtain the vector.

[0009] In the third aspect, the present invention further provides a multi-satellite massive MIMO beam-based channel model for the decoupling design method, wherein the downlink beam-based channel model is represented as the product of the conjugate transpose of the user-side beam matrix, the downlink beam domain channel and the satellite-side beam matrix; the uplink beam-based channel model is represented as the product of the conjugate transpose of the satellite-side beam matrix, the uplink beam domain channel and the user-side beam matrix; the beam matrix is composed of 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 diffusion vector, and the uplink beam domain channel is the product of a diffusion vector and the conjugate transpose of a random vector; the random vector obeys the Rice distribution, and the diffusion vector is a real-valued vector representing the distribution of channel energy on different beams.

[0010] A multi-satellite massive MIMO downlink beam structure precoder decoupling design method based on a beam-based channel model includes: each satellite uses the downlink beam-based channel model and local (not involving other satellites) statistical channel information of each user terminal to design a beam structure precoder for each user, and uses the obtained precoder 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 each user beam set. The beam mapping module for each user maps the low-dimensional beam domain precoded signal of each user into a complete beam domain transmission signal. The beam modulation module multiplies the beam matrix by the beam domain transmission signal vector, and the beam domain transmission signal vector is the sum of the beam domain transmission signal vectors of each user.

[0011] Furthermore, the beam domain precoder depends on the average signal-to-leakage-and-noise ratio (ASLNR) criterion. The beam domain precoder for user k corresponding to satellite s is: by multiplying the spreading vectors of all user terminals corresponding to satellite s by the beam matrix and its conjugate transpose on the left, extracting the resulting vector according to the beam set of user k corresponding to satellite s, and then multiplying it by the square root of the maximum eigenvalue of the user-side channel correlation matrix of the corresponding user, summing the outer products of the vectors obtained, adding the resulting matrix to the matrix obtained by extracting the conjugate transpose of the beam matrix according to the beam set of user k corresponding to satellite s, multiplying the extracted matrix by its conjugate transpose on the right, and then multiplying it by the inverse of the downlink signal-to-noise ratio of user k corresponding to satellite s, and multiplying the inverse matrix of the resulting matrix by the spreading vector of user k corresponding to satellite s by the beam matrix and its conjugate transpose on the left, and multiplying the vector extracted according to the beam set of user k corresponding to satellite s, and then scaling the vector by a coefficient.

[0012] A decoupling design method for a multi-satellite massive MIMO uplink beam structure receiver based on a beam-based channel model includes: each satellite uses the uplink beam-based channel model and statistical channel information of each user terminal to design a beam structure receiver for each user, and uses the obtained receiver to perform uplink linear reception processing; the beam structure receiver includes a beam transformation module, a beam extraction module and each user's beam domain receiver, the beam transformation module transforms the spatial domain reception signal vector on each subcarrier into a beam domain reception signal vector, the beam extraction module extracts the beam domain reception signal vector according to the beam set of each user, and finally uses each user's beam domain receiver and the extracted beam domain reception signal vector to perform linear processing on the signal of each user.

[0013] Furthermore, the beam domain receiver relies on the average signal-to-interference-plus-noise ratio (ASINR) criterion. The beam domain receiver of satellite s corresponding to user k is obtained by multiplying the spreading vectors of all user terminals served by satellite s by the beam matrix and its conjugate transpose on the left, and extracting the obtained vector according to the beam set of satellite s corresponding to user k, and then summing the outer products of the vectors obtained by multiplying the square root of the maximum eigenvalue of the user-side channel correlation matrix of the corresponding user and the square root of the uplink transmission signal-to-noise ratio of the corresponding user, extracting the conjugate transpose of the beam matrix according to the beam set of satellite s corresponding to user k, and adding the obtained matrix to the matrix obtained by right-multiplying the extracted matrix by its conjugate transpose, and multiplying the inverse matrix of the obtained matrix with the spreading vector of satellite s corresponding to user k by the beam matrix and its conjugate transpose on the left, and multiplying the vector extracted according to the beam set of satellite s corresponding to user k.

[0014] Furthermore, the calculation of the beam domain precoder or beam domain receiver only relies on real-valued matrix operations, and the product of the conjugate transpose of the beam matrix and itself can be calculated by the first column of the matrix obtained by the product of the conjugate transpose of its component beam matrices in two directions and itself, and stored in advance; and the product of the conjugate transpose of the beam matrix and itself multiplied right by the diffusion vector of each user can be approximated by increasing the number of sampling points of the direction cosines, and calculated and stored in advance.

[0015] In a fourth aspect, the present invention provides a multi-satellite massive MIMO communication system, including satellites and user terminals, the satellites or gateways associated therewith, and the user terminals implementing the steps of the decoupling design method.

[0016] In a fifth aspect, the present invention provides a computer program product, comprising a computer program / instruction, which implements the steps of the decoupling design method when executed by a processor.

[0017] Beneficial effects: Compared with the existing technology, the present invention makes full use of the characteristics of satellite channels to carry out a multi-satellite large-scale MIMO precoder and receiver decoupling design method. Each satellite uses only local statistical channel information to independently design the downlink precoder and uplink receiver, and uses the designed precoder and receiver to implement downlink precoding transmission and uplink linear reception processing; each user uses only local statistical channel information to independently design the uplink precoder and downlink receiver, and uses the designed precoder and receiver to implement uplink precoding transmission and downlink linear reception processing; further, the decoupled antenna dimension precoder and receiver design can be used to propose a beam structure precoder and receiver design using the beam-based channel model, and the antenna dimension vector design can be converted into a low-dimensional beam domain vector design. In this way, the design and implementation complexity of the precoder and receiver can be greatly reduced while ensuring the system traversal and rate performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings in the following description only illustrate some embodiments of the present invention. For ordinary technicians in this field, they can also obtain drawings of other embodiments based on these drawings without paying any creative work.

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

[0020] Figure 2 The figure is a flowchart of a satellite-side processing method in multi-satellite massive MIMO mobile communications according to an embodiment of the present invention.

[0021] Figure 3 The figure is a flowchart of a user terminal side processing method in multi-satellite massive MIMO mobile communications 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 communications according to an embodiment of the present invention. DETAILED DESCRIPTION

[0023] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0024] The embodiment of the present invention discloses a method for decoupling the precoder and receiver of a multi-satellite massive MIMO system. The method is applied to satellites or gateways and user terminals connected to satellites, 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 and user terminal uses statistical channel information, including average channel energy and spatial angle information, to calculate the precoder corresponding to each satellite and each user terminal, and the receiver corresponding to each user terminal and each satellite. Figure 1 As shown, a multi-satellite massive MIMO precoder and receiver decoupling design method includes a multi-satellite massive MIMO downlink precoder and receiver decoupling design method and a multi-satellite massive MIMO uplink precoder and receiver decoupling design method.

[0025] In one specific embodiment, a method for decoupling a multi-satellite massive MIMO downlink precoder and receiver is described. Each satellite uses a calculated precoder to generate its own transmit signal, implementing multi-satellite massive MIMO downlink transmission. User terminals use a calculated receiver to perform linear reception processing on the signals transmitted by each satellite. Statistical channel information is obtained from feedback from each user or from an uplink sounding process. The feedback from each user can be their geographic location, average channel energy, or spatial angle information. During the uplink sounding process, each user periodically transmits a sounding signal, and the satellite estimates each user's average channel energy and spatial angle information based on the received sounding signals.

[0026] In the multi-satellite massive MIMO downlink precoder and receiver decoupling design method, the decoupling design of the downlink precoder depends on the average signal-to-leakage-and-noise ratio ASLNR criterion and the average signal-to-interference-and-noise ratio ASINR criterion. The satellite side uses the average signal-to-leakage-and-noise ratio ASLNR criterion to calculate the precoder to generate each transmission signal, and the user terminal uses the ASINR criterion to calculate the receiver to perform linear reception processing on the signal sent by each satellite. The satellite side uses the average signal-to-leakage-and-noise ratio ASLNR criterion to calculate the precoder to generate each transmission signal, and the user terminal uses the ASINR criterion to calculate the receiver to perform linear reception processing on the signal sent by each satellite. The decoupling closed-form expression of the precoder of the corresponding user k of satellite s is as follows: The outer product of the satellite side steering vectors of all user terminals corresponding to satellite s is multiplied by the maximum eigenvalue of the corresponding user side channel correlation matrix, and then the sum is calculated. The inverse of the downlink signal-to-noise ratio of user k corresponding to satellite s is then loaded on its diagonal. The inverse matrix of the resulting matrix is multiplied by the satellite side steering vector of user k corresponding to satellite s, and the resulting vector is scaled by a coefficient. The decoupling closed-form expression of the receiver of user k corresponding to satellite s is as follows: the user side channel correlation matrices corresponding to different satellites of user k are multiplied by the corresponding downlink signal-to-noise ratios, the sum is taken for different satellites, and the matrix is added to the identity matrix. The inverse matrix of the resulting matrix is multiplied by the user side channel correlation matrix of satellite s corresponding to user k, and the eigenvalue decomposition of the resulting matrix is performed to obtain the eigenvector corresponding to the maximum eigenvalue.

[0027] The ASINR in a multi-satellite system is the ratio of the average power of the signal sent by the serving satellite to the user to the sum of the average power of the signal sent to other users and the average power of the signal sent by non-serving satellites in the signal formed by the user receiver.

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

[0029] In the multi-satellite massive MIMO uplink precoder and receiver decoupling design method, the decoupling design of the uplink precoder depends on the average signal-to-leakage-and-noise ratio (ASLNR) criterion and the average signal-to-interference-and-noise ratio (ASINR) criterion. The user terminal generates its own transmission signal using the precoder calculated by the average signal-to-leakage-and-noise ratio (ASLNR) criterion, and the satellite side calculates the receiver to perform linear reception processing on the signal of each user using the ASINR criterion. The decoupling closed-form expression of the precoder of user k corresponding to satellite s is as follows: the user side channel correlation matrix of different satellites corresponding to user k is summed for different satellites, and loaded on the diagonal The inverse matrix of the uplink transmission signal-to-noise ratio is multiplied by the user side channel correlation matrix of satellite s corresponding to user k, and the eigenvalue decomposition of the obtained matrix is performed, and the eigenvector corresponding to the maximum eigenvalue is obtained; the decoupled closed-form expression of the receiver corresponding to user k by satellite s is: the outer product of the satellite side steering vectors of all user terminals served by satellite s is multiplied by the maximum eigenvalue of the corresponding user side channel correlation matrix and then multiplied by the corresponding uplink transmission signal-to-noise ratio, and then the sum is added, and the obtained matrix is added to the identity matrix, and the inverse matrix of the obtained matrix is multiplied by the satellite side steering vector of user k corresponding to satellite s to obtain the vector.

[0030] In some lower complexity embodiments, a multi-satellite massive MIMO beam-based channel model is provided, and the downlink beam-based channel model is represented as the product of the conjugate transpose of the user-side beam matrix, the downlink beam domain channel and the satellite-side beam matrix; the uplink beam-based channel model is represented as the product of the conjugate transpose of the satellite-side beam matrix, the uplink beam domain channel and the user-side beam matrix; the beam matrix is composed of 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 diffusion vector, and the uplink beam domain channel is the product of a diffusion vector and the conjugate transpose of a random vector; the random vector obeys the Rice distribution, and the diffusion vector is a real-valued vector representing the distribution of channel energy on different beams.

[0031] In one specific embodiment, a decoupling design method for a multi-satellite massive MIMO downlink beam structure precoder based on a beam-based channel model is provided. Each satellite uses the downlink beam-based channel model and local (not involving other satellites) statistical channel information of each user terminal, including average channel energy and spatial angle information, to design a beam structure precoder for each user. The obtained precoder is then used for downlink precoding transmission. The beam structure precoder consists of 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 for each user beam set. The beam mapping module maps the low-dimensional beam domain precoded signal of each user into a complete beam domain transmit signal. Beam modulation is the multiplication of a beam matrix by a beam domain transmit signal vector. The beam domain transmit signal vector is the sum of the beam domain transmit signal vectors of each user.

[0032] In the multi-satellite massive MIMO downlink beam structure precoder decoupling design method based on the beam-based channel model, the beam domain precoder relies on the average signal-to-leakage-and-noise ratio (ASLNR) criterion. The beam domain precoder for user k corresponding to satellite s is: by multiplying the spreading vectors of all user terminals corresponding to satellite s by the beam matrix and its conjugate transpose, extracting the resulting vector according to the beam set of user k corresponding to satellite s, and then multiplying it by the square root of the maximum eigenvalue of the user-side channel correlation matrix of the corresponding user, summing the outer products of the vectors obtained; adding the resulting matrix to the matrix obtained by extracting the conjugate transpose of the beam matrix according to the beam set of user k corresponding to satellite s, multiplying the extracted matrix by its conjugate transpose, and then multiplying it by the inverse of the downlink transmission signal-to-noise ratio of user k corresponding to satellite s; multiplying the inverse matrix of the resulting matrix by the spreading vector of user k corresponding to satellite s by the beam matrix and its conjugate transpose, and then multiplying it by the vector extracted according to the beam set of user k corresponding to satellite s; and finally scaling the vector by a coefficient.

[0033] In a specific embodiment, a decoupling design method for a multi-satellite massive MIMO uplink beam structure receiver 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 a beam structure receiver for each user, and uses the obtained receiver to perform uplink linear reception processing. The beam structure receiver consists of a beam transformation module, a beam extraction module, and each user's beam domain receiver. The beam transformation module transforms the spatial domain received signal vector on each subcarrier into a beam domain received signal vector. The beam extraction module extracts the beam domain received signal vector based on the beam set of each user. Finally, each user's beam domain receiver and the extracted beam domain received signal vector are used to perform linear processing on the signal of each user.

[0034] In the decoupling design method for a multi-satellite massive MIMO uplink beam structure receiver based on a beam-based channel model, the beam domain receiver relies on the average signal-to-interference-plus-noise ratio (ASINR) criterion. The beam domain receiver for user k corresponding to satellite s is obtained by multiplying the spreading vectors of all user terminals served by satellite s by the beam matrix and its conjugate transpose on the left, and extracting the resulting vector according to the beam set of user k corresponding to satellite s. The outer product of the vector obtained by multiplying the vector by the square root of the maximum eigenvalue of the user-side channel correlation matrix of the corresponding user and the square root of the uplink transmission signal-to-noise ratio of the corresponding user is summed. The resulting matrix is extracted according to the beam set of user k corresponding to satellite s by the conjugate transpose of the beam matrix, and the extracted matrix is right-multiplied by its conjugate transpose. The inverse matrix of the resulting matrix is multiplied by the spreading vector of user k corresponding to satellite s by the beam matrix and its conjugate transpose on the left, and the vector is multiplied according to the vector extracted according to the beam set of user k corresponding to satellite s.

[0035] In a specific embodiment, the calculation of the above-mentioned beam domain precoder and beam domain receiver only relies on real-valued matrix operations, and the product of the conjugate transpose of the beam matrix and itself can be calculated by the first column of the matrix obtained by the product of the conjugate transpose of its component beam matrices in two directions and itself, and stored in advance; and the product of the conjugate transpose of the beam matrix and itself multiplied on the right by the diffusion vector of each user can be approximated by increasing the number of sampling points of the direction cosines, and calculated and stored in advance.

[0036] The following further introduces the method of the embodiment of the present invention in conjunction with specific implementation scenarios. The method of the present invention is not limited to specific scenarios. For other implementations outside the exemplary scenarios of the present invention, those skilled in the art can make adaptive adjustments based on the specific scenarios according to the technical ideas of the present invention and existing knowledge.

[0037] 1. System Configuration

[0038] Consider that each satellite is equipped with an antenna array (which can be a one-dimensional or two-dimensional array, with dozens to hundreds of antennas). The most basic is a two-dimensional uniform panel antenna array (UPA), that is, the antenna units are evenly arranged in the horizontal and vertical directions. Assume that each satellite is equipped with a UPA, and the number of antenna units in the x-axis and y-axis directions is M respectively. x and M y , then M=M x M y The total number of antennas equipped for the satellite. Assuming that each user side is equipped with a UPA, the number of antenna units in the x′ and y′ directions are N respectively. x and N y , then N=N x N y The total number of antennas equipped for the satellite. represents the set of all n×m dimensional complex (real) matrices. The satellite set is denoted as Among them, satellite s serves K s Users form a collection S communicating with user k k Satellites The set of all users served is The size of the collection is

[0039] The number of subcarriers in Orthogonal Frequency Division Multiplex (OFDM) is N c , the cyclic prefix (CP) length is N p , the system sampling time interval is T s , then the OFDM symbol time length is T c =N c T s , the CP time length is T p =N p T s . Remember N t =N c +N p .

[0040] 2. Downlink / Uplink Beam-Based Channel Model

[0041] After the satellite signal is time-frequency compensated on the user side, the channel matrix from satellite s to user k on a certain subcarrier can be expressed as

[0042]

[0043] in L k，s represents the number of multipath channels from satellite s to user k, represents the channel from satellite s to user k The equivalent channel gain of the stripe diameter. and Denote the array response vectors on the satellite side and the user side, respectively, and are expressed as

[0044]

[0045] in and denote the direction cosines of satellite s to user k in the x-direction and y-direction, respectively, and and They represent the user k’s correspondence to satellite s. The stripe diameter corresponds to the direction cosines in the x′ and y′ directions. and Denote the angles corresponding to the x, y, x′ and y′ directions respectively. Let v∈{x, y, x′, y′}, then Defined as

[0046]

[0047] and In order to make The factors that satisfy the conjugate centrosymmetry property, namely This property can be used to reduce the complexity of the subsequent beam structure design. v Indicates the number of antennas in the v direction, And d v , and c represent the antenna spacing in the v direction, the downlink center frequency, and the speed of light, respectively. We call (3) is the scaled direction cosine.

[0048] Next, we use the scaled direction cosines and Perform uniform sampling and derive the beam-based channel model. is the maximum nadir angle of the satellite, then satisfy The corresponding scaled direction cosines satisfy in make in and Represent the number of samples in the t direction and the refined sampling factor respectively. in and Denote the number of samples in the u direction and the refined sampling factor respectively. The beam matrices in the t and u directions are defined as

[0049]

[0050] in and For collection and The approximate scaled direction cosines in , and Defined as

[0051]

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

[0053]

[0054] in represents the spreading vector, which describes the spreading of channel energy between different adjacent beams. Then the satellite side downlink array response vector can be expressed as

[0055]

[0056] in and It can be expressed as

[0057]

[0058] in Denotes the diffusion vector. User-side downlink array response vector It can be expressed as

[0059]

[0060] in and At this time, the downlink channel matrix can be expressed as

[0061]

[0062] in and represents the downlink beam domain channel, where Obeys the Rice distribution, and the Rice factor is κ k，s We call the channel representation in (10) the 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 the diffusion vector, where the random vector follows the Rice distribution and the diffusion vector is a real-valued vector representing the distribution of channel energy on different beams.

[0063] For the uplink, after time-frequency precompensation is performed on the user side, the uplink channel matrix from user k to satellite s on a certain subcarrier is expressed as

[0064]

[0065] in Indicates the channel from user k to satellite s The equivalent channel gain of the stripe diameter. Uplink array response vector and Defined as

[0066]

[0067] in

[0068]

[0069] Indicates the uplink center frequency. and is the uplink beam matrix in the t and u directions, and its definition is similar to (4). The uplink array response vectors on the satellite side and the user side can be re-expressed as

[0070]

[0071] and

[0072]

[0073] in and and Denote the corresponding spreading vectors respectively. Then the uplink channel matrix can be re-expressed as

[0074]

[0075] in and represents the uplink beam domain channel, where Obeys the Rice distribution, and the Rice factor is κ k，s We call the channel representation in (16) the 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 diffusion vector and the conjugate transpose of the random vector; where the random vector follows the Rice distribution, and the diffusion vector is a real-valued vector representing the distribution of the channel energy on different beams.

[0076] It is worth noting that for p∈{dl,ul}, the beam matrix V p and U p It is independent of OFDM symbols and OFDM subcarriers and is the same for different users. as well as Then V p and U p Can be expressed as

[0077]

[0078] and

[0079]

[0080] in and express Point DFT matrix. In addition, The set of its row and column indices and They are and It's worth noting that although the uplink and downlink beam matrices on the satellite and user sides differ due to different center frequencies, they can be constructed from phase-shifted portions of the DFT matrix. This reduces the complexity of the subsequent downlink beam structure precoder (BSP) and uplink beam structure receiver (BSR) designs. Since the subsequent analysis of uplink and downlink is independent, we retain the uplink and downlink superscripts in the equivalent channel gains to distinguish them, and omit the superscripts for the remaining terms for simplicity.

[0081] Due to the limited number of satellite antennas, the channel energy will spread around the adjacent beams with the highest energy. The channel energy tends to be distributed in a diamond shape around the beam with the highest energy, and increasing the fine sampling factor can effectively suppress energy leakage. The diffusion vector is defined as follows: The beam index set corresponding to the element selected in is

[0082]

[0083] where γ represents the number of additionally selected beam indices near the beam with maximum energy in the x- and y-directions, and Then the downlink and uplink channel matrices in (10) and (16) can be approximately expressed as

[0084]

[0085] and

[0086]

[0087] in And the beam selection matrix Defined as

[0088]

[0089] For uplink and downlink, assuming and Obeying the Rice distribution, the average channel energy is The Rice factor is κ k,s, the user side channel correlation matrix can be expressed as

[0090]

[0091] in Represents the user-side beam domain channel correlation matrix.

[0092] 3. Downlink / Uplink Signal Model

[0093] Consider that the user side uses a linear receiver to extract the signal of the target satellite and performs 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 a transmission signal for each user. Specifically, the signal of satellite s received by user k on a certain subcarrier can be expressed as

[0094]

[0095] in is the downlink receiver of user k to satellite s, is the transmission power of satellite s to user i, is the normalized downlink precoder of satellite s to user i, satisfying is a transmission data stream with a mean of 0 and a variance of 1. The total transmission power of satellite s is is a Gaussian asynchronous interference signal with a variance of in Expressed as

[0096]

[0097] and 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 sent to each satellite. The received signal of user k received by satellite s on a certain subcarrier is

[0098]

[0099] in represents the uplink receiver of satellite s to user k, is the transmission power of user i to satellite s, is the normalized uplink precoder, is a transmission data stream with a mean of 0 and a variance of 1. The total transmission power of satellite k is is a Gaussian asynchronous interference signal, and its covariance matrix is Expressed as

[0100]

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

[0102] 4. Downlink / Uplink Decoupling Precoder and Receiver Design

[0103] For a given downlink receiver, the ASLNR maximization criterion is considered for downlink precoder design. Specifically, the ASLNR of satellite s to user k is expressed as

[0104]

[0105] in represents the downlink signal-to-noise ratio. The downlink precoder that maximizes (28) can be expressed as

[0106]

[0107] in is the power normalization factor so that For a given downlink precoder, we consider the downlink receiver design using the ASINR maximization criterion. Specifically, the ASINR of user k to satellite s can be expressed as

[0108]

[0109] in The downlink receiver that maximizes (30) can be expressed as

[0110]

[0111] where ξ max (I) denotes the normalized eigenvector corresponding to the largest eigenvalue of matrix I, and From (29) and (31), we can observe that the design of each satellite downlink precoder and the design of each user receiver depend on each other's information, and the convergence of the 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

[0112]

[0113] in for The power normalization factor. And max(I) represents the maximum eigenvalue of I. That is, the decoupling closed-form expression of the precoder of satellite s corresponding to user k is: by the satellite side rudder vector of all user terminals corresponding to satellite s in Represents the set of users in the system, the outer product multiplied by the maximum eigenvalue of the corresponding user side channel correlation matrix Then sum it up and load the inverse of the downlink signal-to-noise ratio of satellite s corresponding to user k on its diagonal line. The inverse matrix of the obtained matrix is added to the satellite rudder vector g corresponding to user k of satellite s k，s Multiply, and then pass a coefficient The vector obtained after scaling; The decoupling closed-form expression of the receiver of user k corresponding to satellite s is: By calculating the user side channel correlation matrix of user k corresponding to different satellites and the corresponding downlink transmit signal-to-noise ratio Multiply and then sum the different satellites and add them to the unit matrix. Multiply the inverse matrix of the obtained matrix by the user side channel correlation matrix of satellite s corresponding to user k. Then perform eigenvalue decomposition on the obtained matrix and find the eigenvector corresponding to its maximum eigenvalue.

[0114] For both low and high SNRs, the downlink precoder and receiver designs can be independent of each other and depend solely on the sCSI. Notably, each satellite's downlink precoder design depends solely on its local sCSI and is independent of other satellites. Each user's downlink receiver design also depends solely on its local sCSI and is independent of other users. As a result, the computational complexity of the downlink precoder and receiver, as well as the complexity of inter-satellite and satellite-to-ground interactions, can be significantly reduced.

[0115] For a given uplink precoder, the uplink receiver is designed using the ASINR maximization criterion, and the ASINR of satellite s to user k can be considered as The function can be expressed as

[0116]

[0117] in The uplink receiver that maximizes (33) can be expressed as

[0118]

[0119] in For a given uplink receiver, consider designing the uplink precoder using the ASLNR maximization criterion, and use the ASLNR of k pairs of satellites as The function can be expressed as

[0120]

[0121] in and represents the uplink SNR. The uplink precoder that maximizes (35) can be expressed as

[0122]

[0123] in From (34) and (36), we can see that the designs of the uplink precoder and receiver are coupled to each other. For both low and high SNR cases, we can prove that the designs of the uplink precoder and receiver can be decoupled in the following two cases: i. and ii. In both cases, the uplink precoder and uplink receiver The decoupling expression is

[0124]

[0125] That is, the decoupling closed-form expression of the precoder of user k corresponding to satellite s is: by calculating the user side channel correlation matrix of user k corresponding to different satellites Sum the signal-to-noise ratio of different satellites and load it on the diagonal line The inverse matrix of the obtained matrix is multiplied by the user side channel correlation matrix of satellite s corresponding to user k, and then the obtained matrix is decomposed by eigenvalue, and the eigenvector corresponding to the maximum eigenvalue is obtained; the decoupling closed-form expression of the receiver of user k corresponding to satellite s is: by the satellite side rudder vector of all user terminals served by satellite s The outer product multiplied by the maximum eigenvalue of the corresponding user side channel correlation matrix Multiply it by the corresponding uplink signal-to-noise ratio Then sum it up, add the resulting matrix to the identity matrix, and then add the inverse matrix of the resulting matrix to the satellite rudder vector g of user k corresponding to satellite s. k，s The vector obtained after multiplication.

[0126] For low and high SNR, the uplink receivers at each satellite and the uplink precoders at each user can be designed independently and only rely on the local sCSI of each satellite and user.

[0127] 5. Downlink Beam Structure Precoder Design and Uplink Beam Structure Receiver Design

[0128] First, we can prove that when M→∞, and When , (29) can be expressed as

[0129]

[0130] in

[0131]

[0132] and

[0133]

[0134] as well as When the satellite antenna tends to infinity and the satellite beam index sets for any two users do not overlap, the spatial domain downlink precoder The design can be converted into a beam domain vector Due to the sparse beam channel of satellite massive MIMO, The dimension is typically smaller than Therefore, the complexity of designing the downlink precoder can be significantly reduced. We call the spatial domain precoder in (38) is the beam structure precoder, called is the beam domain precoder. In addition, in (40) Indicates the beam index set ASLNR achieved by the beam structure precoder under .

[0135] When the number of users in a multi-satellite massive MIMO system increases, the beam index sets of each satellite for different users may overlap. In this case, it is necessary to consider introducing more beams to participate in the design of the beam structure precoder to improve system performance. It can be proved that when M→∞, a new beam index set is defined Its definition is the same as the set in (19) Similarly, only replace γ in (19) with At this point, you can get

[0136]

[0137] When the collection Elements in When the following conditions are met, the inequality sign is replaced by equality.

[0138]

[0139] Considering more beams in the beam structure precoder design can improve the performance, and (42) gives the beam selection criterion, that is, beams that satisfy (42) should not be considered because the participation of these beams will not improve the performance.

[0140] In actual systems, although the number of antennas on the satellite side is limited, when the satellite side is equipped with a large number of antennas, the proposed beam structure precoder can still achieve near-optimal performance. in And the beam selection matrix Definition and Ω k，s Similar, except that the beam index set Replace with The size of the collection is Therefore, ASLNR can be reformulated as

[0141]

[0142] in and make The maximum beam domain precoder is expressed as

[0143] in Make The decoupling design of the downlink beam structure precoder can be expressed as

[0144] in Make That is, the beam domain precoder of satellite s corresponding to user k is: by left-multiplying the diffusion vector of all user terminals corresponding to satellite s by the beam matrix and its conjugate transpose The obtained vector is extracted according to the beam set of the corresponding user k of satellite s, and then compared with the maximum eigenvalue of the user side channel correlation matrix of the corresponding user The outer product of the vectors obtained after multiplying the square root of is summed up, and the resulting matrix The conjugate transpose of the beam matrix is extracted according to the beam set of the corresponding user k of satellite s, and the extracted matrix is right-multiplied by its conjugate transpose and then multiplied by the inverse of the downlink signal-to-noise ratio of the corresponding user k of satellite s to obtain the matrix Add, multiply the inverse matrix of the obtained matrix with the diffusion vector of user k corresponding to satellite s by the beam matrix and its conjugate transpose, and extract the vector after the beam set of user k corresponding to satellite s The vector obtained by multiplying and scaling by a factor.

[0145] Therefore, the spatial domain downlink precoding derived from (45) can be expressed as

[0146]

[0147] For the uplink beam structure receiver design, we can first prove that when M→∞, and When , (34) can be expressed as

[0148]

[0149] in

[0150]

[0151] and

[0152]

[0153] 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 spatial domain uplink receiver The design can be transformed into a beam domain vector We call the design is the beam domain receiver. The dimension is much lower than Therefore, the design complexity of the uplink receiver can be significantly reduced. We call (47) is the beam structure receiver. In addition, (49) represents the beam index set When the number of users increases and the beam index sets of satellites for different users overlap, it can be proved that when M→∞, for the beam index set and Can get

[0154]

[0155] When the collection Elements in When the following conditions are met, the inequality is equal.

[0156]

[0157] Next, the spatial domain uplink receiver is constrained to satisfy the structure and ASINR can be rewritten as

[0158]

[0159] in make The maximum beam domain receiver can be calculated as

[0160]

[0161] The decoupled beam structure uplink receiver can be expressed as

[0162]

[0163] in The beam domain receiver of satellite s corresponding to user k is obtained by multiplying the diffusion vectors of all user terminals served by satellite s by the beam matrix and its conjugate transpose, and then transforming the resulting vector According to the beam set of satellite s corresponding to user k, we can get Then compare it with the maximum eigenvalue of the user side channel correlation matrix of the corresponding user The square root of the corresponding user's uplink transmission signal-to-noise ratio The outer product of the vectors obtained after multiplying the square root of is summed up, and the resulting matrix The conjugate transpose of the beam matrix is extracted according to the beam set of the corresponding user k of satellite s, and the matrix obtained by right multiplying the extracted matrix by its conjugate transpose is Add, multiply the inverse matrix of the obtained matrix with the diffusion vector of user k corresponding to satellite s by the beam matrix and its conjugate transpose, and extract the vector after the beam set of user k corresponding to satellite s The vector obtained by multiplication.

[0164] The derived spatial domain uplink receiver can be expressed as

[0165]

[0166] 6. Low-complexity design and implementation

[0167] The design complexity of the beam structure downlink precoder and uplink receiver comes from (45) and (54), respectively. First, we prove that and The design of depends only on real-valued matrix operations. N is an inverse permutation matrix and satisfies R N R N =I. Since V t Each column of is conjugate centrosymmetric, so we can get And the matrix V in (45) and (54) H V can be rewritten as

[0168]

[0169] This means that V H V is a real-valued matrix. Since the rudder vector is also conjugate centrosymmetric, so we can get is also a real-valued vector. In addition, it is not difficult to verify that the beam selection matrix is also real-valued. Therefore, the calculation and Relies only on real-valued matrix operations.

[0170] Since V H V does not depend on the specific signal and user, so it can be calculated and stored in advance. Specifically, VH V can be expressed as

[0171]

[0172] in means round down, and It can be calculated directly from its first column, that is,

[0173] [Ξ t ] n，n′ =[Ξ t ] |n-n′|+1，1· (58)

[0174] Therefore, by calculating [Ξ x ] ：，1 and [Ξ y ] ：，1 You can directly get V H V, whose computational and storage complexities are and

[0175] The following can be done by Introduced sampling points, i.e. and To obtain a simple expression for the satellite's side rudder vector. And make Represents the direction cosines closest to the scale The sampling point is defined as

[0176]

[0177] Therefore, the rudder vector It can be approximated as

[0178]

[0179] Note that when hour, Can be It is obtained by cyclic shift and is expressed as

[0180]

[0181] real-valued vector It can be expressed as

[0182]

[0183] in Calculated as

[0184]

[0185] Therefore, through (58), (61), (62) and (63) we can get Its computational complexity is The storage complexity is Downlink beam-domain precoder and uplink beam domain receivers The design complexity is in In comparison, the design complexity of the spatial domain downlink precoder and uplink receiver is

[0186] The complexity of using the designed downlink precoder on each satellite to generate the transmission signal for each user, and using the designed uplink receiver on each satellite to recover the transmission signal for each user is called implementation complexity. Using the designed beam structure downlink precoder, the downlink transmission signal of satellite s can be expressed as

[0187]

[0188] in Therefore, the implementation complexity of the beam structure precoder is The implementation complexity of the spatial domain precoder is

[0189] Using the designed beam structure receiver, the signal of user k recovered by satellite s can be expressed as

[0190]

[0191] in and Therefore, the implementation complexity of the beam structure uplink receiver is The implementation complexity of the spatial domain receiver is

[0192] We assume that the downlink precoder and uplink receiver are designed once for 100 subframes and 14 resource blocks and used to generate the transmit signal. Assume that one subframe has 14 OFDM symbols and one resource block has 12 subcarriers. Then, the total complexity of using the downlink beam structure precoder and uplink beam structure receiver is the superposition of the design complexity and the implementation complexity, which can be expressed as and Where F = 12 × 4 × 100 × 14, The total complexity of using the spatial domain precoder and receiver can be calculated as

[0193] Figure 4The proposed method (DL DPR, DL BSP, UL DPR, UL BSR) in this example, the joint design method of precoder and receiver for uplink and downlink traversal and rate optimization (JPRD, JPRVD), and the precoder design method for single satellite scenario are given. Figure 4 It can be seen that the proposed method can approach the optimal design method for ergodicity and rate, and has a great improvement in ergodicity and rate performance compared with the single-satellite precoding design method.

[0194] An embodiment of the present invention further discloses a multi-satellite massive MIMO communication system, including satellites and user terminals, the satellites or gateways associated therewith, and the user terminals implementing steps of any of the above-mentioned decoupling design methods.

[0195] An embodiment of the present invention further discloses a computer program product, including a computer program / instruction, which performs the steps of any one of the above-mentioned decoupling design methods when executed by a processor.

[0196] Anything not described in detail in the present invention is well known to those skilled in the art.

[0197] 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 modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A multi-satellite massive MIMO downlink precoder and receiver decoupling design method, characterized by: The satellite side uses the average signal-to-leakage-and-noise ratio (ASLNR) criterion to calculate the precoder to generate its own transmit signal. The user terminal uses the average signal-to-interference-and-noise ratio (ASINR) criterion to calculate the receiver and perform linear reception processing on the signals sent by each satellite. The decoupled closed-form expression of the precoder for user k corresponding to satellite s is as follows: multiply the outer product of the satellite-side steering vectors for all user terminals corresponding to satellite s by the maximum eigenvalue of the corresponding user-side channel correlation matrix, then sum them. Then, load the inverse of the downlink transmit signal-to-noise ratio of user k corresponding to satellite s onto its diagonal. Multiply the inverse matrix of the resulting matrix by the satellite-side steering vector for user k corresponding to satellite s, and then scale it by a coefficient to obtain the resulting vector. The decoupled closed-form expression of the receiver for user k corresponding to satellite s is as follows: multiply the user-side channel correlation matrices for different satellites corresponding to user k by the corresponding downlink transmit signal-to-noise ratios, sum them for different satellites, add them to the identity matrix, multiply the inverse matrix of the resulting matrix by the user-side channel correlation matrix for user k corresponding to satellite s, and then perform eigenvalue decomposition on the resulting matrix to obtain the eigenvector corresponding to the maximum eigenvalue.

2. A multi-satellite massive MIMO uplink precoder and receiver decoupling design method, characterized by: User terminals generate their own transmit signals using a precoder calculated using the average signal-to-leakage-and-noise ratio (ASLNR) criterion. The satellite side uses the average signal-to-interference-and-noise ratio (ASINR) criterion to calculate the receiver and perform linear reception processing on each user's signal. The decoupled closed-form expression for the precoder for user k corresponding to satellite s is as follows: summing the user-side channel correlation matrices for different satellites corresponding to user k, loading the inverse of the uplink transmit signal-to-noise ratio on the diagonal, multiplying the inverse matrix of the resulting matrix by the user-side channel correlation matrix for user k corresponding to satellite s, and then performing eigenvalue decomposition on the resulting matrix to obtain the eigenvector corresponding to the maximum eigenvalue. The decoupled closed-form expression for the receiver for user k corresponding to satellite s is as follows: summing the outer product of the satellite-side steering vectors for all user terminals served by satellite s, multiplying them by the maximum eigenvalue of the corresponding user-side channel correlation matrix, and then by the corresponding uplink transmit signal-to-noise ratio, then adding the resulting matrix to the identity matrix. The resulting vector is then obtained by multiplying the inverse matrix of the resulting matrix by the satellite-side steering vector for user k corresponding to satellite s.

3. A multi-satellite massive MIMO beam-based channel model for the decoupling design method according to claim 1 or 2, characterized in that: The downlink beam-based channel model is expressed as the product of the conjugate transpose of the user-side beam matrix, the downlink beam domain channel and the satellite-side beam matrix; the uplink beam-based channel model is expressed as the product of the conjugate transpose of the satellite-side beam matrix, the uplink beam domain channel and the user-side beam matrix; the beam matrix is composed of 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 the diffusion vector, and the uplink beam domain channel is the product of the diffusion vector and the conjugate transpose of the random vector; the random vector obeys the Rice distribution, and the diffusion vector is a real-valued vector, representing the distribution of channel energy on different beams.

4. A precoder decoupling design method for a multi-satellite massive MIMO downlink beam structure, characterized in that: include: Each satellite uses the downlink beam-based channel model and the local statistical channel information of each user terminal to design the beam structure precoder for each user terminal, and uses the obtained precoder for downlink precoding transmission; The downlink beam-based channel model is expressed 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 is composed of the sampling array response vector corresponding to a selected set of scaled direction cosine sampling points. The downlink beam domain channel is the product of a random vector and the conjugate transpose of a diffusion vector. The random vector obeys the Rice distribution, and the diffusion vector is a real-valued vector, which represents the distribution of channel energy on 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 beam set of each user. The beam mapping module for each user maps the low-dimensional beam domain precoded signal of each user into a complete beam domain transmission signal. The beam modulation module is the beam matrix multiplied by the beam domain transmission signal vector. The beam domain transmission signal vector is the sum of the beam domain transmission signal vectors of each user.

5. The method for designing a precoder decoupling system for a multi-satellite massive MIMO downlink beam structure according to claim 4, wherein: The beam domain precoder relies on the average signal-to-leakage-and-noise ratio (ASLNR) criterion. The beam domain precoder for user k corresponding to satellite s is: by multiplying the spreading vectors of all user terminals corresponding to satellite s by the beam matrix and its conjugate transpose, extracting the resulting vector according to the beam set of user k corresponding to satellite s, and then multiplying it by the square root of the maximum eigenvalue of the user-side channel correlation matrix of the corresponding user, summing the outer products of the vectors obtained, adding the resulting matrix to the matrix obtained by extracting the conjugate transpose of the beam matrix according to the beam set of user k corresponding to satellite s, multiplying the extracted matrix by its conjugate transpose, and then multiplying it by the inverse of the downlink signal-to-noise ratio of user k corresponding to satellite s, and multiplying the inverse matrix of the resulting matrix by the spreading vector of user k corresponding to satellite s by the beam matrix and its conjugate transpose, and then multiplying it by the vector extracted according to the beam set of user k corresponding to satellite s, and then scaling the vector by a coefficient.

6. A decoupling design method for a multi-satellite massive MIMO uplink beam structure receiver, characterized in that: include: Each satellite uses the uplink beam-based channel model and the statistical channel information of each user terminal to design each user beam structure receiver, and uses the obtained receiver to perform uplink linear reception processing; The uplink beam-based channel model is expressed 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 vector corresponding to a selected set of scaled direction cosine sampling points. The uplink beam domain channel is the product of the diffusion vector and the conjugate transpose of the random vector; the random vector obeys the Rice distribution, and the diffusion vector is a real-valued vector, which represents the distribution of channel energy on different beams; the beam structure receiver includes a beam transformation module, a beam extraction module and each user's beam domain receiver. The beam transformation module transforms the spatial domain received signal vector on each subcarrier into a beam domain received signal vector. The beam extraction module extracts the beam domain received signal vector according to the beam set of each user. Finally, the signal of each user is linearly processed using the beam domain receiver of each user and the extracted beam domain received signal vector.

7. The multi-satellite massive MIMO uplink beam structure receiver decoupling design method according to claim 6, characterized in that: The beam domain receiver relies on the average signal-to-interference-plus-noise ratio (ASINR) criterion. The beam domain receiver of satellite s corresponding to user k is obtained by multiplying the spreading vectors of all user terminals served by satellite s by the beam matrix and its conjugate transpose on the left, and extracting the obtained vector according to the beam set of satellite s corresponding to user k, and then summing the outer products of the vectors obtained by multiplying the square root of the maximum eigenvalue of the user-side channel correlation matrix of the corresponding user and the square root of the uplink transmission signal-to-noise ratio of the corresponding user, extracting the conjugate transpose of the beam matrix according to the beam set of satellite s corresponding to user k, and adding the obtained matrix to the matrix obtained by multiplying the extracted matrix by its conjugate transpose on the right, and multiplying the inverse matrix of the obtained matrix with the spreading vector of satellite s corresponding to user k by the beam matrix and its conjugate transpose on the left, and multiplying the vector extracted according to the beam set of satellite s corresponding to user k by the inverse matrix.

8. The decoupling design method according to claim 5 or 7, characterized in that: The calculation of the beam domain precoder or beam domain receiver only relies on real-valued matrix operations, and the product of the conjugate transpose of the beam matrix and itself can be calculated by the first column of the matrix obtained by the product of the conjugate transpose of its component beam matrices in two directions and themselves, and stored in advance; and the product of the conjugate transpose of the beam matrix and itself multiplied on the right by the diffusion vector of each user can be approximated by increasing the number of sampling points of the direction cosines, and calculated and stored in advance.

9. A multi-satellite massive MIMO communication system, comprising satellites and user terminals, characterized in that: The satellite or the gateway station associated therewith, and the user terminal implement the steps of the decoupling design method according to any one of claims 1-2, 4-8.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the decoupling design method according to any one of claims 1-2, 4-8 are implemented.

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