Massive MIMO multi-satellite mobile communication uplink transmission method and system

Abstract

The present invention discloses a method and system for uplink transmission of massive MIMO multi-satellite mobile communications. When satellites employ a serial interference cancellation reception scheme, each satellite or gateway uses statistical channel information to calculate the precoding vector for each user terminal corresponding to each satellite, based on the traversal and rate maximization criteria, and feeds this back to each user terminal. When satellites employ a linear reception scheme, each satellite or gateway uses statistical channel information to jointly calculate the precoding vector for each user terminal corresponding to each satellite and the reception processing vector for each satellite corresponding to each user terminal, based on the traversal and rate maximization criteria, dynamically implementing multi-satellite massive MIMO uplink transmission. User terminals utilize the Doppler shift and minimum propagation delay caused by the movement of each satellite to perform frequency and time compensation on each data stream sent to different satellites, followed by linear precoding processing. The present invention can improve the uplink reachability and rate performance of a multi-satellite mobile communication system while having low computational complexity.

Description

Technical Field

[0001] The present invention relates to a multi-satellite mobile communication uplink transmission method and system configured with antenna arrays, and in particular to a multi-satellite mobile communication uplink transmission method and system using large-scale MIMO technology. Background Art

[0002] In recent years, the rapid development of terrestrial mobile communications technology has driven the rapid rise of emerging industries such as mobile internet and autonomous driving. However, some remote areas still face difficulties with internet coverage. To achieve global network coverage, satellite communications are seen as a promising technology with the advantage of wide-area coverage. By utilizing low-, medium-, and high-orbit satellites, satellite communications systems can complement the shortcomings of terrestrial mobile communications systems, achieve global network coverage, and provide new opportunities for future development.

[0003] Massive Multiple-Input Multiple-Output (MIMO) is a key technology for 5G. By leveraging a large number of dynamic beams generated by a large number of antennas at the base station, it can support communication between the base station and dozens of users using the same time-frequency resources. Extending the application of Massive MIMO technology to mobile satellite communications and building a Massive MIMO mobile satellite communication system can significantly improve the spectral and power efficiency of mobile satellite communication systems.

[0004] In recent years, the demand for global internet connectivity has driven the rapid development of mega-satellite constellations. By deploying hundreds or even thousands of low-Earth orbit satellites, mega-satellite constellations can provide internet access to remote and underserved areas. Compared to a single satellite, mega-satellite constellations can further expand the scope of internet service and improve the spectrum efficiency of massive MIMO satellite mobile communication systems, which is of great significance for achieving seamless global coverage and building a space-ground integrated network. Summary of the Invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a large-scale MIMO multi-satellite mobile communication uplink transmission method and system to overcome the shortcomings of the existing technology, improve the reachability and rate performance of the uplink transmission of the multi-satellite mobile communication system, and reduce the implementation complexity.

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

[0007] A massive MIMO multi-satellite mobile communication uplink transmission method is applied to a satellite or a gateway station associated with a satellite, wherein the satellite is equipped with an antenna array and communicates with user terminals equipped with antenna arrays within its coverage area; the method comprises:

[0008] Each satellite or gateway uses statistical channel information and, in accordance with the ergodic reachability and rate maximization criteria, employs the Riemann conjugate gradient (RCG) design method to iteratively calculate the precoding vectors corresponding to each user terminal and each satellite, or jointly calculates the precoding vectors corresponding to each user terminal and each satellite and the receive processing vectors corresponding to each satellite and each user terminal, and then feeds the transmit precoding vectors back to each user terminal. The ergodic reachability and rate include asynchronous interference introduced by multi-satellite scenarios, i.e., signals sent by user terminals to different satellites are asynchronous in time and frequency on a particular satellite.

[0009] Each satellite performs serial interference cancellation processing or linear reception processing on the signal sent by each user terminal;

[0010] During the movement of each satellite or each user terminal, as the statistical channel information changes, the precoding vector corresponding to each satellite or the reception processing vector corresponding to each user terminal is dynamically updated and the uplink transmission process is implemented.

[0011] In a preferred embodiment, the statistical channel information includes spatial angle information and average channel energy, which are obtained by the uplink detection process or through feedback information from each user terminal; during the uplink detection process, each user periodically sends a detection signal, and each satellite estimates the spatial angle information or average channel energy of each user based on the received detection signal; the feedback information from each user terminal is the user's spatial angle information, average channel energy or geographic location information.

[0012] In a preferred embodiment, the calculation of the precoding vector when the satellite adopts the serial interference cancellation reception scheme includes: according to the ergodic reachability and rate maximization criterion, using the Riemann conjugate gradient RCG design method to iteratively calculate the uplink precoding vector, converting the ergodic and rate maximization problem under the user total power constraint in the Euclidean space into a precoding vector design problem of ergodic and rate maximization in the Riemann submanifold space, and obtaining the uplink precoding vector of each satellite corresponding to each user terminal by iteratively solving the ergodic and rate maximization problem in the Riemann submanifold space; the ergodic and rate maximization problem in the Riemann submanifold space calculates the current Riemann gradient in each iteration, and sets the search direction to the negative direction of the Riemann gradient and the direction in the previous iteration. The vector shift of the obtained search direction is superimposed with a new vector obtained by multiplying it by a non-negative coefficient. The vector shift of the search direction is obtained by subtracting the diagonal matrix composed of the inner product of the precoding vector of each user terminal and its search direction divided by the maximum transmit power of the user and the product of the new vector composed of the precoding vectors of all users from the current search direction. The Backtracking algorithm is used to iteratively search for the optimal step size, and the product of the optimal step size and the search direction is added to the user's precoding vector. The precoding vector on the Riemann submanifold space is obtained by multiplying it by the square root of the ratio of the maximum transmit power of each user to the current transmit power. If the obtained precoding vector no longer improves the system and rate performance, the vector is output.

[0013] In a preferred embodiment, the calculation of the precoding vector and the receiving processing vector when the satellite adopts a linear receiving scheme with lower complexity includes: according to the ergodic reachability and rate maximization criterion, using the Riemann conjugate gradient RCG design method to iteratively calculate the uplink precoding vector and the receiving processing vector, converting the ergodic and rate maximization problem under the user total power constraint in the Euclidean space into a design problem of the precoding vector and the receiving processing vector with ergodic and rate maximization in the Riemann submanifold space, and obtaining the precoding vector of each satellite corresponding to each user terminal and each by iteratively solving the ergodic and rate maximization problem in the Riemann submanifold space. The satellite corresponds to a receiving processing vector for each user terminal; in each iteration of the traversal and rate maximization problem in the Riemann submanifold space, the precoding vector is fixed, the Riemann gradient of the sum rate function with respect to the receiving processing vector on the linear manifold is solved, and the search direction is set to the superposition of the negative direction of the Riemann gradient and the new vector obtained by multiplying the search direction obtained in the previous iteration by a non-negative coefficient. The optimal step size is iteratively searched using a backtracking algorithm, the product of the optimal step size and the search direction is added to the receiving processing vector of the user, and if the resulting receiving processing vector no longer improves the system sum rate performance, the vector is output. Next, the received processing vector is fixed, and the Riemann gradient of the sum rate function with respect to the precoding vector on the Riemann submanifold is solved. The search direction is set to the negative direction of the Riemann gradient and the superposition of the new vector obtained by multiplying the vector shift of the search direction obtained in the previous iteration by a non-negative coefficient. The vector shift of the search direction is obtained by subtracting the diagonal elements of the current search direction from the inner product of the precoding vector of each user terminal and its search direction divided by the maximum transmit power of the user and the product of the new vector consisting of the precoding vectors of all users. The Backtracking algorithm is used to iteratively search for the optimal step size, and the product of the optimal step size and the search direction is added to the user's precoding vector. The precoding vector on the Riemann submanifold space is obtained by multiplying by the square root of the ratio of the maximum transmit power of each user to the current transmit power. If the obtained precoding vector no longer improves the system sum rate performance, the vector is output.

[0014] A massive MIMO multi-satellite mobile communication uplink transmission method, the method being applied to a user terminal and comprising:

[0015] The user terminal periodically sends a sounding signal to the satellite, or feeds back the user's spatial angle information, average channel energy, or geographic location information to the satellite. The satellite or gateway uses the statistical channel information and, based on the ergodic reachability and rate maximization criteria, employs the Riemann conjugate gradient (RCG) design method to iteratively calculate the corresponding precoding vectors for each user terminal and each satellite, or jointly calculates the corresponding precoding vectors for each user terminal and each satellite and the corresponding receive processing vectors for each satellite and each user terminal.

[0016] The user terminal uses the Doppler frequency shift caused by the movement of each satellite and the minimum propagation delay of long-distance propagation to perform frequency and time compensation for each data stream sent to different satellites;

[0017] The user terminal uses the transmit precoding vector fed back by each satellite or gateway to perform linear precoding processing on the compensated signal and then transmits the uplink signal.

[0018] In a preferred embodiment, the Doppler frequency shift and the minimum propagation delay for long-distance transmission caused by the satellite movement are estimated by the user terminal based on the received synchronization signal, or calculated based on the position information of the user terminal and the satellite; as the satellite or user terminal moves, the Doppler frequency shift and minimum propagation delay information are dynamically updated, and the frequency and time compensation amounts change adaptively accordingly.

[0019] A satellite-side device for uplink transmission of massive MIMO multi-satellite mobile communications includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the massive MIMO multi-satellite mobile communications uplink transmission method is implemented.

[0020] A massive MIMO multi-satellite mobile communication uplink transmission user terminal side device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the massive MIMO multi-satellite mobile communication uplink transmission method is implemented.

[0021] A massive MIMO multi-satellite mobile communication uplink transmission system includes satellites and user terminals. The satellites are equipped with antenna arrays and communicate with user terminals equipped with antenna arrays within their coverage areas. The satellites or their associated gateways are used to:

[0022] Using statistical channel information and based on the ergodic reachability and rate maximization criteria, the Riemann conjugate gradient (RCG) design method is used to iteratively calculate the precoding vectors corresponding to each user terminal and each satellite, or the precoding vectors corresponding to each user terminal and each satellite and the receive processing vectors corresponding to each satellite and each user terminal. The calculated precoding vectors are then fed back to each user terminal.

[0023] and each satellite performs serial interference cancellation processing or linear reception processing on the signal sent by each user terminal;

[0024] The user terminal is configured to: periodically transmit a sounding signal to a satellite, or feed back the user's spatial angle information, average channel energy, or geographic location information to the satellite for use by the satellite or a gateway station in calculating a transmit precoding vector for each user terminal and a receive processing vector for each satellite; perform frequency and time compensation on an uplink transmit signal using the Doppler frequency shift caused by satellite movement and the minimum propagation delay of long-distance transmission; and perform linear precoding processing on the compensated signal using the transmit precoding vector fed back by the satellite or the gateway station before transmitting the uplink signal.

[0025] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the satellite, gateway or user terminal steps of the massive MIMO multi-satellite mobile communication uplink transmission method.

[0026] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0027] (1) Taking into full consideration that the signals sent by users to different satellites are asynchronous in time and frequency on a certain satellite side, the massive MIMO technology is extended to the multi-satellite mobile communication uplink transmission system, thereby improving the uplink reachability and rate performance of the satellite mobile communication system.

[0028] (2) By utilizing the characteristics of satellite channels and the Riemann conjugate gradient algorithm, the solution of the transmit precoding vector and the receive processing vector does not involve matrix inversion, which greatly reduces the computational complexity.

[0029] (3) The calculation of the transmit precoding vector and the receive processing vector only relies on long-term statistical channel information, and the required information is easier to obtain accurately.

[0030] (4) Each user terminal performs frequency and time compensation on its uplink transmitted signal, which simplifies the system design. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] 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.

[0032] Figure 1 The figure is a flowchart of the satellite-side processing method in massive MIMO multi-satellite mobile communications.

[0033] Figure 2 The figure is a flowchart of a user terminal side processing method in massive MIMO multi-satellite mobile communications.

[0034] Figure 3 Schematic diagram of the massive MIMO multi-satellite mobile communication uplink system.

[0035] Figure 4 This is a comparison chart of uplink and rate performance of massive MIMO multi-satellite mobile communications.

[0036] Figure 5 This is a structural diagram of the satellite-side equipment for uplink transmission of massive MIMO multi-satellite mobile communications.

[0037] Figure 6 This is a structural diagram of the user terminal equipment for uplink transmission of massive MIMO multi-satellite mobile communications.

[0038] Figure 7 This is a structural diagram of the massive MIMO multi-satellite mobile communication uplink transmission system. DETAILED DESCRIPTION

[0039] 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.

[0040] like Figure 1 As shown, the present invention discloses a method for uplink transmission of massive MIMO multi-satellite mobile communications. The method is applied to a satellite or a gateway station associated with a satellite, wherein the satellite is equipped with an antenna array and communicates with user terminals equipped with antenna arrays within its coverage area. The method includes:

[0041] Each satellite or gateway uses statistical channel information and, in accordance with the ergodic reachability and rate maximization criteria, employs the Riemann conjugate gradient (RCG) design method to iteratively calculate the corresponding precoding vectors for each user terminal and each satellite. Alternatively, the receive processing vectors for each satellite and each user terminal and the transmit precoding vectors for each user terminal and each satellite are jointly calculated, and the transmit precoding vectors are fed back to each user terminal. The ergodic reachability and rate account for asynchronous interference introduced by multi-satellite scenarios, i.e., signals sent by user terminals to different satellites are asynchronous in time and frequency on a particular satellite.

[0042] During the movement of each satellite or each user terminal, as the statistical channel information changes, the receiving processing vector corresponding to each user terminal or the transmitting precoding vector corresponding to each satellite is dynamically updated and fed back to each user terminal.

[0043] When each satellite adopts the serial interference cancellation reception scheme, the calculation of the precoding vector includes: based on the ergodic reachability and rate maximization criteria, the uplink precoding vector is iteratively calculated using the Riemann conjugate gradient (RCG) design method, the ergodic and rate maximization problem under the user total power constraint in the Euclidean space is converted into a precoding vector design problem with ergodic and rate maximization in the Riemann submanifold space, and the uplink precoding vector corresponding to each satellite for each user terminal is obtained by iteratively solving the ergodic and rate maximization problem in the Riemann submanifold space.

[0044] When the satellite adopts a linear reception scheme, the calculation of the precoding vector and the reception processing vector includes: based on the ergodic reachability and rate maximization criteria, using the Riemann conjugate gradient (RCG) design method to iteratively calculate the uplink precoding vector and the reception processing vector, converting the ergodic and rate maximization problem under the user total power constraint in the Euclidean space into a design problem of the precoding vector and the reception processing vector with ergodic and rate maximization in the Riemann submanifold space, and obtaining the precoding vector for each satellite corresponding to each user terminal and the reception processing vector for each satellite corresponding to each user terminal by iteratively solving the ergodic and rate maximization problem in the Riemann submanifold space.

[0045] like Figure 2 As shown, the massive MIMO multi-satellite mobile communication uplink transmission method disclosed in the example of the present invention is applied to a user terminal, and the method includes:

[0046] The user terminal periodically sends a sounding signal to the satellite, or feeds back the user's spatial angle information, average channel energy, or geographic location information to the satellite for the satellite or gateway to calculate the precoding vector and receive processing vector;

[0047] The user terminal uses the Doppler frequency shift caused by the movement of each satellite and the minimum propagation delay of long-distance propagation to perform frequency and time compensation on each data stream sent to each satellite;

[0048] Each user terminal uses the transmit precoding vector fed back by the satellite or the gateway to send uplink signals.

[0049] The Doppler frequency shift and minimum propagation delay caused by satellite movement are estimated by the user terminal based on the received synchronization signal, or calculated based on the position information of the user terminal and the satellite. As the satellite or user terminal moves, the Doppler frequency shift and minimum propagation delay information are dynamically updated, and the frequency and time compensation amounts change adaptively accordingly.

[0050] 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.

[0051] (1) System configuration

[0052] Consider equipping each satellite with an antenna array (which can be a one-dimensional or two-dimensional array with dozens to hundreds of antennas). Antenna arrays or large-scale antenna arrays can be arranged in different shapes based on the number and ease of installation. The most basic is a two-dimensional uniform planar array (UPA), where the antenna elements are evenly arranged in the horizontal and vertical directions, and the spacing between adjacent antenna elements can be λ / 2 or λ / 2. Where λ is the carrier wavelength. Figure 3 As shown, assuming that each satellite is equipped with a UPA, the number of antenna units in the x-axis and y-axis directions are M respectively. x and M y , then M r =M x ×M y The total number of antennas equipped for the satellite. Assume that each user side is also equipped with a UPA, and the number of antenna units in the x' and y' directions are N respectively. x′ and N y′ , then N t =N x′ N y′ The total number of antennas equipped for the user side. represents the set of all n×m dimensional complex (real) number matrices. The user set and satellite set are respectively and The set of satellites serving user k is denoted as The cardinality of the set is S k , the set of users served by satellite s is recorded as The cardinality of the set is K s .

[0053] The number of subcarriers in Orthogonal Frequency Division Multiplex (OFDM) is N sc , the cyclic prefix (CP) length is N cp , the system sampling time interval is T s , then the OFDM symbol time length is T sc =N sc T s , the CP time length is T cp =N cp T s . Remember N tot =N sc +N cp .

[0054] (2) Signal and channel model

[0055] remember is the uplink time domain signal sent by user k to satellite s, then the total signal sent by user k to all satellites can be expressed as The time domain received signal of satellite s at time n in one frame can be expressed as

[0056]

[0057] in, is the channel length, is the channel impulse response from user k to satellite s, is the additive Gaussian noise of satellite s. It can be expressed as

[0058]

[0059] in, δ(·) is the Dirac function, (·) H Indicates taking the conjugate transpose of a vector or matrix, L k，s represents the multipath number of the channel from user k to satellite s, ε k，s，l and m k，s，l are the channel complex gain, Doppler shift and propagation delay of the lth path of the channel from satellite s to user k respectively. and are the array response vectors on the user side and the satellite side, respectively, which correspond to the lth path of the channel from user k to satellite s.

[0060] The Doppler frequency shift ε of the lth path of the channel from user k to satellite s k，s，l It mainly consists of two independent parts, namely in and The Doppler shifts are caused by satellite movement and user movement. Because the satellite is far away from the ground user, the Doppler shift caused by satellite movement It can be considered that the different propagation paths l of the user channel are the same, so On the other hand, the Doppler shift caused by user movement l is generally different for different propagation paths.

[0061] Since the satellite is far away from the user, the propagation delay m of the lth path of the channel from user k to satellite s is k，s，l It is larger than that in the terrestrial mobile communication network. It also consists of two parts, namely in Determined by the relative position of the satellite and the user, Determined by the scatterers around the user.

[0062] remember and in and are the arrival angle and departure angle of the lth path of the channel from user k to satellite s, respectively.

[0063] g k，s，l and d k,s,l They can be expressed as

[0064]

[0065] in represents the Kronecker product of two vectors, a w (x) can be expressed as

[0066]

[0067] where d w and n w are the distance between adjacent antenna units and the number of antennas on the w axis, respectively, w∈{x,y,x′,y,}, λ=c / f is the uplink carrier wavelength, c is the speed of light, f is the uplink carrier frequency, (·) T Indicates the transpose of a vector or matrix. If the satellite is equipped with other antenna arrays, just replace a w (x) can be replaced with its corresponding array response vector.

[0068] In satellite communications, since users are far away from satellites, the departure angles corresponding to different multipath signals of the same user can be considered to be approximately the same, that is, Therefore, the array response vector g corresponding to the lth path of the channel from user k to satellite s is k，s，l It can be abbreviated as g k，s，l =g k，s .

[0069] (3) Linear precoding and time-frequency precompensation

[0070] Considering that the user terminal uses linear precoding to generate the transmission signal, It can be expressed as

[0071]

[0072] where w k，s is the precoding vector sent by user k to satellite s, It is the time domain signal transmitted before precoding processing.

[0073] can be rewritten as

[0074]

[0075] remember The user k sends a signal to the satellite s in the frequency domain within the pth OFDM symbol. Then the OFDM modulated signal containing CP can be expressed as

[0076]

[0077] in, N sc The DFT matrix of the point, Defined as

[0078]

[0079] (8) s k，s，p It can be expressed as Assume that the frequency domain transmitted signal s k，s，p，r is a random variable with zero mean and unit variance, and its statistical information remains unchanged within a frame, so,

[0080] Next, the user terminal uses the Doppler frequency shift caused by satellite movement and the minimum propagation delay for long-distance transmission to perform frequency and time compensation on the time-domain transmitted signal. The Doppler frequency shift caused by satellite movement and the minimum propagation delay for long-distance transmission are estimated by the terminal based on the received synchronization signal, or calculated based on information such as the position of the terminal and the satellite. As the satellite or user moves, information such as the Doppler frequency shift and minimum propagation delay are dynamically updated, and the frequency and time compensation amounts change adaptively accordingly. Using the above-mentioned satellite channel Doppler and delay characteristics, we perform frequency and time compensation on the transmitted signal. and Then the transmitted signal after frequency and time compensation can be expressed as

[0081]

[0082] Then the signal sent by user k to satellite s after precoding processing can be expressed as

[0083]

[0084] After time-frequency compensation, the total signal sent by user k to all satellites is expressed as Then the received signal of satellite s can be expressed as

[0085]

[0086] remember is the superposition of the signal sent by the user on the satellite s side to other satellites and the Gaussian noise signal, then It can be expressed as

[0087]

[0088] In formula (12), can be rewritten as

[0089]

[0090] in The length is W k,s The equivalent channel impulse response can be expressed as

[0091]

[0092] Then the received signal of satellite s in the pth OFDM symbol can be expressed as

[0093]

[0094] in On the satellite s side, can be regarded as Gaussian noise, and its covariance matrix can be calculated as

[0095]

[0096] in remember Then the demodulated signal of satellite sOFDM can be expressed as

[0097]

[0098] in is a block diagonal matrix, which can be expressed as Among them H k，s，p，r is the equivalent channel matrix on the rth subcarrier in the pth OFDM symbol from user k to satellite s, x k，s，p，r =w k，s s k，s，p，r ,and H k，s，p，r It can be expressed as

[0099]

[0100] in The signal on the rth subcarrier of the pth OFDM symbol received by satellite s can be expressed as

[0101]

[0102] where z s，p，r Calculated as

[0103]

[0104] in The symbols % and / / represent remainder and truncation respectively. s，p，r The covariance matrix of can be expressed as

[0105] (4) Statistical channel information and its acquisition

[0106] To simplify the discussion, we omit the channel matrix OFDM symbol index and subcarrier index in the is the flat fading channel from user k to satellite s on a certain subcarrier. In this paper, H k，s Obey the following Rice distribution

[0107]

[0108] in is the average channel energy, k k，s is the Ricean factor of the channel from user k to satellite s, ||·|| represents the Euclidean norm of the vector, is the non-random direct path component, is the random scattering path component. k，s，0 represents the direct path direction observed by user k to satellite s, Satisfies cyclically symmetric complex Gaussian distribution And tr(∑ k，s )=1. Here, represents a complex Gaussian distribution with mean vector m and covariance matrix C. k，s Obey the distribution where m k,s and C k，s They are the user side channel components d k，s The mean vector and variance matrix of , and can be expressed as

[0109]

[0110] At this time, the channel average energy and Rice factor can be expressed as β k，s =||m k，s || 2 +tr(C k，s ) and κ k，s =||m k，s || 2 / tr(C k，s ). The channel correlation matrix between the satellite side and the user side can be expressed as

[0111]

[0112]

[0113] Statistical channel information such as the spatial angle information or average channel energy of the user terminal is obtained during the uplink sounding process or through feedback information from each user terminal. During the uplink sounding process, each user periodically sends a sounding signal, and the satellite estimates the spatial angle and average channel energy information of each user based on the received sounding signal. Specifically, the parameter and The estimated value of can be obtained by the classic arrival angle estimation algorithm, such as MUSIC algorithm, ESPRIT algorithm, Unitary ESPRIT algorithm, etc.; the parameter β k，s The estimated value of can be obtained through statistical parameter estimation algorithms.

[0114] The feedback information from each user terminal includes the user's spatial angle information, average channel energy, or geographic location information. This feedback information can be obtained using downlink synchronization signals or sounding signals through channel parameter estimation methods. Geographic location information can also be obtained using the Global Positioning System. If the terminal provides geographic location information, the satellite uses the terminal's geographic location information and satellite position information to derive the spatial angle information for each user.

[0115] (5) Calculation of uplink precoding vector when the satellite adopts serial interference cancellation reception scheme

[0116] After this, we omit sending the signal x k，s，p，r The OFDM symbol index p and subcarrier index r in the , and record x k，s User k sends an uplink signal to satellite s on a certain subcarrier. k，s It can be expressed as x k，s =w k，s s k，s ,in Assume that the user's uplink transmission power meets the constraint The received signal of satellite s can be expressed as

[0117]

[0118] where z s is the superposition signal of asynchronous interference and noise on the satellite s side, and its covariance matrix is And R s Expressed as

[0119]

[0120] Among them (a) is due to Without loss of generality, we assume that satellite s adopts a serial interference cancellation scheme and follows the order from user 1 to user K. s The received data stream is processed in the order of , then the received signal from user k received by satellite s can be expressed as

[0121]

[0122] Then the uplink traversal rate from user k to satellite s can be expressed as

[0123]

[0124] in The covariance matrix of the asynchronous interference signal is included. The uplink sum rate of the system can be expressed as in Expressed as

[0125]

[0126] The upstream traversal and rate maximization problem can be expressed as

[0127]

[0128] in The power constraint of the above problem can be rewritten as Then the following manifold constitutes a Riemann submanifold

[0129]

[0130] Remember the manifold for question Can be converted into a manifold The unconstrained problem on

[0131]

[0132] in f(w) on the manifold The Riemann gradient on can be calculated as

[0133]

[0134] in is f(w) on the manifold The Riemann gradient on can be expressed as

[0135]

[0136] in

[0137]

[0138] When following the direction When searching, an additional step is required to convert w k Projection back to the manifold Will w k Projection back to the manifold The operation on can be expressed as

[0139]

[0140] in Using projection operations Manifold In the (t+1)th iteration, w k The expression is

[0141]

[0142] where α (t) and is the step size and search direction of the tth iteration. It can be expressed as

[0143]

[0144] in Represents the vector η (t-1) The vector shift can be expressed as

[0145]

[0146] in Parameter β (t) for

[0147]

[0148] in for

[0149]

[0150] in<a,b> represents the inner product of vector a and vector b, for

[0151]

[0152] in Expressed as The step size α in formula (41) (t)It can be obtained by the Backtracking algorithm. Let (t, n) represent the nth inner iteration in the tth outer iteration. For a fixed w (t) and η (t) , the objective function can be regarded as the step size α (t，n-1) The function can be expressed as

[0153]

[0154] in remember and It's about α (t，n-1) The function of It can be expressed as

[0155]

[0156] From the above, it can be concluded that when the satellite adopts the serial interference cancellation reception scheme, the Riemann conjugate gradient RCG design method is used to iteratively calculate the uplink precoding vector, and the traversal and rate maximization problem under the user total power constraint in the Euclidean space is transformed into the traversal and rate maximization precoding vector design problem in the Riemann submanifold space. The uplink precoding vector of each user terminal corresponding to each satellite is obtained by iteratively solving the traversal and rate maximization problem in the Riemann submanifold space; the traversal and rate maximization problem in the Riemann submanifold space calculates the current Riemann gradient in each iteration It includes the asynchronous interference introduced by the multi-satellite scenario, that is, the signals sent by the user terminal to different satellites are asynchronous in time and frequency on a certain satellite side, and the search direction η (t) Set to the negative direction of the Riemann gradient and the vector shift of the search direction obtained in the last iteration and a non-negative coefficient β (t) The superposition of the new vectors obtained by multiplication is obtained by subtracting the diagonal matrix consisting of the inner product of the precoding vector of each user terminal and its search direction divided by the maximum transmit power of the user from the current search direction. The product of the new vector composed of the precoding vectors of all users is used to obtain the vector shift in the search direction, and the Backtracking algorithm is used to iteratively search for the optimal step size α (t，n) , add the product of the optimal step size and the search direction to the user's precoding vector, and obtain the precoding vector on the Riemann submanifold space by multiplying it by the square root of the ratio of each user's maximum transmit power to the current transmit power. If the obtained precoding vector no longer improves the system sum rate performance, the vector is output.

[0157] The specific steps of the iterative algorithm based on ergodic reachability and rate when the satellite adopts the serial interference cancellation reception scheme are as follows:

[0158] Step 1: Initialize the precoding vector w (0) , α (0) >0, r∈(0,1), c∈(0,1), t=0, n=1.

[0159] Step 2: Calculate according to formula (36)

[0160] Step 3: Calculate according to formula (35)

[0161] Step 4: Calculate the search direction η according to formula (42) (t) .

[0162] Step 5: Alpha (t，n) ←rα (t，n-1 ), α (t，0) =α (0) .

[0163] Step 6: Calculate according to formula (48)

[0164] Step 7: Calculate according to formula (47)

[0165] Step 8: If Return to step 5.

[0166] Step 9:

[0167] Step 10: If converged, output w (t) , otherwise return to step 2.

[0168] When a satellite employs a serial interference cancellation reception scheme, using an iterative algorithm based on ergodic reachability and rate, the satellite needs to obtain accurate instantaneous channel state information to perform serial interference cancellation on the data streams sent by different users. To reduce computational complexity, this embodiment further proposes that the satellite employ a linear reception processing scheme. Based on the ergodic reachability and rate maximization criteria, this scheme utilizes only statistical channel state information to jointly calculate the user's transmit precoding vector and the satellite's receive processing vector.

[0169] (6) Joint uplink precoding and receive processing vector calculation when the satellite adopts a linear receive processing scheme

[0170] Considering that the satellite adopts a linear receiving processing scheme, the signal received by satellite s from user k can be expressed as

[0171]

[0172] in is the receiving processing vector of satellite s for user k. The uplink traversal rate from user k to satellite s is expressed as

[0173]

[0174] in The traversal and rate are expressed as The traversal and rate maximization problem can be formulated as

[0175]

[0176] in Receive processing vector c on the product manifold Above, expressed as Then the problem It can be transformed into an unconstrained problem on the manifold, that is,

[0177]

[0178] in g(w,c) on the manifold The Riemann gradient of c can be calculated as

[0179]

[0180] in, g(w,c) on the manifold The Riemann gradient of w can be calculated as

[0181]

[0182] in

[0183]

[0184] Fix the precoding vector w of the tth iteration (t) , the received vector of the (t+1)th iteration can be expressed as

[0185]

[0186] in and are the search step size and search direction of the tth iteration respectively, It can be expressed as

[0187]

[0188] For a given c (t+1) , the precoding vector of the (t+1)th iteration can be expressed as

[0189]

[0190] in and are the search step length and search direction of the tth iteration respectively, It can be expressed as

[0191]

[0192] in The parameters in formula (58) and the parameters in (60) It can be obtained similarly from formula (44). Let the step lengths of searching w and c in the nth inner iteration in the tth outer iteration be and And they can be obtained by the Backtracking algorithm. When calculating c with fixed w, the objective function can be regarded as The function of

[0193]

[0194] in It can be expressed as

[0195]

[0196] When c is fixed and w is calculated, the objective function can be regarded as The function of

[0197]

[0198] in remember but It can be expressed as

[0199]

[0200] From the above, it can be seen that when the satellite adopts a linear receiving scheme with lower complexity, the Riemann conjugate gradient RCG design method is used to iteratively calculate the uplink precoding vector and the receiving processing vector, and the traversal and rate maximization problem under the user total power constraint in the Euclidean space is transformed into the design problem of the precoding vector and the receiving processing vector with traversal and rate maximization in the Riemann submanifold space. The precoding vector of each user terminal corresponding to each satellite and the receiving processing vector of each satellite corresponding to each user terminal are obtained by iteratively solving the traversal and rate maximization problem in the Riemann submanifold space; in each iteration of the traversal and rate maximization problem in the Riemann submanifold space, the precoding vector is fixed, and the Riemann gradient grad of the sum rate function with respect to the receiving processing vector on the linear manifold is solved. c g(w (t) , c (t)), which includes the asynchronous interference introduced by the multi-satellite scenario, that is, the signals sent by the user terminal to different satellites are asynchronous in time and frequency on a certain satellite side, and the search direction Set to the negative direction of the Riemann gradient and the search direction obtained in the last iteration and a non-negative coefficient The new vectors obtained by multiplication are superimposed, and the optimal step length is iteratively searched using the Backtracking algorithm. The product of the optimal step size and the search direction is added to the user's receiving processing vector. If the resulting receiving processing vector no longer improves the system sum rate performance, the vector is output. Next, the resulting receiving processing vector is fixed and the Riemannian gradient of the sum rate function with respect to the precoding vector on the Riemann submanifold is solved. And search direction Set to the negative direction of the Riemann gradient and the vector shift of the search direction obtained in the last iteration and a non-negative coefficient The superposition of the new vectors obtained by multiplication is obtained by subtracting the diagonal matrix consisting of the inner product of the precoding vector of each user terminal and its search direction divided by the maximum transmit power of the user from the current search direction. The product of the new vector composed of the precoding vectors of all users is used to obtain the vector shift in the search direction, and the Backtracking algorithm is used to iteratively search for the optimal step length. The product of the optimal step size and the search direction is added to the user's precoding vector, and the precoding vector on the Riemann submanifold space is obtained by multiplying it by the square root of the ratio of the maximum transmit power of each user to the current transmit power. If the obtained precoding vector no longer improves the system sum rate performance, the vector is output.

[0201] When the satellite adopts a linear receiving processing scheme, the specific steps of the iterative algorithm based on ergodic reachability and rate are as follows:

[0202] Step 1: Initialize the receive processing vector c (0) and precoding vector w (0) ,

[0203] Step 2: Calculate according to formula (53)

[0204] Step 3: Calculate according to formula (58)

[0205] Step 4:

[0206] Step 5: Calculate according to formula (62)

[0207] Step 6: Calculate according to formula (61)

[0208] Step 7: If Return to step 4.

[0209] Step 8: c (t+1 )=c (t，n) , n=1.

[0210] Step 9: Calculate according to formula (54)

[0211] Step 10: Calculate according to formula (60)

[0212] Step 11:

[0213] Step 12: Calculate according to formula (64)

[0214] Step 13: Calculate according to formula (63)

[0215] Step 14: If Return to step 11.

[0216] Step 15:

[0217] Step 16: If converged, output c (t) and w (t) , otherwise return to step 2.

[0218] As the satellite or user moves, the channel information of each user, such as the spatial angle and average channel energy, is dynamically updated. The uplink precoding vector of each user corresponding to each satellite and the receiving processing vector of each satellite corresponding to each user change adaptively. Information such as Doppler frequency shift, minimum propagation delay, and the frequency and time compensation of the user terminal also change adaptively.

[0219] Figure 4 The method proposed in this example and the user precoding method in a single-satellite scenario are given for comparison. Figure 4 It can be seen that the ergodic performance and rate performance achieved by the iterative algorithm using only statistical channel state information and a linear reception scheme are similar to the ergodic performance achieved by the iterative algorithm using a nonlinear serial interference cancellation reception scheme. Compared with the user precoding algorithm in the single-satellite scenario, these two algorithms significantly improve the ergodic reachability and rate performance.

[0220] Based on the same inventive concept, Figure 5As shown, an embodiment of the present invention discloses a satellite-side device for uplink transmission of massive MIMO multi-satellite mobile communications, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the method for uplink transmission of massive MIMO multi-satellite mobile communications applied to satellites or gateways is implemented.

[0221] In a specific implementation, the device includes a processor, a communication bus, a memory, and a communication interface. The processor can be a general-purpose central processing unit (CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits used to control the execution of the program of the present invention. The communication bus can include a path for transmitting information between the above components. The communication interface uses any device such as a transceiver for communicating with other devices or communication networks. The memory can be a read-only memory (ROM) or other type of static storage device that can store static information and instructions, a random access memory (RAM) or other type of dynamic storage device that can store information and instructions, an electrically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM) or other optical storage, a disk storage medium or other magnetic storage device, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited to these. The memory can be independent and connected to the processor via a bus. The memory can also be integrated with the processor.

[0222] The memory is used to store application code for executing the solution of the present invention, and the execution is controlled by the processor. The processor is used to execute the application code stored in the memory, thereby implementing the communication method provided by the above embodiment. The processor may include one or more CPUs, or may include multiple processors, each of which may be a single-core processor or a multi-core processor. The processor here may refer to one or more devices, circuits, and / or processing cores for processing data (e.g., computer program instructions).

[0223] Based on the same inventive concept, Figure 6 As shown, an embodiment of the present invention discloses a massive MIMO multi-satellite mobile communication uplink transmission user terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When loaded into the processor, the computer program implements the aforementioned massive MIMO multi-satellite mobile communication uplink transmission method applied to the user terminal. In a specific implementation, the user terminal device includes a processor, a communication bus, a memory, and a communication interface. Its form may include various handheld devices with wireless communication capabilities, vehicle-mounted devices, wearable devices, computing devices, or other processing devices connected to a wireless modem.

[0224] like Figure 7 As shown, an embodiment of the present invention discloses a massive MIMO multi-satellite mobile communication uplink transmission system, including satellites and user terminals, wherein the satellites are equipped with antenna arrays and communicate with user terminals equipped with antenna arrays within their coverage areas; the satellites or the communication gateways associated with the satellites are configured to:

[0225] Using statistical channel information and the ergodic reachability and rate maximization criterion, a Riemann conjugate gradient (RCG) design method is used to iteratively calculate the precoding vectors corresponding to each user terminal and each satellite, or the precoding vectors corresponding to each user terminal and each satellite and the receive processing vectors corresponding to each satellite and each user terminal. Each satellite calculates the transmit precoding vector corresponding to each user terminal and feeds it back to each user terminal. The ergodic reachability and rate include asynchronous interference introduced by multi-satellite scenarios, i.e., signals sent by user terminals to different satellites are asynchronous in time and frequency on the satellite side.

[0226] and each satellite performs serial interference cancellation processing or linear reception processing on the signal sent by each user terminal;

[0227] The user terminal is configured to periodically send a sounding signal to a satellite, or to feed back spatial angle information, average channel energy, or geographic location information of the user terminal to the satellite for use by each satellite or gateway in calculating a transmit precoding vector for each user terminal and a receive processing vector for each satellite; perform frequency and time compensation on each data stream sent to different satellites using the Doppler frequency shift caused by the movement of each satellite and the minimum propagation delay of long-distance transmission; and perform linear precoding processing on the compensated signal using the transmit precoding vector fed back by each satellite or gateway before transmitting the uplink signal.

[0228] The above-mentioned massive MIMO multi-satellite mobile communication uplink transmission system embodiment and the massive MIMO multi-satellite mobile communication uplink transmission method embodiment are based on the same inventive concept. The specific technical implementation details can be referred to the method embodiment and will not be repeated here. The content not involved in this invention is all prior art.

[0229] A computer program product disclosed in an embodiment of the present invention includes a computer program / instruction. When the computer program / instruction is executed by a processor, the steps of the satellite, gateway or user terminal of the massive MIMO multi-satellite mobile communication uplink transmission method are implemented.

[0230] 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 within 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 method for uplink transmission of massive MIMO multi-satellite mobile communications, the method being applied to a satellite or a gateway associated with a satellite, characterized in that: The satellite is configured with an antenna array to communicate with a user terminal configured with an antenna array within its coverage area; the method comprising: Each satellite or gateway uses statistical channel information and, in accordance with the ergodic reachability and rate maximization criteria, employs the Riemann conjugate gradient (RCG) design method to iteratively calculate the precoding vectors corresponding to each user terminal and each satellite, or jointly calculates the precoding vectors corresponding to each user terminal and each satellite and the receive processing vectors corresponding to each satellite and each user terminal, and then feeds the transmit precoding vectors back to each user terminal. The ergodic reachability and rate include asynchronous interference introduced by multi-satellite scenarios, i.e., signals sent by user terminals to different satellites are asynchronous in time and frequency on a particular satellite. Each satellite performs serial interference cancellation processing or linear reception processing on the signal sent by each user terminal; During the movement of each satellite or each user terminal, as the statistical channel information changes, the precoding vector corresponding to each satellite or the reception processing vector corresponding to each user terminal is dynamically updated and the uplink transmission process is implemented.

2. The method for uplink transmission of massive MIMO multi-satellite mobile communications according to claim 1, wherein: The statistical channel information includes spatial angle information and average channel energy, which is obtained during the uplink detection process or through feedback information from each user terminal. During the uplink detection process, each user terminal periodically sends a detection signal, and each satellite estimates the spatial angle information or average channel energy of each user based on the received detection signal. The feedback information from each user terminal is the user's spatial angle information, average channel energy or geographic location information.

3. The method for uplink transmission of massive MIMO multi-satellite mobile communications according to claim 1, wherein: The calculation of the precoding vector when the satellite adopts the serial interference cancellation reception scheme includes: according to the ergodic reachability and rate maximization criterion, the uplink precoding vector is iteratively calculated using the Riemann conjugate gradient RCG design method, the ergodic and rate maximization problem under the user total power constraint in the Euclidean space is converted into a precoding vector design problem of ergodic and rate maximization in the Riemann submanifold space, and the uplink precoding vector of each user terminal corresponding to each satellite is obtained by iteratively solving the ergodic and rate maximization problem in the Riemann submanifold space; the ergodic and rate maximization problem in the Riemann submanifold space calculates the current Riemann gradient in each iteration, and sets the search direction to the negative direction of the Riemann gradient and the search direction obtained in the previous iteration. The vector shift in the search direction is obtained by multiplying a new vector obtained by multiplying the vector shift in the search direction and a non-negative coefficient. The product of a diagonal matrix consisting of the inner product of the precoding vector of each user terminal and its search direction divided by the maximum transmit power of the user and the new vector consisting of the precoding vectors of all users is subtracted from the current search direction to obtain the vector shift in the search direction. The Backtracking algorithm is used to iteratively search for the optimal step size. The product of the optimal step size and the search direction is added to the user's precoding vector. The precoding vector on the Riemann submanifold space is obtained by multiplying by the square root of the ratio of the maximum transmit power of each user to the current transmit power. If the obtained precoding vector no longer improves the system and rate performance, the vector is output.

4. The method for uplink transmission of massive MIMO multi-satellite mobile communications according to claim 1, wherein: The calculation of the precoding vector and the receiving processing vector when the satellite adopts a linear receiving scheme with lower complexity includes: according to the traversal reachability and rate maximization criterion, the uplink precoding vector and the receiving processing vector are iteratively calculated using the Riemann conjugate gradient RCG design method, the traversal and rate maximization problem under the user total power constraint in the Euclidean space is converted into the design problem of the precoding vector and the receiving processing vector with traversal and rate maximization in the Riemann submanifold space, and the precoding vector of each satellite corresponding to each user terminal and the receiving processing vector of each satellite corresponding to each user terminal are obtained by iteratively solving the traversal and rate maximization problem in the Riemann submanifold space; in each iteration of the traversal and rate maximization problem in the Riemann submanifold space, the precoding vector is fixed, the Riemann gradient of the sum rate function with respect to the receiving processing vector on the linear manifold is solved, and the search direction is set to the superposition of the negative direction of the Riemann gradient and the new vector obtained by multiplying the search direction obtained in the previous iteration by a non-negative coefficient, the optimal step size is iteratively searched using the Backtracking algorithm, and the optimal step size is set to the optimal step size. The product of the length and the search direction is added to the user's receiving processing vector. If the resulting receiving processing vector no longer improves the system sum rate performance, the vector is output. Next, the resulting receiving processing vector is fixed, and the Riemann gradient of the sum rate function with respect to the precoding vector on the Riemann submanifold is solved. The search direction is set to the negative direction of the Riemann gradient and the new vector obtained by multiplying the vector shift of the search direction obtained in the previous iteration by a non-negative coefficient. The vector shift of the search direction is obtained by subtracting the diagonal elements of the current search direction from the inner product of the precoding vector of each user terminal and its search direction, divided by the maximum transmit power of the user, and multiplying the new vector consisting of the precoding vectors of all users. The backtracking algorithm is used to iteratively search for the optimal step size. The product of the optimal step size and the search direction is added to the user's precoding vector. The precoding vector on the Riemann submanifold space is obtained by multiplying it by the square root of the ratio of the maximum transmit power of each user to the current transmit power. If the resulting precoding vector no longer improves the system sum rate performance, the vector is output.

5. A method for uplink transmission of massive MIMO multi-satellite mobile communications, the method being applied to a user terminal, characterized in that: The method comprises: The user terminal periodically sends a sounding signal to the satellite, or feeds back the user's spatial angle information, average channel energy, or geographic location information to the satellite. The satellite or gateway uses the statistical channel information to iteratively calculate the precoding vectors corresponding to each user terminal and each satellite using the Riemann conjugate gradient (RCG) design method based on the ergodic reachability and rate maximization criterion, or jointly calculates the precoding vectors corresponding to each user terminal and each satellite and the receive processing vectors corresponding to each satellite and each user terminal. The ergodic reachability and rate include asynchronous interference introduced by multi-satellite scenarios, i.e., signals sent by the user terminal to different satellites are asynchronous in time and frequency on the side of a satellite. The user terminal uses the Doppler frequency shift caused by the movement of each satellite and the minimum propagation delay of long-distance propagation to perform frequency and time compensation for each data stream sent to different satellites; Each user terminal uses the transmit precoding vector fed back by the satellite or the gateway to perform linear precoding processing on the compensated signal and then transmits the uplink signal.

6. The method for uplink transmission of massive MIMO multi-satellite mobile communications according to claim 5, characterized in that: The Doppler frequency shift and minimum propagation delay caused by satellite movement are estimated by the user terminal based on the received synchronization signal, or calculated based on the position information of the user terminal and the satellite. As the satellite or user terminal moves, the Doppler frequency shift and minimum propagation delay information are dynamically updated, and the frequency and time compensation amounts change adaptively accordingly.

7. A satellite-side device for uplink transmission of massive MIMO multi-satellite mobile communications, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the computer program is loaded into a processor, the method for uplink transmission of large-scale MIMO multi-satellite mobile communications is implemented according to any one of claims 1 to 4.

8. A massive MIMO multi-satellite mobile communication uplink transmission user terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the computer program is loaded into a processor, the method for uplink transmission of large-scale MIMO multi-satellite mobile communications is implemented according to any one of claims 5-6.

9. A massive MIMO multi-satellite mobile communication uplink transmission system, comprising satellites and user terminals, characterized in that: The satellite is configured with an antenna array to communicate with user terminals configured with antenna arrays within its coverage area; the satellite or its associated gateway is configured to: Using statistical channel information and the ergodic reachability and rate maximization criterion, a Riemann conjugate gradient (RCG) design method is used to iteratively calculate the precoding vectors corresponding to each user terminal and each satellite, or the precoding vectors corresponding to each user terminal and each satellite and the receive processing vectors corresponding to each satellite and each user terminal. Each satellite calculates the transmit precoding vector corresponding to each user terminal and feeds it back to each user terminal. The ergodic reachability and rate include asynchronous interference introduced by multi-satellite scenarios, i.e., signals sent by user terminals to different satellites are asynchronous in time and frequency on the satellite side. and each satellite performs serial interference cancellation processing or linear reception processing on the signal sent by each user terminal; The user terminal is configured to periodically send a sounding signal to the satellite, or to feed back spatial angle information, average channel energy, or geographic location information of the user terminal to the satellite, so that each satellite or a gateway can calculate a transmit precoding vector for each user terminal and a receive processing vector for each satellite. The frequency and time of each data stream sent to different satellites are compensated by utilizing the Doppler frequency shift caused by the movement of each satellite and the minimum propagation delay of long-distance transmission. The compensated signal is linearly precoded using the transmit precoding vector fed back by each satellite or gateway station before uplink signal transmission.

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 satellite, gateway or user terminal of the massive MIMO multi-satellite mobile communication uplink transmission method according to any one of claims 1 to 6 are implemented.

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