Precoding method, apparatus, medium, and device based on statistical channel information

Abstract

The present disclosure provides a precoding method, device, medium and equipment based on statistical channel information. The method comprises: initializing a precoding matrix of each satellite for each user in the delay Doppler domain; vertically stacking each precoding matrix of each user to obtain a joint precoding matrix corresponding to each user; then obtaining the ergodic rate of each user; determining the weighted sum of the ergodic rates of B users as the initial optimization target; and converting the initial optimization target into a minimum equivalent weighted minimum mean square error objective function according to the joint precoding matrix corresponding to each user and the statistical channel state information, and solving to obtain the target precoding matrix of each satellite for each user. The present disclosure converts the difficult-to-solve initial optimization target combined with the statistical channel state information into a new optimization target that is easier to solve, so as to obtain a better precoding matrix and effectively suppress the multi-satellite multi-user interference.

Description

Technical Field

[0001] This disclosure relates to the field of satellite communication technology, and in particular to a precoding method, apparatus, medium and device based on statistical channel information. Background Technology

[0002] With the development of low-Earth orbit satellite communication systems, high-dynamic broadband access, and multi-satellite cooperative transmission technologies, the wireless links between satellites and user terminals are characterized by significant long propagation delays, high Doppler spread, and strong time-varying characteristics. In such scenarios, traditional orthogonal frequency division multiplexing (OFDM) is highly sensitive to frequency offset and high-speed time-varying channels, and system performance is easily compromised. In contrast, orthogonal time-frequency space (OFS) maps information symbols to the time-delay Doppler domain and then transmits them through inverse symplectic finite Fourier transform and Heisenberg transform, which is more effective in combating performance losses caused by time-varying channels in high-dynamic scenarios. In multi-satellite cooperative transmission scenarios, the useful signal of the same user may come from multiple serving satellites simultaneously. To improve coherent synthesis gain and suppress multi-user interference, the DD domain precoding matrices of each satellite can be jointly designed at the transmitter. However, obtaining instantaneous channel state information of satellite channels is difficult, feedback costs are high, and update lags are significant. Therefore, directly performing slot-by-slot optimal precoding based on instantaneous channel state information is often not feasible in practical systems. Summary of the Invention

[0003] This disclosure proposes a precoding method, apparatus, medium, and device based on statistical channel information to solve or partially solve the above-mentioned problems to a certain extent.

[0004] In a first aspect, this disclosure provides a precoding method based on statistical channel information, the method being applied to multiple satellites communicating with B users; the method includes:

[0005] Initialize the precoding matrix for each satellite in the time-delay Doppler domain for each user; wherein the precoding matrix is ​​constructed based on the equivalent time-delay Doppler domain channel after pre-compensating the deterministic propagation delay; the deterministic propagation delay is determined based on the geometric distance between the satellite and the user; Each precoding matrix for each user is stacked vertically to obtain the joint precoding matrix for each user; The traversal rate for each user is obtained based on the joint precoding matrix and statistical channel state information corresponding to each user. The initial optimization objective is to maximize the weighted sum of the traversal rates of B users. Based on the joint precoding matrix and statistical channel state information corresponding to each user, the initial optimization objective is transformed into minimizing the equivalent weighted minimum mean square error objective function; The objective function is to minimize the equivalent weighted minimum mean square error to obtain the target precoding matrix for each satellite for each user.

[0006] A second aspect of this disclosure provides a precoding apparatus based on statistical channel information, characterized in that the apparatus is applied to multiple satellites, and the multiple satellites communicate with B users; the apparatus includes: An initialization unit is used to initialize the precoding matrix of each satellite for each user in the time-delay Doppler domain; wherein the precoding matrix is ​​constructed based on the equivalent time-delay Doppler domain channel after pre-compensation of the deterministic propagation delay; the deterministic propagation delay is determined based on the geometric distance between the satellite and the user; Stacking units are used to vertically stack each precoding matrix of each user to obtain the joint precoding matrix corresponding to each user. The rate determination unit is used to obtain the traversal rate of each user based on the joint precoding matrix and statistical channel state information corresponding to each user. The initial target determination unit is used to determine the weighted sum of maximizing the traversal rate of B users as the initial optimization target; The transformation unit is used to transform the initial optimization objective into a function that minimizes the equivalent weighted minimum mean square error, based on the joint precoding matrix and statistical channel state information corresponding to each user. The solver unit is used to solve for the objective function of minimizing the equivalent weighted minimum mean square error to obtain the target precoding matrix for each satellite for each user.

[0007] A third aspect of this disclosure provides a computer device including one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and executed by the one or more processors, and the one or more programs include instructions for performing the method of the first aspect.

[0008] A fourth aspect of this disclosure provides a non-volatile computer-readable storage medium comprising a computer program that, when executed by one or more processors, causes the one or more processors to perform the method described in the first aspect.

[0009] The precoding method based on statistical channel information provided in this disclosure, in a multi-satellite cooperative transmission scenario, performs joint precoding on each satellite at the transmitting end based on statistical channel state information to construct a joint precoding matrix. The joint precoding matrix controls the amplitude, phase, and mapping relationship between time-delayed Doppler domain resources when each satellite transmits delayed Doppler domain symbols to each user, thereby enhancing the desired signal for the target user, enabling coherent superposition of signals transmitted from multiple satellites to the same user, and suppressing multi-user interference to other users. Therefore, when optimizing the joint precoding matrix, the initial optimization objective is to maximize the weighted sum of the traversal rates of B users. Since the initial optimization objective is a non-convex function and difficult to solve, it is transformed into a weighted minimum mean square error problem, which is easier to solve. However, under statistical channels, the traditional weighted minimum mean square error problem is not equivalent to the initial optimization objective. Therefore, this disclosure, based on the joint precoding matrix and statistical channel state information, transforms the initial optimization objective into an equivalent objective function that minimizes the equivalent weighted minimum mean square error, to obtain the optimized precoding matrix. This disclosure completes the cooperative precoding in the time-delay Doppler domain based on statistical channel state information, which reduces the dependence on instantaneous channel state information. In the process of optimizing the precoding matrix, the difficult-to-solve initial optimization objective is transformed into a new optimization objective that is easier to solve by combining statistical channel state information, so as to obtain a better precoding matrix and effectively suppress interference between multiple satellites and multiple users. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in this disclosure or related technologies, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 A flowchart of a precoding method based on statistical channel information provided in an embodiment of this disclosure is shown.

[0012] Figure 2 A schematic diagram of the hardware structure of an exemplary computer device provided in an embodiment of this disclosure is shown. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of this disclosure clearer, the following detailed description is provided in conjunction with specific embodiments and the accompanying drawings.

[0014] It should be noted that, unless otherwise defined, the technical or scientific terms used in the embodiments of this disclosure should have the ordinary meaning understood by one of ordinary skill in the art to which this disclosure pertains. The terms "first," "second," and similar terms used in the embodiments of this disclosure do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0015] The precoding method based on statistical channel information disclosed herein is applicable to scenarios where multiple satellites simultaneously provide cooperative transmission services to multiple user terminals. Each satellite is equipped with a uniform planar array antenna, i.e., a UPA array; the number of antenna elements along the x-axis and y-axis are Q and Q, respectively. x and Q y The total number of antenna elements is Q = Q x Q y .

[0016] In one embodiment, the set S of satellites used to provide transmission services meets the following condition: S={1,2,…,A}, where A is the number of satellites; the set U of user terminals meets the following condition: U={1,2,…,B}, where B is the number of users.

[0017] With the development of low-Earth orbit satellite communication systems, high-dynamic broadband access, and multi-satellite cooperative transmission technologies, the wireless link between satellites and user terminals exhibits significant long propagation delays, high Doppler spread, and strong time-varying characteristics. Therefore, this disclosure employs an Orthogonal Time Frequency Space (OTFS) modulation scheme. The symbols to be transmitted are first mapped to the Delay-Doppler (DD) domain resource grid of the OTFS, and then transmitted after undergoing Inverse Symplectic Finite Fourier Transform (ISFFT) and time-domain modulation. After demodulation by the OTFS at the receiver, detection is performed in the DD domain.

[0018] OTFS is a modulation technique, or waveform modulation, similar to OFDM. It transforms the symbols to be transmitted from the time-delay Doppler domain to the time-frequency domain, and then transmits them using time-frequency modulation methods. The DD domain is a two-dimensional domain used to characterize the multipath delay and Doppler frequency shift characteristics in wireless propagation. In an OTFS system, the symbols to be transmitted are preferentially mapped into this domain before being transformed and transmitted.

[0019] The satellite acts as the transmitter, and the user acts as the receiver; the collaborative transmission service process is as follows: Transmitter operation process: For any user u (u∈U), the symbols to be transmitted are organized into an M×N DD-domain symbol matrix, where M represents the number of frequency domain data and N represents the number of time domain data, and then vectorized to obtain the satellite... For users Transmitted DD domain data symbol vector Satellite s (s∈S) uses a DD-domain precoding matrix for user u. The precoded DD domain emission vector is obtained. Then, an ISFFT transform is performed on the precoded DD domain transmit vector to obtain the time-frequency domain signal, which is then transformed by Heisenberg transform to form the time-domain transmit signal of each satellite antenna.

[0020] It is understandable that each satellite corresponds to an independent precoding matrix for each user. The precoding matrix is ​​a linear transformation matrix set on the satellite, which performs linear weighting and vector mapping on the baseband signals of each user, and maps the symbols to be transmitted to the transmission vector of the transmitting antenna / beam.

[0021] The elements in the precoding matrix are complex precoding coefficients, comprising amplitude and phase components, used to control the mapping relationship between the satellite and each DD domain symbol, each antenna component, and possible DD domain neighboring resources for the user. Its function is not simply power allocation, but simultaneously performs: useful signal enhancement, coherent superposition of multiple satellites to the same user, multi-user interference suppression, and satisfaction of satellite power constraints.

[0022] The receiver operates by receiving superimposed signals from multiple satellites. First, the DD domain receive vector is restored using Wigner transform (the inverse of the Heisenberg transform) and Symptotic Finite Fourier Transform (SFFT).

[0023] This disclosure describes a scenario where multiple satellites simultaneously provide collaborative transmission services to multiple user terminals. In the multi-satellite coherent transmission mode, multiple satellites do not independently send different symbols to the same user, but rather coordinate to send the same symbols to the same user, thereby enabling the receiving end to achieve useful signal superposition.

[0024] For any user u (u∈U), the DD domain receive vector obtained after OTFS demodulation is: , It is the superposition result of signals received by user u from all satellites. The following conditions must be met:

[0025] in, The desired signal; Includes users Its own data vector ; This is an interference signal; Multi-user interference items caused to other users, it includes Other user data DD domain data symbol vectors, but these data will also pass through satellites. To users channel Reaching users ; It is additive white Gaussian noise, which is independent of all transmitted data.

[0026] Expected signal The following conditions must be met:

[0027] in, Let be the equivalent DD domain channel matrix from satellite s to user u; It is obtained by applying the OTFS correlation transform to the time-domain equivalent channel. The following conditions must be met:

[0028] in, express Point discrete Fourier transform matrix, This indicates its conjugate transpose. express identity matrix express identity matrix Represents the Kronecker product; This is the time-domain channel matrix, with dimensions MN×QMN.

[0029] Interference signal The following conditions must be met:

[0030] in, ; This refers to users other than user u; That is, satellite S to user The DD-domain precoding matrix; That is, a satellite For users The DD domain data symbol vector being sent.

[0031] It should be noted that in multi-satellite coherent transmission mode, multiple satellites act on the same user's transmitted symbols through their respective equivalent DD domain channel matrices and corresponding precoding matrices; these are then superimposed at the receiver. Here, the better the precoding matrix is ​​designed, the more coherent enhancement the signals from each satellite can achieve at the user end; conversely, they may cancel each other out or enhance interference to other users, resulting in a poor superposition effect of signals at the receiver.

[0032] Furthermore, the degree of coherence enhancement formed by each satellite signal at the user end is determined based on the user's ergodic rate, which is the average achievable rate or long-term transmission capacity of that user in a statistical sense. A better-designed precoding matrix results in a larger sum of weighted ergodic rates for all users; conversely, a poorly designed matrix results in a smaller sum of weighted ergodic rates for all users. Therefore, a better precoding matrix can be obtained by using the sum of weighted ergodic rates for all users as the optimization objective.

[0033] However, obtaining instantaneous Channel State Information (CSI) for satellite channels is difficult, the feedback cost is high, and the update lag is significant. Therefore, performing slot-by-slot optimal precoding directly based on instantaneous CSI is often not feasible in practical systems.

[0034] Therefore, as Figure 1 As shown, this disclosure provides a precoding method based on statistical channel information, which is applied to multiple satellites communicating with B users; the method includes: S100, initialize the precoding matrix for each satellite for each user in the time-delay Doppler domain; wherein, the precoding matrix is ​​constructed based on the equivalent time-delay Doppler domain channel after pre-compensation of the deterministic propagation delay; the deterministic propagation delay is determined based on the geometric distance between the satellite and the user.

[0035] Specifically, in satellite communication systems, the DD domain channel from satellite to user is represented by a multipath superposition model. Each path includes path gain, deterministic propagation delay, Doppler, and array direction vector. The deterministic propagation delay between satellite and user is mainly determined by geometric distance and can be estimated through ephemeris information, user positioning information, link ranging, navigation aid information, or pilot synchronization. This type of deterministic propagation delay is characterized by strong determinism, predictable variation patterns, and mature estimation methods. Therefore, it can be considered a portion that is relatively easy to address using existing synchronization, ranging, timing advance, or navigation aid compensation techniques. After deducting the deterministic propagation delay, residual delay still exists. Residual delay may originate from multipath propagation, scattering and reflection, fractional delay, local environmental changes, synchronization errors, and deviations between statistical CSI and the actual instantaneous channel. Compared to deterministic propagation delay, residual delay is more difficult to obtain accurately and is more prone to modeling and estimation errors, making it the focus of this disclosure.

[0036] Therefore, the DD domain in this embodiment is obtained by pre-compensating for deterministic propagation delay. The easily processed deterministic propagation delay is first stripped away, leaving the remaining channel primarily reflecting the difficult-to-process residual delay, Doppler effect, and DD domain channel error. On one hand, this avoids excessively large differences in large-scale propagation delay between different satellites and the same user, causing the DD domain channels of each satellite to fall at significantly different delay positions, which would be detrimental to unified modeling and joint precoding. On the other hand, it allows the equivalent DD domain channels from multiple satellites to the same user to be placed in a unified, delay-aligned DD domain representation, enabling joint processing of multi-satellite DD domain channels. That is, after pre-compensation, each satellite channel no longer primarily reflects a large deterministic propagation delay offset, but rather mainly reflects residual small-scale delay, Doppler effect, and statistical error.

[0037] In one embodiment, the deterministic propagation delay is first estimated using ephemeris, user location, or pilot synchronization results, and then pre-compensation is performed by methods such as timing advance, receiver synchronization, DD domain cyclic shift, or multiplying by a phase compensation factor in the time and frequency domain.

[0038] After removing the deterministic propagation delay, a unified multi-satellite DD domain channel model is constructed to address the residual delay and DD domain channel error, which are difficult to process accurately and are prone to errors. Based on this model, multi-satellite collaborative precoding optimization driven by statistical CSI is performed.

[0039] In this disclosure, the precoding matrix for each satellite in the time-delay Doppler domain is initialized for each user. The precoding matrix can be initialized using equal-power random initialization, line-of-sight propagation path-direction-based initialization, or unit-structure scaling initialization.

[0040] S200 involves vertically stacking each precoding matrix for each user to obtain the joint precoding matrix for each user.

[0041] Specifically, this stacking method allows the precoding matrices of multiple satellites for the same user to be written as a single matrix variable, thus transforming the multi-satellite collaborative precoding problem into a matrix optimization problem similar to that of a large-scale joint multiple-input multiple-output (MIMO) system.

[0042] As an example: User Joint precoding matrix:

[0043] This matrix is ​​comprised of all service satellites facing the user. The precoding matrices are stacked vertically. S300 obtains the traversal rate for each user based on the joint precoding matrix and statistical channel state information corresponding to each user.

[0044] Specifically, step S300 also includes: S310, based on the statistical channel state information, obtain the joint channel statistical covariance matrix and block diagonal channel covariance matrix for each user in the time-delay Doppler domain.

[0045] Here, we obtain the second-order statistical correlation block between the satellite and the user's DD domain channel as an example: obtaining satellite... and satellite To users The second-order statistical correlation block between DD domain channels. If This matrix represents the distance from a single satellite to the user. Channel autocorrelation; if This matrix represents the cross-correlation of channels from different satellites to the same user. This cross-correlation term is a key manifestation of multi-satellite coherent cooperation in the statistical rate formula. (Satellites) and satellite To users Second-order statistical correlation blocks between DD domain channels The following conditions must be met:

[0046] in, Indicates statistical expectation; This indicates the conjugate transpose. It includes both the mean term of the line-of-sight (LoS) direct path and the covariance term resulting from non-line-of-sight (NLoS) scattering or channel errors. The second-order statistical correlation block between satellite and user DD domain channels refers to the long-term statistical correlation of channels between different satellites and the same user in the time-delay-Doppler domain. It characterizes the long-term spatial correlation of channels for each user and belongs to the slowly varying statistical parameters of the channel, which do not fluctuate with instantaneous small-scale fading.

[0047] Furthermore, based on the second-order statistical correlation block between the satellite and user DD domain channels, the joint channel statistical covariance matrix for each user is obtained. As an example: the joint channel statistical covariance matrix for user u. The following conditions must be met:

[0048] It consists of all It is composed of a block matrix. Because... Include The off-diagonal blocks therefore describe not only the average channel energy of each satellite's own link, but also the signal strength of different satellites at the user's location. Statistical correlation when performing coherent joints.

[0049] Similarly, the block diagonal channel covariance matrix for interference term modeling is obtained. For example, the block diagonal channel covariance matrix for user u... The following conditions must be met:

[0050] in, For each satellite to the user Autocorrelation blocks, It does not contain cross-correlation blocks between different satellites.

[0051] Understandably, for users The desired signal is transmitted by multiple satellites to the same user. The data can form a coherent overlay, therefore it is necessary to retain cross-satellite correlation terms; while for other users... The interference caused by different satellites is usually not used by users. For coherent useful signal processing, the interference statistical covariance is modeled in a block diagonal form.

[0052] S320, for each user, the expected signal statistical covariance matrix of the user is obtained based on the user's joint precoding matrix and joint channel statistical covariance matrix; wherein, the expected signal statistical covariance matrix represents the strength of the expected signal received by the corresponding user.

[0053] Here, the user's expected signal statistical covariance matrix is... The following conditions must be met:

[0054] Indicates user The expected signal statistical covariance matrix is ​​used to characterize the signal from multiple satellites for users. The average power and correlation of the transmitted useful signal in a statistical sense. The larger this matrix, the more powerful the user... The stronger the expected signal.

[0055] S330, for each user, the interference statistical covariance matrix of the user is obtained based on the joint precoding matrix of other users besides the user itself and the user's block diagonal channel covariance matrix; wherein, the interference statistical covariance matrix represents the average intensity of the interference signals received by the corresponding user from other users.

[0056] Here, the user's interference statistical covariance matrix The following conditions must be met:

[0057] Indicates user The received interference statistical covariance matrix. It statistically analyzes the interference from other users. The transmitted signal travels from the satellite to the user. After the channel, in the user The average interference intensity formed at a given location. The larger this matrix, the stronger the user's interference. The stronger the interference, the better.

[0058] S340, based on the expected signal statistical covariance matrix, interference statistical covariance matrix and noise covariance matrix of each user, the traversal rate of each user is obtained; wherein, the noise covariance matrix represents the intensity of additive white Gaussian noise received by the corresponding user.

[0059] Step S340 further includes: S341, obtain the relationship between the transmitted and received signals of each user in the time-delay Doppler domain.

[0060] S342, based on the relationship between the expected signal statistical covariance matrix, interference statistical covariance matrix, noise covariance matrix and the transmitted and received signals in the time-delay Doppler domain for each user, obtain the mutual information of each user.

[0061] S343, correct and normalize the mutual information to obtain the traversal rate for each user.

[0062] Among them, the traversal rate is positively correlated with the statistical covariance matrix of the desired signal; the traversal rate is negatively correlated with the statistical covariance matrix of the interference; and the traversal rate is negatively correlated with the noise covariance matrix.

[0063] Here, based on the aforementioned input-output relationship between the transmitter and receiver, the mutual information of user u can be written in a log-det form similar to the channel capacity of a MIMO system:

[0064] Here, det() represents the matrix determinant; log2() represents the logarithm to the base 2; It represents matrix inversion; the log-det form is a common expression for MIMO / multi-stream channel mutual information or reachable rate, obtained by taking the determinant and logarithm of the matrix formed by the channel and precoding.

[0065] Understandably, in multi-satellite joint transmission scenarios, a single user is equivalent to a virtual MIMO channel, and its mutual information represents the achievable transmission rate of the user. This mutual information is mathematically consistent with the capacity of a classic MIMO channel, and therefore can be represented using a unified log-det form.

[0066] This formula can be understood as follows: the user's traversal rate is determined by the matrix ratio of the desired signal strength to the interference signal strength plus the noise strength. Since an OTFS frame contains MN DD domain data streams, the traversal rate expression is in matrix form, rather than a single scalar signal-to-interference-plus-noise ratio (SINR) form.

[0067] Furthermore, the above mutual information is normalized to the reachable rate Ru of user u; where Ru satisfies the following condition:

[0068] in, Indicates the subcarrier spacing. The duration of a single OTFS time-domain symbol is typically satisfied. ; Indicates the effective duration of an OTFS frame when it does not contain a cycle prefix; This indicates the duration of the cyclic prefix or guard interval. This represents the normalized time-frequency resource quantity after considering the cyclic prefix overhead. If The denominator degenerates into ;like This indicates the effective rate loss due to the cyclic prefix.

[0069] Since instantaneous CSI is difficult to obtain accurately in satellite communications, this disclosure does not directly maximize the instantaneous rate based on the instantaneous channel. Instead, it takes a statistical average of the channel randomness to obtain the user's CSI. The traversal rate is approximately equal to, i.e.

[0070] in, Represents the noise covariance matrix; yes A 1-dimensional identity matrix, not a regular scalar of 1. It corresponds to a single OTFS frame. A unit covariance benchmark for a DD domain data symbol stream. Add to the formula In the capacity formula corresponding to a single-stream communication system The structure; it's just that here, due to the existence of A DD domain data stream, so scalar 1 is generalized to the identity matrix. .

[0071] In the above formula ; This can be understood as the effective signal-to-interference-plus-noise ratio in matrix form. If the precoding matrix... If designed well, then Enlarge Suppressed, user The traversal rate is improved; however, if the precoding matrix is ​​poorly designed, the useful signal is weak and the interference is strong, resulting in a reduced traversal rate.

[0072] S400 sets the weighted sum of the traversal rates of B users as the initial optimization objective.

[0073] The target of this public optimization is precisely all The set of matrices controls the amplitude, phase, and mapping relationships between DD domain resources when each satellite transmits DD domain symbols to each user, thereby enhancing the desired signal for the target user; enabling coherent superposition of signals transmitted by multiple satellites to the same user; and suppressing multi-user interference caused to other users.

[0074] Since this disclosure does not rely on transient CSI, It is not the instantaneous rate of a specific time slot, but rather an approximate expression for the ergonomic rate obtained based on statistical CSI, that is, a rate index under the meaning of averaging random changes in the channel. Therefore, this disclosure uses As a long-term optimization goal, among which Indicates user The business weight or priority. And the constraint of the above initial optimization objective is: the transmission power of each satellite does not exceed its power limit.

[0075] It should be noted that, due to Includes log-det and matrix inverse The function is coupled with multi-user precoding; therefore, the initial optimization objective is usually a non-convex problem. And, improving user... The traversal rate may increase interference from other users, therefore optimization cannot be performed independently for each user. Furthermore, this disclosure is based on statistical CSI, not instantaneous CSI. Therefore, directly solving for the initial optimization objective of maximizing the weighted sum of the traversal rates of B users is very difficult.

[0076] S500 transforms the initial optimization objective into minimizing the equivalent weighted minimum mean square error objective function based on the joint precoding matrix and statistical channel state information corresponding to each user.

[0077] Therefore, this disclosure transforms the initial optimization objective into minimizing the equivalent weighted minimum mean squared error (WMMSE) objective function. However, under statistical Rician channels, the equivalence relations that traditional equivalent weighted minimum mean squared error transformations typically rely on no longer hold. That is, under statistical Rician channels, the "mean product" of the random channel matrix is ​​generally not equal to the "second moment":

[0078] in, It is the channel mean, which usually corresponds to the LoS deterministic component in a Rician channel; It is a second-order statistic of the channel Gram matrix, which includes both the LoS mean term and the covariance term resulting from NLoS scattering or channel error.

[0079] like ,in This is the Loss mean term. If the term is a zero-mean random scattering term, then:

[0080] and

[0081] The two terms are not equal as long as the random scattering term or error covariance is not zero. They are only approximately equal when the Rician factor approaches infinity, the channel is approximately pure Loss of Time (LoS), and the random term disappears.

[0082] Therefore, step S500 also includes: S510: Based on the joint precoding matrix, joint channel statistical covariance matrix and block diagonal channel covariance matrix corresponding to each user, the equivalent mean square error matrix of each user is obtained.

[0083] Step S510 includes: S511, perform matrix square root decomposition on the joint channel statistical covariance matrix of each user to obtain an auxiliary matrix.

[0084] here, Indicates to the user The joint channel statistical covariance matrix is ​​decomposed into its square root to determine the auxiliary matrix. ; yes A square root factor; express The conjugate transpose of .

[0085] The key significance of this decomposition lies in maintaining second-order energy consistency. For any joint precoding matrix... All of them have:

[0086] in, The trace of the matrix; The squared Frobenius norm of a matrix is ​​defined as the sum of the squares of the moduli of all its elements.

[0087] Here, the auxiliary matrix transforms the second-order statistical properties of the random channel into a deterministic equivalent matrix, ensuring that the subsequent MSE expression accurately includes the covariance contribution from the statistical CSI. In simpler terms, It is not the actual physical channel, but the square root representation of the statistical channel energy and correlation.

[0088] Therefore, use When constructing the equivalent mean square error matrix, the statistical channel covariance is not discarded. Instead, the statistical covariance is embedded into the optimization problem in the form of a deterministic matrix product.

[0089] S512 performs matrix square root decomposition on the block diagonal channel covariance matrix of each user to obtain the interference auxiliary matrix.

[0090] Here, the auxiliary matrix of the interference term Its function is to transmit other user signals through the user The average interference power caused by the channel is also written in deterministic matrix form. For users... From user interference terms and This is relevant; if only the channel mean is used, the interference leakage caused by random scattering or channel error will be underestimated. This is used to characterize the covariance of this interference / error.

[0091] In the specific construction, the block diagonal statistical covariance matrix of the interference-related user u can be defined first. :

[0092] in, Then, using the same Cholesky decomposition or eigenvalue decomposition, we can achieve the following:

[0093] Thus, the statistical interference power from other users can be written as the sum of the interference energy terms of all other users, or as the corresponding covariance form. Therefore, Primarily used for constructing the equivalent MSE of the desired signal. It is mainly used to incorporate the interference / error term into the equivalent WMMSE target, so as to avoid underestimating multi-user interference in statistical CSI scenarios.

[0094] S513, based on the joint precoding matrix, auxiliary matrix and interference auxiliary matrix of each user, the equivalent mean square error matrix of each user is obtained.

[0095] Here, the equivalent mean square error matrix of user u can be written as:

[0096] The objective function means: to optimize the linear receiver filter matrix. Weighted minimum mean square error weight matrix and precoding matrix This minimizes the weighted equivalent mean square error (MSE) for all users. Since this equivalent MSE is specifically based on... It is constructed so that it is consistent with the original weighted traversal rate target.

[0097] It's important to note that what is being minimized here is not the traditional equivalent mean square error matrix, but the equivalent WMMSE. Its purpose is to mathematically correlate minimizing the weighted equivalent mean square error matrix with maximizing the weighted traversal rate.

[0098] S520 obtains the preset weights for each user and initializes the linear receiving filter matrix and the weighted minimum mean square error weight matrix for each user.

[0099] Here, the preset weight for each user can be defined by those skilled in the art based on the actual situation.

[0100] The linear receiver filtering matrix is ​​calculated using a closed-form solution optimized by minimum mean square error, based on the statistical covariance matrix of the user's desired signal, the statistical covariance matrix of other user interference, and the noise power term. It is used to perform linear filtering on the signal at the receiver to suppress interference and noise and minimize the equivalent mean square error.

[0101] The weighted minimum mean square error (MMS) matrix is ​​a key matrix in the WMMSE optimization algorithm used for equivalent system transformation and rate maximization problems. It is obtained by inverting the user's equivalent MMS error matrix under the current precoding matrix and the received filter matrix, dynamically representing the user's communication quality and providing weighting coefficients for subsequent precoding matrix updates.

[0102] Here, the linear receiver filtering matrix and the weighted minimum mean square error (MMS) weight matrix for each user are initialized to construct an equivalent weighted minimum mean square error objective function. The specific initialization method can be any method well-known to those skilled in the art.

[0103] S530: Based on the equivalent mean square error matrix, preset weights, linear receiving filter matrix, and weighted minimum mean square error weight matrix for each user, the equivalent weighted minimum mean square error objective function is obtained; wherein, the equivalent mean square error matrix is ​​positively correlated with the equivalent weighted minimum mean square error objective function.

[0104] Here, the equivalent weighted minimum mean square error objective function is as follows:

[0105] in, Indicates user The preset weights.

[0106] S600 is solved with the objective of minimizing the equivalent weighted minimum mean square error objective function to obtain the target precoding matrix for each satellite for each user.

[0107] This disclosure employs an alternating optimization solution, first allocating initial power to each user based on the total satellite power.

[0108] Here, the initial power allocation is just the initialization method of the alternating optimization algorithm, which can be equal power allocation, allocation according to user weight, or allocation according to statistical channel quality.

[0109] In one embodiment, initialization can be based on equal power allocation for each user, or weighted allocation for each user. After allocation, an initial direction matrix is ​​generated, which can be a random semi-unitary matrix, an identity structure matrix, or a maximum ratio transmission direction based on statistical LOS direction vectors, and then normalized. This ensures that the initial matrix satisfies the power constraint. Subsequent iterations will automatically adjust each precoding matrix according to the equivalent WMMSE target; therefore, the initial allocation is not the final allocation, but only serves to provide a feasible initial point.

[0110] Specifically, step S600 includes: S610: Under the condition that the joint precoding matrix and the weighted minimum mean square error weight matrix of each user remain unchanged, update the linear receiver filter matrix of each user with the objective of minimizing the equivalent weighted minimum mean square error objective function.

[0111] Here, with the current precoding matrix fixed, the receive filter matrix is ​​updated based on the current desired signal, interference, and noise statistics. Following the notation in the initial draft of the paper, this can be written as:

[0112] in, Indicates the updated user The linear receiver filtering / equalization matrix; Indicates noise power.

[0113] The meaning of this update formula is: when the current precoding matrix is ​​fixed, the user... Choose a linear receiving filter that minimizes the equivalent mean square error matrix. If the condition number of the total received covariance matrix is ​​poor, a regularized inverse or pseudo-inverse can be used.

[0114] S620, with the joint precoding matrix and linear receiver filtering matrix of each user remaining unchanged, updates the weighted minimum mean square error weight matrix of each user with the objective of minimizing the equivalent weighted minimum mean square error objective function.

[0115] Here, in a fixed position and When the optimal weight matrix that minimizes the equivalent WMMSE objective is equal to the inverse of the equivalent MSE matrix, that is... .

[0116] S630, with the weighted minimum mean square error weight matrix unchanged for each user, updates the joint precoding matrix for each user based on the Lagrangian function and preset transmit power constraints, with the objective of minimizing the equivalent weighted minimum mean square error objective function.

[0117] Here, in a fixed position and Afterwards, the equivalent WMMSE objective is about This transforms into a quadratic optimization problem with power constraints. We construct a Lagrangian function and add the power constraints as multipliers. When using per-user power constraints, it can be written as:

[0118] in, Let the Lagrange multiplier be the equivalent transmit power budget constraint for user u. The equivalent transmit power budget allocated to user u when solving the equivalent WMMSE problem.

[0119] Taking the derivative of the conjugate variable of the joint precoding matrix and setting the derivative to zero yields a linear matrix equation, the general form of which can be written as:

[0120] thereby:

[0121] in, Interference leakage items and auxiliary matrices from all users and , as well as Together constitute; For users The expected signal matching term; Used to ensure that the power constraint is satisfied; I is the identity matrix with the same dimension as matrix Au.

[0122] Furthermore, it can be summarized as follows:

[0123] Seek Then, each satellite was separated according to its stacking position. The above process illustrates how the matrix is ​​optimized: each iteration resolves a precoding matrix that reduces the equivalent WMMSE target based on the current interference, noise, receive filtering, and MSE weights.

[0124] After completing the precoding update for each user, scaling can be performed based on the actual transmit power of each satellite. This scaling ensures that the total transmit power of all satellites does not exceed the corresponding power constraint.

[0125] S640, based on the updated linear receiver filter matrix, the weighted minimum mean square error weight matrix, and the joint precoding matrix, obtains the change value of the equivalent weighted minimum mean square error objective function.

[0126] S650, if the change value of the equivalent weighted minimum mean square error objective function is greater than the preset convergence threshold, then repeat the steps "update the linear receiver filter matrix of each user while keeping the joint precoding matrix and the weighted minimum mean square error weight matrix unchanged" to "obtain the change value of the equivalent weighted minimum mean square error objective function based on the updated linear receiver filter matrix, the weighted minimum mean square error weight matrix, and the joint precoding matrix", until the change value of the equivalent weighted minimum mean square error objective function is equal to or less than the preset convergence threshold or reaches the preset number of iterations, then end, to obtain the target joint precoding matrix.

[0127] Here, if the preset convergence condition is not met, the process repeats from step S610 to step S640 until the preset convergence condition is met.

[0128] S660, the target joint precoding matrix is ​​split to obtain the target precoding matrix for each satellite for each user.

[0129] Here, the optimized joint precoding matrix is ​​split, and the final output is the converged set of DD domain optimized precoding matrices for each satellite and each user. Since the original multi-user precoding problem is non-convex, alternating optimization usually guarantees that the objective function monotonically improves and converges to a stable point or a local optimum that satisfies the KKT conditions.

[0130] The KKT conditions, or Karush-Kuhn-Tucker conditions, are necessary conditions for finding the optimal solution to an optimization problem with inequality constraints. They include gradient conditions, primal feasibility, dual feasibility, and complementary relaxation conditions. In this disclosure, they are used to solve a WMMSE optimization problem with per-user power constraints, determining the values ​​of the Lagrange multipliers to ensure that the precoding matrix satisfies the power constraint requirements.

[0131] This disclosure uses statistical CSI as the basis for DD domain cooperative precoding, adapting to the practical constraints of difficult CSI acquisition and large feedback hysteresis in satellite links, and reducing reliance on instantaneous CSI. Furthermore, it supports multi-satellite coherent cooperative transmission. Multiple serving satellites jointly transmit to the same user, which can improve the useful signal superposition gain and enhance multi-user interference suppression capabilities. This disclosure also provides a precoding apparatus based on statistical channel information, the apparatus being applied to multiple satellites, the multiple satellites communicating with B users; the apparatus includes: An initialization unit is used to initialize the precoding matrix of each satellite for each user in the time-delay Doppler domain; wherein the precoding matrix is ​​constructed based on the equivalent time-delay Doppler domain channel after pre-compensation of the deterministic propagation delay; the deterministic propagation delay is determined based on the geometric distance between the satellite and the user; Stacking units are used to vertically stack each precoding matrix of each user to obtain the joint precoding matrix corresponding to each user. The rate determination unit is used to obtain the traversal rate of each user based on the joint precoding matrix and statistical channel state information corresponding to each user. The initial target determination unit is used to determine the weighted sum of maximizing the traversal rate of B users as the initial optimization target; The transformation unit is used to transform the initial optimization objective into a function that minimizes the equivalent weighted minimum mean square error, based on the joint precoding matrix and statistical channel state information corresponding to each user. The solver unit is used to solve for the objective function of minimizing the equivalent weighted minimum mean square error to obtain the target precoding matrix for each satellite for each user.

[0132] It should be noted that the method of this disclosure embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this disclosure embodiment, and the multiple devices will interact with each other to complete the method described.

[0133] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0134] This disclosure also provides a computer device for implementing the above-described precoding method based on statistical channel information. Figure 2 A schematic diagram of the hardware structure of an exemplary computer device 500 provided in an embodiment of this disclosure is shown.

[0135] like Figure 2As shown, the computer device 500 may include: a processor 502, a memory 504, a network interface 506, a peripheral interface 508, and a bus 510. The processor 502, memory 504, network interface 506, and peripheral interface 508 are interconnected within the computer device 500 via the bus 510.

[0136] Processor 502 may be a central processing unit (CPU), image processor, neural network processor (NPU), microcontroller (MCU), programmable logic device, digital signal processor (DSP), application-specific integrated circuit (ASIC), or one or more integrated circuits. Processor 502 can be used to perform functions related to the techniques described in this disclosure. In some embodiments, processor 502 may also include multiple processors integrated as a single logic component. For example, such as... Figure 2 As shown, processor 502 may include multiple processors 502a, 502b and 502c.

[0137] Memory 504 can be configured to store data (e.g., instructions, computer code, etc.). Figure 2 As shown, the data stored in memory 504 may include program instructions (e.g., one or more programs for implementing the methods of embodiments of this disclosure) and data to be processed (e.g., the memory may store configuration files of other modules, etc.). Processor 502 may also access the program instructions and data stored in memory 504 and execute the program instructions to operate on the data to be processed. Memory 504 may include volatile or non-volatile storage devices. In some embodiments, memory 504 may include random access memory (RAM), read-only memory (ROM), optical disk, magnetic disk, hard disk, solid-state drive (SSD), flash memory, memory stick, etc.

[0138] Network interface 506 can be configured to provide communication with other external devices to computer device 500 via a network. This network can be any wired or wireless network capable of transmitting and receiving data. For example, the network can be a wired network, a local wireless network (e.g., Bluetooth, WiFi, Near Field Communication (NFC), etc.), a cellular network, the Internet, or a combination thereof. It is understood that the type of network is not limited to the specific examples described above.

[0139] The peripheral interface 508 can be configured to connect the computer device 500 to one or more peripheral devices to enable information input and output. For example, peripheral devices may include input devices such as keyboards, mice, touchpads, touch screens, microphones, and various sensors, as well as output devices such as displays, speakers, vibrators, and indicator lights.

[0140] Bus 510 can be configured to transfer information between various components of computer device 500 (such as processor 502, memory 504, network interface 506, and peripheral interface 508), such as internal buses (e.g., processor-memory bus), external buses (USB port, PCI-E bus), etc.

[0141] It should be noted that although the architecture of the computer device 500 described above only shows the processor 502, memory 504, network interface 506, peripheral interface 508, and bus 510, in specific implementations, the architecture of the computer device 500 may also include other components necessary for normal operation. Furthermore, those skilled in the art will understand that the architecture of the computer device 500 described above may only include the components necessary for implementing the embodiments of this disclosure, and does not necessarily include all the components shown in the figures.

[0142] Based on the same inventive concept, corresponding to any of the above embodiments, this disclosure also provides a non-volatile computer-readable storage medium containing a computer program, which, when executed by one or more processors, causes the one or more processors to perform the precoding method based on statistical channel information.

[0143] The computer-readable medium of this embodiment includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transfer medium that can be used to store information accessible by a computing device.

[0144] The computer program stored in the storage medium of the above embodiments is used to cause the one or more processors to perform the method as described in any of the above embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0145] Based on the same inventive concept, corresponding to the precoding method based on statistical channel information in any of the above embodiments, this disclosure also provides a computer program product, which includes one or more computer programs. In some embodiments, the one or more computer programs are executable by one or more processors to cause the one or more processors to perform the precoding method based on statistical channel information. Corresponding to the execution entity for each step in each embodiment of the precoding method based on statistical channel information, the processor executing the corresponding step may belong to the corresponding execution entity.

[0146] The computer program product of the above embodiments is used to cause the processor to execute the precoding method based on statistical channel information as described in any of the above embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0147] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of this disclosure (including the claims) is limited to these examples; within the framework of this disclosure, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of the embodiments of this disclosure as described above, which are not provided in detail for the sake of brevity.

[0148] Additionally, to simplify the description and discussion, and to avoid obscuring the embodiments of this disclosure, the provided drawings may or may not show well-known power / ground connections to integrated circuit (IC) chips and other components. Furthermore, the apparatus may be shown in block diagram form to avoid obscuring the embodiments of this disclosure, and this also takes into account the fact that the details of implementation of these block diagram apparatuses are highly dependent on the platform on which the embodiments of this disclosure will be implemented (i.e., these details should be fully understood by those skilled in the art). While specific details (e.g., circuits) have been set forth to describe exemplary embodiments of this disclosure, it will be apparent to those skilled in the art that the embodiments of this disclosure can be implemented without these specific details or with variations thereof. Therefore, these descriptions should be considered illustrative rather than restrictive.

[0149] Although this disclosure has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed.

[0150] This disclosure is intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A precoding method based on statistical channel information, characterized in that, The method is applied to multiple satellites, which communicate with B users; the method includes: Initialize the precoding matrix for each satellite in the time-delay Doppler domain for each user; wherein the precoding matrix is ​​constructed based on the equivalent time-delay Doppler domain channel after pre-compensating the deterministic propagation delay; the deterministic propagation delay is determined based on the geometric distance between the satellite and the user; Each precoding matrix for each user is stacked vertically to obtain the joint precoding matrix for each user; The traversal rate for each user is obtained based on the joint precoding matrix and statistical channel state information corresponding to each user. The initial optimization objective is to maximize the weighted sum of the traversal rates of B users. Based on the joint precoding matrix and statistical channel state information corresponding to each user, the initial optimization objective is transformed into minimizing the equivalent weighted minimum mean square error objective function; The objective function is to minimize the equivalent weighted minimum mean square error to obtain the target precoding matrix for each satellite for each user.

2. The precoding method based on statistical channel information according to claim 1, characterized in that, The step of obtaining the traversal rate for each user based on the joint precoding matrix and statistical channel state information corresponding to each user includes: Based on the statistical channel state information, the joint channel statistical covariance matrix and block diagonal channel covariance matrix of each user in the time delay Doppler domain are obtained; For each user, the expected signal statistical covariance matrix is ​​obtained based on the user's joint precoding matrix and joint channel statistical covariance matrix; where the expected signal statistical covariance matrix characterizes the strength of the expected signal received by the corresponding user. For each user, the interference statistical covariance matrix is ​​obtained based on the joint precoding matrix of other users besides the user itself and the user's block diagonal channel covariance matrix; where the interference statistical covariance matrix represents the average intensity of the interference signals received by the corresponding user from other users; The traversal rate for each user is obtained by statistically analyzing the expected signal covariance matrix, interference covariance matrix, and noise covariance matrix for each user; where the noise covariance matrix represents the intensity of the additive white Gaussian noise received by the corresponding user.

3. The precoding method based on statistical channel information according to claim 2, characterized in that, The step of obtaining the traversal rate for each user based on the expected signal statistical covariance matrix, interference statistical covariance matrix, and noise covariance matrix includes: Obtain the relationship between the transmitted and received signals of each user in the time-delay Doppler domain; Based on the relationship between the expected signal statistical covariance matrix, interference statistical covariance matrix, noise covariance matrix, and the transmitted and received signals in the time-delay Doppler domain for each user, the mutual information of each user is obtained. The mutual information is corrected and normalized to obtain the traversal rate for each user.

4. The precoding method based on statistical channel information according to claim 3, characterized in that, The traversal rate is positively correlated with the statistical covariance matrix of the desired signal; the traversal rate is negatively correlated with the statistical covariance matrix of the interference; and the traversal rate is negatively correlated with the noise covariance matrix.

5. The precoding method based on statistical channel information according to claim 2, characterized in that, The step of transforming the initial optimization objective into minimizing the equivalent weighted minimum mean square error objective function based on the joint precoding matrix and statistical channel state information corresponding to each user includes: Based on the joint precoding matrix, joint channel statistical covariance matrix and block diagonal channel covariance matrix corresponding to each user, the equivalent mean square error matrix of each user is obtained. Obtain the preset weights for each user, and initialize the linear receiving filter matrix and the weighted minimum mean square error weight matrix for each user; Based on the equivalent mean square error matrix, preset weights, linear receiving filter matrix, and weighted minimum mean square error weight matrix for each user, the equivalent weighted minimum mean square error objective function is obtained; where the equivalent mean square error matrix is ​​positively correlated with the equivalent weighted minimum mean square error objective function.

6. The precoding method based on statistical channel information according to claim 5, characterized in that, The equivalent mean square error matrix for each user is obtained based on the joint precoding matrix, joint channel statistical covariance matrix, and block diagonal channel covariance matrix corresponding to each user, including: The joint channel statistics covariance matrix of each user is decomposed by the square root of the matrix to obtain the auxiliary matrix; The block diagonal channel covariance matrix of each user is decomposed into a square root matrix to obtain the interference auxiliary matrix; The equivalent mean square error matrix for each user is obtained based on the joint precoding matrix, auxiliary matrix, and interference auxiliary matrix for each user.

7. The precoding method based on statistical channel information according to claim 5, characterized in that, The objective function, which minimizes the equivalent weighted minimum mean square error, is solved to obtain the target precoding matrix for each satellite and each user. This includes: Under the condition that the joint precoding matrix and the weighted minimum mean square error weight matrix remain unchanged for each user, the linear receiver filter matrix of each user is updated with the objective of minimizing the equivalent weighted minimum mean square error objective function. Under the condition that the joint precoding matrix and the linear receiver filtering matrix of each user remain unchanged, the weighted minimum mean square error weight matrix of each user is updated with the objective of minimizing the equivalent weighted minimum mean square error objective function. Under the condition that the weighted minimum mean square error weight matrix remains unchanged for each user, the joint precoding matrix of each user is updated according to the Lagrangian function and the preset transmit power constraint, with the objective of minimizing the equivalent weighted minimum mean square error objective function. Based on the updated linear receiver filter matrix, the weighted minimum mean square error weight matrix, and the joint precoding matrix, the change value of the equivalent weighted minimum mean square error objective function is obtained; If the change value of the equivalent weighted minimum mean square error objective function is greater than the preset convergence threshold, then repeat the steps "update the linear receiver filter matrix of each user while keeping the joint precoding matrix and the weighted minimum mean square error weight matrix unchanged" to "obtain the change value of the equivalent weighted minimum mean square error objective function based on the updated linear receiver filter matrix, the weighted minimum mean square error weight matrix and the joint precoding matrix", until the change value of the equivalent weighted minimum mean square error objective function is equal to or less than the preset convergence threshold or reaches the preset number of iterations, then end, to obtain the target joint precoding matrix; The target joint precoding matrix is ​​split to obtain the target precoding matrix for each satellite and each user.

8. A precoding apparatus based on statistical channel information, characterized in that, The device is applied to multiple satellites, and the multiple satellites communicate with B users; the device includes: An initialization unit is used to initialize the precoding matrix of each satellite for each user in the time-delay Doppler domain; wherein the precoding matrix is ​​constructed based on the equivalent time-delay Doppler domain channel after pre-compensation of the deterministic propagation delay; the deterministic propagation delay is determined based on the geometric distance between the satellite and the user; Stacking units are used to vertically stack each precoding matrix of each user to obtain the joint precoding matrix corresponding to each user. The rate determination unit is used to obtain the traversal rate of each user based on the joint precoding matrix and statistical channel state information corresponding to each user. The initial target determination unit is used to determine the weighted sum of maximizing the traversal rate of B users as the initial optimization target; The transformation unit is used to transform the initial optimization objective into a function that minimizes the equivalent weighted minimum mean square error, based on the joint precoding matrix and statistical channel state information corresponding to each user. The solver unit is used to solve for the objective function of minimizing the equivalent weighted minimum mean square error to obtain the target precoding matrix for each satellite for each user.

9. A computer device comprising one or more processors, a memory; and one or more programs, wherein the one or more programs are stored in the memory and executed by the one or more processors, the one or more programs comprising instructions for performing the method of any one of claims 1 to 7.

10. A non-volatile computer-readable storage medium comprising a computer program, which, when executed by one or more processors, causes the one or more processors to perform the method of any one of claims 1 to 7.

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