Sky-wave massive MIMO multi-stream robust precoding method and system

Abstract

The application discloses a sky-wave massive MIMO multi-flow robust precoding method and system. Firstly, space-time encoding is implemented on signals sent to each user at a base station side. A multi-flow robust precoder designed by using a beam base posterior channel model and a maximum average signal leakage noise ratio criterion is used to implement precoding on the space-time encoded signals to obtain base station sending signals. In order to reduce the calculation complexity, the multi-flow robust precoder is further limited to a beam structure. The corresponding beam structure multi-flow robust precoding process is to use the beam base posterior channel model and the maximum average signal leakage noise ratio criterion to design a beam domain multi-flow robust precoder. The beam domain multi-flow robust precoder is used to implement beam domain precoding, beam mapping, multi-user signal summation and beam transformation on the space-time encoded signals to obtain the base station sending signals. The application can effectively obtain the diversity gain of sky-wave massive MIMO downlink transmission through space-time encoding and reduce the calculation complexity through beam structure design.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and in particular relates to a skywave massive MIMO multi-stream robust precoding method and system. Background Technology

[0002] Skywave communication utilizes ionospheric reflection to support long-distance wireless transmission and is an important technology for achieving wide-area coverage. However, traditional point-to-point skywave systems typically face limited data rates and low link reliability. Massive MIMO, by introducing greater spatial freedom at the base station, can serve as a reliable technology to improve the performance of skywave communication. Massive MIMO can serve a large number of users with the same time-frequency resources and can achieve signal enhancement and interference suppression through spatial signal processing. Therefore, introducing massive MIMO into skywave communication systems is of great significance for improving the spectral efficiency, transmission reliability, and coverage of long-distance wireless communication.

[0003] For skywave massive MIMO systems, precoding plays a crucial role in improving downlink transmission quality. When the base station transmitter knows the instantaneous channel state information, precoders such as Maximum Ratio Transmission (MRT), Regularized Zero-Forcing (RZF), and Weighted Minimum Mean-Squared Error (WMMSE) can achieve good performance. However, when the signal reaches the user side after long-distance transmission, the instantaneous channel state information obtained by the skywave massive MIMO base station is usually outdated. In this case, robust precoding methods that can overcome the channel aging effect to some extent can be used.

[0004] For single-antenna user scenarios, existing robust precoding methods are all single-stream precoding, which cannot fully capture multipath diversity gain under inaccurate channel conditions. To overcome this problem, combining space-time coding and precoding is an effective means to achieve multi-stream precoding and obtain diversity gain. Most work combining space-time coding and precoding is geared towards point-to-point MIMO systems; therefore, introducing space-time coding into multi-user massive MIMO precoding is of great significance. Furthermore, to address the issue of excessively high dimensionality in massive MIMO precoders, exploring low-complexity multi-stream robust precoding methods by further considering the channel characteristics of skywave massive MIMO is also of significant value. Summary of the Invention

[0005] Purpose of the invention: To address the shortcomings of existing technologies, this invention proposes a robust precoding method and system for skywave massive MIMO multi-stream, which utilizes the sparsity of beam domain channels and combines space-time coding to effectively obtain diversity gain while ensuring low computational complexity.

[0006] Technical Solution: To solve the above-mentioned technical problems, in a first aspect, the present invention provides a multi-stream robust precoding method for skywave massive MIMO, which combines space-time coding with robust precoding to achieve multi-stream robust precoding; the space-time coding encodes the signals of each user on multiple consecutive time symbols into space-time codes; the multi-stream robust precoding is achieved by precoding the space-time coded signals using a robust precoder to generate base station transmission signals; the multi-stream robust precoder utilizes a beam-based posterior channel model and is designed to maximize the average signal-to-noise ratio. Specifically, it obtains the multi-stream robust precoder by performing generalized eigenvalue decomposition on the spatial domain posterior channel correlation matrix and the matrix pair formed by the sum of the spatial domain posterior channel correlation matrices and noise covariance matrices of all users, and selecting the generalized eigenvector corresponding to the generalized eigenvalue with the largest preset number of streams. In the generalized eigenvalue decomposition, the sparsity of the skywave massive MIMO beam domain channel is utilized, and the generalized eigenvector of the original matrix pair is obtained by solving for the eigenvector corresponding to the largest eigenvalue of a low-dimensional auxiliary matrix and performing a linear transformation on the eigenvector.

[0007] Secondly, this invention provides a skywave massive MIMO multi-stream robust precoding method that combines space-time coding with robust precoding to achieve multi-stream robust precoding. The space-time coding encodes the signals of each user across multiple consecutive time symbols into space-time codes. The multi-stream robust precoding is achieved by precoding the space-time coded signals using a robust precoder to generate the base station's transmitted signals. The multi-stream robust precoder utilizes a beam-based posterior channel model to constrain the multi-stream robust precoder to a beam structure, and designs a beam-domain multi-stream robust precoder by maximizing the average signal-to-leakage-to-noise ratio. The multi-stream robust precoder is constrained to a beam structure. The window function is multiplied by the extracted beam matrix and then by the structure of the beam-domain multi-stream robust pre-encoder. The window function is a real diagonal matrix, the extracted beam matrix is ​​composed of the columns containing the non-zero beams of the corresponding user extracted from the beam matrix, and the beam-domain multi-stream robust pre-encoder is a low-dimensional complex matrix multiplied by the number of non-zero beam points of the corresponding user and the dimension of the number of data streams of that user. The beam-domain multi-stream robust pre-encoder is used for beam-structured multi-stream robust precoding. The beam-structured multi-stream robust precoding generates the base station transmission signal by performing beam-domain multi-stream precoding, beam mapping, multi-user signal summation, and beam transformation on the spatiotemporally encoded transmission signals of each user.

[0008] Furthermore, the multi-stream robust precoder is a complex matrix consisting of the number of base station antennas multiplied by the number of data streams of each user; the process of precoding using the multi-stream robust precoder involves multiplying the precoder of each user with the spatially coded signal of each user and summing the results over all users.

[0009] Furthermore, the beam-based posterior channel model models the channel vector of each user as a product of the beam matrix and the sparse beam domain channel vector, wherein the beam matrix has a phase-shifted discrete Fourier transform matrix structure, and the beam domain channel vector is modeled as a complex Gaussian distribution vector that follows a given mean and variance.

[0010] Furthermore, the average signal-to-noise ratio (SNR) for each user is defined as the ratio of the expected signal energy transmitted to the current user by the base station using the user's precoder to the expected energy of the signal leaking to other users plus the expected noise energy.

[0011] Furthermore, in the skywave massive MIMO multi-stream robust precoding method described in the first aspect, the low-dimensional auxiliary matrix and the linear transformation of the eigenvectors of the low-dimensional auxiliary matrix are calculated by multiplying the matrix composed of the instantaneous channel and statistical channel information in the spatial domain, its conjugate transpose, and the matrix composed of the sum of the spatial domain posterior channel correlation matrix and the noise covariance matrix of all users by inverse multiplication.

[0012] Furthermore, in the second aspect of the skywave massive MIMO multi-stream robust precoding method, the solution steps for the beam-domain multi-stream robust precoder are as follows: after designing and obtaining the window function, firstly, the posterior channel correlation matrix of the spread beam domain for each user is calculated; then, the matrix composed of the sum of the posterior channel correlation matrix of the spread beam domain for all users and the noise covariance matrix is ​​calculated; finally, the low-dimensional matrix composed of the non-zero beam positions of each user is extracted from the matrix calculated in the first two steps, and generalized eigenvalue decomposition is performed on the generalized eigenvector corresponding to the generalized eigenvalue with the largest preset stream number to obtain the beam-domain multi-stream robust precoder.

[0013] Furthermore, the spread beam domain posterior channel correlation matrix is ​​calculated from the beam spread matrix, the beam domain instantaneous channel vector, and the beam domain statistical channel information. This calculation process can be simplified by utilizing the approximate sparsity of the beam spread matrix and the sparsity of the beam domain channel. The beam spread matrix is ​​obtained by multiplying the conjugate transpose of the beam matrix by the window function matrix and then by the beam matrix.

[0014] Furthermore, the beam-domain multi-stream precoding process described in the second aspect involves multiplying the beam-domain multi-stream robust precoder of each user with the spatiotemporally encoded signal of each user. The beam mapping involves mapping the precoded signal of each user onto its respective non-zero beam index. The beam transform is the result of multiplying the window function by the beam matrix and then by the sum of the precoded signals of each user. The beam transform can be effectively implemented using the Fast Fourier Transform.

[0015] Thirdly, the present invention provides a computer system including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is executed by the processor, it implements the steps of the skywave massive MIMO multi-stream robust precoding method described in the first or second aspect.

[0016] Beneficial effects: Compared with the prior art, the present invention utilizes the sparse characteristics of the beam domain channel of skywave massive MIMO and the space-time coding design of a multi-stream robust precoding method. Compared with the single-stream robust precoding method, the multi-stream robust precoder and beam domain multi-stream robust precoder proposed in this scheme have greater diversity gain. Among them, the beam domain multi-stream robust precoder can significantly reduce the design complexity of the precoder and the implementation complexity of the precoding. Attached Figure Description

[0017] Figure 1 This is a block diagram of a multi-stream robust precoding system according to an embodiment of the present invention;

[0018] Figure 2 This is a comparison chart of the bit error rate (BER) performance of multi-stream robust precoding in this embodiment of the invention with other precoding methods. Detailed Implementation

[0019] To better understand the purpose, solution, and effects of this invention, the following detailed description of the skywave large-scale MIMO multi-stream robust precoding method of this invention is provided in conjunction with the accompanying drawings.

[0020] The skywave massive MIMO multi-stream robust precoding method disclosed in this invention embodiment is illustrated in the system block diagram of the multi-stream robust precoding method. Figure 1At the base station, the signals sent to each user are first spatiotemporally coded. A multi-stream robust precoder, designed using a beam-based posterior channel model and the maximum average signal-to-noise ratio (SNR) criterion, is then used to precode the spatiotemporally coded signals to obtain the base station's transmitted signals. To reduce computational complexity, the multi-stream robust precoder can be further restricted to a beam structure. The corresponding beam structure multi-stream robust precoding process involves designing a beam-domain multi-stream robust precoder using a beam-based posterior channel model and the maximum average SNR criterion, and then performing beam-domain precoding, beam mapping, multi-user summation, and beam transform on the spatiotemporally coded signals to obtain the base station's transmitted signals.

[0021] The method of this invention is mainly applicable to skywave massive MIMO systems equipped with large-scale antenna arrays on the base station side to simultaneously serve multiple users.

[0022] In one possible implementation, the skywave massive MIMO multi-stream robust precoding method described in this embodiment combines space-time coding with robust precoding to achieve multi-stream robust precoding. The space-time coding encodes the signals of each user over multiple consecutive time symbols into space-time codes. The multi-stream robust precoding is achieved by precoding the space-time coded signals using a robust precoder to generate base station transmit signals. The multi-stream robust precoder utilizes a beam-based posterior channel model and is designed to maximize the average signal-to-noise ratio. Specifically, it is obtained by decomposing the generalized eigenvalues ​​of the spatial domain posterior channel correlation matrix and the matrix pair consisting of the sum of the spatial domain posterior channel correlation matrices and the noise covariance matrix of all users, and selecting the generalized eigenvector corresponding to the generalized eigenvalue with the largest preset number of streams. In the generalized eigenvalue decomposition, the sparsity of the skywave massive MIMO beam domain channel is utilized to solve for the eigenvector corresponding to the largest eigenvalue of a low-dimensional auxiliary matrix and perform a linear transformation on the eigenvector to obtain the generalized eigenvector of the original matrix pair.

[0023] In one possible implementation, to further reduce computational complexity, the skywave massive MIMO multi-stream robust precoding method described in this embodiment combines space-time coding with robust precoding to achieve multi-stream robust precoding. The space-time coding encodes the signals of each user across multiple consecutive time symbols into space-time codes. The multi-stream robust precoding is achieved by precoding the space-time coded signals using a robust precoder to generate the base station transmission signal. The multi-stream robust precoder utilizes a beam-based posterior channel model to constrain the multi-stream robust precoder to a beam structure, and obtains a beam-domain multi-stream robust precoder by maximizing the average signal-to-leakage-to-noise ratio. The multi-stream robust precoder is constrained to be a structure of a window function multiplied by the extracted beam matrix and then multiplied by a beam-domain multi-stream robust precoder. The window function is a real diagonal matrix, the extracted beam matrix is ​​composed of the columns containing the non-zero beams corresponding to the user extracted from the beam matrix, and the beam-domain multi-stream robust precoder is a low-dimensional complex matrix multiplied by the number of non-zero beam points for the corresponding user and the dimension of the user's data streams. The beam-domain multi-stream robust precoder is used for beam-structured multi-stream robust precoding. The beam-structured multi-stream robust precoding generates the base station transmission signal by performing beam-domain multi-stream precoding, beam mapping, multi-user signal summation, and beam transformation on the spatiotemporally encoded transmission signals of each user.

[0024] The following detailed explanation of the implementation process of the downlink precoding method involved in this invention is based on a specific communication system example. It should be noted that this invention is not only applicable to the specific system model described in this embodiment, but also to other system models with different configurations.

[0025] I. System Model

[0026] Considering a skywave massive MIMO-Orthogonal Frequency Division Multiplexing (OFDM) system, the base station is equipped with A uniform linear array of antennas serves simultaneously A single-antenna user. Assume the channel is... It remains unchanged within a series of consecutive OFDM symbols and we only focus on Downlink transmission on each subcarrier. For continuous The first OFDM symbol Each subcarrier transmits a signal that can be represented as follows: ,in Representing the The first antenna The transmission signal of one OFDM symbol. User After OFDM demodulation, subcarrier upper continuous The received signal on one OFDM symbol can be represented as

[0027] (1)

[0028] in and users respectively The channel frequency response vector and additive white Gaussian noise, Indicates noise power. This represents the Nth-order identity matrix. For skywave massive MIMO systems, the channel vector... Spatial correlation can be expressed as

[0029] (2)

[0030] in For users The diameter number, For subcarrier spacing, , and The first The complex gain, time delay, and direction parameters of the stripe. Furthermore, For pointing The direction vector, its first The elements are

[0031] (3)

[0032] Through the exist Uniform sampling , Channel vector It can be approximated as a beam-based channel model

[0033] (4)

[0034] in The total number of sampled beams, and the refinement factor. Beam matrix and beam domain channel vector Defined respectively

[0035] (5)

[0036] (6)

[0037] in Due to the small-angle spread of the skywave channel, Typically sparse, and their non-zero element index sets constitute non-zero beam sets. ,Right now This property is called beam-domain channel sparsity. Combining (3) and (5), the beam matrix... This can be further expressed as the discrete Fourier transform matrix of the phase-shifting part.

[0038] (7)

[0039] in express 3D discrete Fourier transform matrix, ,and Depend on The first of the first order identity matrix line and front Column composition, express The first dimension of the discrete Fourier transform matrix List.

[0040] Generally speaking, beam domain channel vector The prior follows a complex Gaussian distribution. The beam domain prior channel covariance matrix Let be a real diagonal matrix, where the beam domain channel coupling vector is defined as

[0041] (8)

[0042] Based on the characteristics of skywave massive MIMO channels, the beam domain channel coupling vector exhibits properties such as independence from subcarriers, long-term invariance, and sparsity. Therefore, the beam domain channel coupling vector is typically used as the known beam domain statistical channel state information at the base station. In time-division duplex mode, the instantaneous beam domain channel state information... This can be obtained by performing uplink channel estimation on the training data segment. Considering channel aging, the instantaneous channel state information in the beam domain used for downlink transmission can be modeled as follows:

[0043] (9)

[0044] in It is a time-related factor, and It is a random vector. Therefore Posterior distribution ,in The posterior mean and posterior variance are respectively and The above channel model is called the beam-based posterior channel model, that is: according to the above formulas (4), (7) and (9), the beam-based posterior channel model divides the channel vectors of each user into... Modeled as a beam matrix With sparse beam domain channel vectors The form of multiplication, where the beam matrix It has a phase-shifted discrete Fourier transform matrix structure and a beam domain channel vector. The model is a complex Gaussian distribution vector that follows a given mean and variance. In this embodiment, the beam-based posterior channel model will be subsequently used for downlink precoding design.

[0045] II. Robust Precoding for Space-Time Coding

[0046] Space-time coding is used for downlink multi-stream precoding, encoding the signals of each user across multiple consecutive time symbols into space-time codes. For example, Alamoti codes are used in this embodiment. (User...) In subcarrier The transmit signal on is set to After being encoded by Alamoti, it is obtained

[0047] (10)

[0048] The complex number symbol Selected from the collection of modulated constellations Assume that the transmitted symbols of each user are independent and identically distributed and have unit average power, i.e. ,therefore

[0049] (11)

[0050] Therefore, the base station on the subcarrier The transmitted signal is transmitted through Generate, where For users In subcarrier A multi-stream pre-encoder with a power constraint. Therefore, users In subcarrier The received signal on two consecutive OFDM symbols can be written as

[0051] (12)

[0052] Among them, interference items This is caused by "leakage" of signals that the base station intends to transmit to other users. Typically, downlink precoding aims to improve system performance by reducing the impact of interference and noise. Therefore, multi-stream robust precoders... This can be designed by maximizing the signal-to-leakage-to-noise ratio for each user. It should be noted that this embodiment uses Alamoti code as an example, but the present invention is not limited to this specific space-time block code. More generally, the multi-stream robust precoder is a complex matrix of the number of base station antennas multiplied by the number of data streams for each user; the precoding process using the multi-stream robust precoder involves multiplying the precoder of each user with the space-time encoded signal of each user and summing the results over all users. According to (11) and (12), the user... In subcarrier The signal-to-noise ratio is defined as follows:

[0053] (13)

[0054] However, directly designing a precoder by maximizing the signal-to-leakage-to-noise ratio for each user is not feasible because base stations typically lack accurate instantaneous channel state information, possessing only posterior statistical information of the channel. Therefore, further definitions of users are needed. In subcarrier The average signal-to-noise ratio (SNR) is the ratio of the expected signal energy transmitted to the current user at the base station using the user's precoder to the expected energy plus noise energy of the signal leaking to other users. Specifically, it is expressed as follows:

[0055] (14)

[0056] The posterior channel correlation matrices in the spatial domain and beam domain are defined as follows:

[0057] (15)

[0058] (16)

[0059] The expression for the average signal-to-leakage-to-noise ratio (SNR) utilizes both the posterior mean and variance of the channel, making it possible to solve for the precoder by maximizing the average SNR. Furthermore, space-time coding needs to satisfy the following irrelevant constraints:

[0060] (17)

[0061] Therefore, the multi-stream robust precoder design problem can be expressed as:

[0062] (18)

[0063] After designing and obtaining the multi-stream robust precoder, the downlink transmission process on the base station side includes space-time coding and downlink precoding, and for the ... The process of performing downlink precoding on the space-time coded signal on each subcarrier can be written as follows:

[0064] (19)

[0065] With the increasing number of antennas in skywave massive MIMO base stations, the design complexity and implementation complexity of multi-stream robust precoders become very high. To overcome this problem, the multi-stream robust precoder is further constrained to a beamforming structure.

[0066] (20)

[0067] Where the diagonal matrix A window function to reduce beam spread. Beam selection matrix. The Listed as ,in For users Non-zero beam index set The elements arranged from smallest to largest Each element. For users In subcarrier A beam-domain multi-stream robust pre-encoder. As shown above, the multi-stream robust pre-encoder is limited to... The window function is multiplied by the decimated beam matrix and then multiplied by the beam-domain multi-stream robust precoder. The structure, the extracted beam matrix is ​​composed of the columns containing the corresponding non-zero beams of the extracted user, and the beam domain multi-stream robust pre-encoder. This is a low-dimensional complex matrix representing the number of non-zero beam points corresponding to a user multiplied by the dimension of the user's data stream number. It can be proven that restricting the multi-stream robust precoder to a beam structure does almost no loss in average signal-to-noise ratio performance. At this point, the user... In subcarrier The average signal-to-noise ratio can be rewritten as

[0068] (twenty one)

[0069] The extracted spread beam domain posterior channel correlation matrix posterior channel correlation matrix in the spread beam domain and beam spread matrix Therefore, the design problem of a beam-domain multi-stream robust pre-encoder can be expressed as:

[0070] (twenty two)

[0071] in , Compared to the original optimization problem (18), the number of variables to be optimized in optimization problem (22) is reduced from [previous number]. It dropped to This is expected to significantly reduce computational complexity.

[0072] The following discussion focuses on how to implement downlink precoding using a beam-domain multi-stream robust precoder. Once the multi-stream robust precoder is designed... After that, subcarrier The downlink precoding at this point can be represented as

[0073] (twenty three)

[0074] Specifically, beam domain precoding A beam-domain multi-stream robust pre-encoder is implemented on the space-time coded signal, and then a beam selection matrix is ​​used. After beam mapping, the precoded signals from all users are summed. Then, Generated through beamforming, where beamforming involves combining the precoded signals of all users with a diagonal matrix. Multiplication, Fast Fourier Transform, and the use of window functions Adding a window involves three steps.

[0075] III. Robust Pre-encoder Design

[0076] First, the original multi-stream robust pre-encoder design problem (18) is solved. In this embodiment, a beam-domain multi-stream robust pre-encoder is obtained by maximizing the average signal-to-leakage-to-noise ratio. Specifically, power constraints are utilized. The average signal-to-noise ratio (14) can be written in the form of the generalized trace Rayleigh quotient.

[0077] (twenty four)

[0078] However, the matrix in the denominator is user-dependent. To simplify the precoder design, a monotonic transformation is employed. This transformation is in This ensures optimality. Therefore, the transformed objective function can be written as follows:

[0079] (25)

[0080] in It is irrelevant to the user. Therefore, Also a generalized trace Rayleigh quotient, and the optimal solution of (18) can be maximized under constraints. The optimal solution is obtained from matrix pairs. The two largest generalized eigenvalues ​​correspond to the generalized eigenvectors. That is, in this embodiment, the spatial domain posterior channel correlation matrix is ​​used to construct the generalized eigenvectors. and the sum of the posterior channel correlation matrix and the noise covariance matrix of all user space domains. The matrix pairs formed The generalized eigenvalue decomposition is performed, and the generalized eigenvectors corresponding to the two largest generalized eigenvalues ​​are selected to obtain the multi-stream robust pre-encoder.

[0081] However, due to the matrix and The dimensions are very large, making direct generalized eigenvalue decomposition (GEM) highly complex. This embodiment utilizes the sparsity of the beam domain channel in skywave massive MIMO in GEM decomposition. It obtains the generalized eigenvectors of the original matrix pairs by solving for the eigenvector corresponding to the largest eigenvalue of a low-dimensional auxiliary matrix and performing a linear transformation on this eigenvector. The low-dimensional auxiliary matrix and the linear transformation on its eigenvectors are both matrices composed of spatial domain instantaneous channel and statistical channel information, their conjugate transposes, and the inverse of the matrix formed by the sum of the spatial domain posterior channel correlation matrices and noise covariance matrices of all users. The result is obtained through multiplication. Specifically, based on the sparsity of the beam domain channel in skywave massive MIMO, It possesses a low-rank structure, a feature that can be used to reduce the computational complexity of generalized eigenvalue decomposition. Specifically, It can be represented as the product of a matrix consisting of instantaneous channel information and statistical channel information in the spatial domain and its conjugate transpose, i.e. ,in

[0082] (26)

[0083] in To estimate the spatial domain channel vector, the matrix pair is then used. The generalized eigenvectors can be obtained by modifying the low-dimensional auxiliary matrix. This is obtained by eigenvalue decomposition. It can be proven that the matrix pairs... Non-zero generalized eigenvalues ​​and matrices The non-zero eigenvalues ​​are consistent, and Corresponding non-zero generalized eigenvalues The generalized eigenvectors can be constructed as ,in For matrix Corresponding eigenvalues The eigenvectors. Furthermore, Included in The calculation. To calculate efficiently. Rewrite it as The spatial domain prior channel covariance matrix Utilizing the structure of the beam matrix, and They can be written as

[0084] (27)

[0085] (28)

[0086] because It is a diagonal matrix, therefore For one The generated partial cyclic matrix. Therefore, It can be done Point Fast Fourier Transform Calculation.

[0087] Based on the above discussion, the design of a multi-stream robust pre-encoder includes the following steps:

[0088] Step 1: For each user, calculate the spatial domain posterior channel correlation matrix according to (27) and (28). Calculated according to (26) ;

[0089] Step 2: Calculate the sum of the posterior channel correlation matrix and the noise covariance matrix for all user space domains. ;

[0090] Step 3: Calculate the low-dimensional auxiliary matrix for each user. For low-dimensional auxiliary matrices Perform eigenvalue decomposition and select the eigenvectors corresponding to the two largest eigenvalues. and ,set up , Multi-stream robust pre-encoder Scaling to meet power constraints.

[0091] Next, the design problem of a beam-domain multi-stream robust pre-encoder is solved (22). In this embodiment, the window function is first processed. The design issue. The purpose of adding windows is to enhance... The energy concentration, its energy diffusion is determined by the beam spread matrix. This results in... Therefore, the objective is transformed into design that makes the matrix... The window function with the highest energy concentration in the diagonal band. Using the structure of the beam matrix, we have...

[0092] (29)

[0093] in Therefore, the matrix For completely composed of sequences Given a definite Topulitz matrix, therefore, maximizing the matrix... The problem of energy concentration within the diagonal band can be formulated as maximizing the sequence. In the index The problem of nearby energy, among which Energy is defined as

[0094] (30)

[0095] because , Therefore, the sequence The period is The periodic sequence, i.e. , Considering The periodicity, defined The set of nearby energy concentration indices is ,in Let be the unilateral diffusion length. Therefore, the window function can be designed to maximize... In the index set The energy ratio within the body can be expressed as follows:

[0096] (31)

[0097] It can be proven that maximizing The optimal window function can be chosen as a real-valued, centrally symmetric vector. Specifically, this optimal window function is a matrix. The eigenvector corresponding to the largest eigenvalue, where To ensure the matrix The diagonal element has unit energy, and scaling the window function makes... Furthermore, the real-valued centrally symmetric structure of the window function makes... , Therefore, the matrix It can be rewritten as an approximately sparse real-valued symmetric Topletz matrix.

[0098] (32)

[0099] This structure indicates that the matrix Only a small number of real-valued parameters are required for characterization, which helps reduce the design complexity of beam-domain multi-stream robust pre-encoders.

[0100] After determining the window function, the design of a beam-domain multi-stream robust pre-encoder is discussed next. The average signal-to-noise ratio in optimization problem (22) can be equivalently replaced by the following optimization objective:

[0101] (33)

[0102] in Therefore, the optimal solution to problem (22) can be obtained by finding the matrix pairs. The generalized eigenvectors corresponding to the two largest generalized eigenvalues ​​are obtained. That is, the solution steps for the beam-domain multi-stream robust precoder in this embodiment are: after designing and obtaining the window function, first calculate the spread beam-domain posterior channel correlation matrix for each user. Next, the matrix consisting of the sum of the posterior channel correlation matrix and the noise covariance matrix of all users in the beam domain is calculated. Finally, a low-dimensional matrix consisting of the non-zero beam positions of each user is extracted from the matrix calculated in the first two steps. Generalized eigenvalue decomposition is performed, and the generalized eigenvectors corresponding to the two largest generalized eigenvalues ​​are selected to obtain the beam-domain multi-stream robust pre-encoder. Since the dimensionality of the beam-domain multi-stream robust pre-encoder has been reduced to [missing information], [the following is a continuation of the previous sentence]. Matrix pairs The generalized eigenvalue decomposition has low complexity. Therefore, the design complexity of the beam-domain multi-stream robust precoder mainly comes from the calculation of the following matrices.

[0103] (34)

[0104] The main aspects involved and The calculation. Specifically, using the matrix shown in (32). Structure, sequence Most terms have minimal energy that can be approximated as zero; therefore, a selection set is defined.

[0105] (35)

[0106] in ,and This is a preset threshold. Therefore... It can be approximated as .therefore, It can be approximated as

[0107] (36)

[0108] Formula (36) shows It can be retained The main loop diagonal elements are approximated. Therefore, dense matrix-vector multiplication can be performed using a small number of operations. The shifting and scaling operations are replaced. On the other hand, The following formula can be used to approximate the calculation.

[0109] (37)

[0110] in , ,and

[0111] (38)

[0112] (39)

[0113] It is evident that formula (37) can avoid and The complete multiplication calculation. Therefore, Beam spread matrix can be used The approximate sparsity of the beam domain channel and the approximate simplified calculation of the sparsity are given by formulas (36) and (37).

[0114] Based on the above discussion, the design of a beam-domain multi-stream robust pre-encoder includes the following steps:

[0115] Step 1: For each user, calculate the posterior channel correlation matrix in the spread beam domain according to (36) and (37). ;

[0116] Step 2: Calculate the matrix formed by the sum of the posterior channel correlation matrix and the noise covariance matrix in the spread beam domain for all users. ;

[0117] Step 3: Calculate the non-zero beam position for each user. Next, calculate the matrix pairs. The generalized eigenvectors corresponding to the two largest generalized eigenvalues and Multi-stream robust pre-encoder Scaling to meet power constraints.

[0118] VI. Implementation Results

[0119] To enable those skilled in the art to better understand the present invention, the performance results of the downlink precoding method in this embodiment under a specific configuration are given below.

[0120] Considering a skywave massive MIMO-OFDM communication system, the system parameters are configured as follows: carrier frequency , the number of subcarriers Number of base station antennas Base station antenna spacing The refinement factor and the one-sided diffusion length are respectively set as and The base station is The service is provided to one user, with a time correlation factor of 0.6 and a modulation method of quadrature phase shift keying.

[0121] To measure downlink precoding performance Figure 2The BER performance of Regularized Zero-Forcing (RZF) precoders, Single-Stream Robust Precoders (SSRP), Multi-Stream Robust Precoders (MSRP), and Beam-Domain Multi-Stream Robust Precoders (BMSRP) were compared under different transmit powers. RZF is designed based on outdated instantaneous channel state information. Single-stream or multi-stream robust precoders utilize the posterior mean and covariance of the channel to maximize the average signal-to-noise ratio (SNR) for each user. Each user receiver employs space-time decoding and maximum likelihood decoding to recover the transmitted signal. Because the outdated instantaneous channel state information has weak correlation with the actual data segment channel, traditional RZF suffers from severe performance loss and exhibits a significant error plateau in the high-power region. In contrast, SSRP, MSRP, and BMSRP utilize both the posterior mean and covariance of the channel, demonstrating stronger robustness to channel aging. Furthermore, MSRP achieves a significant gain compared to SSRP, especially in the medium-to-high power region, confirming the effectiveness of multi-stream precoding using space-time coding when instantaneous channel state information is imperfect. The proposed BMSRP achieves BER performance close to that of MSRP with a much lower required precoder design dimensionality. For BMSRP, the threshold... Control Matrix The sparse approximation of . When When the value is small, the BMSRP curve is almost the same as... When they coincide, they can be discarded. Most of the cyclic diagonal elements are negligible. With Increase More components are truncated, which may result in a slight decrease in BER, especially in the high-power region.

[0122] This invention also provides a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it implements the steps of the skywave massive MIMO multi-stream robust precoding method described in any of the foregoing embodiments.

[0123] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A robust precoding method for multi-stream large-scale MIMO using the skywave method, characterized in that, Multi-stream robust precoding is achieved by combining space-time coding with robust precoding. The space-time coding encodes the signals of each user across multiple consecutive time symbols into space-time codes. The multi-stream robust precoding is implemented by precoding the space-time coded signals using a robust precoder to generate the base station transmission signal. The multi-stream robust precoder utilizes a beam-based posterior channel model and is designed to maximize the average signal-to-noise ratio. Specifically, it is obtained by decomposing the generalized eigenvalues ​​of the spatial domain posterior channel correlation matrix and the matrix pair consisting of the sum of the spatial domain posterior channel correlation matrices and the noise covariance matrix of all users, and selecting the generalized eigenvector corresponding to the generalized eigenvalue with the largest preset number of streams. In the generalized eigenvalue decomposition, the sparsity of the beam domain channel of skywave massive MIMO is utilized. The generalized eigenvector of the original matrix pair is obtained by solving for the eigenvector corresponding to the largest eigenvalue of a low-dimensional auxiliary matrix and performing a linear transformation on the eigenvector.

2. A robust precoding method for multi-stream large-scale MIMO using the skywave method, characterized in that: Multi-stream robust precoding is achieved by combining space-time coding with robust precoding. The space-time coding encodes the signals of each user across multiple consecutive time symbols into space-time codes. Multi-stream robust precoding is implemented by precoding the space-time coded signals using a robust precoder to generate the base station's transmitted signals. The multi-stream robust precoder utilizes a beam-based posterior channel model to constrain the multi-stream robust precoder to a beam structure. A beam-domain multi-stream robust precoder is designed by maximizing the average signal-to-leakage-to-noise ratio (SNR), where the multi-stream robust precoder is constrained by multiplying a window function by the decimated beam matrix and then by... The structure of the beam-domain multi-stream robust precoder includes a window function that is a real diagonal matrix. The extracted beam matrix is ​​formed by extracting the columns containing the non-zero beams of the corresponding user from the beam matrix. The beam-domain multi-stream robust precoder is a low-dimensional complex matrix consisting of the number of non-zero beam points of the corresponding user multiplied by the dimension of the number of data streams of that user. The beam-domain multi-stream robust precoder is used for beam-structured multi-stream robust precoding. The beam-structured multi-stream robust precoding generates the base station transmission signal by performing beam-domain multi-stream precoding, beam mapping, multi-user signal summation, and beam transformation on the spatiotemporally encoded transmission signals of each user.

3. The skywave massive MIMO multi-stream robust precoding method according to claim 1 or 2, characterized in that, The multi-stream robust precoder is a complex matrix consisting of the number of base station antennas multiplied by the number of data streams of each user; the process of precoding using the multi-stream robust precoder is to multiply the precoder of each user with the spatially coded signal of each user and sum over all users.

4. The skywave massive MIMO multi-stream robust precoding method according to claim 1 or 2, characterized in that, The beam-based posterior channel model models the channel vector of each user as a product of the beam matrix and the sparse beam domain channel vector, wherein the beam matrix has a phase-shifted discrete Fourier transform matrix structure, and the beam domain channel vector is modeled as a complex Gaussian distribution vector that follows a given mean and variance.

5. The skywave massive MIMO multi-stream robust precoding method according to claim 1 or 2, characterized in that, The average signal-to-noise ratio (SNR) for each user is defined as the ratio of the expected signal energy transmitted to the current user at the base station using the user's precoder to the expected energy of the signal leaking to other users plus the expected noise energy.

6. The skywave massive MIMO multi-stream robust precoding method according to claim 1, characterized in that, The low-dimensional auxiliary matrix and the linear transformation of the eigenvectors of the low-dimensional auxiliary matrix are both calculated by multiplying the matrix composed of the instantaneous channel and statistical channel information in the spatial domain, its conjugate transpose, and the matrix composed of the sum of the spatial domain posterior channel correlation matrix and the noise covariance matrix of all users by inverse multiplication.

7. The skywave massive MIMO multi-stream robust precoding method according to claim 2, characterized in that, The solution steps for the beam-domain multi-stream robust precoder are as follows: After designing and obtaining the window function, firstly, calculate the posterior channel correlation matrix of the spread beam domain for each user. Then, calculate the matrix composed of the sum of the posterior channel correlation matrix of the spread beam domain for all users and the noise covariance matrix. Finally, extract the low-dimensional matrix composed of the non-zero beam positions of each user from the matrix calculated in the first two steps and perform generalized eigenvalue decomposition. Select the generalized eigenvector corresponding to the generalized eigenvalue with the largest preset stream number to obtain the beam-domain multi-stream robust precoder.

8. The skywave massive MIMO multi-stream robust precoding method according to claim 7, characterized in that, The spread beam domain posterior channel correlation matrix is ​​calculated from the beam spread matrix, the beam domain instantaneous channel vector, and the beam domain statistical channel information. This calculation process can be simplified by utilizing the approximate sparsity of the beam spread matrix and the sparsity of the beam domain channel. The beam spread matrix is ​​obtained by multiplying the conjugate transpose of the beam matrix by the window function matrix and then by the beam matrix.

9. The skywave massive MIMO multi-stream robust precoding method according to claim 2, characterized in that, The beam-domain multistream precoding process involves multiplying the beam-domain multistream robust precoder of each user with the spatiotemporally encoded signal of each user. The beam mapping process involves mapping the precoded signal of each user onto its respective non-zero beam index. The beam transform process involves multiplying the window function by the beam matrix and then by the sum of the precoded signals of each user. The beam transform can be effectively implemented using the Fast Fourier Transform.

10. A computer system 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 executed by the processor, it implements the steps of the skywave massive MIMO multi-stream robust precoding method according to any one of claims 1-9.

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