Pre-coding method for multi-user MIMO-OTFS system

Abstract

The invention belongs to the field of wireless communication, and discloses a pre-coding method for a multi-user MIMO-OTFS system. The method comprises the following steps: establishing an optimization problem according to a pre-coding matrix, a complete channel matrix, a system noise variance, a user weight and a total transmitting power constraint in a multi-user MIMO-OTFS communication model; a complete channel matrix in the optimization problem is approximated to be an LoS path approximation channel matrix, a matrix SVD is obtained, precoding matrix design is carried out based on a right singular matrix in an SVD decomposition result, and a directional component and a power component are included; substituting the designed precoding matrix into an optimization problem, constructing a sub-optimization problem about the power component and the complex gain of each sub-channel, optimizing the transmitting power of each sub-channel, and outputting the optimal power component; and constructing a final precoding matrix according to the direction component and the optimal power component. According to the method, efficient utilization of system resources can be realized, and the calculation complexity can be greatly reduced while the WSR performance is ensured.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication, and specifically relates to a precoding method for weighted sum rate maximization in multi-user MIMO-OTFS systems. Background Technology

[0002] With the rapid development of 5G and future 6G technologies, many scenarios requiring high mobility and high reliability communication have emerged, such as high-speed rail communication, vehicle communication, and drone communication. Traditional OFDM modulation experiences a sharp performance degradation in these scenarios. This is because high mobility causes the channel to change over time, resulting in dispersion in both time and frequency dimensions, which disrupts the orthogonality between OFDM subcarriers and causes severe inter-carrier interference.

[0003] Orthogonal Time Frequency Space (OTFS) modulation is a novel modulation technique for achieving reliable transmission in highly mobile scenarios. Based on the concept of time-frequency lattice and symbol mapping, this technique modulates data jointly in the time and frequency domains, enabling the signal to maintain high robustness even under conditions of high Doppler frequency offset and frequency-selective fading. Unlike traditional modulation methods that are susceptible to interference and experience significant performance degradation in complex channels, OTFS can balance channel influences in both the time and frequency domains, thereby improving transmission stability and reliability.

[0004] Combining OTFS modulation technology and MIMO systems leverages the advantages of both, achieving faster data transmission rates and higher spectral efficiency. Current research primarily focuses on channel estimation, signal detection, and beamforming. For example, Chinese patent application CN202411466856.8 proposes a fractional delay and Doppler estimation method suitable for massive MIMO-OTFS communication systems. This method utilizes the beamforming gain and asymptotic orthogonality of massive MIMO channels to distinguish different target echo signals; after angle estimation, a two-stage estimation strategy is employed to significantly improve the accuracy of fractional delay and Doppler estimation. Chinese patent application CN202510284569.3 proposes a single-user MIMO-OTFS system and its capacity method. This method designs corresponding transmit and receive beam matrices for different levels of channel state information to optimize channel capacity under various CSI conditions. Notably, this method achieves communication performance close to channel capacity while relying on only a small amount of channel information and with low signal processing complexity. Chinese patent application CN202410334355.8 proposes a digital precoding method suitable for broadband massive MIMO-OTFS systems. This method first establishes an input-output relationship model for broadband MIMO-OTFS and designs a digital precoding scheme accordingly. The data stream to be transmitted is precoded and then transmitted to the user. This scheme enables data transmission without inter-symbol interference while maintaining low-complexity data detection performance.

[0005] In multi-user scenarios, precoding design aimed at maximizing the weighted sum rate is a fundamental and critical problem, but it still lacks in-depth research in multi-user MIMO-OTFS systems. Since the size of the channel matrix depends on the product of the OTFS grid size and the number of transmit and receive antennas, traditional coding designs face extremely high computational complexity due to the channel matrix, while complex coupling relationships exist between users in the delay-Doppler domain. Summary of the Invention

[0006] The purpose of this invention is to provide a precoding method for multi-user MIMO-OTFS systems. This method aims to improve communication performance by comprehensively optimizing interference and power allocation among multiple users, as well as precoding design, thereby achieving efficient utilization of system resources and significantly reducing computational complexity while ensuring WSR performance.

[0007] To achieve the above-mentioned objectives, the present invention provides the following technical solution: A precoding method for a multi-user MIMO-OTFS system, the method comprising: (1) Based on the precoding matrix in the multi-user MIMO-OTFS communication model Complete channel matrix System noise variance User weight and total transmit power constraints Construct an optimization problem; (2) Utilizing the characteristics of the MIMO-OTFS channel, the complete channel matrix in the optimization problem is obtained. Approximate channel matrix of the Loss path And using an approximate channel matrix The structural properties directly yield the SVD matrix, and then the right singular matrix in the SVD decomposition result is used as the basis. Perform precoding matrix Design, the precoding matrix obtained from the design Including directional components and power components ; (3) The precoding matrix designed in step (2) Substituting into the optimization problem constructed in step (1), construct the power component... This problem involves a sub-optimization problem of the complex gain of each sub-channel, optimizing the transmit power of each sub-channel, and outputting the optimal power component. ; (4) Based on the direction components in step (2) and the optimal power component in step (3) Construct the final precoding matrix .

[0008] The precoding method provided by this invention is an innovative low-complexity singular value decomposition (SVD) precoding method. While ensuring the performance of user weighted total rate (WSR), it effectively suppresses inter-user interference and significantly reduces computational complexity, making it highly feasible for practical deployment in next-generation high-mobility wireless communication systems.

[0009] Step 1 describes the multi-user MIMO-OTFS system and establishes a multi-user MIMO-OTFS communication model, including: A description of a multi-user MIMO-OTFS system: The base station side and the user side, wherein the base station side is a single base station (BS) configuration. One transmitting antenna supports DDS domain signal processing; on the user side there is One user, configuration for each user The root receiving antenna supports DDS domain signal processing, among which In this system, the transmitted signal is an OTFS signal; where the OTFS delay-Doppler grid size is... ,in and These represent the number of grid points for Doppler and time delay, respectively.

[0010] The signal transmitted by the base station contains all The information for a user can be expressed as follows: ; in, Satisfy unity power constraint ,and Indicates the first Signal vectors of each user Represents the conjugate transpose of a matrix or vector. Represents the conjugate transpose of a signal vector; It is a dimension of The identity matrix. The transmitted signal will pass through the precoding matrix. Multiplexing in the time-delay-Doppler-spatial domain, the precoded signal can be represented as: ; in, Indicates the first DD domain signal frames transmitted on the root transmitting antenna. Each All of them must undergo the inverse symplectic finite Fourier transform (ISFFT) to convert the information from the time-delay-Doppler domain to the time-frequency domain. Its mathematical form is: ; in, The normalized Discrete Fourier Transform (DFT) matrix satisfies .all A parallel ISFFT operation can be represented as and Multiplication, thereby achieving signal conversion The signal is converted to the time domain for wireless transmission. The base station's transmit power can be expressed as: ; in, Representing the expectation, therefore, the precoding matrix Maximum power constraint must be met , It is the F-norm. This indicates the system's maximum power constraint.

[0011] Next, the transmission channel is modeled: this channel is a DDS domain channel composed of the Kronecker product of the time-frequency (TF) domain channel and the spatial domain channel. Therefore, the user... Equivalent DDS domain channel matrix : ; in For users The number of paths, For users The Path channel sub-gain Let be the spatial response matrix along the path, where , , , The imaginary unit, Indicates the spacing between adjacent antennas. Indicates the wavelength of the signal. and These are the angle of arrival and the angle of departure, respectively. Represents the conjugate transpose of a matrix; For users The delay-Doppler (DD) domain channel matrix, It is a dimension of M M An identity matrix of dimension 1 The matrix representing the normalized discrete Fourier transform (DFT) is denoted by . , The deferred permutation matrix is ​​defined by the following structure: , It is the Doppler phase rotation matrix, which is defined as follows: , Represents integer delay points, and These correspond to integer and fractional Doppler shifts, respectively.

[0012] Establishing a multi-user MIMO-OTFS communication model includes: The user The received signal after processing by the MIMO-OTFS system is: , in For users The first term of the received signal vector in the DDS domain For users The target signal, For users The received symbol vector in the DDS domain, For other users to users Multi-user interference items, The receiver's white Gaussian noise follows a set pattern. .

[0013] In step (1), the precoding matrix in the multi-user MIMO-OTFS communication model is used. Complete channel matrix System noise variance User weight and total transmit power constraints The optimization problem is: Taking into account both communication and interference effects, the optimization problem is formulated as a weighted sum rate (WSR) maximization problem, which can be expressed as: ; constraint: ; in, and These represent the number of grid points for Doppler and time delay, respectively. () represents the determinant of a matrix. For user weight, For dimension The identity matrix, Represents the conjugate transpose of a matrix or vector. For the precoding matrix Conjugate transpose matrix, Channel matrix The conjugate transpose of the matrix. For the first One user, To exclude the first Users other than the specified user This represents the system noise variance. It is the F-norm.

[0014] Step (2) includes the following sub-steps: (2-1) The complete channel matrix An approximation of the channel matrix that retains only the Loss of Sorrow (LoS) path. ; (2-2) Approximate channel matrix Perform SVD decomposition to obtain the SVD decomposition results; (2-3) Construct a composite multi-user received signal model based on SVD The composite right singular splicing matrix is ​​obtained. ; (2-4) Based on the composite right singular splicing matrix after splicing by all users Perform precoding design to obtain the precoding matrix. ,in Represented as a composite right singular splicing matrix The false rebellion.

[0015] In step (2-1), the complete channel matrix is... An approximation of the channel matrix that retains only the Loss of Sorrow (LoS) path. : (2-1-1) The complete channel matrix An approximation of the channel matrix that retains only the Loss of Sorrow (LoS) path. : ; in For users The path complex gain corresponding to the Loss path, For users The spatial response matrix corresponding to the Loss path. Represents the Krone integrability operation. For users The channel matrix in the delay-Doppler (DD) domain corresponding to the LosS path; (2-1-2) This leads to the approximate channel matrix. Complete structural expression: ; in, Represented as The steering vector of the root antenna, , , The imaginary unit, This indicates the spacing between adjacent antennas, typically... Indicates the wavelength of the signal. and users respectively The arrival angle and departure angle of the Loss path; It is a dimension of M M An identity matrix of dimension 1 It is a dimension of The normalized discrete Fourier transform (DFT) matrix, where , The deferred permutation matrix is ​​defined by the following structure: , It is the Doppler phase rotation matrix, which is defined as follows: , Represents integer delay points, and These correspond to integer and fractional Doppler shifts, respectively.

[0016] In step (2-2), the approximate channel matrix is... Perform SVD decomposition: For approximate channel matrix Perform SVD decomposition: ; in and They are users The left singular value matrix (LSM) and the right singular value matrix (RSM), It is based on the approximate channel matrix The singular values ​​are the diagonal singular matrix with diagonal elements; based on the approximate channel matrix. Structural properties can be directly obtained through SVD decomposition: Left Singular Matrix (LSM) It can be expressed as: ; Diagonal Singular Matrix SM It can be expressed as: ; Right Singular Matrix RSM It can be expressed as: .

[0017] Furthermore, based on the approximate channel matrix in step 3... Based on the SVD decomposition results, a low-complexity precoding design is developed, including: In step (2-3), a composite multi-user received signal model is constructed: All Received signal vector of each user Vertical concatenation is performed to form a system-level composite receive vector: ; in, This can be represented as the transpose of a matrix or vector. Based on the SVD decomposition results of each user channel, the equivalent input-output relationship of this composite signal vector can be further expressed as: ; The composite matrix in this model is formed by concatenating the channel parameter matrices of each user, and its complete structural expression is as follows: Composite gain matrix , is a block diagonal matrix containing the channel gains of all users: ; Composite Left Singular Matrix and composite singular value matrix These are block diagonal matrices formed by concatenating the left singular matrices and singular value matrices of each user: ; ; Composite right singular matrix It is formed by horizontally concatenating all right singular matrices: ; Composite noise vector It is formed by horizontally concatenating all noise vectors: .

[0018] In step (2-4), precoding design is performed based on the SVD concatenated by all users: The precoding matrix is: ,in Represented as The pseudo-inverse; using its inherent structural relationships can significantly reduce computational complexity. Represented as: ; It is a diagonal matrix, defined as follows: diagonal elements Indicates allocation to the corresponding number The power of a virtual singular path.

[0019] As can be seen from steps (2-1) and (2-2), this method fully utilizes the inherent structure of the approximate Loss channel in the time-delay-Doppler-spatial domain, significantly reducing the computational complexity of SVD and matrix inversion, with a complexity of O(n). .

[0020] In step (3), based on the complex gain of each sub-channel, a water-filling algorithm is designed to optimize the transmit power of each sub-channel, eliminate inter-user interference, and, under transmit power constraints, maximize the weighted sum rate to ultimately obtain the optimal power allocation solution, including: (3-1) Constructed with respect to power components The sub-optimization problem for the complex gain of each sub-channel is expressed as an SVD-based expression: ; constraint: ; in, Represents the trace of a matrix. and These represent the number of grid points for Doppler and time delay, respectively. It is the determinant of a matrix. For user weight, For the first One user, For users The path complex gain corresponding to the Loss path, For system noise variance, For the first Singular value matrix of each user For the first Power component matrix of each user for The conjugate transpose of .

[0021] In step (3), with a given directional component With fixed premises, for the subproblem of power allocation in the original optimization problem, we construct a formula regarding... The sub-optimization problem.

[0022] (3-2) Transmit power allocation design to maximize weighted sum rate: The transmit power of each sub-channel is optimized to output the optimal power component. The sub-optimization problem can be transformed into a power allocation problem, which can be expressed as: ; ; in, Represented as the first The weights corresponding to each virtual singular channel and Diagonal matrices The diagonal One element, The weighting coefficients are defined as follows: .

[0023] To solve this problem, the Lagrange function is constructed: ; in, It is a Lagrange multiplier, for Find the partial derivative: ; Set the expression to 0 and combine it with the constraints. Then the optimal power allocation for each virtual singular path can be obtained: ; in, This represents the optimal power allocation result for each virtual singular path. Therefore, the optimal power allocation matrix is ​​expressed as: .

[0024] The final form of the pre-encoded code is obtained: .

[0025] The present invention also provides a precoding matrix obtained by the above method. G In multi-user MIMO-OTFS systems, the signals transmitted by the base station are processed by a multi-precoding matrix. G* The data is pre-coded and then transmitted to the user, and the base station's transmit power is allocated and then transmitted to the user.

[0026] This invention proposes a low-complexity approximate channel SVD method to address the high complexity of traditional SVD methods due to channel dimensionality. In MU-MIMO-OTFS systems, this method proposes a comprehensive transmit-receive joint framework to achieve joint multiplexing in the delay-Doppler-space (DDS) domain. This method constructs a non-convex optimization problem encompassing OTFS modulation, multi-user precoding, inter-user interference, and power constraints to maximize the weighted sum rate. Unlike traditional methods, this method proposes an innovative low-complexity SVD precoding method that effectively suppresses multi-user interference. The algorithm leverages the dominant line-of-sight channel characteristics and analytically obtains the channel SVD by utilizing the structural features of the DD and spatial domains, thus significantly reducing computational complexity. Furthermore, this method reduces the need for precise channel state information, making it more feasible for practical deployment. Simultaneously, this method designs an optimal weighted water-filled power allocation scheme, significantly reducing computational complexity and channel state information requirements while incurring only a minimal WSR performance loss. This scheme has great potential for practical application in next-generation high-mobility wireless communication systems. Attached Figure Description

[0027] Figure 1 This is a diagram illustrating a multi-user MIMO-OTFS scenario for high mobility, provided in an embodiment of the present invention. Figure 2 A block diagram of the downlink of a multi-user MIMO-OTFS system; Figure 3 A comparison chart of WSR performance for different methods; Figure 4 A graph comparing the complexity of different methods; Figure 5 A graph showing the relationship between relevant parameters and WSR performance; Figure 6 The impact of the number of users on WSR performance. Detailed Implementation

[0028] The present invention will now be described in further detail with reference to the accompanying drawings.

[0029] Example 1: MU-MIMO-OTFS System In this embodiment, a multi-user multiple-input multiple-output (MIMO)-orthogonal time-frequency-space (OTFS) communication system is considered, including: The base station side is configured as a single base station (BS). One transmitting antenna supports DDS domain signal processing; on the user side there is One user, configuration for each user The root receiving antenna supports DDS domain signal processing, among which In this system, the transmitted signal is an OTFS signal; where the OTFS delay-Doppler grid size is... ,in and These represent the number of grid points for Doppler and time delay, respectively.

[0030] The signal transmitted by the base station contains all The information for a user can be expressed as follows: ; in, Satisfy unity power constraint ,and Indicates the first Signal vectors of each user Represents the conjugate transpose of a matrix or vector. Represents the conjugate transpose of a signal vector; It is a dimension of The identity matrix; The transmitted signal will pass through a precoding matrix Multiplexing in the time-delay-Doppler-spatial domain, the precoded signal can be represented as: ; in, Indicates the first DD domain signal frames transmitted on the root transmitting antenna. Each All of them must undergo the inverse symplectic finite Fourier transform (ISFFT) to convert the information from the time-delay-Doppler domain to the time-frequency domain. Its mathematical form is: ; in, The normalized Discrete Fourier Transform (DFT) matrix satisfies ,all A parallel ISFFT operation can be represented as and Multiplication, thereby achieving signal conversion Convert to the time domain for wireless transmission.

[0031] The base station's transmit power can be expressed as: ; Therefore, the precoding matrix Maximum power constraint must be met , It is the F-norm. This indicates the system's maximum power constraint.

[0032] Next, the transmission channel is modeled: this channel is a DDS domain channel composed of the Kronecker product of the time-frequency (TF) domain channel and the spatial domain channel. Therefore, the user... Equivalent DDS domain channel matrix : ; in For users The number of paths, For users The Path channel sub-gain Let be the spatial response matrix along the path, where , , , The imaginary unit, Indicates the spacing between adjacent antennas. Indicates the wavelength of the signal. and These are the angle of arrival and the angle of departure, respectively. Represents the conjugate transpose of a matrix; For users The delay-Doppler (DD) domain channel matrix, It is a dimension of M M An identity matrix of dimension 1 The matrix representing the normalized discrete Fourier transform (DFT) is denoted by . , The deferred permutation matrix is ​​defined by the following structure: , It is the Doppler phase rotation matrix, which is defined as follows: , Represents integer delay points, and These correspond to integer and fractional Doppler shifts, respectively.

[0033] user The received signal after processing by the MIMO-OTFS system is: ; in For users The first term of the received signal vector in the DDS domain For users The target signal, For users The received symbol vector in the DDS domain, For other users to users Multi-user interference items, The receiver's white Gaussian noise follows a set pattern. .

[0034] Example 2: Low-complexity precoding design for MU-MIMO-OTFS systems Using the MU-MIMO-OTFS communication system described in Example 1, the precoding design method includes the following steps: S1. Based on the precoding matrix in the multi-user MIMO-OTFS communication model Complete channel matrix System noise variance User weight and total transmit power constraints The optimization problem is: Taking into account both communication and interference effects, the optimization problem is formulated as a weighted sum rate (WSR) maximization problem, which can be expressed as: ; constraint: ; in, and These represent the number of grid points for Doppler and time delay, respectively. () represents the determinant of a matrix. For user weight, For dimension The identity matrix, Represents the conjugate transpose of a matrix or vector. For the precoding matrix Conjugate transpose matrix, Channel matrix The conjugate transpose of the matrix. For the first One user, To exclude the first Users other than the specified user This represents the system noise variance. It is the F-norm.

[0035] S2. Utilizing the characteristics of the MIMO-OTFS channel, the complete channel matrix in the optimization problem is... Approximate channel matrix of the Loss path And using an approximate channel matrix The structural properties directly yield the SVD matrix, and then the right singular matrix in the SVD decomposition result is used as the basis. Perform precoding matrix Design, the precoding matrix obtained from the design Including directional components and power components Specifically, it includes the following sub-steps: S2-1, Complete the channel matrix An approximation of the channel matrix that retains only the Loss of Sorrow (LoS) path. : ; in For users The path complex gain corresponding to the Loss path, For users The spatial response matrix corresponding to the Loss path. Represents the Krone integrability operation. For users The channel matrix in the delay-Doppler (DD) domain corresponding to the LosS path; S2-2, and then the approximate channel matrix is ​​obtained. Complete structural expression: ; in, Represented as The steering vector of the root antenna, , , The imaginary unit, This indicates the spacing between adjacent antennas, typically... Indicates the wavelength of the signal. and users respectively The arrival angle and departure angle of the Loss path; It is a dimension of M M An identity matrix of dimension 1 It is a dimension of The normalized discrete Fourier transform (DFT) matrix, where , The deferred permutation matrix is ​​defined by the following structure: , It is the Doppler phase rotation matrix, which is defined as follows: , Represents integer delay points, and These correspond to integer and fractional Doppler shifts, respectively.

[0036] 2-3. Approximate Channel Matrix Perform SVD decomposition: ; in and They are users The left singular value matrix (LSM) and the right singular value matrix (RSM), It is based on the approximate channel matrix The singular values ​​are the diagonal singular matrix with diagonal elements; based on the approximate channel matrix. Structural properties can be directly obtained through SVD decomposition: Left Singular Matrix (LSM) It can be expressed as: ; Diagonal Singular Matrix SM It can be expressed as: ; Right Singular Matrix RSM It can be expressed as: .

[0037] S2-4. Constructing a composite multi-user received signal model: All Received signal vector of each user Vertical concatenation is performed to form a system-level composite receive vector: ; Based on the SVD decomposition results of each user channel, the equivalent input-output relationship of this composite signal vector can be further expressed as: ; The composite matrix in this model is formed by concatenating the channel parameter matrices of each user, and its complete structural expression is as follows: Composite gain matrix , is a block diagonal matrix containing the channel gains of all users: ; Composite Left Singular Matrix and composite singular value matrix These are block diagonal matrices formed by concatenating the left singular matrices and singular value matrices of each user:

[0038]

[0039] Composite Left Singular Matrix It is formed by horizontally concatenating all right singular matrices: ; Composite noise vector It is formed by horizontally concatenating all noise vectors: .

[0040] S2-5. Pre-encoding design based on the SVD concatenated by all users: precoding ,in Represented as The pseudo-inverse; using its inherent structural relationships can significantly reduce computational complexity: ; It is a diagonal matrix, defined as follows: diagonal elements This represents the power allocated to the corresponding virtual singular path.

[0041] S3. The precoding matrix designed in S2 Substituting into the optimization problem, we construct information about the power components. This problem involves a sub-optimization problem of the complex gain of each sub-channel, optimizing the transmit power of each sub-channel, and outputting the optimal power component. Specifically, it includes the following sub-steps: S3-1, Construction regarding power components The sub-optimization problem for the complex gain of each sub-channel is expressed as an SVD-based expression: ; constraint: ; in, Represents the trace of a matrix. and These represent the number of grid points for Doppler and time delay, respectively. () represents the determinant of a matrix. For user weight, For the first One user, For users The path complex gain corresponding to the Loss path, For system noise variance, For the first A user singular value matrix For the first Power component matrix of each user for The conjugate transpose of .

[0042] S3-2, Transmit power allocation design to maximize weighted sum rate: First, the power allocation problem can be expressed as:

[0043]

[0044] in, Represented as the first The weights corresponding to each virtual singular channel and Diagonal matrices The diagonal One element, The weighting coefficients are defined as follows: .

[0045] To solve this problem, the Lagrange function is constructed: ; in, It is a Lagrange multiplier. (Correct) Find the partial derivative: ; Set the expression to 0 and combine it with the constraints. Then the optimal power allocation for each virtual singular path can be obtained: ; in, This represents the optimal power allocation result for each virtual singular path. Therefore, the optimal power allocation matrix is ​​expressed as: .

[0046] The final form of the pre-encoded code is obtained: .

[0047] As can be seen from S2-1 and S2-2, this method fully utilizes the inherent structure of the approximate LoS channel in the time-delay-Doppler-spatial domain, significantly reducing the computational complexity of SVD and matrix inversion, with a complexity of O(n). .

[0048] In this embodiment, the main simulation parameters are set as follows: number of users The base station is equipped with Each user is equipped with a single transmitting antenna. The root receiving antenna and the DD grid size are set to... Number of channel paths Integer delay Randomly generated within the range [0, M-1], with Doppler shift (integer or fractional). Randomly generated within the range [0, N-1]. Assume the secondary gain of the Los path follows a normalized Gaussian distribution. Because there is a significant power difference between the Los path and the NLos path, the NLos path has a weaker secondary gain. obey Run 100 Monte Carlo simulations and analyze the average results.

[0049] Figure 3 The WSR performance of different methods under different transmit powers was compared. The curve corresponding to "WMMSE" represents the classic WMMSE precoding method. The curves corresponding to "SVD-LoS CSI, Equal Power" and "SVD-LoS CSI, Waterfilling" represent the average power allocation and waterfilling power allocation of the proposed method, respectively. The curves corresponding to "SVD-Perfect CSI, Equal Power" and "SVD-Perfect CSI CSI, Waterfilling" represent the average power allocation and waterfilling power allocation of the traditional SVD method under full CSI, respectively. As can be seen from the figures, the WMMSE algorithm outperforms the SVD-based method across the entire signal-to-noise ratio (SNR) range. Meanwhile, the WSR performance of the low-complexity SVD method using LosS CSI is slightly lower than that of the SVD method using perfect CSI. However, despite this small performance difference, the advantage of the proposed low-complexity SVD algorithm is that it only requires LosS CSI, while the traditional SVD method relies on full CSI. Regarding power allocation strategies, for the SVD-based method, the waterfilling scheme shows a significant performance gain compared to the equal power allocation scheme, especially in the high SNR region.

[0050] like Figure 4 As shown in the figure, the complexity of different methods under different parameters is compared. It can be seen from the figure that the complexity of the SVD algorithm using approximate Loss CSI is much lower than that of the SVD method and the WMMSE method under full CSI.

[0051] like Figure 5 As shown, simulations were performed to examine the impact of different parameters on WSR performance. It can be seen that adding a transmitting antenna... and receiving antenna The quantity can continuously improve WSR and expand the dimensionality of OTFS meshes. Or the number of channel paths Reducing it will cause WSR performance to decrease.

[0052] like Figure 6 As shown, the number of users is displayed. The relationship between WSR performance and the overall system speed. It can be observed that although the total system speed increases with the number of users, the gain gradually decreases due to the marginal effect.

[0053] Therefore, this invention achieves satisfactory WSR performance while significantly reducing computational complexity and the need for channel state information.

[0054] In summary, this invention discloses a low-complexity precoding method for maximizing the weighted sum rate in multi-user MIMO-OTFS systems. First, based on a multi-user MIMO-OTFS system, a non-convex problem is constructed with the goal of maximizing the system's weighted sum rate while considering transmit power constraints and reducing inter-user interference. Second, a Loss-of-Spot (LoS) channel-based SVD algorithm is proposed, significantly reducing the complexity of traditional SVD calculations and greatly reducing the need for channel state information. Then, a water-filling algorithm is used to rationally allocate power to each virtual singular path, ultimately obtaining the optimal power allocation solution. Finally, simulation results verify the effectiveness and low computational complexity of the algorithm, demonstrating that while the proposed scheme's WSR performance is slightly lower than the SVD method based on perfect channel state information, it significantly reduces computational complexity and the need for channel state information. The water-filling algorithm can adaptively allocate more power to sub-channels with better gain, thereby improving the overall transmission rate of the system.

[0055] It should be noted that the above embodiments are merely preferred examples of the present invention and do not constitute a limitation on the scope of protection of the present invention. Any equivalent substitutions, structural adjustments, or improvements made in accordance with the present invention specification and drawings, or any direct or indirect application of the present invention to other related technical fields, should be included within the scope of protection of the present invention.

Claims

1. A precoding method for a multi-user MIMO-OTFS system, characterized in that, The method includes: (1) Based on the precoding matrix in the multi-user MIMO-OTFS communication model Complete channel matrix System noise variance User weight and total transmit power constraints Construct an optimization problem; (2) Utilizing the characteristics of the MIMO-OTFS channel, the complete channel matrix in the optimization problem is obtained. Approximate channel matrix of the Loss path And using an approximate channel matrix The structural properties directly yield the SVD matrix, and then the right singular matrix in the SVD decomposition result is used as the basis. Perform precoding matrix Design, the precoding matrix obtained from the design Including directional components and power components ; (3) The precoding matrix designed in step (2) Substituting into the optimization problem constructed in step (1), construct the power component... This problem involves a sub-optimization problem of the complex gain of each sub-channel, optimizing the transmit power of each sub-channel, and outputting the optimal power component. ; (4) Based on the direction components in step (2) and the optimal power component in step (3) Construct the final precoding matrix .

2. The precoding method for a multi-user MIMO-OTFS system according to claim 1, characterized in that, In step (1), the multi-user MIMO-OTFS system includes a base station side and a user side, with the base station side configured as a single base station (BS). One transmitting antenna, located on the user side. One user, configuration for each user Root receiving antenna; The optimization problem to be constructed is: ； constraint: ; in, and These represent the number of grid points for Doppler and time delay, respectively. It is the determinant of a matrix. For user weight, For dimension The identity matrix, Represents the conjugate transpose of a matrix or vector. For the precoding matrix Conjugate transpose matrix, Channel matrix The conjugate transpose of the matrix. For the first One user, To exclude the first Users other than the specified user This represents the system noise variance. It is the F-norm.

3. The precoding method for a multi-user MIMO-OTFS system according to claim 1, characterized in that, Step (2) includes the following sub-steps: (2-1) The complete channel matrix An approximation of the channel matrix that retains only the Loss of Sorrow (LoS) path. ; (2-2) Approximate channel matrix Perform SVD decomposition to obtain the SVD decomposition results; (2-3) Construct a composite multi-user received signal model based on SVD The composite right singular splicing matrix is ​​obtained. ; (2-4) Based on the composite right singular splicing matrix after splicing by all users Perform precoding design to obtain the precoding matrix. ,in Represented as a composite right singular splicing matrix The false rebellion.

4. The precoding method for a multi-user MIMO-OTFS system according to claim 3, characterized in that, In step (2-1), the complete channel matrix is... An approximation of the channel matrix that retains only the Loss of Sorrow (LoS) path. : ； in, For users The path complex gain corresponding to the Loss path, For users The spatial response matrix corresponding to the Loss path. Represents the Krone integrability operation. For users The channel matrix in the delay-Doppler (DD) domain corresponding to the LosS path; This leads to the approximate channel matrix. Complete structural expression: ； in, Represented as The steering vector of the root antenna, , , The imaginary unit, This indicates the spacing between adjacent antennas, typically... Indicates the wavelength of the signal. and users respectively The arrival angle and departure angle of the Loss path; It is a dimension of M M The identity matrix, It is a dimension of The normalized discrete Fourier transform (DFT) matrix, where , The deferred permutation matrix is ​​defined by the following structure: , It is the Doppler phase rotation matrix, which is defined as follows: , Represents integer delay points, and These correspond to integer and fractional Doppler shifts, respectively.

5. The precoding method for a multi-user MIMO-OTFS system according to claim 3, characterized in that, In step (2-2), the approximate channel matrix is... Perform SVD decomposition: ； in and They are users The left singular value matrix (LSM) and the right singular value matrix (RSM), It is based on the approximate channel matrix The diagonal singular matrices with singular values ​​as diagonal elements are represented as follows: ； ； 。 6. The precoding method for a multi-user MIMO-OTFS system according to claim 3, characterized in that, In step (2-3), all Received signal vector of each user Vertical concatenation results in a system-level composite receive vector: ； Based on the SVD decomposition results of each user channel, the equivalent input-output relationship of the composite receive vector can be further expressed as: ； The composite matrix in this model is formed by concatenating the channel parameter matrices of each user, and its complete structural expression is as follows: Composite gain matrix , is a block diagonal matrix containing the channel gains of all users: ； Composite Left Singular Matrix and composite singular value matrix These are block diagonal matrices formed by concatenating the left singular matrices and singular value matrices of each user: ； ； Composite right singular matrix It is formed by horizontally concatenating all right singular matrices: ； Composite noise vector It is formed by horizontally concatenating all noise vectors: 。 7. The precoding method for a multi-user MIMO-OTFS system according to claim 3, characterized in that, In step (2-4), the precoding matrix obtained is as follows: ； in, Represented as The false rebellion, Represented as: ； in, Let be a diagonal matrix, defined as: ； diagonal elements This represents the power allocated to the corresponding virtual singular path.

8. The precoding method for a multi-user MIMO-OTFS system according to claim 7, characterized in that, In step (3), the constructed power component The sub-optimization problem for the complex gain of each sub-channel is expressed as an SVD-based expression: ； constraint: ; in, Represents the trace of a matrix. and These represent the number of grid points for Doppler and time delay, respectively. It is the determinant of a matrix. For user weight, For the first One user, For users The path complex gain corresponding to the Loss path, For system noise variance, For the first Singular value matrix of each user For the first Power component matrix of each user for The conjugate transpose of .

9. The precoding method for a multi-user MIMO-OTFS system according to claim 7, characterized in that, The transmit power of each sub-channel is optimized to output the optimal power component. The method is as follows: Transform the sub-optimization problem into: ； ； in, and Diagonal matrices The diagonal One element, The weighting coefficients are defined as follows: ; To solve this problem, the Lagrange function is constructed: ； in, It is a Lagrange multiplier, for Find the partial derivative: ； Set the expression to 0 and combine it with the constraints. Then the optimal power allocation for each virtual singular path can be obtained: ； in, This represents the optimal power allocation result for each virtual singular path; therefore, the optimal power allocation matrix is ​​expressed as: .

10. The method according to any one of claims 1-9, characterized in that, The user MIMO-OTFS system includes a base station side and a user side, wherein the base station side is a single base station (BS) configuration. One transmitting antenna supports DDS domain signal processing; on the user side there is One user, configuration for each user The root receiving antenna supports DDS domain signal processing, among which In this system, the transmitted signal is an OTFS signal; where the OTFS delay-Doppler grid size is... ,in and These represent the number of grid points for Doppler and time delay, respectively. The signal transmitted by the base station contains all Information for each user, expressed as: ； in, Satisfy unity power constraint ,and Indicates the first Signal vectors of each user Represents the conjugate transpose of a matrix or vector. Represents the conjugate transpose of a signal vector; It is a dimension of The identity matrix; The transmitted signal will pass through a precoding matrix Multiplexing in the time-delay-Doppler-spatial domain, the precoded signal is: ； in, Indicates the first Each DD domain signal frame transmitted on the root transmitting antenna All of them must undergo the inverse symplectic finite Fourier transform (ISFFT) to convert the information from the time-delay-Doppler domain to the time-frequency domain. Its mathematical form is: ； in, The normalized Discrete Fourier Transform (DFT) matrix satisfies ,all A parallel ISFFT operation is represented as and Multiplication, thereby achieving signal conversion Convert to the time domain for wireless transmission; Therefore, the transmit power at the base station is expressed as: ； in, Representing expectation, precoding matrix Maximum power constraint must be met , It is the F-norm. This indicates the system's maximum power constraint; user Equivalent DDS domain channel matrix : ； in For users The number of paths, For users The Path channel sub-gain Let be the spatial response matrix along the path, where , , , The imaginary unit, Indicates the spacing between adjacent antennas. Indicates the wavelength of the signal. and These are the angle of arrival and the angle of departure, respectively. Represents the conjugate transpose of a matrix; For users The time-delay-Doppler domain channel matrix, It is a dimension of M M An identity matrix of dimension 1 The normalized Discrete Fourier Transform (DFT) matrix represents the matrix, where , The deferred permutation matrix is ​​defined by the following structure: , It is the Doppler phase rotation matrix, which is defined as follows: , Represents integer delay points, and These correspond to integer and fractional Doppler shifts, respectively.

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