Channel smoothing method based on manifold optimization

Abstract

The invention discloses a channel smoothing method based on manifold optimization, and relates to the technical field of channel smoothing. The method comprises the following steps: constructing a multiple-input multiple-output orthogonal frequency division multiplexing system which comprises N receiving antennas, M transmitting antennas and K subcarriers; the method comprises the following steps: on the basis of a multiple-input-multiple-output orthogonal frequency division multiplexing system, taking maximization of the smoothness of a beam forming channel in the multiple-input-multiple-output orthogonal frequency division multiplexing system as a target, considering channel estimation constraints, and constructing a channel smoothing model; and solving the channel smoothing model by adopting a manifold optimization algorithm to obtain a channel smoothing strategy of the beam forming channel. According to the method provided by the invention, the difference vector between adjacent subcarriers and the amplitude of each subcarrier can be effectively reduced, the destructiveness of a corresponding beam forming channel is reduced, and the channel estimation and data packet accuracy is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of channel smoothing, and in particular to a channel smoothing method based on manifold optimization. Background Art

[0002] Channel smoothing is a technique used to enhance channel estimation in communication systems. It can perform some degree of averaging or filtering on channel characteristics to reduce the impact of time-varying channel characteristics or frequency-selective fading on signal transmission, thereby improving the reliability and quality of signal transmission.

[0003] However, current channel smoothing technologies often suffer from various undesirable factors in actual communication channels, such as multipath, Doppler shift, and noise interference. These factors can cause signal distortion and fading during transmission, impacting communication system performance. Channel smoothing technology can effectively counteract these adverse effects, improving the stability and reliability of communication systems and enhancing the accuracy and efficiency of data transmission.

[0004] Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier modulation technology widely used in modern communications. In OFDM systems, channel smoothing exploits the correlation or smoothness of channel responses in the frequency domain to split a high-rate data stream into multiple lower-rate sub-streams. These sub-streams are then modulated onto mutually orthogonal sub-carriers for parallel transmission. Because the sub-carriers are orthogonal, they can overlap in the spectrum, but at the receiving end, correlation demodulation techniques can still be used to correctly separate and recover the sub-streams, effectively improving spectrum efficiency.

[0005] However, when existing orthogonal frequency division multiplexing systems are applied to Wi-Fi beamforming multiple-input multiple-output (MIMO) systems, the beamforming vectors provided by the receiver are destructive. This results in high difference vectors between adjacent subcarriers and high amplitudes for each subcarrier, making the corresponding beamforming channels destructive as well. This in turn leads to high channel estimation errors and packet error rates. Summary of the Invention

[0006] To overcome the existing problem in OFDM applied to WiFi beamforming multiple-input multiple-output systems, where the difference vectors between adjacent subcarriers and the amplitude of each subcarrier are high, resulting in a destructive beamforming channel and, in turn, high channel estimation errors and packet error rates, the present invention aims to propose a channel smoothing method based on manifold optimization. This method can effectively reduce the difference vectors between adjacent subcarriers and the amplitude of each subcarrier, mitigate the destructiveness of the corresponding beamforming channel, and improve channel estimation and packet error rates.

[0007] To achieve the purpose of the present invention, the present invention adopts the following technical solutions:

[0008] A channel smoothing method based on manifold optimization, the method comprising the following steps:

[0009] Build a multiple-input multiple-output orthogonal frequency division multiplexing system, including: N receive antennas, M transmit antennas and K subcarriers;

[0010] Based on a MIMO OFDM system, a channel smoothing model is constructed with the goal of maximizing the smoothness of the beamforming channel in the MIMO OFDM system and considering the channel estimation constraints.

[0011] The manifold optimization algorithm is used to solve the channel smoothing model and obtain the channel smoothing strategy of the beamforming channel.

[0012] In the above technical solution, by constructing a multi-input multi-output orthogonal frequency division multiplexing system, the technical problems existing in the prior art can be better studied. Based on the technical problems, with the goal of maximizing the smoothness of the beamforming channel in the multi-input multi-output orthogonal frequency division multiplexing system, considering the channel estimation constraints, a channel smoothing model is constructed, and the channel smoothing model is iteratively solved using a manifold optimization algorithm. Based on the channel smoothing strategy of the beamforming channel obtained, when OFDM is applied to a multi-input multi-output system for WiFi beamforming, the difference vector between adjacent subcarriers and the amplitude of each subcarrier can be effectively reduced, the destructiveness of the corresponding beamforming channel can be reduced, and the channel estimation and data packet accuracy can be improved. In addition, the manifold optimization algorithm used can effectively avoid the calculation of the Hessian matrix in the process of solving the channel smoothing model, thereby improving computational efficiency and reducing resource waste.

[0013] Furthermore, based on the MIMO OFDM system, the channel estimation constraint on the i-th subcarrier is set, and the expression is:

[0014]

[0015] Use FIR filter to constrain channel estimation Perform channel smoothing to obtain channel estimation And estimate the channel Perform singular value decomposition, the expression is:

[0016]

[0017] Among them, H i ∈C M×N represents the channel of the MIMO OFDM system, Z i ∈C M×N represents additive noise, V i ∈C M×N represents the right singular value vector, U i represents the left singular vector matrix, Λ i represents the singular value matrix, V i H Represents the right singular value vector after singular value decomposition on the channel.

[0018] Furthermore, based on the channel estimation constraint and the right singular value vector V i , and minimize the front and back right singular value vector V on the channel i The distance between them is used to maximize the smoothness of the beamforming channel in the MIMO OFDM system and to construct a channel smoothing model, which is expressed as:

[0019]

[0020] Among them, Q i ∈C N×M represents the vector to be solved, represents the identity matrix, represents a unitary matrix constraint.

[0021] Furthermore, the channel smoothing model is simplified by using matrix norm expansion and trace operation simplification method, and the expression is:

[0022]

[0023] Among them, Q i ∈C N×M Represents the vector to be solved, Tr(*) represents the trace operation of the matrix, R i Equal to V i+1 H V i , V i ∈C M ×N represents the right singular value vector after singular value decomposition, Represents the identity matrix.

[0024] In the above technical solution, by constructing a multi-input multi-output orthogonal frequency division multiplexing system, the channel estimation constraint on the i-th subcarrier set in the system can be calculated, and then the right singular value vector after singular value decomposition is calculated based on the channel estimation constraint, and according to the problem of insufficient smoothness of the right singular value vector after singular value decomposition in the existing system, a channel smoothing model is constructed, so as to maximize the smoothness of the beamforming channel in the multi-input multi-output orthogonal frequency division multiplexing system. The right singular value vector after singular value decomposition is smoothed and optimized to improve the performance of the beamforming channel; in addition, the channel smoothing model is simplified by using matrix norm expansion and trace operation simplification methods, which can improve computational efficiency and reduce resource waste.

[0025] Furthermore, the process of solving the channel smoothing model using the manifold optimization algorithm includes:

[0026] The objective function of the channel smoothing model is simplified to an unconstrained optimization form on the Riemannian manifold;

[0027] An iterative optimization method based on the Barzilai-Borwein algorithm is used, combined with a gradient descent strategy, to transform the objective function in the unconstrained optimization form into a least squares problem.

[0028] Solving the least squares problem to obtain a Riemann BB step length, and calculating a signal vector received on the manifold based on the Riemann BB step length;

[0029] The simplified channel smoothing model is derived according to the received signal to calculate a piecewise function of the gradient in the Euclidean space, and a smoothed beamforming vector is reconstructed based on the piecewise function.

[0030] Furthermore, the objective function of the channel smoothing model is simplified to an unconstrained optimization form on the Riemannian manifold as follows:

[0031]

[0032] Among them, f(Q i ) represents the cost value in the channel smoothing model; the smaller the cost value, the greater the smoothness.

[0033] Furthermore, the objective function of the unconstrained optimization form is transformed into a least squares problem, which is expressed as:

[0034] min t ||s k ty k ||2

[0035] The least squares problem is solved to obtain the Riemann BB step length, which is expressed as:

[0036]

[0037] Based on the Riemann BB step length, the update vector on the Riemann manifold is calculated as follows:

[0038]

[0039] Based on the update vector on the Riemann manifold, the signal vector received on the manifold is calculated, and the expression is:

[0040]

[0041] in, represents the vector transport operator on the Riemannian manifold, η k Indicates the current point x k The optimized direction vector at g. k Indicates the current point x k The gradient vector of represents the update vector s k The transpose of .

[0042] Furthermore, the simplified channel smoothing model is derived according to the received signal to calculate the piecewise function of the gradient in the Euclidean space, which is expressed as:

[0043]

[0044] The smoothed beamforming vector is reconstructed based on the piecewise function, and the expression is:

[0045]

[0046] Where sub represents the number of subcarriers, Q i ∈C N×M Represents the vector to be solved, R i Equal to V i+1 H V i , V i ∈C M×N represents the right singular value vector after singular value decomposition, Represents the optimal rotation matrix obtained by solving.

[0047] A computer device comprises a memory, a processor and a computer program stored in the memory and running on the processor, wherein when the processor executes the computer program, the steps of a channel smoothing method based on manifold optimization are implemented.

[0048] A computer-readable storage medium stores a computer program. The computer program is executed by a processor to implement the steps of a channel smoothing method based on manifold optimization.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] The present invention proposes a channel smoothing method based on manifold optimization. By constructing a multi-input multi-output orthogonal frequency division multiplexing (OFDM) system, it is possible to better study the technical problems existing in the prior art. Based on the technical problems, with the goal of maximizing the smoothness of the beamforming channel in the MIMO OFDM system, a channel smoothing model is constructed considering channel estimation constraints. The channel smoothing model is iteratively solved using a manifold optimization algorithm. Based on the obtained channel smoothing strategy for the beamforming channel, when OFDM is applied to a multi-input multi-output (OFDM) system for WiFi beamforming, the difference vector between adjacent subcarriers and the amplitude of each subcarrier are effectively reduced, the destructiveness of the corresponding beamforming channel is mitigated, and the channel estimation and data packet accuracy are improved. In addition, the manifold optimization algorithm used can effectively avoid the calculation of the Hessian matrix in the process of solving the channel smoothing model, thereby improving computational efficiency and reducing resource waste. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 A flow chart of the steps of a channel smoothing method based on manifold optimization provided in an embodiment of the present application;

[0052] Figure 2 This is a schematic diagram of the convergence of the channel smoothing model as the number of iterations increases in the experiment provided in the embodiment of the present application;

[0053] Figure 3 Schematic diagram showing the performance comparison between the channel smoothing model and the existing model in the experiment provided in the embodiment of the present application;

[0054] Figure 4 This is a performance diagram of the channel smoothing model under different numbers of receiving antennas and data streams in the experiment provided in the embodiment of the present application. DETAILED DESCRIPTION

[0055] To facilitate understanding of the present invention, the present invention will be described more fully below with reference to the accompanying drawings. Preferred embodiments of the present invention are shown in the accompanying drawings. However, the present invention may be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and comprehensive understanding of the present disclosure.

[0056] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this invention pertains. The terms used in this specification of the present invention are for the purpose of describing specific embodiments only and are not intended to limit the present invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0057] Example 1:

[0058] This embodiment provides a channel smoothing method based on manifold optimization, see Figure 1 , the method comprises the following steps:

[0059] Step S1: Construct a multiple-input multiple-output orthogonal frequency division multiplexing (MIMO OFDM) system, including: N receiving antennas, M transmitting antennas and K subcarriers;

[0060] Step S2: Based on a MIMO OFDM system, a channel smoothing model is constructed with the goal of maximizing the smoothness of the beamforming channel in the MIMO OFDM system and considering channel estimation constraints.

[0061] Step S3: A manifold optimization algorithm is used to solve the channel smoothing model to obtain a channel smoothing strategy for the beamforming channel.

[0062] As a preferred embodiment, in step S1, based on a multiple-input multiple-output orthogonal frequency division multiplexing system, a channel estimation constraint on the i-th subcarrier is set, and the expression is:

[0063]

[0064] Among them, H i ∈C M×N is the MIMO OFDM channel, Z i ∈C M×N This is additive noise. This is a channel sounding frame, which is non-beamforming (non-BFed). Therefore, an FIR filter can be used at the receiving end to smooth the passing channel, and the FIR filter window value is fixed to 5.

[0065] exist After passing through the FIR filter, the channel estimation after channel smoothing can be obtained At this time Performing singular value decomposition (SVD) yields the following equation:

[0066]

[0067] Among them, V i ∈C M×N represents the right singular value vector, U i represents the left singular vector matrix, Λ i represents the singular value matrix, Represents the right singular value vector after singular value decomposition on the channel. The quantized V iwill be packed into CSI frames and sent to the access point (AP), which will use V i The beamforming vector is generated by calculating the y-axis. The channel sounding protocol in 802.11ax includes the AP's channel sounding frame and the STA's CSI report frame. The AP uses a forced zero precoder. On the i-th subcarrier, the beamforming matrix formed by the AP is expressed as:

[0068]

[0069] in, Depend on The largest right singular value vector of P. i It is a diagonal matrix with power normalization factors on the diagonal.

[0070] In the case of channel estimation, the signal passes through the beamforming matrix T i After that, the signal transmitted on the i-th subcarrier can be expressed as:

[0071] Y i =H i T i X i +Z i (4)

[0072] is the received signal vector, is the signal vector sent, is the additive noise vector. H i ∈C M×N Is the street estimation matrix, which is used to estimate the influence of the channel. STA can use the leading code of the MIMO data frame to estimate the beamforming channel,

[0073] h i =H i T i +z i (5)

[0074] z i Is the channel estimation error. The received signal vector Y i With the beamforming matrix h i Multiply to remove the channel effect and get the signal vector X i .Right now This step actually eliminates interference and enhances the received signal, making it clearer and more reliable. However, due to the rank inversion effect, the singular vectors of the channel matrix obtained after performing SVD decomposition may have destructive effects on the subcarriers. These effects are transmitted to the AP through the CSI report frame, resulting in the beamforming vector T i The roughness of h iThe roughness affects the reception and demodulation of signals.

[0075] As a preferred embodiment, according to the beamforming vector T i The roughness of h i The problem of non-smoothness affecting signal reception and demodulation is based on channel estimation constraints. and the right singular value vector V i , and minimize the front and back right singular value vector V on the channel i The distance between them is used to maximize the smoothness of the beamforming channel in the MIMO OFDM system and to construct a channel smoothing model, which is expressed as:

[0076]

[0077] Among them, Q i ∈C N×M represents the vector to be solved, represents the identity matrix, represents a unitary matrix constraint.

[0078] By using matrix norm expansion and trace operation simplification, Equation (6) can be rewritten as:

[0079]

[0080]

[0081] Furthermore, due to N r is known and computable, and using constant elimination, we remove N from the simplified optimization expression. r The channel smoothing model is simplified by the term, and the expression is:

[0082]

[0083] Among them, Q i ∈C N×M Represents the vector to be solved, Tr(*) represents the trace operation of the matrix, represents the sum of the main diagonal elements of the matrix, R i Equal to V i+1 H V i , V o ∈C M×N represents the right singular value vector after singular value decomposition, Represents the identity matrix. After this series of operations, the optimization expression is simplified, the unitary matrix constraint is retained, and the computational complexity is reduced. After removing the constant term, the form of the optimization objective function is more concise, and the optimization algorithm does not need to calculate the N r Related meaningless quantities.

[0084] It can be understood that by constructing a multi-input multi-output orthogonal frequency division multiplexing system, the channel estimation constraint on the i-th subcarrier set in the system can be calculated, and then the right singular value vector after singular value decomposition is calculated based on the channel estimation constraint, and according to the problem of insufficient smoothness of the right singular value vector after singular value decomposition in the existing system, a channel smoothing model is constructed, so as to maximize the smoothness of the beamforming channel in the multi-input multi-output orthogonal frequency division multiplexing system. The right singular value vector after singular value decomposition is smoothed and optimized to improve the performance of the beamforming channel; in addition, the channel smoothing model is simplified by using matrix norm expansion and trace operation simplification methods, which can improve computational efficiency and reduce resource waste.

[0085] As a preferred embodiment, the process of solving the channel smoothing model using the manifold optimization algorithm includes:

[0086] The objective function of the channel smoothing model is simplified to an unconstrained optimization form on the Riemannian manifold;

[0087] An iterative optimization method based on the Barzilai-Borwein algorithm is used, combined with a gradient descent strategy, to transform the objective function in the unconstrained optimization form into a least squares problem.

[0088] Solving the least squares problem to obtain a Riemann BB step length, and calculating a signal vector received on the manifold based on the Riemann BB step length;

[0089] The simplified channel smoothing model is derived according to the received signal to calculate a piecewise function of the gradient in the Euclidean space, and a smoothed beamforming vector is reconstructed based on the piecewise function.

[0090] Specifically, the objective function of the channel smoothing model is simplified to an unconstrained optimization form on the Riemann manifold as follows:

[0091]

[0092] Among them, f(Q i ) represents the cost value in the channel smoothing model; the smaller the cost value, the greater the smoothness.

[0093] The Barzilai-Borwein (BB) algorithm will be used on the Riemannian manifold to solve this optimization expression. The BB algorithm belongs to the category of first-order optimization algorithms, which only depends on the gradient of the cost function and does not contain second-order information such as the Hessian matrix. and To express it, then the first-order method can be expressed as x (k+1) =x (k) -α k g (k) , where the step size αk It can be fixed or obtained by line search. The first-order method is simple, but converges slowly. The Newton method is given by x (k+1) =x (k) -(F (k) ) -1 g (k) , which converges faster but requires the calculation of the Hessian matrix. The Barzilai-Borwein (BB) method uses α k g (k) To approximate (F (k) ) -1 , which can avoid the calculation of the Hessian matrix, simplify the calculation process, and thus improve the optimization efficiency.

[0094] Specifically, the objective function of the unconstrained optimization form is transformed into a least squares problem, which is expressed as:

[0095] min t ||s k ty k ||2(10)

[0096] In Euclidean space, the basic idea of the BB method is to solve the least squares problem for k ≥ 1, where s k ∶=x k+1 -x k and Let x k+1 ≠x k , the unique solution is obtained by the least squares method

[0097] when When , the least squares problem is solved to obtain the Riemann BB step length, which is expressed as:

[0098]

[0099] Similar to the Euclidean case, the Riemann BB method approximates the effect of the Riemann Hessian of f at a specific point by scalar multiples of the identity matrix. This avoids the high cost of calculating the Riemann Hessian and captures local second-order information. The convergence speed is significantly better than the traditional first-order method. Specifically, in the (k+1)th step, the Hessian is used as the arrive The linear mapping effect ( Denotes the manifold M at point x k Tangent space on ). Consider the vector η k =-α k g k , instead of the difference x k+1 -xk , the vector belongs to and transfer it to

[0100] Then, based on the Riemann BB step length, the update vector on the Riemann manifold is calculated, and the expression is:

[0101]

[0102] Among them, Equation (12) describes a key step in the optimization on Riemannian manifold: vector transmission. k Represents the update vector on the manifold, that is, from point x k Move to point x k+1 The desired vector. is a vector transport operator on a Riemannian manifold. k is the current point x k The optimized direction vector at g. k , current point x k Gradient vector of . Step size - α k Used to control the update amplitude.

[0103] Here, let x k and x k+1 There is a vector transfer between them. In order to obtain y k , we need to subtract the two gradients in different tangent spaces. Perform the operation on g k Transfer to Then, based on the update vector on the Riemann manifold, the signal vector received on the manifold is calculated, and the expression is:

[0104]

[0105] in, represents the vector transport operator on the Riemannian manifold, η k Indicates the current point x k The optimized direction vector at g. k Indicates the current point x k The gradient vector of represents the update vector s k The transpose of .

[0106] Furthermore, the simplified channel smoothing model is differentiated according to the received signal to calculate the piecewise function of the gradient in the Euclidean space. The process includes:

[0107] The Riemann correspondence of the Secant equation (10) can be rewritten as:

[0108] s k t=yk (14)

[0109] about The least squares approximation of Therefore, the Riemann BB step size is of the form:

[0110]

[0111] Through the symmetry of formula (10), which comes from the properties of least squares approximation and the relationship between the gradient change and the update vector, the Riemann BB step size can be generated.

[0112]

[0113] exist and The tensor-tensor product between is defined as:

[0114]

[0115] From Euclidean space ε to The orthogonal projection operator is:

[0116]

[0117] Furthermore, suppose that the retraction R applied on the manifold is a retraction based on t-QR, expressed as:

[0118] in and express In the t-QR decomposition of Factor, satisfied in and

[0119] The gradient of the smooth function f defined on St(n,p,l) is:

[0120]

[0121] in In R n×p×l is defined on , and coincides with f on St(n,p,l): and

[0122] The vector transmission on St(n,p,l) is,

[0123]

[0124] in is the vector transfer operator, is the orthogonal projection operator, is any retraction on St(n,p,l), Retraction operator, is the tangent vector at point Q.

[0125] The simplified channel smoothing model is differentiated to calculate the piecewise function of the gradient in Euclidean space, which is expressed as:

[0126]

[0127] Obviously, this expression should be a piecewise function;

[0128] Based on the piecewise function, a beamforming smoothing algorithm 1 based on the BB algorithm is designed to reconstruct a smoothed beamforming vector, which is expressed as:

[0129]

[0130] Where sub represents the number of subcarriers, Q i ∈C N×M Represents the vector to be solved, R i Equal to V i+1 H V i , V i ∈C M×N represents the right singular value vector after singular value decomposition, Represents the optimal rotation matrix obtained by solving.

[0131] The process of designing the beamforming smoothing algorithm 1 based on the BB algorithm includes defining the parameters of the line search as follows: the step size reduction factor σ belongs to the interval (0,1); the parameter γ is sufficiently reduced to be within (0,1); an integer parameter M is used for non-monotonic line search, where M>0; the upper and lower bounds of the step size are denoted as α max >α min > 0. The retraction and vector transfer operators are defined in equations (19) and (21). Set the initial value: starting point Q0.

[0132]

[0133]

[0134] In this embodiment, by constructing a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system, technical problems existing in the prior art can be better studied. Based on the technical problems, with the goal of maximizing the smoothness of the beamforming channel in the MIMO orthogonal frequency division multiplexing (OFDM) system, a channel smoothing model is constructed, channel estimation constraints are considered, and the channel smoothing model is iteratively solved using a manifold optimization algorithm. Based on the obtained channel smoothing strategy for the beamforming channel, when OFDM is applied to a multiple-input multiple-output (MIMO) system for WiFi beamforming, the difference vector between adjacent subcarriers and the amplitude of each subcarrier can be effectively reduced, thereby mitigating the destructiveness of the corresponding beamforming channel and improving channel estimation and data packet accuracy. Furthermore, the manifold optimization algorithm employed can effectively avoid the calculation of the Hessian matrix during the solution of the channel smoothing model, thereby improving computational efficiency and reducing resource waste.

[0135] Example 2:

[0136] Based on the method steps in Example 1, corresponding experimental data are provided for illustration, as follows:

[0137] In the simulation, the latest 802.11ax standard was considered for MIMO. The simulation bandwidth was 80 MHz, consisting of 242 active subcarriers. There were four transmit antennas and four receive antennas, for a total of four space-time streams. The APEP length was 2000 bytes. MCS7 (64QAM, binary convolutional coding (BCC) with a coding rate of 5 / 6) was used. Binary convolutional coding was employed. The delay model was Model-D. There was no large-scale fading effect on the channel output, and the channel output was not normalized. The transmit and receive distance was 1 meter. Three schemes were evaluated.

[0138] aNormal: The transmitter uses unsmoothed beamforming vectors, and the receiver does not perform channel smoothing.

[0139] Test b: The transmitter uses the smoothed beamforming vectors obtained by the closed-form solution, and the receiver applies channel smoothing.

[0140] c-manifold: The transmitter uses the smoothed beamforming vector as shown in Algorithm 1, and the receiver applies channel smoothing.

[0141] See also Figure 2 , which shows that as the number of iterations increases, the cost value (f(Q i The three lines in the figure represent the iterative convergence of the manifold optimization algorithm at different signal-to-noise ratios (SNRs). As can be seen, the manifold optimization algorithm converges to approximately -1300 after approximately 20 iterations, while the value before manifold optimization was approximately -1180. Therefore, it can be concluded that manifold optimization brings an improvement of approximately 120.

[0142] Figure 3 and Figure 4 The bit error rate (PER) performance is shown. Figure 3 For MCS7, the manifold optimization-based solution proposed in this invention achieves a gain of approximately 1.8 dB compared to the traditional solution. For comparison, the manifold optimization solution in this experiment also achieved a gain of approximately 0.3 dB compared to the traditional method. This is because the objective function proposed in this invention more comprehensively considers smoothing across all subcarriers, rather than focusing solely on the unsmoothed performance between adjacent subcarriers.

[0143] In order to verify the applicability of the proposed method, the present invention tests the performance under different receiving antennas and data stream numbers. Figure 2 The case of 4 transmit antennas, 4 receive antennas and 4 data streams is shown in Figure 3 The case of 2 transmit antennas, 2 receive antennas and 2 data streams is shown. Figure 3 In the figure, we can see that the advantages of the proposed method are more significant. The scheme using manifold optimization achieves a gain of about 8dB compared to the traditional scheme, and a gain of 6dB compared to the method in the traditional method.

[0144] Example 3:

[0145] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein when the processor executes the computer program, steps of a channel smoothing method based on manifold optimization are implemented.

[0146] Example 4:

[0147] This embodiment provides a computer-readable storage medium storing a computer program. The computer program is executed by a processor to implement steps of a channel smoothing method based on manifold optimization.

[0148] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention's description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A channel smoothing method based on manifold optimization, characterized in that: The method comprises the following steps: Build a multiple-input multiple-output orthogonal frequency division multiplexing system, including: N receive antennas, M transmit antennas and K subcarriers; Based on a MIMO OFDM system, a channel smoothing model is constructed with the goal of maximizing the smoothness of the beamforming channel in the MIMO OFDM system and considering the channel estimation constraints. The manifold optimization algorithm is used to solve the channel smoothing model and obtain the channel smoothing strategy of the beamforming channel.

2. The channel smoothing method based on manifold optimization according to claim 1, characterized in that Based on the MIMO OFDM system, the channel estimation constraint on the i-th subcarrier is set as follows: Use FIR filter to constrain channel estimation Perform channel smoothing to obtain channel estimation And estimate the channel Perform singular value decomposition, the expression is: Among them, H i ∈C M×N represents the channel of the MIMO OFDM system, Z i ∈C M×N represents additive noise, V i ∈C M×N represents the right singular value vector, U i represents the left singular vector matrix, Λ i represents the singular value matrix, Represents the right singular value vector after singular value decomposition on the channel.

3. The channel smoothing method based on manifold optimization according to claim 2, characterized in that: Based on channel estimation constraints and the right singular value vector V i , and minimize the front and back right singular value vector V on the channel i The distance between them is used to maximize the smoothness of the beamforming channel in the MIMO OFDM system and to construct a channel smoothing model, which is expressed as: Among them, Q i ∈C N×M represents the vector to be solved, represents the identity matrix, represents a unitary matrix constraint.

4. The channel smoothing method based on manifold optimization according to claim 3, characterized in that: The channel smoothing model is simplified by using matrix norm expansion and trace operation simplification method, and the expression is: Among them, Q i ∈C N×M Represents the vector to be solved, Tr(*) represents the trace operation of the matrix, R i Equal to V i+1 H V i , V i ∈C M×N represents the right singular value vector after singular value decomposition, Represents the identity matrix.

5. The channel smoothing method based on manifold optimization according to claim 4, characterized in that: The process of solving the channel smoothing model using the manifold optimization algorithm includes: The objective function of the channel smoothing model is simplified to an unconstrained optimization form on the Riemannian manifold; An iterative optimization method based on the Barzilai-Borwein algorithm is used, combined with a gradient descent strategy, to transform the objective function in the unconstrained optimization form into a least squares problem. Solving the least squares problem to obtain a Riemann BB step length, and calculating a signal vector received on the manifold based on the Riemann BB step length; The simplified channel smoothing model is derived according to the received signal to calculate a piecewise function of the gradient in the Euclidean space, and a smoothed beamforming vector is reconstructed based on the piecewise function.

6. The channel smoothing method based on manifold optimization according to claim 5, characterized in that: The objective function of the channel smoothing model is simplified to an unconstrained optimization form on the Riemann manifold as follows: Among them, f(Q i ) represents the cost value in the channel smoothing model; the smaller the cost value, the greater the smoothness.

7. The channel smoothing method based on manifold optimization according to claim 6, characterized in that: The objective function of the unconstrained optimization form is transformed into a least squares problem, which is expressed as: min t ||s k t-y k ||2 The least squares problem is solved to obtain the Riemann BB step length, which is expressed as: Based on the Riemann BB step length, the update vector on the Riemann manifold is calculated as follows: Based on the update vector on the Riemann manifold, the signal vector received on the manifold is calculated, and the expression is: in, represents the vector transport operator on the Riemannian manifold, η k Indicates the current point x k The optimized direction vector at g. k Indicates the current point x k The gradient vector of represents the update vector s k The transpose of .

8. The channel smoothing method based on manifold optimization according to claim 7, characterized in that: The simplified channel smoothing model is differentiated according to the received signal to calculate the piecewise function of the gradient in Euclidean space, which is expressed as: The smoothed beamforming vector is reconstructed based on the piecewise function, and the expression is: Where sub represents the number of subcarriers, Q i ∈C N×M Represents the vector to be solved, R i Equal to V i+1 H V i , V i ∈C M×N represents the right singular value vector after singular value decomposition, represents the optimal rotation matrix obtained by solving.

9. A computer device, characterized in that: The method comprises a memory, a processor, and a computer program stored in the memory and running on the processor, wherein when the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and the computer program is executed by a processor to implement the steps of the method according to any one of claims 1 to 8.

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