ZP-OTFS channel estimation method based on depth expansion

Abstract

This paper discloses a ZP-OTFS channel estimation method based on deep unwrapping. The method comprises the following steps: generating a DD-domain signal based on the structure of a DD-domain transmitted data frame of a ZP-OTFS system; obtaining a transmitted time-domain signal through a Zak transform of the DD-domain signal, and transmitting the signal through a time-domain channel to obtain a discrete time-domain received signal; transforming the OTFS time-domain channel estimation problem into a sparse signal recovery problem based on the discrete time-domain received signal; and constructing a LISTA network to solve the sparse signal recovery problem and estimate the ZP-OTFS system channel. By constructing and training a learning network, the method achieves high-precision OTFS channel estimation. The proposed channel estimation method has lower channel estimation error than existing compressed sensing and deep learning methods.

Description

Technical Field

[0001] The present invention relates to the technical field of channel estimation, and in particular to a ZP-OTFS channel estimation method based on depth expansion. Background Art

[0002] Orthogonal Time Frequency Space (OTFS) modulation technology has received widespread attention for its excellent performance in high-speed scenarios. OTFS maps symbols into the delay-Doppler domain and spreads each symbol throughout the time-frequency space through a two-dimensional orthogonal function. Each symbol experiences the same time-frequency fading; the receiver's equalization algorithm obtains the same time-frequency diversity gain, thereby improving the reliability of wireless communication systems in high-speed scenarios. ZP-OTFS is a variant of the OTFS system that has the characteristic of inserting pilot symbols as padding according to a specific rule in the DD domain's transmitted symbol grid, and is applied to channel estimation. Pilot padding simplifies the relationship between DD domain input and output symbols, avoids inter-block interference of transmitted data in the time domain, and does not bring additional overhead to the OTFS system.

[0003] Accurate channel estimation is a prerequisite for stable reception at the receiver end of a ZP-OTFS system. Existing ZP-OTFS channel estimation methods mostly use zero-filled guard bands and traditional compressed sensing methods. These methods increase pilot overhead and are sensitive to parameters, resulting in inaccurate estimation results. To achieve better channel estimation performance, model-driven deep learning has recently demonstrated its potential in communication tasks. This approach combines performance-guaranteed algorithms with neural networks to ensure high performance. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology, take advantage of the sparsity of the ZP-OTFS channel and the deep unfolding network, apply the deep unfolding network to the ZP-OTFS system, and aim to further improve the channel estimation performance of the ZP-OTFS system. The specific technical solution is as follows:

[0005] The ZP-OTFS channel estimation method based on depth expansion includes the following steps:

[0006] Generate DD domain signals according to the structure of data frames sent in the DD domain of the ZP-OTFS system;

[0007] The DD domain signal is transformed into a time domain transmit signal through Zak transform, and then transmitted through the time domain channel to obtain a time domain discrete receive signal;

[0008] Based on the discrete received signal in time domain, the OTFS time domain channel estimation problem is transformed into a sparse signal recovery problem;

[0009] The LISTA network is constructed to solve the sparse signal recovery problem and complete the channel estimation of the ZP-OTFS system.

[0010] Furthermore, the calculation formula of the DD domain signal is:

[0011]

[0012] Where X represents the DD domain signal, X d and X p They represent the data signal and pilot signal in the DD domain, M and N are the delay and Doppler dimensions respectively.

[0013] Furthermore, the calculation formula of the time domain transmitted signal is:

[0014]

[0015] in, represents the time domain transmitted signal, and vec(·) represents matrix vectorization, X represents the DD domain signal, s d and s p represent the time domain data signal and pilot signal respectively, IDZT(·) represents the inverse discrete Fourier transform of the matrix, represents the discrete Fourier transform coefficients, represents the Kronecker product, I M represents the identity matrix;

[0016] is the time domain channel matrix, and the specific calculation formula is:

[0017]

[0018] Where, Q = (l max +1)(2k max +1), where l max and k max They represent the maximum delay and Doppler spread of the channel, h i is the channel coefficient of the i-th path, Π is the standard permutation matrix, Δ=diag(z 0 ,z 1 ,…,z MN-1 ) and z=e j2π / MN ;

[0019] The time-domain discrete received signal is obtained from the time-domain transmitted signal and the channel matrix. The specific calculation formula is:

[0020] r=Hs=[Φ1,Φ2,…,Φ Q h+w=Φh+w=Φ d h+Φ p h+w (4)

[0021] Where r represents the time domain received signal, represents the channel vector, represents the time domain signal matrix, Φ d and Φ p are the data and pilot signal matrices respectively, and w represents the channel noise.

[0022] Furthermore, the specific steps of converting the OTFS time domain channel estimation problem into a sparse signal recovery problem based on the time domain received signal are as follows:

[0023] The channel vector h is recovered from the received signal r using a sparse recovery method. The sparse recovery method uses a pilot received signal that is not interfered with by data to estimate h. The calculation formula for the pilot received signal in the time domain is:

[0024] r p,w =φ p,w h+w w (5)

[0025] in, represents the pilot received signal in the time domain that is not interfered by the data signal, represents the noise vector, represents the time domain pilot matrix;

[0026] Transform h into a channel estimation problem. The specific formula is:

[0027]

[0028] st||h||0<ε (7)

[0029] Among them, ε represents the 2 The relevant threshold parameter, ||·||, represents the norm;

[0030] because Norm constraint, transforming the channel estimation problem into a solvable form:

[0031]

[0032] Where ξ represents the regularization parameter.

[0033] Furthermore, the steps of constructing the LISTA network include: expanding each iteration process of the iterative shrinkage threshold algorithm into a deep neural network consisting of a fixed number of stages to construct the LISTA network.

[0034] Furthermore, the calculation formula of the iterative shrinkage threshold algorithm is:

[0035]

[0036] Among them, s η represents the soft shrinkage function, η represents the constant threshold, λ max Representation matrix The maximum eigenvalue of , I represents the identity matrix;

[0037] In a deep neural network, the formula for calculating the input-output relationship of the L-th layer neural network is:

[0038]

[0039] Among them, V a ,V b and Respectively and η are learning parameters;

[0040] In the LISTA network, the loss function is defined as The dataset is in, represents the real channel, and l represents the number of layers of the neural network.

[0041] According to another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored, characterized in that when the program is executed by a processor, the ZP-OTFS channel estimation method based on depth expansion of the present invention is implemented.

[0042] According to another aspect of the present invention, a computer device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the ZP-OTFS channel estimation method based on depth expansion of the present invention is implemented.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] 1. To simplify the implementation of the OTFS system, the present invention uses discrete Zak transform to optimize the structure of the OTFS system and implements the ZP-OTFS system through pilot padding in the delay-Doppler domain, which provides a convenient premise for channel estimation.

[0045] 2. In order to improve estimation accuracy and reduce computation time, the present invention proposes a deep unfolding network LISTA, which maps the iterations of the traditional iterative algorithm ISTA to several stages of a deep unfolding network with learnable parameters, thus having stronger adaptability and lower computation time. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments made with reference to the following drawings:

[0047] Figure 1 is a flow chart of the method of the present invention;

[0048] Figure 2 It is a deep unfolding network structure used for channel estimation of ZP-OTFS system in the present invention;

[0049] Figure 3 It is the convergence performance diagram of the LISTA algorithm proposed in the present invention;

[0050] Figure 4 This is a performance comparison chart of different algorithms of the present invention under different signal-to-noise ratio conditions. DETAILED DESCRIPTION

[0051] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0052] The following is a further detailed description of the embodiments of the present invention in conjunction with the accompanying drawings:

[0053] like Figure 1 As shown, the present invention includes the following steps:

[0054] The DD domain signal is generated based on the structure of the DD domain transmission data frame of the ZP-OTFS system, and the transmission time domain signal is obtained through Zak transform. Furthermore, the time domain reception signal is obtained by transmitting it through the time domain channel;

[0055] By utilizing the signal sparsity of OTFS in delay-Doppler domain, OTFS time-domain channel estimation is formulated as a sparse signal recovery problem.

[0056] The iterative process of the traditional compressed sensing algorithm is expanded into a deep neural network consisting of a fixed number of stages, and the LISTA network is constructed. This algorithm can be used to effectively and more accurately estimate the ZP-OTFS system channel.

[0057] According to the placement of data and pilot in the DD domain of the ZP-OTFS system, the DD domain transmission signal can be expressed as

[0058]

[0059] In the ZP-OTFS system, the back of the data matrix ZP Behavior 0, first Ml ZP In order to make full use of DD domain resources, the back of the pilot matrix ZP The rows contain pilot symbols, subject to distribution, while the rest of the lines are 0. The DD domain signal can be converted into a time domain signal through the inverse discrete Zak transform (IDZT). At the transmitter, the time domain transmission signal can be expressed as,

[0060]

[0061] in, and X is the ZP-OTFSDD domain signal.

[0062] like Figure 2 As shown, based on the received ZP-OTFS signal, the present invention designs a deep neural network consisting of a fixed number of layers, including:

[0063] According to the ZP-OTFS modulation and demodulation process, the time domain received signal is:

[0064] r=[Φ1,Φ2,…,Φ Q h+w=Φh+w=Φ d h+Φ p h+w (3)

[0065] in, represents the channel vector, is the time domain signal matrix. is the time domain channel matrix, which can be expressed as

[0066]

[0067] in, is the standard permutation matrix, is a diagonal Doppler matrix, and z = e j2π / (MN)

[0068] The channels in the OTFSDD domain are in, represents the channel coefficient, and Q=(l max +1)(2k max +1), where l max and k max Denote the maximum delay and Doppler of the channel, respectively. Let P be the number of channel paths in the DD domain. The sparsity of the OTFS channel is the ratio of P to Q. Using sparse recovery methods, the channel vector h can be recovered from the received signal r. Consider using a pilot signal that is not interfered with by data to estimate h. Therefore, the pilot signal can be rewritten as follows:

[0069]

[0070] in, represents the vector affected by the pilot, represents the noise vector, Represents the time domain pilot matrix. In the above estimation formula, h is a typical channel estimation (compressed sensing CS) problem, which can be expressed as

[0071]

[0072] st||h||0<ε (7)

[0073] where ε is given by 2 Related threshold parameters. Norm constraint, the above formula is non-convex, so it is converted into a solvable form as

[0074]

[0075] From the above analysis, we can see that the signal will be received from the low dimension of N×1 dimension The Q×1-dimensional high-dimensional channel h is recovered from the ZP-OTFS system, thus transforming the channel estimation problem of the ZP-OTFS system into a sparse signal recovery problem.

[0076] Iterative Shrinkage and Thresholding Algorithm ISTA is one of the common methods to solve the above problem. Through this method, the solution to the above problem can be expressed as

[0077]

[0078] Among them, s η is the soft contraction function in software, which can be expressed as [s η ] g =sign([h] g )(|[h] g |-η) + ,in,[·] g is the gth element of the vector; sign(·) represents the sign of the scalar; (·) + represents max(·,0); η is a constant threshold; λ max is a matrix The largest eigenvalue of ; I is the identity matrix.

[0079] The accuracy of the ISTA algorithm's recovery is affected by the initial value of η. To further improve channel estimation accuracy, we employ the Learned Iterative Shrinkage and Thresholding Algorithm (LISTA). This method uses a fixed number of iterations and overcomes the shortcomings of the ISTA algorithm by learning η from data. The key to the LISTA algorithm is to expand each iteration of ISTA into a neural network layer. The input-output relationship of the lth layer of the neural network can be expressed as:

[0080]

[0081] Figure 2 Represents the Lth layer of the LISTA algorithm neural network. The solid line in the figure represents forward propagation, and the dotted line represents backpropagation. The parameters of the LISTA algorithm are updated by backpropagating the gradient of the loss function, which is defined as The dataset is in For the real channel.

[0082] The ZP-OTFS channel estimation method based on LISTA is as follows:

[0083] Step 1: Initialize parameters: V a ,V b , Create a dataset

[0084] Step 2: From the dataset Get a set of data from

[0085] Step 3: Forward Propagation: Calculating the Neural Network The output of , and calculate the loss function

[0086] Step 4: Backpropagation: Update the parameters V using backpropagation a ,V b ,

[0087] Step 5: Repeat steps 2, 3, and 4 until convergence;

[0088] Output: trained neural network

[0089] Figure 3Figure 2 shows the convergence performance for different numbers of neural network layers. Our proposed LISTA-based ZP-OTFS channel estimation algorithm converges well, reaching convergence after 20 iterations. Furthermore, a greater number of neural network layers leads to faster convergence and a smaller mean square error (MSE) at convergence. Furthermore, there is a significant difference between different M and N. This is because larger OTFS frames increase the number of grid points in the DD domain, making the channel sparser and improving the estimation.

[0090] Figure 4 In this paper, the MSE performance of the model-based learning method LISTA proposed in this paper is compared with that of representative non-learning algorithms (including least squares method, OMP and ISTA). The number of iterations of LS, OMP and FISTA is 100. A neural network with 11 layers is used based on the LISTA and algorithm. Figure 4 As can be seen from the figure, the model-based algorithm outperforms existing methods such as LS, OMP, and FISTA, especially at low signal-to-noise ratios. Furthermore, to achieve good performance, the number of layers required in the unfolded network is typically much smaller than the number of iterations required by the iterative solver. Therefore, it can be concluded that LISTA achieves better performance with less computational effort compared to existing methods. This means that the LISTA-based algorithm further improves performance and reduces computational complexity.

[0091] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0092] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0093] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0094] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0095] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A ZP-OTFS channel estimation method based on depth expansion, characterized in that: The following steps are involved: Generate DD domain signals according to the structure of data frames sent in the DD domain of the ZP-OTFS system; The DD domain signal is transformed into a time domain transmit signal through Zak transform, and then transmitted through the time domain channel to obtain a time domain discrete receive signal; Based on the discrete received signal in time domain, the OTFS time domain channel estimation problem is transformed into a sparse signal recovery problem; Construct the LISTA network to solve the sparse signal recovery problem and complete the channel estimation of the ZP-OTFS system; The calculation formula of the time domain transmitted signal is: （2） in, represents the time domain transmitted signal, and , represents matrix vectorization, Indicates DD domain signal, represent the time domain data signal and pilot signal respectively, represents the inverse discrete Fourier transform of the matrix, represents the discrete Fourier transform coefficients, represents the Kronecker product represents the identity matrix; is the time domain channel matrix, and the specific calculation formula is: （3） in, ,in and They represent the maximum delay and Doppler spread of the channel, For the The channel coefficients of the paths, is the standard permutation matrix, and ; The time-domain discrete received signal is obtained from the time-domain transmitted signal and the channel matrix. The specific calculation formula is: （4） in, represents the time domain received signal, represents the channel vector, represents the time domain signal matrix, are the data and pilot signal matrices respectively, represents the channel noise; The specific steps of transforming the OTFS time domain channel estimation problem into a sparse signal recovery problem based on the time domain received signal are as follows: Using the sparse recovery method, the channel vector Receive signal from The sparse recovery method uses the pilot received signal that is not interfered by the data to estimate , the calculation formula of the pilot received signal in the time domain is: （5） in, represents the pilot received signal in the time domain that is not interfered by the data signal, represents the noise vector, represents the time domain pilot matrix; Will Transformed into a channel estimation problem, the specific formula is: （6） （7） in, Represents Related threshold parameters, represents the norm; because Norm constraint, transforming the channel estimation problem into a solvable form: （8） in, represents the regularization parameter.

2. The method according to claim 1, characterized in that The calculation formula for the DD domain signal is: （1） in, Indicates DD domain signal, They represent the data signal and pilot signal in the DD domain, M and N are the delay and Doppler dimensions respectively.

3. The method according to claim 1, characterized in that The steps of constructing the LISTA network include: expanding each iteration process of the iterative shrinkage threshold algorithm into a deep neural network consisting of a fixed number of stages to construct the LISTA network.

4. The method according to claim 3, characterized in that The calculation formula of the iterative shrinkage threshold algorithm is: （9） in, represents the soft shrinkage function, represents a constant threshold, Representation matrix The maximum eigenvalue of represents the identity matrix; In a deep neural network, the formula for calculating the input-output relationship of the L-th layer neural network is: (10) in, , Respectively , and The learning parameters of In the LISTA network, the loss function is defined as , the data set is ,in, represents the real channel, Indicates the number of layers of the neural network.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the ZP-OTFS channel estimation method based on depth expansion according to any one of claims 1 to 4 is implemented.

6. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the ZP-OTFS channel estimation method based on depth expansion according to any one of claims 1 to 4 is implemented.

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