Off-network channel estimation method and device based on backtracking momentum gradient descent
By introducing the momentum term and damping parameter mechanism of the backtracking momentum gradient descent algorithm, combined with Armijo backtracking line search, the channel estimation difficulty caused by multipath propagation effect in underwater acoustic communication is solved, the channel estimation accuracy and iteration efficiency are improved, the hardware processing latency and energy consumption are reduced, and the reliability of the underwater acoustic communication system is enhanced.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-22
- Publication Date
- 2026-03-24
AI Technical Summary
In existing underwater acoustic communication, frequency-selective fading caused by multipath propagation makes symbol recovery difficult. Traditional sparse channel estimation algorithms conflict with the parallel characteristics of hardware architecture in the case of scarce computing resources on underwater platforms. Furthermore, gradient descent algorithms have slow convergence speed and severe oscillation in high-dimensional optimization problems, which limits the accuracy and efficiency of channel estimation.
An off-network channel estimation method based on backtracking momentum gradient descent is adopted. A momentum term acceleration mechanism and a parameter update mechanism similar to the damped Hamiltonian differential equation are introduced. Combined with the Armijo backtracking line search method, the step size and damping parameters in the gradient descent are adaptively updated to improve the iteration convergence speed and robustness.
It significantly improves channel estimation accuracy and iteration convergence speed, reduces hardware processing latency and energy consumption, and enhances the communication reliability of underwater acoustic communication systems.
Smart Images
Figure CN121727901A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to an off-network channel estimation method and device based on backtracking momentum gradient descent, which has high channel estimation accuracy and high off-network optimization efficiency, and belongs to the field of underwater acoustic communication technology. Background Technology
[0002] As one of the most fundamental technologies for connecting heterogeneous underwater devices, the immaturity of underwater acoustic communication technology has constrained the development of underwater IoT-related technologies such as cooperative positioning, target tracking, and data collection. One of the main challenges facing underwater acoustic communication is the severe multipath propagation effect, which causes frequency-selective fading of multi-carrier communication signals at the receiving end, resulting in difficulties in symbol recovery.
[0003] In the Orthogonal Frequency Division Multiplexing (OFDM) framework, to address severe multipath propagation effects, it is essential to acquire underwater channel state information to balance frequency-selective fading in the received signal. Therefore, accurate channel estimation is crucial for communication between underwater IoT nodes. Since underwater acoustic channels are typically sparse, compressed sensing algorithms are widely used for underwater acoustic channel estimation. Orthogonal Matching Pursuit (OMP), a commonly used compressed sensing-based channel estimation algorithm, estimates underwater acoustic channels under the assumption that multipath delays are confined to a fixed-interval discrete time-delay grid. However, the actual multipath delay distribution is continuous, and this difference leads to significant off-grid delay estimation errors in traditional sparse channel estimation algorithms. Therefore, to reduce off-grid errors and improve channel estimation accuracy, off-grid channel estimation has become one of the core research topics in underwater acoustic communication. Given the limited computational resources of underwater platforms, off-grid channel estimation methods must meet the system's requirements for low complexity and high real-time performance. Among existing off-grid channel estimation algorithms based on orthogonal matching pursuit, gradient descent-based algorithms achieve higher estimation accuracy. However, when using gradient descent to solve optimization problems, this algorithm is prone to oscillations near local minima of the objective function, which hinders rapid convergence to local optima. Furthermore, due to changes in directional curvature in high-dimensional space, the convergence speed of this algorithm significantly slows down when dealing with high-dimensional optimization problems. This iterative computation mode inherently conflicts with the parallel capabilities of hardware architecture, significantly increasing hardware processing latency and energy consumption, thus limiting the practical application of this algorithm. Summary of the Invention
[0004] To address the shortcomings of existing technologies, this invention proposes an off-network channel estimation method and device based on backtracking momentum gradient descent. It introduces a momentum term acceleration mechanism and a parameter update mechanism that mimics the damped Hamiltonian differential equation to improve the iteration convergence speed. Furthermore, it adopts the Armijo backtracking line search method to adaptively update the step size and damping parameters in the accelerated gradient descent, thereby further accelerating convergence and enhancing the robustness of the iteration process.
[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:
[0006] An off-network channel estimation method based on backtracking momentum gradient descent includes the following steps:
[0007] S1. Obtain the transmit pilot symbol set and the receive pilot symbol set. Construct the transmit pilot symbol set into a diagonal matrix and calculate the frequency domain observation symbol after pilot normalization by least squares estimation.
[0008] S2. Set the number of pilot subcarriers, the total number of delay grid points, the delay oversampling factor and the pilot interval, determine the pilot subcarrier index set, calculate the delay value of each delay grid point, construct the corresponding dictionary atoms and dictionary matrix, initialize the residual to the frequency domain observation symbols obtained in step S1, and preset the channel sparsity.
[0009] S3. Calculate the correlation vector using the current residual and dictionary matrix, determine the index corresponding to the largest element in the correlation vector, update the grid dictionary matrix and grid time delay vector, calculate the orthogonal projection amplitude of the frequency domain observation symbol on the grid dictionary matrix, and update the residual.
[0010] S4. Count the number of times step S3 is executed. If the number of times reaches the preset channel sparsity, use the grid delay vector as the initial value for off-network channel delay optimization, initialize the step size hyperparameter, damping hyperparameter and speed parameter, and execute step S5; if it does not reach the preset channel sparsity, return to step S3.
[0011] S5. Calculate the intermediate variables for off-grid delay estimation, determine whether the step size hyperparameter satisfies the Armijo criterion, if not, shrink the step size until it does, and adjust the damping hyperparameter synchronously; calculate the gradient of the objective function used for off-grid channel optimization based on the current off-grid delay estimate, update the velocity parameter using the gradient, and then update the off-grid delay estimate.
[0012] S6. Calculate the absolute difference between the offline delay parameters and the absolute difference between the objective function in the two iterations. If either of them is less than the preset threshold, the channel estimation result is obtained; otherwise, return to step S5 to continue the iteration.
[0013] Furthermore, in step S1, the diagonal matrix is constructed from the transmitted pilot symbols according to the diagonal elements, and the calculation relationship of the frequency domain observation symbols is: the frequency domain observation symbols are equal to the product of the inverse of the diagonal matrix and the received pilot symbols.
[0014] Further, in step S2, the initial element of the pilot subcarrier index set is a negative value equal to half the total number of subcarriers, and subsequent elements are generated by adding the pilot interval to the previous element, as shown below: , It is the pilot spacing. This refers to the number of active subcarriers, including data subcarriers and pilot subcarriers;
[0015] The time delay value at each time delay grid point is the ratio of the grid point index to the product of the time delay oversampling factor and the baseband sampling frequency, expressed as: , It is the oversampling factor of the delay. It is the first The delay value of each delay grid point This refers to the baseband sampling frequency.
[0016] The dictionary matrix is formed by concatenating dictionary atoms column by column. Each dictionary atom represents the frequency response of the time delay value at each time delay grid point on the pilot subcarrier, expressed as:
[0017] ;
[0018] It is the first in the dictionary matrix. One atom, representing time delay. Frequency response on pilot subcarriers, This is the total number of grid points for the delay.
[0019] Furthermore, in step S3, the relevant vector is calculated by multiplying the conjugate transpose of the dictionary matrix with the residual, and is expressed as: , The residual in the current iteration, It is a dictionary matrix;
[0020] pass Determine the index of the largest element in the relevant vector and update the grid dictionary matrix composed of the selected atoms. Update the grid delay vector composed of the estimated delays. ;
[0021] The orthogonal projection amplitude is calculated by multiplying the pseudo-inverse of the grid dictionary matrix with the frequency domain observation symbol, and is expressed as: , For frequency domain observation symbols, The pseudo-inverse of the grid dictionary matrix composed of selected atoms;
[0022] The update relation for the residuals is: the updated residuals equal the frequency domain observation symbols minus the product of the grid dictionary matrix and the orthogonal projection amplitude, expressed as: .
[0023] Furthermore, in step S4, the initial value of the damping hyperparameter is the ratio of 1.2 to the step size hyperparameter; the velocity parameter is initialized as a zero vector consistent with the preset channel sparsity dimension.
[0024] Further, in step S5, the intermediate variable for off-network delay estimation is calculated by summing the products of the initial value of the off-network channel delay, the speed parameter, and half of the step size hyperparameter, and is expressed as: ; This is the initial value of the off-network channel delay. For speed parameters, This refers to the step size hyperparameter.
[0025] Step size shrinkage is achieved by multiplying the current step size hyperparameter by a constant in the interval (0,1);
[0026] The objective function used for off-network channel optimization is the negative of the absolute value of the product of the conjugate transpose of the frequency domain observation symbol, the projection matrix, and the frequency domain observation symbol. The projection matrix is composed of the product of the matrix consisting of the dictionary atoms corresponding to the current off-network channel delay and its pseudo-inverse, and is expressed as: , , This represents a matrix composed of dictionary atoms corresponding to the current off-network channel delay. For frequency domain observation symbols;
[0027] The formula for updating the velocity parameter is: , For damping hyperparameters, This is the current estimated offline latency. The gradient of the corresponding objective function;
[0028] The formula for updating the offline latency estimation is: .
[0029] Further, in step S6, the preset threshold condition is: the average value of the difference in the offline delay parameter is less than the preset delay threshold, or the absolute value of the difference in the objective function is less than the preset objective function threshold;
[0030] The channel estimation result is the product of the dictionary matrix corresponding to the off-network optimized delay and the product of the pseudo-inverse of the matrix and the frequency domain observation symbol.
[0031] The present invention also provides an electronic device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the off-network channel estimation method based on backtracking momentum gradient descent as described above.
[0032] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the off-network channel estimation method based on backtracking momentum gradient descent as described above.
[0033] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the off-network channel estimation method based on backtracking momentum gradient descent as described above.
[0034] Beneficial effects: The present invention has significant advantages in channel estimation performance: (1) The present invention significantly improves the channel estimation accuracy of the orthogonal matching pursuit (OMP) algorithm through off-network channel optimization; (2) The present invention utilizes the momentum term acceleration mechanism of the backtracking momentum gradient descent (AGD) algorithm and the parameter update mechanism that imitates the damped Hamiltonian differential equation to significantly improve the iteration convergence speed and hyperparameter robustness of the algorithm; (3) The present invention adopts the Armijo backtracking line search method to adaptively update the step size and damping parameters in the accelerated gradient descent, further accelerating convergence and enhancing the robustness of the iteration process; (4) The present invention obtains high-precision channel information for channel equalization, which can significantly enhance the communication reliability of the underwater acoustic communication system, while reducing the hardware processing delay and energy consumption of the communication system. Attached Figure Description
[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments are briefly introduced below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort, wherein:
[0036] Figure 1 This is a flowchart of the method of the present invention;
[0037] Figure 2 It is a performance comparison of different channel estimation methods under the condition that the multipath delay is strictly aligned with the baseband delay grid, at different signal-to-noise ratios;
[0038] Figure 3 It compares the performance of different channel estimation methods under different signal-to-noise ratios, provided that the multipath delay is uniformly distributed within the constraints.
[0039] Figure 4 This refers to the change of the objective function value of different channel estimation methods with the number of iterations;
[0040] Figure 5 This is a performance comparison of different channel estimation methods under different signal-to-noise ratios when the number of iterations is fixed at 5.
[0041] Figure 6 This is a comparison of experimental communication performance of different array elements and different channel estimation methods (the dashed lines in the figure represent the average results of each channel estimation method on all array elements).
[0042] Figure 7 This is a comparison of the number of experimental iterations and convergence times for different array elements and different channel estimation methods (the dashed lines in the figure represent the average results of each channel estimation method on all array elements). Detailed Implementation
[0043] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to specific embodiments and accompanying drawings.
[0044] Figure 1 The flowchart of the off-network channel estimation method based on backtracking momentum gradient descent proposed in this invention is shown below. Figure 1 The method includes the following steps:
[0045] (1) Pilot normalization: using transmitted pilot symbols With the received pilot symbol The frequency domain observation symbols after pilot normalization are obtained through least squares estimation. ,in A diagonal matrix consisting of transmitted pilot symbols. For pilot subcarrier index set, It is the pilot spacing. It is the number of active subcarriers (including data subcarriers and pilot subcarriers). It is an element in the pilot subcarrier index set;
[0046] (2) Initialization of trellis channel estimation: Construct the dictionary matrix:
[0047]
[0048] Among them, pilot subcarrier index set , It is the pilot spacing. This is the number of pilot subcarriers, which is equal to the number of elements in the pilot subcarrier index set. It is an element in the pilot subcarrier index set. It is the data subcarrier frequency interval. It is the total number of grid points with delay, the first one. The delay value of each delay grid point , It is the oversampling factor of the delay. The baseband sampling frequency for the received signal. It is the first in the dictionary matrix. One atom, representing time delay. Frequency response on pilot subcarrier, initial residual The preset channel sparsity is .
[0049] (3) OMP grid channel estimation: using the residuals in the current iteration With dictionary matrix Calculate the correlation vector Search for the index with the highest relevance value. ,in, It is the time-delay grid point index; update the grid dictionary matrix composed of selected atoms. Update the grid delay vector composed of the estimated delays. ; Calculate frequency domain observation symbols Orthogonal projection amplitude on selected atoms Update # The residual of the next iteration .
[0050] (4) Determine whether the number of iterations has reached the preset channel sparsity. If the initial value of the off-network channel delay optimization in step (5) is reached, then let it be... Initialize step size hyperparameters With damping hyperparameter Initialize speed parameters If the iteration continues, proceed to step (5); otherwise, return to step (3) and continue iterating.
[0051] (5) AGD Off-Network Channel Optimization and Armijo Backtracking Search Hyperparameter Update: Calculating the first Intermediate variables for estimating offline delay in the second iteration Determine if the step size hyperparameter satisfies the Armijo criterion at this point. If it does, maintain the first... Next iteration step size If the condition is not met, then a constant is used. Shrink the step size, so that Repeat this process until the Armijo criterion is satisfied, and then set the damping hyperparameter. Changes with step size; Update the first The velocity parameter of the next iteration The objective function for off-network channel optimization is... , , This represents a matrix composed of atoms corresponding to the current off-network channel delay. The gradient is calculated based on the objective function used for off-network channel optimization, which is essentially calculating the gradient of the objective function based on the intermediate variables of the off-network delay estimation. For the first The gradient of the objective function corresponding to the intermediate variable of the off-grid delay estimation in the next iteration is updated; Offline delay estimation in the next iteration .
[0052] (6) Determine the first Next and first Does the offline delay parameter and the objective function in the next iteration satisfy the iteration termination condition? or In other words, whether the average value of the offline latency parameter difference is less than the preset latency threshold. Or whether the absolute value of the difference in the objective function is less than the preset objective function threshold. If the conditions are met, then calculate the channel estimation result. The orthogonal projection amplitude Otherwise, return to step (5) to continue iterative optimization.
[0053] In this invention, updating the off-grid delay estimate via velocity parameters is equivalent to indirectly driving the delay towards a local optimum through gradient descent. Simultaneously, when the iterative optimization direction is consistent with the previous iteration, the velocity parameters accelerate the movement of the iteration point towards the optimum. When the iteration direction changes, the velocity parameters smooth out potential oscillations during iteration, thereby accelerating the iterative convergence speed of the optimization method. Thus, the velocity parameters reflect the role of momentum. This invention borrows the momentum term acceleration mechanism from the backtracking momentum gradient descent algorithm and the parameter update mechanism mimicking the damped Hamiltonian differential equation, significantly improving the algorithm's iterative convergence speed and hyperparameter robustness.
[0054] The performance simulation evaluation was carried out according to the above process. The system parameters are: bandwidth 1 kHz, carrier frequency 6.5 kHz, sampling rate 48 kHz, total number of subcarriers 512, polar code rate 1 / 2, symbol modulation mode 4QAM, and number of OFDM symbols 20.
[0055] Figure 2 Images (a) and (b) show the channel estimation normalized mean square error (NMSE) and bit error rate (BER) evaluation results for different channel estimation methods, respectively. A total of seven methods are compared:
[0056] 1) Standard OMP Algorithm
[0057] 2) Oversampling factor Oversampling OMP algorithm
[0058] 3) AGD-Armijo(MP) algorithm optimized using Armijo backtracking search
[0059] 4) The OMP algorithm using Wan interpolation (Wan)
[0060] 5) OMP algorithm optimized using fixed-parameter gradient descent (GD) (GD-Fixed)
[0061] 6) The OMP algorithm optimized by GD (GD-Armijo) is searched using Armijo backtracking.
[0062] 7) The OMP algorithm optimized by Armijo backtracking search AGD (AGD-Armijo) (the method of this invention)
[0063] Except for the oversampling algorithm, the oversampling factor of all other methods is uniformly set to 1. To meet the requirements of the Wan interpolation method ( Consider a multipath channel model with a sparsity of 3 and a maximum delay spread of approximately 9 ms. The multipath delay is strictly aligned with the baseband delay grid, and it is assumed that there is no relative motion between the transmitter and receiver, or that ideal Doppler compensation has been completed before channel estimation.
[0064] Because the multipath delay is strictly aligned with the baseband delay grid, the standard OMP algorithm can achieve zero off-network error without additional off-network optimization. Three negative gradient-based OMP off-network channel estimation algorithms (GD-Fixed, GD-Armijo, and AGD-Armijo (the method of this invention)) achieve high channel estimation accuracy by minimizing the objective function through off-network optimization. Therefore, the OMP algorithm and the negative gradient OMP off-network channel estimation algorithm show nearly identical performance in channel estimation NMSE and bit error rate. The Wan algorithm's channel estimation NMSE and BER performance are slightly worse than the standard OMP and negative gradient OMP off-network channel estimation algorithms. This performance gap stems from noise altering the inner product peak shape, leading to a decrease in the fitting degree of the interpolation formula in the Wan algorithm. The AGD-Armijo(MP) algorithm exhibits the worst NMSE performance because the off-network atoms lack orthogonality, and each iteration only adjusts the amplitude of a single path, introducing estimation error. However, due to its off-network optimization characteristics, the delay estimation error of AGD-Armijo(MP) is smaller than that of the oversampling algorithm. Compared to path amplitude estimation error, delay estimation error has a more significant impact on the phase of data symbols after channel equalization, leading to a higher BER. Therefore, although the oversampling algorithm has better NMSE performance than the AGD-Armijo(MP) algorithm, its bit error rate performance is actually worse.
[0065] exist Figure 3 In this study, an off-network delay offset is introduced based on a typical multipath channel to establish a random multipath channel model with controllable off-network effect. The off-network delay offset follows a uniform distribution within a preset maximum threshold. Figure 3 Figures (a) and (b) show the channel estimation NMSE and BER evaluation results for different channel estimation methods. Except for the multipath delay setting method, other conditions are the same. Figure 2 The results are identical. Under these conditions, the channel estimation NMSE and BER performance rankings of all methods remain consistent. These two performance metrics primarily depend on the accuracy of off-grid delay estimation. The standard OMP algorithm, due to its strict grid estimation and large grid spacing, performs the worst. The three negative gradient-based OMP-OGCE algorithms exhibit nearly consistent performance and are the best among all algorithms. Of the remaining three methods, the Wan algorithm performs the worst due to the largest off-grid delay error. The AGD-Armijo(MP) algorithm is affected by both off-grid delay error and amplitude error, and its performance falls between that of the Wan algorithm and the oversampling algorithm. The oversampling algorithm achieves the best performance due to its relatively small off-grid delay error and amplitude error.
[0066] Figure 4 The changes in the objective function values of three negative gradient methods with the number of iterations are shown to evaluate the convergence speed of each method. A multipath channel model with a sparsity of 3 is considered, in which the multipath delay is randomly distributed within the constraints, with a maximum delay spread of approximately 11 ms. It is assumed that there is no relative motion between the transmitter and receiver or that ideal Doppler compensation has been completed before channel estimation.
[0067] The GD-Fixed algorithm has the slowest convergence speed because its step size needs to be set to a small value to avoid continuous oscillation near the critical point, resulting in limited progress towards convergence in each iteration. The GD-Armijo algorithm exhibits better performance than GD-Fixed. Its step size update mechanism allows for a larger initial step size and adaptive adjustment, resulting in faster convergence. The average number of iterations required to meet the convergence condition is 14.85. The AGD-Armijo algorithm (the method of this invention) exhibits the best performance. Under the same step size update rule, AGD has a faster convergence speed than GD. The average number of iterations required to meet the convergence condition is 7.02, a reduction of 52.7% compared to the GD-Armijo algorithm.
[0068] Figure 5Figures (a) and (b) show the NMSE and BER evaluation results of different channel estimation methods under different signal-to-noise ratios when the number of iterations is fixed at 5. The GD-Fixed algorithm exhibits the worst channel estimation accuracy and bit error rate performance because its off-network optimization fails to meet the convergence condition, resulting in significant off-network error. The GD-Armijo algorithm achieves a significant performance improvement over GD-Fixed. The AGD-Armijo algorithm significantly outperforms both GD-Fixed and GD-Armijo algorithms. This result corroborates the convergence speed evaluation conclusion at the 5th iteration, proving that the AGD-Armijo algorithm has better estimation efficiency.
[0069] Experimental data verification:
[0070] In February 2025, a channel measurement experiment was conducted in the Songhua Lake area of Jilin Province. The water depth was 52 meters. The transmitter used a single sound source deployed at a depth of 13.3 meters, and the receiver was a 24-element vertical acoustic barometric hydrophone array with the top element at a depth of 12 meters. The communication distance was 4.4 kilometers. Both the transmitter and receiver positions were fixed. The system parameters were: bandwidth 1 kHz, carrier frequency 5.5 kHz, sampling rate 48 kHz, total number of subcarriers 512, polar code rate 1 / 2, symbol modulation scheme 4QAM, and number of OFDM symbols 20.
[0071] Figure 6 The performance comparison results of the standard OMP algorithm, GD-Armijo algorithm, and AGD-Armijo algorithm (the method of this invention) are presented for different array elements. Figure 6 In the diagram, (a) represents the received signal-to-noise ratio (SNR), (b) represents the channel estimation non-MSE (NMSE), (c) represents the BER before decoding, and (d) represents the BER after decoding. The oversampling factor for all methods is uniformly set to... When the estimated path amplitude is less than The iteration terminates when the time is right.
[0072] The difference in channel estimation NMSE between different array elements stems from the difference in received signal-to-noise ratio. For example... Figure 6 As shown in (a), the channel estimation NMSE and the received signal-to-noise ratio are both negatively correlated. Figure 6 (b) shows that, on all array elements, the channel estimation NMSE of the OMP off-network channel estimation algorithm (GD-Armijo algorithm, AGD-Armijo algorithm (the method of this invention)) is consistently lower than that of the standard OMP algorithm, which proves that the OMP off-network channel estimation algorithm has better channel estimation accuracy. Figure 6(c) shows that the OMP off-network channel estimation algorithm achieves better pre-decoding BER performance in most array element channels. However, due to the large array aperture and the differences in channel structure between different array elements, the performance gap between the standard OMP and OMP off-network channel estimation algorithms narrows on some array elements, and the bit error rate of the OMP off-network channel estimation algorithm is even slightly higher than that of the standard OMP in some array elements. After channel decoding, as shown in (c), Figure 6 As shown in (d), the OMP off-network channel estimation algorithm still maintains better BER performance in most channels.
[0073] Figure 7 The paper presents a comparison of the number of iterations required for the GD-Armijo algorithm and the AGD-Armijo algorithm (the method of this invention) across different array elements. The AGD-Armijo algorithm (the method of this invention) requires fewer iterations than the GD-Armijo algorithm to converge on all array elements, demonstrating the advantage of the AGD-Armijo algorithm in estimation efficiency.
[0074] The above results show that the method proposed in this embodiment has higher channel estimation accuracy and higher estimation efficiency than various channel estimation algorithms, proving its effectiveness and engineering application value in underwater acoustic communication systems.
[0075] The present invention also provides an electronic device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the off-network channel estimation method based on backtracking momentum gradient descent as described above.
[0076] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the off-network channel estimation method based on backtracking momentum gradient descent as described above.
[0077] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the off-network channel estimation method based on backtracking momentum gradient descent as described above.
[0078] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus (systems), electronic devices, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0079] This invention is described with reference to a flowchart of a method according to embodiments of the invention. It should be understood that each step in the flowchart and combinations thereof can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate instructions for implementing the process. Figure 1 A device for performing a specified function in one or more processes. The processor involved in each embodiment may be a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic device, a quantum computing-based data processing logic device, an artificial intelligence processor, etc., and is not limited thereto.
[0080] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 The function specified in one or more processes.
[0081] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 Steps of a specified function in one or more processes.
Claims
1. An off-network channel estimation method based on backtracking momentum gradient descent, characterized in that, Includes the following steps: S1. Obtain the transmit pilot symbol set and the receive pilot symbol set. Construct the transmit pilot symbol set into a diagonal matrix and calculate the frequency domain observation symbol after pilot normalization by least squares estimation. S2. Set the number of pilot subcarriers, the total number of delay grid points, the delay oversampling factor and the pilot interval, determine the pilot subcarrier index set, calculate the delay value of each delay grid point, construct the corresponding dictionary atoms and dictionary matrix, initialize the residual to the frequency domain observation symbols obtained in step S1, and preset the channel sparsity. S3. Calculate the correlation vector using the current residual and dictionary matrix, determine the index corresponding to the largest element in the correlation vector, update the grid dictionary matrix and grid time delay vector, calculate the orthogonal projection amplitude of the frequency domain observation symbol on the grid dictionary matrix, and update the residual. S4. Count the number of times step S3 is executed. If the number of times reaches the preset channel sparsity, use the grid delay vector as the initial value for off-network channel delay optimization, initialize the step size hyperparameter, damping hyperparameter and speed parameter, and execute step S5; if it does not reach the preset channel sparsity, return to step S3. S5. Calculate the intermediate variables for off-grid delay estimation, determine whether the step size hyperparameter satisfies the Armijo criterion, and if not, shrink the step size until it does, and adjust the damping hyperparameter synchronously. The gradient of the objective function used for off-network channel optimization is calculated based on the current off-network delay estimate. The speed parameter is then updated using the gradient, and the off-network delay estimate is updated accordingly. S6. Calculate the absolute difference between the offline delay parameters and the absolute difference between the objective function in the two iterations. If either of them is less than the preset threshold, the channel estimation result is obtained; otherwise, return to step S5 to continue the iteration.
2. The method according to claim 1, characterized in that, In step S1, the diagonal matrix is constructed from the transmitted pilot symbols along the diagonal elements. The calculation relationship of the frequency domain observation symbols is: the frequency domain observation symbols are equal to the product of the inverse of the diagonal matrix and the received pilot symbols.
3. The method according to claim 1, characterized in that, In step S2, the initial element of the pilot subcarrier index set is a negative value equal to half the total number of subcarriers, and subsequent elements are generated by adding the pilot interval to the previous element, as shown below: , It is the pilot spacing. This refers to the number of active subcarriers, including data subcarriers and pilot subcarriers; The time delay value at each time delay grid point is the ratio of the grid point index to the product of the time delay oversampling factor and the baseband sampling frequency, expressed as: , It is the oversampling factor of the delay. It is the first The delay value of each delay grid point This refers to the baseband sampling frequency. The dictionary matrix is formed by concatenating dictionary atoms column by column. Each dictionary atom represents the frequency response of the time delay value at each time delay grid point on the pilot subcarrier, expressed as: ； It is the first in the dictionary matrix. One atom, representing time delay. Frequency response on pilot subcarriers, This is the total number of grid points for the delay.
4. The method according to claim 3, characterized in that, In step S3, the relevant vector is calculated by multiplying the conjugate transpose of the dictionary matrix with the residual, and is expressed as: , The residual in the current iteration, It is a dictionary matrix; pass Determine the index of the largest element in the relevant vector and update the grid dictionary matrix composed of the selected atoms. Update the grid delay vector composed of the estimated delays. ; The orthogonal projection amplitude is calculated by multiplying the pseudo-inverse of the grid dictionary matrix with the frequency domain observation symbol, and is expressed as: , For frequency domain observation symbols, The pseudo-inverse of the grid dictionary matrix composed of selected atoms; The update relation for the residuals is: the updated residuals equal the frequency domain observation symbols minus the product of the grid dictionary matrix and the orthogonal projection amplitude, expressed as: .
5. The method according to claim 1, characterized in that, In step S4, the initial value of the damping hyperparameter is the ratio of 1.2 to the step size hyperparameter; the velocity parameter is initialized as a zero vector consistent with the preset channel sparsity dimension.
6. The method according to claim 1, characterized in that, In step S5, the intermediate variable for off-network delay estimation is calculated by summing the products of the initial value of the off-network channel delay, the velocity parameter, and half of the step size hyperparameter, and is expressed as: ; This is the initial value of the off-network channel delay. For speed parameters, This refers to the step size hyperparameter. Step size shrinkage is achieved by multiplying the current step size hyperparameter by a constant in the interval (0,1); The objective function used for off-network channel optimization is the negative of the absolute value of the product of the conjugate transpose of the frequency domain observation symbol, the projection matrix, and the frequency domain observation symbol. The projection matrix is composed of the product of the matrix consisting of the dictionary atoms corresponding to the current off-network channel delay and its pseudo-inverse, and is expressed as: , , This represents a matrix composed of dictionary atoms corresponding to the current off-network channel delay. For frequency domain observation symbols; The formula for updating the velocity parameter is: , For damping hyperparameters, This is the current estimated offline latency. The gradient of the corresponding objective function; The formula for updating the offline latency estimation is: .
7. The method according to claim 1, characterized in that, In step S6, the preset threshold condition is: the average value of the difference between the offline delay parameters is less than the preset delay threshold, or the absolute value of the difference between the objective functions is less than the preset objective function threshold. The channel estimation result is the product of the dictionary matrix corresponding to the off-network optimized delay and the product of the pseudo-inverse of the matrix and the frequency domain observation symbol.
8. An electronic device, characterized in that, include: One or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the off-network channel estimation method based on backtracking momentum gradient descent as described in any one of claims 1-7.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the off-network channel estimation method based on backtracking momentum gradient descent as described in any one of claims 1-7.
10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the off-network channel estimation method based on backtracking momentum gradient descent as described in any one of claims 1-7.