Channel estimation method and device, equipment and storage medium

Abstract

The invention discloses a channel estimation method, device and equipment and a storage medium, and relates to the technical field of data processing, and the method comprises the steps: determining a solving interval of fractional Doppler frequency shift according to a signal feature corresponding to a received signal in a time delay Doppler frequency domain; performing gradient iterative optimization on the fractional Doppler frequency shift based on a preset optimization function and the solution interval to obtain a target fractional Doppler frequency shift; and estimating the amplitude and the phase deviation of the channel gain of each path according to the target fractional Doppler frequency shift, and determining the channel estimation result of each path. Gradient iteration optimization is performed on the fractional Doppler frequency shift through the preset optimization function, the fractional Doppler frequency shift is accurately solved, and the channel estimation precision is improved.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to channel estimation methods, apparatus, devices and storage media. Background Technology

[0002] Most existing algorithms for fractional-delay Doppler scenarios rely on virtual sampling, which involves dividing the Doppler domain into a finer grid and finding the maximum likelihood point as the estimation result. Virtual grids alone cannot achieve accuracy beyond the grid resolution. Although some improved methods attempt to overcome resolution limitations and reduce inter-path interference, their computational complexity is often high.

[0003] The above content is only used to help understand the technical solution of this application and does not represent an admission that the above content is prior art. Summary of the Invention

[0004] The main objective of this application is to provide a channel estimation method, apparatus, device, and storage medium, which aims to solve the technical problem that current algorithms for fractional delay Doppler scenarios rely on virtual sampling, and cannot achieve accuracy beyond the grid resolution using only virtual grids, resulting in low channel estimation accuracy.

[0005] To achieve the above objectives, this application proposes a channel estimation method, which includes:

[0006] The solution interval for the fractional Doppler frequency shift is determined based on the signal characteristics corresponding to the received signal in the time-delay Doppler frequency domain. Based on the preset optimization function and the solution interval, the fractional Doppler frequency shift is optimized by gradient iteration to obtain the target fractional Doppler frequency shift; The amplitude and phase shift of the channel gain for each path are estimated based on the target fractional Doppler frequency shift, and the channel estimation result for each path is determined.

[0007] In one embodiment, the signal features include peak features and phase features, and the step of determining the solution interval of the fractional Doppler frequency shift based on the signal features corresponding to the received signal in the time-delay Doppler frequency domain includes: The truncated observation signal is obtained by extracting the received signal in the time-delay Doppler frequency domain based on the preset embedded pilot signal; The solution interval for the fractional Doppler frequency shift is determined based on the peak and phase characteristics of the channel response vector of the observed signal on the time delay axis.

[0008] In one embodiment, the step of performing gradient iterative optimization of the fractional Doppler frequency shift based on a preset optimization function and the solution interval to obtain the target fractional Doppler frequency shift includes: Based on the solution interval, determine the initial estimate corresponding to the fractional Doppler frequency shift; Based on the initial estimate, the preset optimization function, and the preset adaptive step size adjustment strategy, the fractional Doppler frequency shift is iteratively optimized by gradient to obtain the target fractional Doppler frequency shift.

[0009] In one embodiment, the preset optimization function includes a first optimization function based on waveform amplitude cross-correlation, and the step of performing gradient iterative optimization of the fractional Doppler frequency shift based on the initial estimate, the preset optimization function, and a preset adaptive step size adjustment strategy to obtain the target fractional Doppler frequency shift includes: Starting from the initial estimate, calculate the gradient of the first optimization function with respect to the fractional Doppler frequency shift in the current iteration; Based on the sign of the gradient and the preset step size, the estimated value of the fractional Doppler frequency shift is updated. If the updated estimated value exceeds the solution range, or the sign of the gradient changes before and after the current iteration, the step size is halved based on the preset adaptive step size adjustment strategy, and the value is rolled back to the estimated value before the update. Repeat the above steps until the absolute value of the gradient is less than a preset threshold, or the number of iterations reaches the maximum number of iterations, to obtain the target fractional Doppler frequency shift; The formula for calculating the first optimization function is as follows: ; in, Indicates the inner product. It is the amplitude of the received signal y[k] in its general form.

[0010] In one embodiment, the preset optimization function further includes a second optimization function based on the residual. The step of performing gradient iterative optimization of the fractional Doppler frequency shift based on the initial estimate, the preset optimization function, and a preset adaptive step size adjustment strategy to obtain the target fractional Doppler frequency shift includes: Starting from the initial estimate, calculate the gradient of the second optimization function with respect to the fractional Doppler frequency shift in the current iteration; Based on the sign of the gradient and the preset step size, the estimated value of the fractional Doppler frequency shift is updated. If the updated estimated value exceeds the solution range, or the sign of the gradient changes before and after the current iteration, the step size is halved based on the preset adaptive step size adjustment strategy, and the value is rolled back to the estimated value before the update. Repeat the above steps until the absolute value of the gradient is less than a preset threshold, or the number of iterations reaches the maximum number of iterations, to obtain the target fractional Doppler frequency shift; The formula for calculating the second optimization function is as follows: ; in, This represents the second optimization function. It is the first The estimated magnitude of the path channel gain. It is the amplitude of the received signal y[k] in its general form. It is the pilot energy, and N represents the size in the Doppler domain.

[0011] In one embodiment, the step of estimating the magnitude and phase shift of the channel gain for each path based on the target fractional Doppler frequency shift and determining the channel estimation result for each path includes: The ideal channel response vector for each path is reconstructed based on the target fractional Doppler frequency shift; Based on the ideal channel response vector and the received signal, the amplitude and phase offset of the channel gain for each path are estimated, and the channel estimation result for each path is determined.

[0012] In one embodiment, the step of estimating the magnitude and phase shift of the channel gain for each path based on the ideal channel response vector and the received signal, and determining the channel estimation result for each path, includes: Energy normalization is performed based on the ideal channel response vector and the energy estimate corresponding to the received signal to estimate the magnitude of the channel gain for each path. The minimum mean square error is calculated for the ideal channel response vector and the received signal to estimate the phase shift of the channel gain for each path; The channel estimation result for each path is determined based on the amplitude and the phase offset.

[0013] Furthermore, to achieve the above objectives, this application also proposes a channel estimation apparatus, the channel estimation apparatus comprising: The solution interval determination module is used to determine the solution interval of the fractional Doppler frequency shift based on the signal characteristics corresponding to the received signal in the time delay Doppler frequency domain. The gradient iteration solution module is used to perform gradient iteration optimization of the fractional Doppler frequency shift based on a preset optimization function and the solution interval to obtain the target fractional Doppler frequency shift. The channel parameter estimation module is used to estimate the amplitude and phase shift of the channel gain for each path based on the target fractional Doppler frequency shift, and to determine the channel estimation result for each path.

[0014] In addition, to achieve the above objectives, this application also proposes a channel estimation device, the device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the channel estimation method as described above.

[0015] In addition, to achieve the above objectives, this application also proposes a storage medium, which is a computer-readable storage medium, on which a computer program is stored, and which, when executed by a processor, implements the steps of the channel estimation method described above.

[0016] One or more technical solutions proposed in this application have at least the following technical effects: This application determines the solution interval for the fractional Doppler frequency shift based on the signal characteristics corresponding to the received signal in the time-delay Doppler frequency domain; it performs gradient iterative optimization of the fractional Doppler frequency shift based on a preset optimization function and the solution interval to obtain the target fractional Doppler frequency shift; it estimates the amplitude and phase shift of the channel gain for each path based on the target fractional Doppler frequency shift and determines the channel estimation result for each path. Compared with the current algorithms for fractional time-delay Doppler scenarios that rely on virtual sampling, which cannot achieve accuracy beyond the grid resolution using only a virtual grid, resulting in low channel estimation accuracy, this application performs gradient iterative optimization of the fractional Doppler frequency shift using a preset optimization function to accurately solve the fractional Doppler frequency shift and improve the channel estimation accuracy. Attached Figure Description

[0017] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating the channel estimation method of this application in Embodiment 1. Figure 2 This is a schematic diagram of the embedded pilot structure provided in Embodiment 1 of the channel estimation method of this application; Figure 3 A complete and truncated schematic diagram of the channel response amplitude provided for Embodiment 1 of the channel estimation method of this application; Figure 4 This is a schematic diagram showing the optimization function values ​​corresponding to the complete and truncated channel responses provided in Embodiment 1 of the channel estimation method of this application; Figure 5 The flowchart of the OTFS channel estimation algorithm based on gradient optimization is provided in Embodiment 2 of the channel estimation method of this application; Figure 6 Exclusive pilot signal provided for embodiment two of the channel estimation method of this application A schematic diagram illustrating the variation of MSE with SNR; Figure 7 This is a schematic diagram showing the variation of NMSE of the channel response under exclusive pilot signal as a function of SNR, provided in Embodiment 2 of the channel estimation method of this application. Figure 8 This is a schematic diagram illustrating the variation of NMSE with SNR in the embedded pilot channel response provided in Embodiment 2 of the channel estimation method of this application. Figure 9 This is a schematic diagram of the module structure of the channel estimation device according to an embodiment of this application; Figure 10 This is a schematic diagram of the device structure of the hardware operating environment involved in the channel estimation method in the embodiments of this application.

[0020] The purpose, features, and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0021] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application.

[0022] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0023] The main solution of this application is as follows: This application determines the solution interval of the fractional Doppler frequency shift based on the signal characteristics corresponding to the received signal in the time-delay Doppler frequency domain; performs gradient iterative optimization of the fractional Doppler frequency shift based on a preset optimization function and the solution interval to obtain the target fractional Doppler frequency shift; estimates the amplitude and phase shift of the channel gain of each path based on the target fractional Doppler frequency shift, and determines the channel estimation result of each path.

[0024] In this embodiment, for ease of description, the following description uses a computing service device as the execution subject.

[0025] Current algorithms for fractional delay Doppler scenarios rely on virtual sampling, and virtual grids alone cannot achieve accuracy beyond grid resolution, resulting in low channel estimation accuracy.

[0026] This application provides a solution that uses a preset optimization function to perform gradient iterative optimization of the fractional Doppler frequency shift, accurately solves the fractional Doppler frequency shift, and improves the channel estimation accuracy.

[0027] As can be seen from the above embodiments, this application determines the solution interval of the fractional Doppler frequency shift based on the signal characteristics corresponding to the received signal in the time-delay Doppler frequency domain; performs gradient iterative optimization of the fractional Doppler frequency shift based on a preset optimization function and the solution interval to obtain the target fractional Doppler frequency shift; estimates the amplitude and phase shift of the channel gain for each path based on the target fractional Doppler frequency shift, and determines the channel estimation result for each path. Compared with current algorithms for fractional time-delay Doppler scenarios that rely on virtual sampling, which cannot achieve accuracy beyond the grid resolution using only a virtual grid, resulting in low channel estimation accuracy, this application performs gradient iterative optimization of the fractional Doppler frequency shift using a preset optimization function to accurately solve the fractional Doppler frequency shift and improve channel estimation accuracy.

[0028] It should be noted that the executing entity in this embodiment can be a computing service device with data processing, network communication, and program execution functions, such as a tablet computer, personal computer, or mobile phone, or an electronic device capable of performing the above functions, including a large-model channel estimation system for financial scenarios. The following description uses a computer as an example to illustrate this embodiment and the subsequent embodiments.

[0029] Based on this, embodiments of this application provide a channel estimation method, referring to... Figure 1 , Figure 1 This is a flowchart illustrating an embodiment of the channel estimation method of this application.

[0030] In this embodiment, the channel estimation method includes steps S10 to S30: Step S10: Determine the solution interval of the fractional Doppler frequency shift based on the signal characteristics corresponding to the received signal in the time-delay Doppler frequency domain.

[0031] It should be noted that the time-delay Doppler frequency domain refers to the time-delay frequency domain and the Doppler frequency domain, i.e., the DD domain. The receiver uses OTFS (orthogonal time-frequency space) demodulation (Wigner transform and symplectic finite Fourier transform SFFT) to convert the time-domain signal r(t) back to the time-delay-Doppler domain to obtain the received signal Y[k,l]. y[k,l]=h[k,l] x[k,l]+n[k,l]; The above equation describes the process by which the transmitted signal x[k,l] is distorted by the DD domain channel h[k,l], and then combined with DD domain noise n[k,l] to finally form the received signal y[k,l]. The transmitted signal is represented as the symbol X[k,l] on a two-dimensional grid, where k is the Doppler index and l is the time delay index.

[0032] Understandably, the signal features include peak features and phase features. The solution range of the fractional Doppler frequency shift is determined by the peak features and phase features corresponding to the received signal in the time-delay Doppler frequency domain. Specifically, the solution range of the fractional Doppler is determined based on the amplitude abrupt change and phase jump characteristics of the received signal near the peak, providing an initial search range for gradient iteration.

[0033] Furthermore, step S10 also includes: intercepting the received signal in the time-delay Doppler frequency domain based on a preset embedded pilot signal to obtain a truncated observation signal; and determining the solution interval of the fractional Doppler frequency shift based on the peak characteristics and phase characteristics corresponding to the channel response vector of the observation signal on the time-delay axis.

[0034] It should be noted that in the OTFS system, the relationship between the transmitted and received signals in the DD domain is given by the following formula: (1) in, This represents the received and transmitted signals in the DD domain. and These represent the indices for time delay and the Doppler axis, respectively. The variance is Gaussian channel noise. The channel impulse response, based on the bioorthogonality assumption, can be expressed as: (2) in, It is the number of transmission paths. and They are the first The amplitude and phase of the path channel gain. and They represent the first The path delay and Doppler shift. It is the Dirac impulse function. and It is given by the following formula: (3) in, It is the duration of the symbol. It is the subcarrier spacing.

[0035] Understandably, the preset embedded pilot reference Figure 2 The embedded pilot structure shown in the diagram is achieved by employing, for example... Figure 2 The impulse pilot structure shown is an embedded pilot arrangement. This indicates the position coordinates of the pilot signal in the DD grid. , It is the length of the guard interval in the DD domain, where and It is the largest Doppler shift and time delay. It is pilot energy. Corresponding data symbols. Introducing guard intervals. This is to reduce interference caused by the fractional Doppler effect.

[0036] In specific implementation, the received signal in the time-delay Doppler frequency domain is truncated based on a preset embedded pilot signal to obtain the truncated observation signal; the solution interval for the fractional Doppler frequency shift is determined according to the peak and phase characteristics corresponding to the channel response vector of the observation signal on the time delay axis. In broadband systems, it is assumed that the time delay is distinguishable. Furthermore, considering the time-delay-Doppler decomposition, the method of this application can be extended to the fractional time delay scenario. Therefore, this paper does not consider the case of fractional time delay. In the integer time delay scenario, when hour Otherwise, it equals 0. Therefore, for a specific time delay tap, the received signal vector... It is given by the following formula: ; (4) Among them, fractional Doppler frequency shift Integer part containing Doppler and fractional part In embedded pilots, truncated signals are used. Perform channel estimation, such as Figure 2 As shown. and These represent the dimensions in the Doppler domain and the time delay domain, respectively.

[0037] Step S20: Perform gradient iterative optimization on the fractional Doppler frequency shift based on the preset optimization function and the solution interval to obtain the target fractional Doppler frequency shift.

[0038] It should be noted that the preset optimization functions include a first optimization function based on waveform amplitude cross-correlation and a second optimization function based on residuals. The fractional Doppler frequency shift is then iteratively optimized using either the first optimization function based on waveform amplitude cross-correlation or the second optimization function based on residuals, along with the solution interval, to obtain the target fractional Doppler frequency shift.

[0039] Furthermore, step S20 further includes: determining an initial estimate of the fractional Doppler frequency shift based on the solution interval; performing gradient iterative optimization of the fractional Doppler frequency shift based on the initial estimate, the preset optimization function, and the preset adaptive step size adjustment strategy to obtain the target fractional Doppler frequency shift.

[0040] It should be noted that gradient iterative optimization can be achieved by iteratively solving the first or second optimization function using gradient ascent or descent methods. Starting with an initial value within the solution interval, the first or second optimization function is iteratively solved using gradient ascent or descent methods until the convergence condition is met, obtaining an estimate of the fractional Doppler frequency shift. A preset adaptive step size adjustment strategy is employed during the iteration process. The target fractional Doppler frequency shift is output upon completion of the iteration.

[0041] Step S30: Estimate the amplitude and phase shift of the channel gain for each path based on the target fractional Doppler frequency shift, and determine the channel estimation result for each path.

[0042] It should be noted that the amplitude and phase shift of the channel gain for each path are estimated based on the target fractional Doppler frequency shift, and the channel estimation result for each path is determined.

[0043] In the specific implementation, after receiving the signal at the receiver, a channel response vector of length N is obtained along the time delay axis. First, the integer solution interval is determined based on the signal peak value and phase characteristics. Then, the proposed gradient ascent / descent method is used to solve for the fractional Doppler shift. After obtaining the fractional Doppler shift, the ideal channel response can be reconstructed, and it is used together with the actual received signal to estimate the amplitude of the channel gain and the phase deflection. Finally, the channel estimation results for each path are output, including the channel delay, Doppler shift, and channel gain.

[0044] This embodiment determines the solution interval of the fractional Doppler frequency shift based on the signal characteristics corresponding to the received signal in the time-delay Doppler frequency domain; performs gradient iterative optimization of the fractional Doppler frequency shift based on a preset optimization function and the solution interval to obtain the target fractional Doppler frequency shift; estimates the amplitude and phase shift of the channel gain for each path based on the target fractional Doppler frequency shift, and determines the channel estimation result for each path. Compared with the current algorithm for fractional time-delay Doppler scenarios, which relies on virtual sampling and cannot achieve accuracy beyond the grid resolution using only a virtual grid, resulting in low channel estimation accuracy, this application performs gradient iterative optimization of the fractional Doppler frequency shift using a preset optimization function to accurately solve the fractional Doppler frequency shift and improve the channel estimation accuracy.

[0045] Based on the above Figure 1 The first embodiment shown is followed by an embodiment two of the emotion recognition method of this application. Based on the first embodiment of this application, the same or similar content as the first embodiment can be referred to the above description, and will not be repeated hereafter.

[0046] In this embodiment, the preset optimization function includes a first optimization function based on waveform amplitude cross-correlation. The step of performing gradient iterative optimization of the fractional Doppler frequency shift based on the initial estimate, the preset optimization function, and a preset adaptive step size adjustment strategy to obtain the target fractional Doppler frequency shift includes: starting from the initial estimate, calculating the gradient of the first optimization function with respect to the fractional Doppler frequency shift in the current iteration; updating the estimated value of the fractional Doppler frequency shift according to the sign of the gradient and a preset step size; if the updated estimated value exceeds the solution interval, or the sign of the gradient changes before and after the current iteration, halving the step size based on the preset adaptive step size adjustment strategy and reverting to the estimated value before the update; repeating the above steps until the absolute value of the gradient is less than a preset threshold, or the number of iterations reaches the maximum number of iterations, to obtain the target fractional Doppler frequency shift. The formula for calculating the first optimization function is as follows: (5) in, Indicates the inner product. It is the amplitude of the received signal y[k] in its general form.

[0047] It should be noted that the first optimization function is constructed based on the amplitude of the channel response. This correlation function reaches its maximum value at the correct fractional Doppler. Therefore, The maximum likelihood estimate can be obtained by the following formula: (6) Unlike traditional methods that directly calculate cross-correlation values ​​at virtual sampling points for parameter estimation, this application utilizes the convexity of the optimization function, referencing... Figure 3 The diagrams shown depict the full and truncated channel response amplitudes, as well as... Figure 4 The diagram shows the optimization function values ​​corresponding to the complete and truncated channel responses, as shown below. Figure 3 (a) and Figure 4 As shown in (a), this helps to accurately solve for the fractional Doppler value within each integer interval. Therefore, the fractional Doppler frequency shift can be precisely determined by locating the zero-crossing points of the derivative of the optimization function. This method overcomes the inherent accuracy limitations of the virtual sampling grid. The derivative of the optimization function is given by the following equation: (7) At the non-differentiable point, set the derivative value to 0.

[0048] In one possible implementation, the preset optimization function further includes a second optimization function based on the residual. The step of performing gradient iterative optimization of the fractional Doppler frequency shift based on the initial estimate, the preset optimization function, and a preset adaptive step size adjustment strategy to obtain the target fractional Doppler frequency shift includes: starting from the initial estimate, calculating the gradient of the second optimization function with respect to the fractional Doppler frequency shift in the current iteration; updating the estimated value of the fractional Doppler frequency shift according to the sign of the gradient and a preset step size; if the updated estimated value exceeds the solution interval, or the sign of the gradient changes before and after the current iteration, halving the step size based on the preset adaptive step size adjustment strategy and reverting to the estimated value before the update; repeating the above steps until the absolute value of the gradient is less than a preset threshold, or the number of iterations reaches the maximum number of iterations, to obtain the target fractional Doppler frequency shift. The formula for calculating the second optimization function is as follows: (8) in, This represents the second optimization function. It is the first The estimated magnitude of the path channel gain. It is the amplitude of the received signal y[k] in its general form. It is the pilot energy, and N represents the size in the Doppler domain.

[0049] It should be noted that in embedded pilot structures, the location of the maximum value is inherently shifted due to signal truncation. Even in the absence of noise and data signal interference, the estimation error of the cross-correlation function is caused by the truncation of the channel response. Figure 4 As shown in (b), the truncated channel response is... The maximum cross-correlation value occurs at 2.19, while the true value should be 2.2. This offset leads to the use of... Estimation errors are unavoidable. To address this issue, this application further defines a residual-based optimization function for embedded pilots as follows: (8) in It is the first The estimated magnitude of the path channel gain. Similar to the correlation function, the corresponding maximum likelihood estimate is given by the following equation: (9) in The derivative is given by the following formula: ; (10) The residual function formula (9) estimates the channel response by minimizing the residual between the channel response and the waveform. .like Figure 4 As shown in (b), the minimum value of the residual function will not be shifted due to signal truncation.

[0050] Gradient descent / ascent is used to numerically locate the zero-crossings of these derivatives (Equations (7) and (10)) to achieve accurate fractional Doppler shift estimation, where the Doppler shift is updated in each iteration according to the following equation: (11) in This represents the adaptive halving step size, and the `sign` function determines the optimization direction based on the sign of the derivative. To ensure... The interval remains within integers, with an initial step size of 0.1. The step size is halved when either of the following conditions is met: (1) the derivative changes sign, or (2) the updated... Out of integer range. The optimization process must be constrained to the correct integer range. This occurs when the maximum number of iterations is reached or the derivative magnitude falls below a predefined threshold. When the iteration is complete, the optimization process terminates.

[0051] because and Differentiability is only within an integer interval, therefore determining the solution interval is crucial. Utilizing the characteristics of the OTFS received signal, this application determines the Doppler interval by analyzing the peak and phase relationships. As derived from equation (4), the received signal exhibits a linear phase change, while simultaneously displaying abrupt phase jumps near its peak amplitude. Assuming the received signal with the maximum amplitude is... Then, the side of the peak point where the phase transition occurs is... The search range.

[0052] Furthermore, step S30 further includes: reconstructing the ideal channel response vector of each path based on the target fractional Doppler frequency shift; estimating the amplitude and phase shift of the channel gain of each path based on the ideal channel response vector and the received signal, and determining the channel estimation result of each path.

[0053] In the specific implementation, refer to Figure 5 The flowchart of the gradient-optimized OTFS channel estimation algorithm shown illustrates how, after receiving the signal at the receiver, a channel response vector of length N is obtained along the time delay axis. First, the integer solution interval is determined based on the signal peak value and phase characteristics. Then, the proposed gradient ascent / descent method is used to solve for the fractional Doppler shift. After obtaining the fractional Doppler shift, the ideal channel response can be reconstructed, and this, along with the actual received signal, is used to estimate the amplitude of the channel gain and the phase deflection. Finally, the channel estimation results for each path are output, including the channel delay, Doppler shift, and channel gain.

[0054] Further, the step of estimating the amplitude and phase shift of the channel gain for each path based on the ideal channel response vector and the received signal, and determining the channel estimation result for each path, includes: performing energy normalization processing based on the energy estimate value corresponding to the ideal channel response vector and the received signal; calculating the minimum mean square error of the channel gain for each path based on the amplitude of the channel gain for the ideal channel response vector and the received signal; estimating the phase shift of the channel gain for each path; and determining the channel estimation result for each path based on the amplitude and the phase shift.

[0055] It should be noted that, understandably, the amplitude and phase of the channel gain are estimated separately. First, the amplitude of the channel gain is estimated using the following formula. : (12) in It is the channel response reconstructed in the truncated region, whose energy during the coarse estimation period is approximately... In the case of exclusive pilot signal, Become , ,and .

[0056] Then, the phase shift can be estimated using the minimum mean square error method based on the following formula: (13) The closed-form solution can be expressed as: (14) in, Extract the phase angle of a complex number.

[0057] The process of the gradient-based search CE algorithm proposed in this application is summarized in Algorithm 1. The gradient-based channel estimation algorithm in Algorithm 1 is as follows: Input: Pilot response , , , ,

[0058] Output: ; For to do A rough solution can be obtained using formula (12).

[0059] Finding the solution interval and initialize

[0060] initialization

[0061] Repeat

[0062] Calculate according to formulas (7) and (10) and

[0063] Update according to formula (11)

[0064] If or then

[0065]

[0066] End if Until or

[0067] Solve according to formula (12)

[0068] Solve according to formula (14)

[0069] End for Return , ,

[0070] The algorithm has a maximum time delay range It iterates through all possible integer delays. For each delay tap, it first obtains the residual-based function. A rough estimate is then made. Then, the solution interval around the peak amplitude is determined. And assign initial fractional Doppler values. In each iteration, the gradients of the correlation-based and residual-based optimization functions are calculated according to formulas (7) and (10), respectively, and are expressed as follows: and Based on these gradients, updates are performed using gradient ascent / descent algorithms. If the sign of the derivative value changes or is updated... Beyond the solution interval Then step size Halve and retain the previous estimate The iterative process terminates and obtains the result when the condition at the end of III-A is met. Finally, the estimated channel response is reconstructed. This is used to estimate based on formulas (12) and (14) respectively. and phase shift .

[0071] Furthermore, this application theoretically verifies the effectiveness of the estimator by deriving a closed-form expression for the single-path Cramer-Rao Lower Bound (CRLB) in the OTFS system. Simulation results show that the two proposed gradient-based algorithms are effective estimators for both fractional Doppler and channel response in the case of exclusive pilots. In embedded pilots, the residual-based optimization function outperforms existing comparative algorithms. The Cramer-Rao Lower Bound (CRLB) analysis can be used to evaluate whether the proposed CE algorithm is an effective estimator when each path has a fixed channel gain and fractional Doppler frequency shift. The probability density function of the received pilot channel response is given by the following equation: ; (15) in Includes parameters , and .

[0072] The Fisher information matrix (FIM) can be derived as follows: (16) The inverse of the corresponding FIM is: (17) The CRLB for each parameter is the main diagonal element in (26). Furthermore, the CRLB for the pilot channel response is calculated as follows: ; (18) In terms of computational complexity, the proposed algorithm achieves linear complexity. For each integer time-delay tap, the complexity of searching the solution interval is O(log n). The time complexity of gradient descent / ascent methods is O(n). , where L represents the average number of iterations for the gradient descent / ascent method. The complexity of channel gain estimation is O(n). Therefore, the overall algorithm complexity is O(n log n). This linear complexity is attributed to avoiding large matrix inversions and the efficient convergence of gradient descent / ascent methods. This application utilizes... For example, to further verify the estimation accuracy of this application, the channel estimation performance of the proposed method is compared with that of current methods using normalized mean square error. Experimental results also include... The mean square error is compared with the theoretical lower bound of the variance. This application considers exclusive pilots without data symbols and such... Figure 2 The embedded pilot is shown in two cases. The signal dimensions in the delay-Doppler domain are set to M=64 and N=64. The carrier frequency is 3GHz, and the subcarrier spacing is 7.5kHz. The normalized maximum Doppler frequency shift and delay are respectively... and The channel consists of P=5 paths, randomly distributed over different integer time delays. Above. The pilot signal energy is 30dB. To facilitate comparison with the derived single-path CRLB, this application sets a fixed complex path gain for the P paths. The threshold of the gradient-based algorithm... The maximum number of iterations is set to and the maximum number of iterations are respectively set to And 30. Reference Figure 6 The exclusive pilot signal shown The diagram illustrating the MSE versus SNR shows the MSE performance of fractional Doppler estimation using a dedicated pilot. The two proposed methods outperform other algorithms at low SNR and approach CRLB at high SNR, demonstrating their effectiveness as estimators. This advantage stems from the fact that gradient-based algorithms are not limited by grid resolution. Once the correct solution interval is determined, the fractional Doppler shift can be accurately solved. Therefore, as the SNR increases, noise does not lead to incorrect solution intervals, and the estimation performance approaches the theoretical lower bound. In contrast, virtual grid-based cross-correlation algorithms are inherently limited by grid resolution, and their accuracy saturates with increasing SNR. Combining virtual sampling with a first-order linear approximation can overcome the resolution limitation, but this method is highly sensitive to noise and only performs well at higher SNRs. (Reference) Figure 7 The diagram illustrates the variation of NMSE of the channel response with SNR under exclusive pilot conditions, comparing the estimated NMSE of the channel response using different methods when using exclusive pilot. Similar to the fractional Doppler estimation results, the proposed method achieves a lower NMSE than other algorithms and approaches CRLB at high SNR. This is because, in integer delay scenarios, the accuracy of fractional Doppler estimation primarily determines the accuracy of the reconstructed channel response. This verifies that the proposed method is also an effective estimator for the channel response. For comparison, this application retains the fractional Doppler component only in the SBL-based estimation algorithm. The virtual grid resolution is set to r=0.2, and this application retains the fractional Doppler component at each integer delay tap. Paths, among which This method achieves higher accuracy at the cost of increased computational complexity, but still falls short of CRLB. Two other low-complexity algorithms exhibit higher NMSE values. Figure 8The diagram showing the NMSE of the channel response under embedded pilots as a function of SNR illustrates the NMSE performance of different methods for channel response estimation when using embedded pilots. It can be seen that the method proposed in this application achieves a lower NMSE than other algorithms. Specifically, the residual-based optimization function produces a lower NMSE than the correlation-based optimization function because it avoids estimation errors caused by truncation effects. Similar to the exclusive pilot case, the SBL-based algorithm preserves the NMSE at r=0.2. One path. Its performance is about 5dB lower than the residual-based method. The other two low-complexity algorithms also exhibit high NMSE values ​​similar to the exclusive pilot case. The error plateau observed at high SNR is mainly caused by fractional interference from the data signal, where the noise effect is negligible. This error is unavoidable unless the signal interference is distinguished from the channel response. Therefore, this application proposes a gradient-based ascending / descending channel estimation algorithm for OTFS systems with fractional Doppler effect. This application reveals the convexity of the proposed correlation and residual-based optimization function. Based on this property, a gradient-based algorithm is proposed to estimate the accurate fractional Doppler value. In addition, this application derives a closed-form expression for the single-path Cramer-Rao lower bound of the OTFS system to theoretically verify the effectiveness of the proposed estimator. Simulation results show that the two optimization functions are close to the derived CRLB when using exclusive pilots and exhibit excellent channel estimation performance in embedded pilot schemes.

[0073] This embodiment determines the solution interval for the fractional Doppler frequency shift based on the signal characteristics corresponding to the received signal in the time-delay Doppler frequency domain; it performs gradient iterative optimization of the fractional Doppler frequency shift based on a preset optimization function and the solution interval to obtain the target fractional Doppler frequency shift; it estimates the amplitude and phase shift of the channel gain for each path based on the target fractional Doppler frequency shift and determines the channel estimation result for each path. Compared with current algorithms for fractional time-delay Doppler scenarios that rely on virtual sampling, which cannot achieve accuracy beyond the grid resolution using only a virtual grid, resulting in low channel estimation accuracy, this embodiment performs gradient iterative optimization of the fractional Doppler frequency shift using a preset optimization function to accurately solve the fractional Doppler frequency shift and improve channel estimation accuracy.

[0074] It should be noted that the above examples are only for understanding this application and do not constitute a limitation on the channel estimation method of this application. Any simple transformations based on this technical concept are within the protection scope of this application.

[0075] This application also provides a channel estimation apparatus, please refer to... Figure 9 The channel estimation device includes: The solution interval determination module 10 is used to determine the solution interval of fractional Doppler based on the signal characteristics corresponding to the received signal in the time delay Doppler frequency domain. The gradient iteration solution module 20 is used to perform gradient iteration optimization on the fractional Doppler based on a preset optimization function and the solution interval to obtain the target fractional Doppler frequency shift. The channel parameter estimation module 30 is used to estimate the amplitude and phase shift of the channel gain for each path based on the target fractional Doppler frequency shift, and to determine the channel estimation result for each path.

[0076] Furthermore, the signal features include peak features and phase features. The solution interval determination module 10 is also used to extract the received signal in the time-delay Doppler frequency domain based on a preset embedded pilot signal to obtain the truncated observation signal; and to determine the solution interval of the fractional Doppler frequency shift according to the peak features and phase features corresponding to the channel response vector of the observation signal on the time delay axis.

[0077] Furthermore, the gradient iteration solution module 20 is also used to determine the initial estimate corresponding to the fractional Doppler frequency shift based on the solution interval; and to perform gradient iteration optimization on the fractional Doppler frequency shift based on the initial estimate, the preset optimization function, and the preset adaptive step size adjustment strategy to obtain the target fractional Doppler frequency shift.

[0078] Furthermore, the preset optimization function includes a first optimization function based on waveform amplitude cross-correlation, and the gradient iteration solution module 20 is also used to calculate the gradient of the first optimization function with respect to the fractional Doppler frequency shift in the current iteration, starting from the initial estimated value; The estimated value of the fractional Doppler frequency shift is updated based on the sign of the gradient and the preset step size. If the updated estimated value exceeds the solution range, or if the sign of the gradient changes before or after the current iteration, the step size is halved based on a preset adaptive step size adjustment strategy, and the value is rolled back to the estimated value before the update. Repeat the above steps until the absolute value of the gradient is less than a preset threshold, or the number of iterations reaches the maximum number of iterations, to obtain the target fractional Doppler frequency shift; The formula for calculating the first optimization function is as follows: ; in, Indicates the inner product. It is the amplitude of the received signal y[k] in its general form.

[0079] Furthermore, the preset optimization function also includes a second optimization function based on the residual, and the gradient iteration solution module 20 is further used to calculate the gradient of the second optimization function with respect to the fractional Doppler frequency shift in the current iteration, starting from the initial estimate; The estimated value of the fractional Doppler frequency shift is updated based on the sign of the gradient and the preset step size. If the updated estimated value exceeds the solution range, or if the sign of the gradient changes before or after the current iteration, the step size is halved based on a preset adaptive step size adjustment strategy, and the value is rolled back to the estimated value before the update. Repeat the above steps until the absolute value of the gradient is less than a preset threshold, or the number of iterations reaches the maximum number of iterations, to obtain the target fractional Doppler frequency shift; The formula for calculating the second optimization function is as follows: ; in, This represents the second optimization function. It is the first The estimated magnitude of the path channel gain. It is the amplitude of the received signal y[k] in its general form. It is the pilot energy, and N represents the size in the Doppler domain.

[0080] Furthermore, the channel parameter estimation module 30 is also used to reconstruct the ideal channel response vector of each path based on the target fractional Doppler frequency shift; estimate the amplitude and phase shift of the channel gain of each path based on the ideal channel response vector and the received signal, and determine the channel estimation result of each path.

[0081] Furthermore, the channel parameter estimation module 30 is also used to perform energy normalization processing based on the ideal channel response vector and the energy estimate corresponding to the received signal, and estimate the amplitude of the channel gain for each path; perform minimum mean square error calculation on the ideal channel response vector and the received signal, and estimate the phase offset of the channel gain for each path, and determine the channel estimation result for each path based on the amplitude and the phase offset.

[0082] The channel estimation apparatus provided in this application, employing the channel estimation method described in the above embodiments, can solve the technical problem that current algorithms for fractional delay Doppler scenarios rely on virtual sampling, and cannot achieve accuracy exceeding grid resolution using only a virtual grid, resulting in low channel estimation accuracy. Compared with the prior art, the beneficial effects of the channel estimation apparatus provided in this application are the same as those of the channel estimation method provided in the above embodiments, and other technical features in the channel estimation apparatus are the same as those disclosed in the methods of the above embodiments, and will not be repeated here.

[0083] This application provides a channel estimation device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, which are executed by the at least one processor to enable the at least one processor to perform the channel estimation method in Embodiment 1 above.

[0084] The following is for reference. Figure 10 The diagram illustrates a structural schematic of a channel estimation device suitable for implementing embodiments of this application. The channel estimation device in these embodiments may include, but is not limited to, mobile terminals such as mobile phones, laptops, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Description), PMPs (Portable Media Players), in-vehicle terminals (e.g., in-vehicle navigation terminals), and fixed terminals such as digital TVs and desktop computers. Figure 10 The channel estimation device shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0085] like Figure 10 As shown, the channel estimation device may include a processing unit 1001 (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory 1002 or a program loaded from a storage device 1003 into a random access memory 1004. The random access memory 1004 also stores various programs and data required for the operation of the channel estimation device. The processing unit 1001, the read-only memory 1002, and the random access memory 1004 are interconnected via a bus 1005. An input / output interface 1006 is also connected to the bus. Typically, the following systems can be connected to the input / output interface 1006: input devices 1007 including, for example, a touchscreen, touchpad, keyboard, mouse, image sensor, microphone, accelerometer, gyroscope, etc.; output devices 1008 including, for example, a liquid crystal display (LCD), speaker, vibrator, etc.; storage devices 1003 including, for example, magnetic tape, hard disk, etc.; and communication devices 1009. Communication device 1009 allows the channel estimation device to communicate wirelessly or wiredly with other devices to exchange data. While the figure shows channel estimation devices with various systems, it should be understood that implementation or possession of all the systems shown is not required. More or fewer systems may be implemented alternatively.

[0086] Specifically, according to the embodiments disclosed in this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments disclosed in this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from storage device 1003, or installed from read-only memory 1002. When the computer program is executed by processing device 1001, it performs the functions defined in the methods of the embodiments disclosed in this application.

[0087] The channel estimation device provided in this application, employing the channel estimation method described in the above embodiments, can solve the technical problem that current algorithms for fractional delay Doppler scenarios rely on virtual sampling, and cannot achieve accuracy exceeding grid resolution using only a virtual grid, resulting in low channel estimation accuracy. Compared with the prior art, the beneficial effects of the channel estimation device provided in this application are the same as those of the channel estimation method provided in the above embodiments, and other technical features of this channel estimation device are the same as those disclosed in the previous embodiment method, and will not be repeated here.

[0088] It should be understood that the various parts disclosed in this application can be implemented using hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0089] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0090] This application provides a computer-readable storage medium having computer-readable program instructions (i.e., a computer program) stored thereon, the computer-readable program instructions being used to execute the channel estimation method in the above embodiments.

[0091] The computer-readable storage medium provided in this application may be, for example, a USB flash drive, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems or devices, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system or device. The program code contained on the computer-readable storage medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination thereof.

[0092] The aforementioned computer-readable storage medium may be included in the channel estimation device; or it may exist independently and not assembled into the channel estimation device.

[0093] The aforementioned computer-readable storage medium carries one or more programs. When the aforementioned one or more programs are executed by the channel estimation device, the channel estimation device: sequentially polls the motion control chip corresponding to each axis within a preset control cycle via a high-speed serial bus, and obtains the encoder data corresponding to each axis fed back by the motion control chip corresponding to each axis; determines the encoder type corresponding to each axis based on the encoder data corresponding to each axis; selects a target control strategy from the preset control strategies based on the encoder type corresponding to each axis, and performs closed-loop control on each axis according to the target control strategy.

[0094] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a Local Area Network (LAN) or a Wide Area Network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0095] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0096] The modules described in the embodiments of this application can be implemented in software or hardware. The names of the modules do not necessarily limit the functionality of the unit itself.

[0097] The readable storage medium provided in this application is a computer-readable storage medium that stores computer-readable program instructions (i.e., a computer program) for executing the above-described channel estimation method. This addresses the technical problem that current algorithms for fractional delay Doppler scenarios rely on virtual sampling, and the virtual grid alone cannot achieve accuracy exceeding the grid resolution, resulting in low channel estimation accuracy. Compared to the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as those of the channel estimation method provided in the above embodiments, and will not be repeated here.

[0098] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the channel estimation method described above.

[0099] The computer program product provided in this application can solve the technical problem that current algorithms for fractional delay Doppler scenarios rely on virtual sampling, and cannot achieve accuracy beyond the grid resolution using only a virtual grid, resulting in low channel estimation accuracy. Compared with the prior art, the beneficial effects of the computer program product provided in this application are the same as those of the channel estimation method provided in the above embodiments, and will not be repeated here.

[0100] The above description is only a part of the embodiments of this application and does not limit the scope of this application. All equivalent structural transformations made under the technical concept of this application and using the content of this application specification and drawings, or direct / indirect applications in other related technical fields, are included within the protection scope of this application.

Claims

1. A channel estimation method, characterized in that, The method includes: The solution interval for the fractional Doppler frequency shift is determined based on the signal characteristics corresponding to the received signal in the time-delay Doppler frequency domain. Based on the preset optimization function and the solution interval, the fractional Doppler frequency shift is optimized by gradient iteration to obtain the target fractional Doppler frequency shift; The amplitude and phase shift of the channel gain for each path are estimated based on the target fractional Doppler frequency shift, and the channel estimation result for each path is determined.

2. The channel estimation method as described in claim 1, characterized in that, The signal characteristics include peak characteristics and phase characteristics. The step of determining the solution interval of the fractional Doppler frequency shift based on the signal characteristics corresponding to the received signal in the time-delay Doppler frequency domain includes: The truncated observation signal is obtained by extracting the received signal in the time-delay Doppler frequency domain based on the preset embedded pilot signal; The solution interval for the fractional Doppler frequency shift is determined based on the peak and phase characteristics of the channel response vector of the observed signal on the time delay axis.

3. The channel estimation method as described in claim 1, characterized in that, The step of performing gradient iterative optimization of the fractional Doppler frequency shift based on a preset optimization function and the solution interval to obtain the target fractional Doppler frequency shift includes: Based on the solution interval, determine the initial estimate corresponding to the fractional Doppler frequency shift; Based on the initial estimate, the preset optimization function, and the preset adaptive step size adjustment strategy, the fractional Doppler frequency shift is iteratively optimized by gradient to obtain the target fractional Doppler frequency shift.

4. The channel estimation method as described in claim 3, characterized in that, The preset optimization function includes a first optimization function based on waveform amplitude cross-correlation. The step of performing gradient iterative optimization of the fractional Doppler frequency shift based on the initial estimate, the preset optimization function, and a preset adaptive step size adjustment strategy to obtain the target fractional Doppler frequency shift includes: Starting from the initial estimate, calculate the gradient of the first optimization function with respect to the fractional Doppler frequency shift in the current iteration; The estimated value of the fractional Doppler frequency shift is updated based on the sign of the gradient and the preset step size. If the updated estimated value exceeds the solution range, or if the sign of the gradient changes before or after the current iteration, the step size is halved based on a preset adaptive step size adjustment strategy, and the value is rolled back to the estimated value before the update. Repeat the above steps until the absolute value of the gradient is less than a preset threshold, or the number of iterations reaches the maximum number of iterations, to obtain the target fractional Doppler frequency shift; The formula for calculating the first optimization function is as follows: ； in, Indicates the inner product. It is the amplitude of the received signal y[k] in its general form.

5. The channel estimation method as described in claim 3, characterized in that, The preset optimization function further includes a second optimization function based on the residual. The step of performing gradient iterative optimization of the fractional Doppler frequency shift based on the initial estimate, the preset optimization function, and a preset adaptive step size adjustment strategy to obtain the target fractional Doppler frequency shift includes: Starting from the initial estimate, calculate the gradient of the second optimization function with respect to the fractional Doppler frequency shift in the current iteration; The estimated value of the fractional Doppler frequency shift is updated based on the sign of the gradient and the preset step size. If the updated estimated value exceeds the solution range, or if the sign of the gradient changes before or after the current iteration, the step size is halved based on a preset adaptive step size adjustment strategy, and the value is rolled back to the estimated value before the update. Repeat the above steps until the absolute value of the gradient is less than a preset threshold, or the number of iterations reaches the maximum number of iterations, to obtain the target fractional Doppler frequency shift; The formula for calculating the second optimization function is as follows: ； in, This represents the second optimization function. It is the first The estimated magnitude of the path channel gain. It is the amplitude of the received signal y[k] in its general form. It is the pilot energy, and N represents the size in the Doppler domain.

6. The channel estimation method as described in claim 1, characterized in that, The step of estimating the amplitude and phase shift of the channel gain for each path based on the target fractional Doppler frequency shift, and determining the channel estimation result for each path, includes: The ideal channel response vector for each path is reconstructed based on the target fractional Doppler frequency shift; Based on the ideal channel response vector and the received signal, the amplitude and phase offset of the channel gain for each path are estimated, and the channel estimation result for each path is determined.

7. The channel estimation method as described in claim 6, characterized in that, The step of estimating the amplitude and phase offset of the channel gain for each path based on the ideal channel response vector and the received signal, and determining the channel estimation result for each path, includes: Energy normalization is performed based on the ideal channel response vector and the energy estimate corresponding to the received signal to estimate the magnitude of the channel gain for each path; The minimum mean square error is calculated for the ideal channel response vector and the received signal to estimate the phase shift of the channel gain for each path; The channel estimation result for each path is determined based on the amplitude and the phase offset.

8. A channel estimation device, characterized in that, The device includes: The solution interval determination module is used to determine the solution interval of the fractional Doppler frequency shift based on the signal characteristics corresponding to the received signal in the time delay Doppler frequency domain. The gradient iteration solution module is used to perform gradient iteration optimization of the fractional Doppler frequency shift based on a preset optimization function and the solution interval to obtain the target fractional Doppler frequency shift. The channel parameter estimation module is used to estimate the amplitude and phase shift of the channel gain for each path based on the target fractional Doppler frequency shift, and to determine the channel estimation result for each path.

9. A channel estimation device, characterized in that, The channel estimation device includes: a memory, a processor, and a channel estimation program stored in the memory and executable on the processor, the channel estimation program being configured to implement the channel estimation method as described in any one of claims 1 to 7.

10. A storage medium, characterized in that, The storage medium stores a channel estimation program, which, when executed by a processor, implements the steps of the channel estimation method as described in any one of claims 1 to 7.

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