A method for compensating for a large doppler frequency offset in an LDACS system

Abstract

The application belongs to the technical field of civil aviation broadband communication, and specifically discloses a large Doppler frequency offset compensation method for an LDACS system, which comprises the following steps: performing channel estimation on pilot signals received in a time domain and separating the pilot signals to obtain a plurality of signals, and calculating a carrier frequency offset estimation value of each signal; scanning a frequency axis of the transmitted pilot signals to obtain frequency variation, and constructing a multipath signal model according to the frequency variation; respectively obtaining the maximum signal of the multipath signal model at different time scaling scales; resampling the multipath signal model in the time domain of S1, and outputting the maximum signal at each time scaling scale and adding the maximum signals to obtain an optimal decision signal; and the method has the following advantages: on the basis of compensating the Doppler frequency shift of a line-of-sight channel, the Doppler frequency shift caused by the multipath effect in signal propagation is also compensated, and the transmission reliability of an aircraft in an air route stage at a high altitude is improved; the signal is completely represented in a time-frequency domain, and the compensation accuracy is improved.

Description

Technical Field

[0001] This invention relates to the field of civil aviation broadband communication technology, and more specifically, to a method for compensating for the ultra-large Doppler frequency offset in an LDACS system. Background Technology

[0002] During high-altitude flight, a major challenge for civil aviation communications is how to counteract the massive Doppler frequency shift generated by high-speed flight. In the current era of voice control, the communication modulation method uses amplitude modulation, which is insensitive to Doppler frequency shift. However, in the future era of digital control, data message control will replace voice control, and the communication modulation method will become OFDM modulation. Doppler frequency shift will seriously affect the orthogonality between OFDM subcarriers, causing great trouble for signal reception and demodulation, and compromising the reliability of data transmission.

[0003] Currently, there is limited research on the estimation of ultra-high-altitude Doppler frequency offset during the high-altitude flight path phase in the field of civil aviation communications. Furthermore, the Doppler compensation methods used in ground communications are not suitable for long-distance, fast-time-varying channels in aviation communications. At the same time, traditional methods of performing Doppler compensation in the frequency domain have high computational complexity, and most of them only consider the Doppler frequency shift of the line-of-sight channel, often neglecting the compensation for the Doppler frequency shift spread caused by multipath propagation.

[0004] Meanwhile, traditional compensation methods based on Fourier transform have limitations because Fourier transform can only obtain frequency components of a finite-length signal, but cannot determine the occurrence times of different frequency components. Furthermore, its complexity increases rapidly with signal length, requiring the design of appropriate window functions for signal processing in practical applications, which can lead to the Gibbs effect. In contrast, wavelet transform represents the signal in both the time and frequency domains, its computational complexity is adjusted according to its wavelet series, and it has advantages in processing non-stationary signals.

[0005] To address the aforementioned issues, a method for compensating for the ultra-large Doppler frequency offset in LDACS systems is proposed. Summary of the Invention

[0006] The present invention aims to provide a method for compensating for the ultra-large Doppler frequency offset of an LDACS system, so as to solve or improve at least one of the above-mentioned technical problems.

[0007] In view of this, the first aspect of the present invention is to provide a method for compensating for the ultra-large Doppler frequency offset of an LDACS system.

[0008] The first aspect of the present invention provides a method for super-Doppler frequency offset compensation in an LDACS system, comprising the following steps: S1, performing channel estimation on the received pilot signal in the time domain, separating multiple signals, and calculating the carrier frequency offset estimate for each signal; S2, scanning the frequency axis of the transmitted pilot signal to obtain frequency changes, and constructing a multipath signal model based on the frequency changes; S3, obtaining the signal with the largest value at different time scaling scales of the multipath signal model; S4, using the carrier frequency offset estimate as a sampling factor, resampling the multipath signal model in the time domain of S1, and outputting the signal with the largest value at each time scaling scale and summing them to obtain the optimal decision signal.

[0009] The present invention provides a super-large Doppler frequency offset compensation method for LDACS system, which compensates for the Doppler frequency shift of the line-of-sight channel and also compensates for the Doppler frequency shift spread caused by multipath effect in signal propagation, thereby improving the transmission reliability of aircraft in the high-altitude flight phase.

[0010] Time-domain resampling is performed to separate each signal path. While the initial frequency of each path is the same, their Doppler frequency offsets differ, resulting in different frequencies at the receiver. Wavelet transform is used to maximize the signal of each path. Since the frequency offset manifests as signal scaling in the time domain, time-domain resampling eliminates this offset using a time-domain scaling factor, restoring the frequency to its state before the offset was eliminated, thus completing frequency normalization. Finally, the normalized signals are merged by adding the normalized signals from each path to obtain the optimal decision signal, which is then fed into the decision-maker for judgment. This completes the compensation for multipath Doppler frequency offset.

[0011] In addition, the technical solution provided by the embodiments of the present invention also has the following additional technical features:

[0012] In any of the above technical solutions, step S1 specifically includes: S101, performing channel estimation on the received pilot signal in the time domain to obtain the channel response matrix; S102, performing multipath feature extraction on the channel response matrix to obtain each signal in the time domain; S103, calculating the carrier frequency offset estimate of each signal based on the cross-correlation signal between the currently received time domain signal and the local pilot signal.

[0013] In any of the above technical solutions, the pilot signal is transmitted synchronously with the data symbols at the transmitting end and can be acquired at both the receiving and transmitting ends; and step S101 includes: establishing a relationship model considering the received pilot signal and the transmitted pilot signal, y = Hx + z; and establishing a cost function that minimizes the distance between the receiving end and the transmitting end based on the model, y = Hx + z. The cost function is minimized to obtain the optimal channel response matrix representing the relationship. Where y represents the received pilot signal, H represents the channel response, x represents the transmitted pilot signal, and z represents noise. Let J(H) denote the conjugate transpose, and J(H) denote the objective function that minimizes the distance. This represents the optimal estimated channel response matrix.

[0014] In this technical solution, there are two approaches to estimating Doppler frequency shift. One approach is to obtain the position and velocity information of the source and receiver and then calculate the frequency shift according to the Doppler formula. The drawback of this method is that it can only estimate the single-point frequency offset of the direct path and cannot estimate the multipath Doppler spread. Moreover, for aircraft, the position and velocity information is difficult to obtain accurately. To overcome the above problems, this patent proposes to use a channel estimation method to obtain Doppler information.

[0015] Channel estimation methods are divided into blind channel estimation and non-blind channel estimation. Blind channel estimation uses the structure and statistical characteristics of the received signal itself to obtain channel state information. Although it can reduce resource overhead, its performance is poor. Non-blind channel estimation refers to transmitting pilot signals, which can be obtained by both the source and the receiver, in addition to transmitting data symbols, and then using the pilot signals for channel estimation. In aviation communications, aircraft fly at high speeds, the channel is dynamically changing, and OFDM symbols are complex with many subcarriers. The accuracy of blind channel estimation is insufficient to meet the requirements of the rapidly changing channel state. This patent uses a pilot-based non-blind channel estimation method, employing the least squares estimation method to obtain channel state information.

[0016] The model considering the received signal is as follows:

[0017] y = Hx + z

[0018] Where y represents the received signal, H represents the channel response, x represents the transmitted signal, and z represents Gaussian white noise. σ 2 Let I represent the variance, and let I represent the identity matrix.

[0019] The goal of the least squares estimation method is to find the distance between and that is minimized, which means minimizing the following cost function:

[0020]

[0021] in, Let J(H) denote the conjugate transpose, and J(H) denote the objective function. Taking the derivative of the cost function with respect to the variables, we get:

[0022]

[0023] The solution obtained by the least squares estimation method is:

[0024]

[0025] In practical applications, x represents the local pilot signal. Let y represent the optimal estimated channel response matrix, and y represent the pilot signal received by the receiver. Thus, the channel response matrix is ​​obtained.

[0026] In any of the above technical solutions, step S102 includes: setting H in the relational model as a multi-order matrix, and solving and decomposing the channel response matrix to obtain... Calculate the channel response for each signal and obtain the signal relation model based on the relation model. Where U represents an m*m order chief matrix, Π i T represents a diagonal matrix whose diagonal elements have values ​​only at (n,n). T Let T be the conjugate transpose of T, where T is an n*n matrix, N represents the number of multipaths, and y represents the number of multipaths. np This indicates the nth signal received.

[0027] In this technical solution, based on the expression of the received signal, it is known that the received signal is a set of signals with different frequency offsets and time delays modulated by different multipaths. To separate the signals, this method employs singular value decomposition to extract the channel response of each path.

[0028] Suppose H is an m*n matrix whose elements all belong to the real or complex number field. Then there exists a decomposition such that:

[0029] H=UΣT T

[0030] Where U represents an m*m order Σ matrix, Σ represents a positive semi-definite m*n order diagonal matrix, and T T It is the conjugate transpose of T, and is an n*n matrix. Σ (a diagonal matrix, but not necessarily a square matrix) contains the elements Σ on its diagonal. i These are the singular values ​​of M.

[0031] The general form of Σ is as follows:

[0032]

[0033] The above decomposition constructs a matrix Σ, which has only diagonal elements, with all other elements being 0. Another convention is that the diagonal elements of Σ are arranged in descending order. In practical engineering, after a certain number of singular values ​​(r), all other singular values ​​are set to zero. This means that the dataset contains only r important features, with the rest being noise or redundant data.

[0034] In this method, the channel response matrix is ​​decomposed into a diagonal matrix Σ by singular value decomposition. The number of eigenvalues ​​represents the number of multipaths, and the magnitude of the eigenvalues ​​represents the amplitude of each multipath. When the diagonal matrix is ​​not full rank, it means that there are few multipaths, and all multipath information is extracted. However, when the diagonal matrix is ​​full rank, there may be incomplete extraction of multipath information. In this case, two pilot symbols are used to estimate the channel, and the dimension of the channel response matrix is ​​increased to avoid incomplete extraction of multipath information.

[0035] In obtaining The channel response matrix is ​​then written as:

[0036]

[0037] Among them, (Π1,Π2,…,Π) n ) represents a diagonal matrix, T T Let U represent the left singular vector after eigenvalue decomposition, and let U represent the right singular vector after eigenvalue decomposition. U has only one diagonal element, which is an eigenvalue of the Σ matrix.

[0038] Π1=diag(Σ1,0,…,0)

[0039] Π2=diag(0,Σ2,…,0)

[0040] …

[0041] Π n =diag(0,…,0,Σ) n )

[0042] Will After decomposing the signal into different multipath components, it is necessary to calculate the frequency offset of each multipath component. This requires extracting the multipath components from the received signal based on the decomposed channel response matrix. Given the received signal as y = Hx + z, and considering that the frequency offset of each multipath component has already been calculated... The received signal is rewritten as:

[0043]

[0044] The signal of the nth multipath is:

[0045]

[0046] In any of the above technical solutions, step S103 includes: establishing a cross-correlation signal for each signal, for Calculate the carrier frequency offset estimate for each signal. Among them, y np (n) represents the received multipath separation pilot signal, x * (i) represents the transmitted pilot signal, R represents the cross-correlation signal from multipath separation, and N represents the multipath separation cross-correlation signal.cp express, This represents the estimated carrier frequency offset.

[0047] In this technical solution, signals from different multipaths are separated to obtain (y 1p ,y 2p ,…,y np The traditional method for calculating frequency offset based on pilot signals is as follows, assuming the pilot length is N. sp Cross-correlation of the received signal and the local pilot signal yields:

[0048]

[0049] Among them, y np (n) represents the received pilot signal after multipath separation, x * (i) represents the local pilot signal, and R represents the cross-correlation signal. Therefore, the carrier frequency offset estimate is expressed as:

[0050]

[0051] in, This represents the estimated carrier frequency offset.

[0052] This method utilizes the cross-correlation of adjacent pilots at this stage to calculate the frequency offset of different multipaths, and (y 1p ,y 2p ,…,y np Substituting these values ​​into the calculation formula, we obtain the frequency offset estimate of the multipath component. This prepares for the next step of frequency offset compensation based on multi-scale wavelet transform.

[0053] In any of the above technical solutions, the step of scanning the frequency axis of the transmitted pilot signal to obtain frequency changes specifically includes: E1, acquiring and reading the transmitted pilot signal; E2, using formula W... X (a,b)=∫x(t)ψ a,b (t)dt, calculate the wavelet coefficients of the pilot signal; E3, change the wavelet scaling factor b, scan along the time axis to calculate the wavelet coefficients until the signal is fully processed; E4, change the wavelet shift factor a, return to step E2, complete the scan of the frequency axis, until the time axis scan is complete; where a represents the wavelet shift factor, b represents the wavelet scaling factor, W X (a,b) represents the amplitude of the wavelet component at the translation and scaling factors, and ψ(t) represents the basis function of the wavelet transform.

[0054] In this technical solution, the wavelet transform is able to observe signals in both the time and frequency domains simultaneously, overcoming the limitation of the Fourier transform, which can only observe signals in the frequency domain. At the same time, wavelets with different scaling factors can analyze signals at different resolution levels. Moreover, wavelet transform does not require the use of dynamic time windows to observe signals and can dynamically track frequency offset changes, thus improving the accuracy of frequency offset compensation.

[0055] In any of the above technical solutions, the multipath signal model is defined by the following formula: Where ε(t) represents noise, n l Represents the scaling factor, ρ l Let y(t) represent the impulse response amplitude, y(t) represent the received pilot signal, and s(k) represent the basis function coefficients. The translation coefficient s(k) = W is adjusted for different scaling factors nl of the wavelet. X (kT,n l ), τ l K represents the time shift, and K represents the time domain delay.

[0056] In any of the above technical solutions, step S3 includes: S301, setting y(t) as a superposition signal of basis functions ψ(t) at different scales, and performing matched filtering on the signal at each scale to maximize the signal at each scale; S302, performing autocorrelation detection on each signal to find the signal point with the largest value at that scale; wherein, the number of basis functions ψ(t) is equal to the number of time scaling scales, and the scale of the basis functions corresponds to the time scaling scale of the signal.

[0057] In this technical solution, the received signal y(t) is regarded as wavelet basis functions ψ at different scales. l The number of wavelet bases in the superimposed signal (t) is related to the number of time scaling scales. Multipath features have been extracted in the above steps, yielding the frequency offsets of different multipaths. It can be seen that the frequency offset manifests in the time domain as signal scaling; here, the frequency offset will be... Convert to scale scaling factor Then, based on the characteristics of wavelet transform, the wavelet of the corresponding scale is found.

[0058] Then, when performing Doppler compensation on the received signal using a diversity system, matched filtering is applied to the signal at each scale. The matching relationship between the matched filter and the wavelet basis function is as follows:

[0059]

[0060] in, This represents the complex conjugate of the Coiflets wavelet basis functions.

[0061] This step treats signals at other scales as noise, thereby maximizing the signal at this scale, and performs autocorrelation detection after matched filtering to find the maximum signal point at this scale.

[0062] In any of the above technical solutions, the matching relationship between the matched filter and the wavelet basis function is as follows: The multipath signal model is derived as follows: Among them, h l (t)=ρ l δ(t), and h l (t) represents the amplitude ρ l The impulse function, δ(t) representation, This represents the complex conjugate of ψ(t).

[0063] In this technical solution, matched filtering is used to treat signals at other scales as noise, thereby maximizing the signal at this scale.

[0064] Specifically, the formula after matching is:

[0065] The beneficial effects of this invention compared to the prior art are as follows:

[0066] Based on compensating for the Doppler frequency shift in the line-of-sight channel, the Doppler frequency shift spread caused by multipath effects in signal propagation is also compensated, thereby improving the transmission reliability of aircraft during the high-altitude flight phase.

[0067] By leveraging the ability of wavelet transform to observe signals simultaneously in both the time and frequency domains, it surpasses the limitation of Fourier transform, which can only observe signals in the frequency domain. Furthermore, wavelets with different scaling factors can analyze signals at different resolution levels. Moreover, wavelet transform does not require the use of dynamic time windows to observe signals and can dynamically track frequency offset changes, thereby improving the accuracy of frequency offset compensation.

[0068] Additional aspects and advantages of embodiments of the invention will become apparent in the following description or may be learned by practice of embodiments of the invention. Attached Figure Description

[0069] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0070] Figure 1 This is a flowchart illustrating the steps of the LDACS system's ultra-high Doppler frequency offset compensation method of the present invention.

[0071] Figure 2 This is a flowchart of the multi-scale wavelet compensation based on the present invention. Detailed Implementation

[0072] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments are combined with each other.

[0073] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention is also practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0074] The following reference Figures 1 to 2 This invention describes a method for compensating for the ultra-large Doppler frequency offset of an LDACS system according to an embodiment of the present invention.

[0075] Step 101: Signal modeling for the high-altitude flight phase of an aircraft:

[0076] In high-altitude flight path scenarios, the aircraft channel model consists of two components: a direct component, referring to the channel with a straight line connecting the transmitter and receiver; and a diffuse component, representing the components of the refraction and scattering paths. The ratio of the direct component to the diffuse component is generally described using the Rice factor.

[0077]

[0078] Among them, C los Indicates the amplitude of the direct component. K represents the variance of the diffuse component. rice This represents the Rice factor. During the phase where the aircraft approaches the control tower, the aircraft's angle of attack increases, and the direct component is much larger than the diffuse component. The diffuse component is ignored, and the air traffic channel follows a single-path model. When the aircraft leaves the control tower, the angle of attack decreases, and the ratio of the direct component to the diffuse component decreases. At this point, the diffuse component cannot be ignored, and the air traffic channel follows a two-path model. Due to multipath propagation, there are multiple sub-path signals with different arrival directions, and their Doppler frequency offsets are also different. The frequency shift of the diffuse component is a Doppler frequency shift spread within a certain range.

[0079] Based on the existing ground-to-air channel model constructed by research, the receiver Doppler frequency offset mainly includes direct path Doppler frequency offset and multipath Doppler spread. The receiver time-domain signal after generating Doppler frequency offset is represented as follows:

[0080]

[0081] Where y(t) represents the time-domain received signal with Doppler frequency offset, L represents the number of multipath paths, l represents the multipath index, x(t) represents the transmitted signal, and n l τ represents the time-domain scaling value caused by Doppler frequency offset. lh represents the delay of the l-th multipath. l (t) represents the channel impulse response of the l-th multipath, where ε(t) represents additive white Gaussian noise, and multipath refers to different time scaling scales.

[0082] Step 102 Channel estimation:

[0083] There are two approaches to estimating Doppler frequency shift. One approach is to obtain the position and velocity information of the source and receiver and then calculate the frequency shift using the Doppler formula. However, this method can only estimate the single-point frequency offset of the direct path and cannot estimate the multipath Doppler spread. Furthermore, for aircraft, the position and velocity information is difficult to obtain accurately. To overcome these problems, this patent proposes to use a channel estimation method to obtain Doppler information.

[0084] Channel estimation methods are divided into blind channel estimation and non-blind channel estimation. Blind channel estimation uses the structure and statistical characteristics of the received signal itself to obtain channel state information. Although it can reduce resource overhead, its performance is poor. Non-blind channel estimation refers to transmitting pilot signals, which are known to both the source and the receiver, in addition to transmitting data symbols, and then using these pilot signals for channel estimation. In aviation communications, aircraft fly at high speeds, the channel is dynamically changing, and OFDM symbols are complex with many subcarriers. The accuracy of blind channel estimation is insufficient to meet the requirements of rapidly changing channel states. This patent uses a pilot-based non-blind channel estimation method, employing the least squares estimation method to obtain channel state information.

[0085] The model considering the received signal is as follows:

[0086] y = Hx + z

[0087] Where y represents the received signal, H represents the channel response, x represents the transmitted signal, and z represents Gaussian white noise. σ 2 Let I represent the variance, and let I represent the identity matrix.

[0088] The goal of the least squares estimation method is to find the distance between and that is minimized, which means minimizing the following cost function:

[0089]

[0090] in, Let J(H) denote the conjugate transpose, and J(H) denote the objective function. Taking the derivative of the cost function with respect to the variables, we get:

[0091]

[0092] The solution obtained by the least squares estimation method is:

[0093]

[0094] In practical applications, x represents the local pilot signal. Let y represent the optimal estimated channel response matrix, and y represent the pilot signal received by the receiver. Thus, the channel response matrix is ​​obtained.

[0095] Step 103 Multipath Feature Extraction:

[0096] Based on the expression for the received signal, it is known that the received signal is a set of signals with different frequency offsets and time delays modulated by different multipaths. In order to separate the signals, this method uses singular value decomposition to extract the channel response of each path.

[0097] Suppose H is an m*n matrix whose elements all belong to the real or complex number field. Then there exists a decomposition such that:

[0098] H=UΣT T

[0099] Where U represents an m*m order Σ matrix, Σ represents a positive semi-definite m*n order diagonal matrix, and T T It is the conjugate transpose of T, and is an n*n matrix. Σ (a diagonal matrix, but not necessarily a square matrix) contains the elements Σ on its diagonal. i These are the singular values ​​of M.

[0100] The general form of Σ is as follows:

[0101]

[0102] The above decomposition constructs a matrix Σ, which has only diagonal elements, with all other elements being 0. Another convention is that the diagonal elements of Σ are arranged in descending order. In practical engineering, after a certain number (r) of singular values, all other singular values ​​are set to zero. This means that the dataset contains only r important features, and the rest are noise or redundant data.

[0103] In this method, the channel response matrix is ​​decomposed into a diagonal matrix Σ by singular value decomposition. The number of eigenvalues ​​represents the number of multipaths, and the magnitude of the eigenvalues ​​represents the amplitude of each multipath. When the diagonal matrix is ​​not full rank, it means that there are few multipaths, and all multipath information is extracted. However, when the diagonal matrix is ​​full rank, there may be incomplete extraction of multipath information. In this case, two pilot symbols are used to estimate the channel, and the dimension of the channel response matrix is ​​increased to avoid incomplete extraction of multipath information.

[0104] In obtaining The channel response matrix is ​​then written as:

[0105]

[0106] Among them, (Π1,Π2,…,Π)n ) represents a diagonal matrix, T T Let U represent the left singular vector after eigenvalue decomposition, and let U represent the right singular vector after eigenvalue decomposition. U has only one diagonal element, which is an eigenvalue of the Σ matrix.

[0107] Π1=diag(Σ1,0,…,0)

[0108] Π2=diag(0,Σ2,…,0)

[0109] …

[0110] Π n =diag(0,…,0,Σ) n )

[0111] Will After decomposing the signal into different multipath components, it is necessary to calculate the frequency offset of each multipath component. This requires extracting the multipath components from the received signal based on the decomposed channel response matrix. Given the received signal as y = Hx + z, and considering that the frequency offset of each multipath component has already been calculated... The received signal is rewritten as:

[0112]

[0113] The signal of the nth multipath is:

[0114]

[0115] Step 104: Carrier frequency offset estimation of multipath characteristic signals:

[0116] At this point, the signals from different multipaths have been separated, and (y) has been obtained. 1p ,y 2p ,…,y np The traditional method for calculating frequency offset based on pilot signals is as follows, assuming the pilot length is N. sp Cross-correlation of the received signal and the local pilot signal yields:

[0117]

[0118] Among them, y np (n) represents the received pilot signal after multipath separation, x * (i) represents the local pilot signal, R represents the cross-correlation signal, and x * Therefore, the carrier frequency offset estimate is expressed as:

[0119]

[0120] in, This represents the estimated carrier frequency offset.

[0121] This method utilizes the cross-correlation of adjacent pilots at this stage to calculate the frequency offset of different multipaths, and (y 1p ,y 2p ,…,y np Substituting these values ​​into the calculation formula, we obtain the frequency offset estimate of the multipath component. This prepares for the next step of frequency offset compensation based on multi-scale wavelet transform.

[0122] Step 104: Doppler frequency offset compensation based on multi-scale wavelet transform:

[0123] According to the formula, when frequency shifts are manifested in the time domain, different frequency shifts compress or expand the signal on the time axis. The scaling of the signal at different time scales caused by the Doppler frequency shifts of different multipaths is called scale diversity. This method aims to utilize the scale diversity brought about by Doppler expansion and use multi-scale wavelet transform to reconstruct the signal, thereby achieving frequency normalization and the construction of optimal decision variables.

[0124] The wavelet transform expression for the transmitted signal x(t) is:

[0125]

[0126] Where ψ(t) represents the basis functions of the wavelet transform, s(k) represents the basis function coefficients, k represents , and T represents . The wavelet transform process is as follows:

[0127] (1) Prepare the signal to be subjected to wavelet transform;

[0128] (2) Wavelet analysis: After reading the signal to be transformed, select the wavelet basis function (Coiflets wavelet is selected here) and its scale value, and calculate the wavelet coefficients using the wavelet transform formula.

[0129]

[0130] Where a represents the wavelet translation coefficient, b represents the wavelet scaling coefficient, and W X (a,b) represents the amplitude of the wavelet component at the translation and scaling factors, and ψ(t) represents the Coiflets wavelet basis function.

[0131] (3) Change the translation amount b, scan along the time axis, and calculate the wavelet coefficients to know the signal focus.

[0132] (4) Change the time scale a and repeat steps (2) and (3) to complete the scan of the frequency axis.

[0133] Let h l (t)=ρ l δ(t), i.e., h l (t) amplitude is ρ lThe impulse function, the received signal y(t), is expressed as:

[0134]

[0135] Where ε(t) represents noise, n l ρ represents the scaling factor. l This indicates the magnitude of the impulse response.

[0136] The received signal y(t) is considered as wavelet basis functions ψ at different scales. l The number of wavelet bases of the superimposed signal (t) is related to the number of multipaths. The multipath features have been extracted in step 103 to obtain the frequency offsets of different multipaths. It can be seen that the frequency offset manifests in the time domain as signal scaling; here, the frequency offset will be... Convert to scale scaling factor Then, based on the characteristics of wavelet transform, the wavelet of the corresponding scale is found.

[0137] The received signal is then subjected to Doppler compensation using a diversity system. Different multipath signals have different Doppler frequency offsets, corresponding to different time scaling variations in the time domain and different wavelet scaling coefficients in the wavelet transform. Matched filtering is then applied to the signal at each scale, where the relationship between matched filtering and the wavelet basis function is as follows:

[0138]

[0139] in, This represents the complex conjugate of the Coiflets wavelet basis functions.

[0140] This step treats signals at other scales as noise, thereby maximizing the signal at this scale, and performs autocorrelation detection after matched filtering to find the signal point with the largest value at this scale.

[0141] Next, time-domain resampling is performed. The above steps yielded signals that separated each multipath signal. While each path's initial frequency is the same, their Doppler frequency offsets differ, resulting in different frequencies at the receiver. Wavelet transform is used to maximize the signal of each path. Since the frequency offset manifests as signal scaling in the time domain, time-domain resampling eliminates this offset. The sampling factor is a time-domain scaling factor, thus restoring the frequency to its state before the frequency offset was eliminated, completing frequency normalization. Finally, the normalized signals are merged by adding the normalized signals of each path to obtain the optimal decision signal, which is then fed into the decision-maker for judgment. This completes the compensation for the multipath Doppler frequency offset.

[0142] In the description of this invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this invention, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0143] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for compensating for ultra-high frequency doppler offset in an LDACS system, characterized in that, Includes the following steps: S1, perform channel estimation on the received pilot signal in the time domain, separate multiple signals, and calculate the carrier frequency offset estimate for each signal; S2, scan the frequency axis of the pilot signal to obtain the frequency change, and construct a multipath signal model based on the frequency change; S3, respectively obtain the maximum signal of the multipath signal model at different time scaling scales; S4 uses the carrier frequency offset estimate as a sampling factor to resample the multipath signal model in the time domain of S1, and outputs the maximum signal at each time scaling scale and adds them together to obtain the optimal decision signal.

2. The method for compensating for ultra-large Doppler frequency offset in an LDACS system according to claim 1, characterized in that, Step S1 specifically includes: S101, perform channel estimation on the received pilot signal in the time domain to obtain the channel response matrix; S102, Multipath feature extraction is performed on the channel response matrix to obtain each signal in the time domain; S103, calculate the estimated carrier frequency offset of each signal based on the cross-correlation signal between the currently received time-domain signal and the local pilot signal.

3. The method for super Doppler frequency offset compensation in an LDACS system according to claim 2, characterized in that, The pilot signal is transmitted synchronously with the data symbols at the transmitting end and can be acquired at both the receiving and transmitting ends; The steps in S101 include: Establish a model that considers the relationship between the received pilot signal and the transmitted pilot signal, for ; Based on the model, a cost function that minimizes the distance between the transmitter and receiver is established. ; The cost function is minimized to obtain the channel response matrix representing the optimal relationship. ; in, Indicates the received pilot signal, Indicates channel response, Indicates the pilot signal to be transmitted. Indicates noise, This indicates the conjugate transpose. The objective function representing the minimum distance, This represents the optimal estimated channel response matrix.

4. The method for compensating for ultra-large Doppler frequency offset in an LDACS system according to claim 3, characterized in that, The steps in S102 include: In the context of setting the relational model Given a multi-order matrix, and by solving the decomposition of the channel response matrix, we obtain... ; Calculate the channel response for each signal and obtain the signal relation model based on the relation model. ; Where U represents an m*m order chief matrix, T represents a diagonal matrix whose diagonal elements have values ​​only at the position (n,n). T Let T represent the conjugate transpose of T, where T is an n*n matrix. Indicates the number of multipaths, Indicates the received number n signal.

5. The method for compensating for ultra-large Doppler frequency offset in an LDACS system according to claim 4, characterized in that, The steps in S103 include: Establish the cross-correlation signal for each signal, for ; Calculate the carrier frequency offset estimate for each signal. ; in, Indicates the received multipath separation pilot signal, Indicates the pilot signal to be transmitted. Cross-correlation signals representing multipath separation This represents the estimated carrier frequency offset. This indicates the length of the cyclic prefix pilot.

6. The method for super Doppler frequency offset compensation in an LDACS system according to claim 1, characterized in that, The step of scanning the frequency axis of the pilot signal to obtain frequency changes is as follows: E1, acquire and read the transmitted pilot signal; E2, using the formula Calculate the wavelet coefficients of the pilot signal; E3, change the wavelet scaling factor Wavelet coefficients are calculated by scanning along the time axis; E4, change the wavelet shift coefficient Return to step E2 to complete the scan of the frequency axis until the scan of the time axis is completed; in, Represents the wavelet translation coefficients. Represents the wavelet scaling factor. This represents the amplitude of the wavelet component at the translation and scaling factors. These represent the basis functions of the wavelet transform.

7. The method for compensating for ultra-large Doppler frequency offset in an LDACS system according to claim 6, characterized in that, The multipath signal model is given by the following formula: ； in, Indicates noise, Indicates scaling factor, Indicates the impulse response amplitude, Indicates the received pilot signal, Represents the basis function coefficients, and for different scaling factors The wavelet changes its translation coefficient. = , The time shift, K, represents the time-domain delay.

8. The method for compensating for ultra-large Doppler frequency offset in an LDACS system according to claim 7, characterized in that, The steps in S3 include: S301, Set as basis functions of different scales The superimposed signals are processed, and matched filtering is applied to the signals at each scale to maximize the signal at each scale. S302, perform autocorrelation detection on each signal to find the signal point with the largest signal at this scale; Wherein, basis functions The number of basis functions is equal to the number of time scaling scales, and the scale of the basis functions corresponds to the time scaling scale of the signal.

9. A method for compensating for ultra-large Doppler frequency offset in an LDACS system according to claim 8, characterized in that, The matching relationship between the matched filter and the wavelet basis function is as follows: The multipath signal model is derived using the following formula: ； in, ,and For amplitude impulse function Represents the standard impact function, express .

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