An AFDM channel estimation method based on a structured pilot design and a two-stage estimation framework

Abstract

The application discloses an AFDM channel estimation method based on a structured pilot design and a two-stage estimation framework, and belongs to the technical field of wireless communication and signal processing. The application solves the problem of low channel parameter estimation accuracy of current methods. The application firstly jointly designs a pilot subcarrier set, DAFT parameters and related pilot parameters, so that pilot symbols form a structured sparse pattern in a DD domain, and through parameter screening, ensures that a pilot active area meets separation requirements under a double fractional delay-Doppler channel condition; a zero protection area corresponding to the pilot is set in a DAFT domain, and pilot-data separation is implemented at a receiving end, so as to suppress pilot energy leakage and adjacent data symbol interference, and obtain reliable channel estimation observation; then, the separated pilot related components are mapped to the DD domain to construct a channel estimation observation matrix, and based on parameters of each propagation path, an equivalent channel matrix of the AFDM system is reconstructed. The method can be applied to channel estimation of the AFDM system.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication and signal processing technology, specifically relating to an AFDM (Affine Frequency Division Multiplexing) channel estimation method based on structured pilot design and a two-stage estimation framework. Background Technology

[0002] In high-mobility communication scenarios such as vehicle-to-everything (V2X), high-speed rail, and low-orbit satellite communication, wireless channels exhibit rapid changes in both the time and frequency domains, exhibiting significant biselective fading characteristics. Traditional orthogonal frequency division multiplexing (AFDM) systems are prone to severe inter-carrier interference in these scenarios, leading to performance degradation. AFDM is a multi-carrier modulation method suitable for biselective channel environments. It maps information symbols onto orthogonally chirped subcarriers using the inverse discrete affine fourier transform (IDAFT), distributing the energy of each symbol across the entire time-frequency plane. This allows for more effective utilization of diversity gain in biselective channels and can be adapted to different channel environments by adjusting the DAFT parameters.

[0003] Channel estimation is a crucial step in achieving reliable reception in AFDM systems. Existing AFDM channel estimation methods typically rely on the separability, stability, or sparsity of the equivalent channel in the DAFT domain for pilot design and path parameter estimation. However, in real-world propagation environments, limitations in time delay and Doppler resolution inevitably result in fractional components in the normalized time delay and Doppler offset of the equivalent channel. This leads to the diffusion of the equivalent channel response for each propagation path in the DAFT domain, further generating aliasing (referred to as a double fractional channel). In this case, pilot design and parameter estimation methods based on the separability of the DAFT domain path are difficult to apply directly, easily leading to problems such as pilot response aliasing and decreased accuracy in path parameter recovery.

[0004] Therefore, there is an urgent need to provide an AFDM channel estimation method suitable for dual fractional channel conditions, so that even when the propagation path response spreads and overlaps, the pilot correlation signal can still be effectively separated and the channel parameters can be accurately recovered, thereby improving the communication performance and reliability of the AFDM system in high mobility scenarios. Summary of the Invention

[0005] This invention addresses the problem of low channel parameter estimation accuracy in current methods due to pilot response aliasing and low path parameter recovery accuracy. It proposes an AFDM channel estimation method based on structured pilot design and a two-stage estimation framework.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is: an AFDM channel estimation method based on structured pilot design and a two-stage estimation framework, the method specifically including the following steps:

[0007] Step 1: Record the total number of subcarriers in the AFDM system as... Let the grid dimension of the DD domain be denoted as And satisfy , Let be the dimension of the time-delay domain grid. Let be the dimension of the Doppler domain grid. and All are positive integers;

[0008] The set of subcarriers carrying pilot information at the transmitting end is denoted as . ,gather The number of subcarriers included is And satisfy , The interval between adjacent subcarriers carrying pilot information. and All are positive integers;

[0009] Step 2: Set DAFT domain parameters and They are respectively:

[0010]

[0011]

[0012] in, and All are constants;

[0013] Step 3: In the DAFT field, based on the set For pilot symbols Zero protection zone and data symbols By performing joint configuration, the composite signal distribution at the transmitting end is obtained. ;

[0014] Then analyze the distribution of the composite signal Perform IDAFT transformation to obtain the AFDM time-domain transmit signal. After inserting a cyclic prefix into the AFDM time-domain transmit signal, transmit the time-domain signal with the cyclic prefix inserted through a dual fractional channel.

[0015] Step 4: The receiving end receives the time-domain signal after the channel has been processed, and performs cyclic prefix removal and DAFT transform on the received signal in sequence to obtain the received DAFT domain composite signal. ;

[0016] Then according to the set The maximum normalized delay, maximum normalized Doppler offset, and fractional parameter leakage range of the channel are used to determine the composite signal. Pilot active region in According to the active pilot region Calculate the pilot correlation receive vector ;

[0017] Step 5: Assess the pilot-related received vector. Perform an IDAFT transform, then map the IDAFT transform result to the DD domain to obtain the DD domain pilot correlation matrix. ;

[0018] Step 6: Based on the DD domain pilot correlation matrix By jointly estimating the parameters of each propagation path, a parameter set for each propagation path is obtained. ;

[0019] in, For the first Gain of each propagation path For the first Integer delay components of each propagation path, For the first Fractional delay components of each propagation path, For the first Integer Doppler components of the propagation path, For the first Fractional Doppler components of each propagation path, Number of propagation paths;

[0020] Step 7: Reconstruct the equivalent channel matrix of the AFDM system based on the parameters of each propagation path. The channel estimation results are obtained.

[0021] The beneficial effects of this invention are:

[0022] This invention first designs the pilot subcarrier set, DAFT parameters, and related pilot parameters based on the representation characteristics of subcarriers in the delay-Doppler domain of an AFDM system. This design enables the pilot symbols to form a structured sparse pattern in the DD domain. Parameter selection ensures that the active pilot region meets the separation requirements under the dual fractional delay-Doppler channel condition. A zero-protection zone corresponding to the pilot is set in the DAFT domain, and pilot-data separation is implemented at the receiver. This suppresses pilot energy leakage and interference from adjacent data symbols caused by fractional delay and fractional Doppler, resulting in reliable channel estimation observations. Subsequently, at the receiver, the separated pilot correlation components are mapped to the DD domain to construct the channel estimation observation matrix. Based on the off-network sparse recovery method, the gain, delay, and Doppler parameters of each propagation path are jointly estimated, and the equivalent channel matrix of the AFDM system is reconstructed. This improves the channel estimation accuracy, data detection performance, and communication reliability of the AFDM system in high-mobility scenarios. Attached Figure Description

[0023] Figure 1 This is a flowchart of an AFDM channel estimation method based on structured pilot design and a two-stage estimation framework according to the present invention.

[0024] Figure 2 This is the first set of pilot parameters. Schematic diagram of the corresponding DD domain structured sparse pilot pattern;

[0025] Figure 3 It is the second set of pilot parameters Schematic diagram of the corresponding DD domain structured sparse pilot pattern;

[0026] Figure 4 It is the third set of pilot parameters Schematic diagram of the corresponding DD domain structured sparse pilot pattern;

[0027] Figure 5 It is the fourth set of pilot parameters Schematic diagram of the corresponding DD domain structured sparse pilot pattern;

[0028] Figure 6 It is the fifth group of pilot parameters Schematic diagram of the corresponding DD domain structured sparse pilot pattern;

[0029] Figure 7 It is the sixth group of pilot parameters Schematic diagram of the corresponding DD domain structured sparse pilot pattern;

[0030] Figures 2-7 This illustrates the distribution patterns, quantity, shape, and location variations of pilot patterns in the DD domain under different pilot parameter configurations.

[0031] Figure 8 A schematic diagram of the DAFT domain pilot, zero protection zone, and active receiving area;

[0032] Used to illustrate the joint configuration of the transmitter (Tx) pilot symbols, zero protection zone, and data signal, as well as the extraction range of the receiver (Rx) pilot active region;

[0033] Figure 9 This is a schematic diagram of the pilot signal;

[0034] Figure 10 A schematic diagram for transmitting composite signals;

[0035] Figure 11 A schematic diagram for receiving composite signals;

[0036] Figure 12 This is a schematic diagram of pilot correlation signals;

[0037] Figures 9-12 Used to illustrate the changes in pilot-related signals during the transmission configuration, channel transmission and reception, and pilot extraction processes;

[0038] Figure 13 This is a comparison curve of the normalized mean square error (NMSE) performance of the method of the present invention and the comparative method;

[0039] Figure 14 This is a graph comparing the bit error rate (BER) performance of the method of this invention with that of the comparative method. Detailed Implementation

[0040] When a propagation path has both fractional delay and fractional Doppler, the equivalent responses of each propagation path in the DAFT domain will spread and overlap, making it difficult to separate the active pilot region, thus affecting the accuracy of pilot extraction and path parameter recovery. To address the above-mentioned shortcomings of existing AFDM channel estimation methods under dual fractional channel conditions, this invention first proposes a pilot design method suitable for single-input single-output AFDM systems, which constructs a structured sparse pilot pattern in the DD domain and ensures the separability of the active pilot region at the receiver. Then, a two-stage AFDM channel estimation method suitable for dual fractional channel conditions is proposed. In the first stage, the pilot correlation signal is extracted in the DAFT domain to separate the pilot from the data. In the second stage, the separated pilot correlation signal is mapped to the DD domain, an observation matrix is ​​constructed, and off-network sparse recovery is performed to complete the channel parameter estimation and equivalent channel matrix reconstruction.

[0041] Specific implementation method one: Combining Figure 1 This embodiment describes an AFDM channel estimation method based on structured pilot design and a two-stage estimation framework. The method specifically includes the following steps:

[0042] Step 1: Record the total number of subcarriers in the AFDM system as... Let the grid dimension of the DD domain be denoted as And satisfy , Let be the dimension of the time-delay domain grid. Let be the dimension of the Doppler domain grid. and All are positive integers;

[0043] The set of subcarriers carrying pilot information at the transmitting end is denoted as . ,gather The number of subcarriers included is ,gather The subcarriers within the AFDM system are arranged discretely at equal intervals, allowing multiple subcarriers carrying pilot information to form a regular distribution in the DD domain. This provides a foundation for the subsequent construction of structured sparse pilot patterns and satisfies... , The interval between adjacent subcarriers carrying pilot information. and All are positive integers;

[0044] Step 2: To ensure the sparsity of the pilot DD domain pattern and to allow the shape and position of the pilot pattern to be controlled by relevant parameters, set the DAFT domain parameters. and They are respectively:

[0045]

[0046]

[0047] in, and All are constants;

[0048] parameter Used to control the number of active points in the pilot pattern; Parameter Used to control the shape of the active point distribution; parameters and Used to control the position of the pilot pattern in the DD domain. For example... Figures 2 to 7 As shown, under different pilot parameter configurations, the pilot patterns in the DD domain can exhibit different quantities, shapes, and positional distributions. By setting the aforementioned pilot parameters, the joint design of structured sparse pilot patterns in the DD domain can be achieved.

[0049] Step 3: To enable the receiver to form an extractable and separable pilot receiving area, in the DAFT domain, based on the set... For pilot symbols Zero protection zone and data symbols By performing joint configuration, the composite signal distribution at the transmitting end is obtained. , ;

[0050] Then analyze the distribution of the composite signal Perform IDAFT transformation to obtain the AFDM time-domain transmit signal. After inserting a cyclic prefix into the AFDM time-domain transmit signal, transmit the time-domain signal with the cyclic prefix inserted through a dual fractional channel.

[0051] Step 4: The receiving end receives the time-domain signal after the channel has been processed, and performs cyclic prefix removal and DAFT transform on the received signal in sequence to obtain the received DAFT domain composite signal. , Composite signal It includes pilot signals, data signals, and noise terms;

[0052] Then according to the set The maximum normalized delay, maximum normalized Doppler offset, and fractional parameter leakage range of the channel are used to determine the composite signal. Pilot active region in According to the active pilot region Calculate the pilot correlation receive vector ;

[0053] Step 5: Assess the pilot-related received vector. Perform an IDAFT transform, and then map the IDAFT transform result to the DD domain (preferably using the discrete Zak transform) to obtain the DD domain pilot correlation matrix. ;

[0054] Step 6: Based on the DD domain pilot correlation matrix By jointly estimating the parameters of each propagation path, a parameter set for each propagation path is obtained. ;

[0055] in, For the first Gain of each propagation path For the first Integer delay components of each propagation path, For the first Fractional delay components of each propagation path, For the first Integer Doppler components of the propagation path, For the first Fractional Doppler components of each propagation path, The number of distinguishable propagation paths;

[0056] Specifically, a sparse mapping relationship between the wireless propagation channel and the pilot pattern in the DD domain is established, transforming the AFDM channel estimation problem into an off-grid sparse recovery problem in the DD domain, and then the parameters of each propagation path are estimated. The preferred off-grid sparse recovery method is Spare Bayesian Learning (SBL), but Orthogonal Matching Pursuit (OMP) or other off-grid sparse recovery algorithms can also be used.

[0057] Step 7: Reconstruct the equivalent channel matrix of the AFDM system based on the parameters of each propagation path. The channel estimation results are obtained.

[0058] Specific Implementation Method Two: This implementation method is a further limitation of Specific Implementation Method One, wherein the set The set of indices for the subcarriers contained herein is:

[0059]

[0060] in, For set The index of the first subcarrier carrying pilot information (which can be randomly given). For set Subcarrier index carrying pilot information;

[0061] when Less than or equal to hour, ;

[0062] when Greater than hour, .

[0063] The other steps and parameters are the same as in Specific Implementation Method 1.

[0064] Specific Implementation Method 3: This implementation method further defines Specific Implementation Method 2, wherein the spacing between adjacent subcarriers carrying pilot information is... and constant The method for determining it is as follows:

[0065] Step 1: Set the time delay direction protection interval in the DD domain and Doppler direction protection interval They are respectively:

[0066]

[0067]

[0068] in:

[0069] For maximum normalized delay, For the maximum normalized Doppler shift, The effective range of the time delay domain, The effective range of the Doppler domain;

[0070] Step 2: Initialize the parameter set And calculate the upper bound of the number of non-zero points in the pilot pattern in the DD domain. :

[0071]

[0072] in, To round down;

[0073] Step 3, Initialization ;

[0074] Step 4, Calculation The value;

[0075] like Then the active region of the pilot signal can meet the separation requirements only through the time delay dimension, and the parameters are... Take any integer, and set the parameter group Add parameter set ;

[0076] like Therefore, relying solely on time delay separation is insufficient to guarantee that the active regions of the pilot signals do not overlap; it is necessary to simultaneously satisfy the separation constraints of both the time delay dimension and the Doppler dimension. The following conditions must be met: , set the parameters that meet the conditions Add parameter set ;

[0077] in, To round up;

[0078] Step 5: Determine if the condition is met. ;

[0079] If not satisfied Then let Return to step 4;

[0080] If satisfied Then we get the final parameter set. From the parameter set A set of parameters is randomly selected to design the composite signal distribution at the transmitting end.

[0081] The other steps and parameters are the same as in Specific Implementation Method Two.

[0082] The feasible parameter set obtained in this embodiment Any set of parameters can ensure that the active regions corresponding to each pilot satisfy the minimum separation condition in the DD domain, that is, ensure that the active regions in the DD domain corresponding to different pilots have sufficient separation, thereby suppressing inter-pilot interference caused by double fractional time delay and Doppler shift.

[0083] Specific Implementation Method Four: This implementation method further defines Specific Implementation Method Three. The composite signal distribution at the transmitting end is as follows:

[0084]

[0085] in:

[0086] Composite signal distribution at the transmitting end The first in A symbol, For pilot signals, For the first The zero-protection zone of each pilot frequency, For data symbols, The energy of data symbols.

[0087] The other steps and parameters are the same as in Specific Implementation Method 3.

[0088] Specific Implementation Method Five: This implementation method further defines Specific Implementation Method Four, and the zero protection zone range... , As an intermediate variable, It is an integer. for The absolute value, Zero protection zone width;

[0089] when Greater than hour, ;

[0090] when Less than or equal to hour, ;

[0091] Traversal After each value is taken, the first value is obtained. Zero protection zone of each pilot. .

[0092] The other steps and parameters are the same as in Specific Implementation Method Four.

[0093] Specific Implementation Method Six: This implementation method is a further limitation of Specific Implementation Method Five, wherein the zero protection zone width... for:

[0094]

[0095] in: This represents the maximum active region width determined by pilot energy diffusion under the two-fractional-channel condition;

[0096]

[0097] in, The range of fractional parameters for the DAFT domain.

[0098] The other steps and parameters are the same as in Specific Implementation Method 5.

[0099] This implementation determines the zero-protection zone width based on the pilot energy leakage range caused by fractional delay and fractional Doppler, in order to cover the active pilot receiving area and suppress interference from adjacent data symbols on pilot estimation. For example... Figure 8 As shown, by jointly configuring pilot symbols, zero protection zones, and data signals in the DAFT domain, the receiver can form an extractable and separable active pilot region.

[0100] Specific Implementation Method Seven: This implementation method is a further limitation of Specific Implementation Method Six, wherein the composite signal Pilot active region in Represented as:

[0101] in, As an intermediate variable;

[0102] when Greater than hour, ;

[0103] when Less than or equal to hour, ;

[0104] Traversal and The value yields the pilot active region. Pilot active region In composite signals The position corresponding to the above is the composite signal. Location of the intermediate pilot frequency correlated signal.

[0105] The other steps and parameters are the same as in Specific Implementation Method Six.

[0106] Specific Implementation Method Eight: This implementation method is a further limitation of Specific Implementation Method Seven, wherein the method based on the pilot active region... Calculate the pilot correlation receive vector Specifically:

[0107] Construct the receive window matrix:

[0108]

[0109] in: For receiving window matrix, , For matrix The Middle Line number Column elements;

[0110] According to the receiving window matrix From composite signal Extract the signal components related to pilot estimation:

[0111]

[0112] in: composite signal The signal components related to pilot estimation in the signal.

[0113] The other steps and parameters are the same as in Specific Implementation Method Seven.

[0114] Specific Implementation Method Nine: This implementation method is a further limitation of Specific Implementation Method Eight, wherein the DD domain pilot correlation matrix for:

[0115]

[0116] in: This indicates that the length is The vector is converted to a dimension of Operations on matrices of length 10 ... The first element of the vector to the second element The nth element is used as the first row of the matrix, and the nth element is used as the first row of the matrix. The elements up to the first Each element is used as the second row of the matrix;

[0117] The dimension is The normalized discrete Fourier transform matrix, , for The conjugate transpose of the matrix. The dimension is The normalized discrete Fourier transform matrix;

[0118] and Let be a discrete Chirp diagonal matrix, and , for The conjugate transpose of the matrix. for The conjugate transpose of ;

[0119]

[0120]

[0121] in, is the base of the natural logarithm. Represents a diagonal matrix. It is the imaginary unit.

[0122] The other steps and parameters are the same as in Specific Implementation Method 8.

[0123] The DD-domain pilot correlation matrix in this embodiment characterizes the active distribution of pilot signals in the DD domain and the diffusion characteristics caused by fractional time delay and fractional Doppler, serving as the observation basis for off-grid sparse recovery. Figures 9 to 12 As shown, interference can be effectively reduced by separating pilot signals from data. After further mapping in the DD domain, pilot-related signals can be effectively separated in the DD domain, providing an observational basis for subsequent channel parameter estimation.

[0124] Specific Implementation Method Ten: This implementation method is a further limitation of Specific Implementation Method Nine. The specific process of step seven is as follows:

[0125]

[0126] in: It is a diagonal matrix. ; This is the frequency offset matrix. ; Represents the time offset matrix;

[0127]

[0128]

[0129]

[0130] in: It is a forward circular matrix. for The conjugate transpose of .

[0131] The other steps and parameters are the same as in Specific Implementation Method Nine.

[0132] By performing DD domain off-network estimation and equivalent channel reconstruction in the second stage, the channel estimation accuracy of the AFDM system under dual-selectivity dual-fractional-channel conditions can be improved, thereby enhancing communication reliability.

[0133] Simulation section

[0134] To verify the effectiveness of the AFDM channel estimation method proposed in this invention, Monte Carlo simulations were performed on a single-input single-output AFDM system. In the simulation, the grid dimension of the DD domain was taken as... Total number of system carriers Maximum normalized delay of the channel Maximum Normalized Doppler Migration The maximum number of propagation paths is 4. The pilot parameters of the DD domain estimation algorithm are set to... The time delay resolution is 0.5. The DAFT domain estimation algorithm uses a single embedded pilot architecture with an index of 0 and frequency modulation parameters. The Doppler resolution is 0.5. To ensure fairness in the comparison, all comparison algorithms use the same system and channel parameter settings.

[0135] Under the above simulation conditions, using the normalized mean square error (NMSE) as the channel estimation performance evaluation index, the method of this invention is compared with the comparative method under different conditions. The variation of channel estimation accuracy with SNR, where This is the pilot energy. (From...) Figure 13 As can be seen, the method of this invention exhibits superior NMSE performance under low, medium, and high signal-to-noise ratio (SNR) conditions, and its estimation performance advantage further extends with increasing SNR. In particular, the DD domain estimation algorithm performs better in the SNR range greater than 10 dB. The estimation performance under the given conditions is better than that under the DAFT domain. The performance of the Off-grid algorithm is shown in the figure below; however, in the DD domain algorithm, the Off-grid algorithm consistently maintains its performance advantage over the On-grid algorithm. This indicates that the present invention, through the combination of structured pilot design, DAFT domain pilot-data separation, and DD domain off-network sparse recovery, can effectively suppress the impact of pilot energy diffusion and data interference on estimation accuracy under dual fractional channel conditions, thereby improving the channel estimation performance of the AFDM system.

[0136] Under the above simulation conditions, the impact of different channel estimation methods on the data detection performance at the receiver is further examined, and the BER results of VAMP and MMSE detectors are used as evaluation metrics. To ensure fairness among the detection modules during BER performance comparison, the frequency modulation parameter of the data frame is uniformly set to [value missing]. .Depend on Figure 14 As can be seen, when using the channel estimation results obtained by the method of this invention for data detection, under the two detectors, it exhibits the same characteristics as... Figure 13The same performance comparison pattern holds true: the BER performance of the DD domain algorithm is superior to that of the DAFT domain algorithm, and the performance of the Off-Grid scheme in the DD domain is even better than that of the On-Grid algorithm. This result demonstrates that the method of this invention not only improves the accuracy of channel parameter estimation but also provides more reliable channel state information for subsequent detectors through more accurate equivalent channel matrix reconstruction, thereby improving the bit error rate performance of the AFDM system in a fractional-delay-Doppler channel.

[0137] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. An AFDM channel estimation method based on structured pilot design and a two-stage estimation framework, characterized in that, The method specifically includes the following steps: Step 1: Record the total number of subcarriers in the AFDM system as... Let the grid dimension of the DD domain be denoted as And satisfy , Let be the dimension of the time-delay domain grid. Let be the dimension of the Doppler domain grid. and All are positive integers; The set of subcarriers carrying pilot information at the transmitting end is denoted as . ,gather The number of subcarriers included is And satisfy , The interval between adjacent subcarriers carrying pilot information. and All are positive integers; Step 2: Set DAFT domain parameters and They are respectively: in: and All are constants; Step 3: In the DAFT field, based on the set For pilot symbols Zero protection zone and data symbols By performing joint configuration, the composite signal distribution at the transmitting end is obtained. ; Then analyze the distribution of the composite signal Perform IDAFT transformation to obtain the AFDM time-domain transmit signal. After inserting a cyclic prefix into the AFDM time-domain transmit signal, transmit the time-domain signal with the cyclic prefix inserted through a dual fractional channel. Step 4: The receiving end receives the time-domain signal after the channel has been processed, and performs cyclic prefix removal and DAFT transform on the received signal in sequence to obtain the received DAFT domain composite signal. ; Then according to the set The maximum normalized delay, maximum normalized Doppler offset, and fractional parameter leakage range of the channel are used to determine the composite signal. Pilot active region in According to the active pilot region Calculate the pilot correlation receive vector ; Step 5: Assess the pilot-related received vector. Perform an IDAFT transform, then map the IDAFT transform result to the DD domain to obtain the DD domain pilot correlation matrix. ; Step 6: Based on the DD domain pilot correlation matrix By jointly estimating the parameters of each propagation path, a parameter set for each propagation path is obtained. ; in: For the first Gain of each propagation path For the first Integer delay components of each propagation path, For the first Fractional delay components of each propagation path, For the first Integer Doppler components of the propagation path, For the first Fractional Doppler components of each propagation path, Number of propagation paths; Step 7: Reconstruct the equivalent channel matrix of the AFDM system based on the parameters of each propagation path. The channel estimation results are obtained.

2. The AFDM channel estimation method based on structured pilot design and a two-stage estimation framework according to claim 1, characterized in that, The set The set of indices for the subcarriers contained herein is: in: For set The first subcarrier index carrying pilot information within the array. For set Subcarrier index carrying pilot information; when Less than or equal to hour, ; when Greater than hour, .

3. The AFDM channel estimation method based on structured pilot design and a two-stage estimation framework according to claim 2, characterized in that, The interval between adjacent subcarriers carrying pilot information and constant The method for determining it is as follows: Step 1: Set the time delay direction protection interval in the DD domain and Doppler direction protection interval They are respectively: in: For maximum normalized delay, For the maximum normalized Doppler shift, The effective range of the time delay domain, The effective range of the Doppler domain; Step 2: Initialize the parameter set And calculate the upper bound of the number of non-zero points in the pilot pattern in the DD domain. : in: To round down; Step 3, Initialization ; Step 4, Calculation The value; like Then the parameters Take any integer, and set the parameter group Add parameter set ; like Then the parameter The following conditions must be met: , set the parameters that meet the conditions Add parameter set ; in: To round up; Step 5: Determine if the condition is met. ; If not satisfied Then let Return to step 4; If satisfied Then we get the final parameter set. From the parameter set A set of parameters is randomly selected to design the composite signal distribution at the transmitting end.

4. The AFDM channel estimation method based on structured pilot design and a two-stage estimation framework according to claim 3, characterized in that, The composite signal distribution at the transmitting end is as follows: in: Composite signal distribution at the transmitting end The first in A symbol, For pilot signals, For the first The zero-protection zone of each pilot frequency, For data symbols, The energy of data symbols.

5. The AFDM channel estimation method based on structured pilot design and a two-stage estimation framework according to claim 4, characterized in that, The zero protection zone , As an intermediate variable, It is an integer. for The absolute value, Zero protection zone width; when Greater than hour, ; when Less than or equal to hour, ; Traversal After each value is taken, the first value is obtained. Zero protection zone of each pilot. .

6. The AFDM channel estimation method based on structured pilot design and a two-stage estimation framework according to claim 5, characterized in that, The width of the zero protection zone for: in: This represents the maximum active region width determined by pilot energy diffusion under the two-fractional-channel condition; in, The range of fractional parameters for the DAFT domain.

7. The AFDM channel estimation method based on structured pilot design and a two-stage estimation framework according to claim 6, characterized in that, The composite signal Pilot active region in Represented as: in: As an intermediate variable; when Greater than hour, ; when Less than or equal to hour, ; Traversal and The value yields the pilot active region. Pilot active region In composite signals The position corresponding to the above is the composite signal. Location of the intermediate pilot frequency correlated signal.

8. The AFDM channel estimation method based on structured pilot design and a two-stage estimation framework according to claim 7, characterized in that, The based on pilot active region Calculate the pilot correlation receive vector Specifically: Construct the receive window matrix: in: For receiving window matrix, , For matrix The Middle Line number Column elements; According to the receiving window matrix From composite signal Extract the signal components related to pilot estimation: in: composite signal The signal components related to pilot estimation in the signal.

9. The AFDM channel estimation method based on structured pilot design and a two-stage estimation framework according to claim 8, characterized in that, The DD domain pilot correlation matrix for: in: This indicates that the length is The vector is converted to a dimension of Matrix operations; The dimension is The normalized discrete Fourier transform matrix, for The conjugate transpose of the matrix. The dimension is The normalized discrete Fourier transform matrix; and For discrete Chirp diagonal matrices, for The conjugate transpose of the matrix. for The conjugate transpose of ; in: is the base of the natural logarithm. Represents a diagonal matrix. It is the imaginary unit.

10. The AFDM channel estimation method based on structured pilot design and a two-stage estimation framework according to claim 9, characterized in that, The specific process of step seven is as follows: in: It is a diagonal matrix; This is the frequency offset matrix; Represents the time offset matrix; in: It is a forward circular matrix. for The conjugate transpose of .

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