Monostatic AFDM-ISAC Sensing Method Based on Fractional Delay-Doppler Feature Extraction and Pilot Optimization ML Estimation

Abstract

This invention relates to a monostatic AFDM-ISAC sensing method based on fractional delay-Doppler feature extraction and pilot-optimized ML estimation, belonging to the field of target sensing technology. This invention addresses the problems of high computational complexity and lack of flexible adjustability in traditional methods. Utilizing the dispersion characteristics of fractional delay and fractional Doppler frequency offset in the AFDM equivalent channel matrix, this invention proposes a method to extract key dispersion features to sparsify the equivalent channel matrix during ML estimation. Furthermore, the equivalent channel matrix is ​​simplified by leveraging the zero-filling characteristic of pilots, and column extraction is performed on the ML-estimated equivalent channel matrix to simplify the likelihood function estimation. Vector multiplication replaces matrix multiplication, achieving target parameter estimation with lower computational complexity while maintaining the same sensing accuracy. The trade-off between sensing accuracy and complexity is jointly determined by the delay dispersion parameter and the pilot proportion, allowing for flexible adjustment of sensing performance. This method can be applied to the integrated sensing process of monostatic communication and sensing.

Description

Technical Field

[0001] This invention belongs to the field of target perception technology, specifically relating to a monostatic AFDM-ISAC perception method based on fractional delay-Doppler feature extraction and pilot optimization ML estimation. Background Technology

[0002] Existing AFDM-ISAC sensing methods based on affine frequency division multiplexing can be broadly classified into two types. One is the AFDM-ISAC method based on full data sensing (Ni, Yuanhan, et al. "An AFDM-based integrated sensing and communications." 2022 International Symposium on Wireless Communication Systems (ISWCS). IEEE, 2022.). This method performs maximum likelihood (ML) estimation of the sensing channel in the discrete affine Fourier transform (DAFT) domain based on the input-output relationship of the transmitted and received signals to calculate the target range and velocity parameters. The other is the AFDM-ISAC method based on pilot sensing (Bemani, Ali, Nassar Ksairi, and Marios Kountouris. "Integrated sensing and communications with affinefrequency division multiplexing." IEEE Wireless Communications Letters (2024.).). This method employs a special pilot structure design to acquire the pilot signal portion orthogonal to the communication data at the receiver for ML estimation to calculate the target parameters. Both methods utilize the characteristic that AFDM waveforms can obtain the optimal diversity order under dual-dispersion channels to perform sensing channel ML estimation and target solution within an AFDM symbol block.

[0003] However, traditional pilot-sense-based AFDM-ISAC methods utilize the entire equivalent channel matrix and the transmitted and received pilot symbol vectors for machine learning (ML) estimation to estimate target parameters. Furthermore, the trade-off between sensing accuracy and complexity is determined by the proportion of pilots to the entire AFDM symbol block, thus lacking flexibility in AFDM-ISAC systems. Moreover, under specific sensing accuracy requirements, the computational complexity of traditional pilot-sense-based AFDM-ISAC methods remains high. Therefore, proposing a new method to address these issues is currently a pressing need. Summary of the Invention

[0004] The purpose of this invention is to address the problems of high computational complexity and lack of flexible adjustability in traditional pilot-based AFDM-ISAC methods, and to propose a monostatic AFDM-ISAC sensing method based on fractional delay-Doppler feature extraction and pilot optimization ML estimation.

[0005] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a monostatic AFDM-ISAC sensing method based on fractional delay-Doppler feature extraction and pilot optimization ML estimation, the method specifically including the following steps:

[0006] At the launch end

[0007] Step 1: Perform serial-to-parallel conversion, constellation mapping, and pilot insertion on the original bitstream sequentially to generate a symbol vector. ;

[0008] Step 2: For the symbol vector Perform inverse discrete affine Fourier transform to generate a time-domain AFDM signal;

[0009] Step 3: Add a chirped cyclic prefix to the time-domain AFDM signal, then perform parallel-to-serial conversion and digital-to-analog conversion on the signal after adding the chirped cyclic prefix, and then send the digital-to-analog converted signal to the channel through the radio frequency antenna of the transmitter.

[0010] At the sensing receiver

[0011] Step 4: Receive analog signals from the channel using the radio frequency antenna of the sensing receiver, and then convert the received analog signals into digital signals through analog-to-digital conversion.

[0012] Step 5: Perform serial-to-parallel conversion, chirped cyclic prefix removal, and discrete affine Fourier transform on the digital signal obtained in Step 4 to generate the received symbol vector. ;

[0013] Step 6: Extract the received symbol vector The distance and velocity of the sensed target are calculated based on the extracted pilot information and the maximum likelihood estimation method.

[0014] The beneficial effects of this invention are:

[0015] This invention utilizes the dispersion characteristics of fractional time delay and fractional Doppler frequency offset in the AFDM equivalent channel matrix. It proposes a method to extract key dispersion features to sparsify the equivalent channel matrix during ML estimation. Furthermore, it simplifies the equivalent channel matrix using the zero-filling characteristic of pilots, and then performs column extraction on the ML-estimated equivalent channel matrix to simplify the likelihood function estimation. Vector multiplication replaces matrix multiplication, achieving target parameter estimation with lower computational complexity while maintaining the same sensing accuracy. Moreover, since this method utilizes the key features of fractional time delay and Doppler frequency offset in the pilot-related equivalent channel matrix and the received pilot symbol vector for ML estimation, the trade-off between sensing accuracy and complexity is jointly determined by the time delay dispersion parameter and the pilot proportion, allowing for flexible adjustment of sensing performance. Attached Figure Description

[0016] Figure 1 It is a monobase single-antenna AFDM-ISAC system model;

[0017] Figure 2 This is a flowchart of a monostatic AFDM-ISAC sensing method based on fractional delay-Doppler feature extraction and pilot optimization ML estimation according to the present invention;

[0018] Figure 3 This is a schematic diagram showing the correspondence between AFDM transmit and receive symbols;

[0019] Figure 4(a) is the equivalent channel matrix containing all fractional delay and fractional Doppler information;

[0020] Figure 4(b) is derived from the parameters The sparse equivalent channel matrix for control;

[0021] Figure 4(c) shows the sparse equivalent channel matrix after pruning;

[0022] Figure 5 This is a graph showing the RMSE simulation results;

[0023] (a) shows the distance simulation results, and (b) shows the velocity simulation results. Detailed Implementation

[0024] Specific implementation method one: Combining Figure 2 This embodiment describes a monostatic AFDM-ISAC sensing method based on fractional delay-Doppler feature extraction and pilot optimization ML estimation. This method is applicable to monostatic single-antenna ISAC systems. A general monostatic single-antenna AFDM-ISAC system model is as follows: Figure 1As shown, the AFDM-ISAC transceiver uses a single antenna to transmit AFDM signals for both communication and sensing, and receives reflected signals from the target at the sensing receiver (ISAC Rx). Since the communication aspect of this invention is the same as that of traditional AFDM, it will not be discussed further; only the sensing aspect will be discussed. The sensing method specifically includes the following steps:

[0025] At the launch end

[0026] Step 1: Perform serial-to-parallel conversion, constellation mapping, and pilot insertion on the original bitstream sequentially to generate a symbol vector. ;

[0027] Step 2: For the symbol vector Perform inverse discrete affine Fourier transform (IDAFT) to generate a time-domain AFDM signal;

[0028] Step 3: Add a chirped cyclic prefix (CPP) to the time-domain AFDM signal, then perform parallel-to-serial conversion and digital-to-analog conversion on the signal after adding the chirped cyclic prefix, and then send the digital-to-analog converted signal to the channel through the radio frequency antenna of the transmitter.

[0029] At the sensing receiver

[0030] Step 4: Receive analog signals from the channel using the radio frequency antenna of the sensing receiver, and then convert the received analog signals into digital signals through analog-to-digital conversion.

[0031] Step 5: Perform serial-to-parallel conversion, chirped cyclic prefix removal, and Discrete Affine Fourier Transform (DAFT) processing on the digital signal obtained in Step 4 to generate the received symbol vector. ;

[0032] Step 6: Extract the received symbol vector The distance and velocity of the sensed target are calculated based on the extracted pilot information and the maximum likelihood estimation method.

[0033] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the received symbol vector... for:

[0034] (1)

[0035] in, Indicates by The target reflection produced One wireless link; Indicates the first Gain of each path Indicates the first The equivalent channel matrix of each path, It is a length of AFDM transmit symbol vector, The superscript T indicates transpose. They represent The first in One AFDM transmission symbol, , They represent The first in One AFDM received symbol, It follows a mean of 0 and a variance of 0. Gaussian white noise, i.e. .

[0036] The other steps and parameters are the same as in Specific Implementation Method 1.

[0037] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the pilot signal insertion process is specifically as follows:

[0038] Step 11: Insert a single pilot symbol P at any position in the constellation mapping result;

[0039] Step 1 and 2: Insert 0s on both sides of the pilot symbol as pilot protection intervals;

[0040] Step 13: Insert 0s on both sides of the pilot protection interval as data protection intervals.

[0041] Other steps and parameters are the same as in specific implementation method one or two.

[0042] Structure such as Figure 3 As shown, Indicates the index of the transmitted data symbol. and This represents the index of the data protection interval and the pilot protection interval, where P indicates a value of... A single pilot symbol, surrounded by... and Protection. The Data part represents the data portion of the received symbol vector, and the Pilot part represents the pilot-related portion of the received symbol vector.

[0043] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the number of zero elements in the guard intervals on both sides of a single pilot symbol is equal; that is, the number of zero elements in the pilot guard interval on one side of a single pilot symbol is added to the number of zero elements in the data guard interval, and then the number of zero elements in the pilot guard interval on the other side of a single pilot symbol is added to the number of zero elements in the data guard interval. The two sums are equal. It should be noted that the insertion position of a single pilot symbol P can be any position in the constellation mapping result. When the position of pilot symbol P is relatively early, the zeros on the left side of pilot symbol P can extend to the end of the constellation mapping result; when the position of pilot symbol P is relatively late, the zeros on the right side of pilot symbol P can extend to the beginning of the constellation mapping result to ensure that the number of zeros inserted on both sides of pilot symbol P is equal. When the position of pilot symbol P is neither early nor late, that is, under normal circumstances:

[0044] The number of zero elements on each side of a single pilot symbol serving as a guard interval is: ;

[0045] in, Indicates the maximum integer delay. , For the maximum physical delay, The sampling interval is... Indicates rounding up. For the maximum Doppler frequency shift, , For the duration of an AFDM transmitted symbol, For the maximum physical Doppler frequency shift, The Doppler frequency shift dispersion parameter, This indicates the number of zero elements on each side of a single pilot symbol that serve as a guard interval.

[0046] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0047] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the equivalent channel matrix is:

[0048] (2)

[0049] in, Represents the emission symbol vector element index, Represents the received symbol vector element index, Representing the equivalent channel matrix The Middle Line number Column elements, The base of the natural logarithm. Represents the imaginary unit. and They represent the first The integer and fractional parts of the fractional delay of the path. , For any irrational number or less rational numbers, It is an intermediate variable.

[0050] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0051] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the intermediate variable... for:

[0052] (3)

[0053] in, Indicates the first The equivalent delay of the path, , and They represent the first The integer and fractional parts of the fractional Doppler frequency offset of each path. Indicates indicator functions, sets ,gather elements in intermediate variables , , Indicates rounding down;

[0054] when When the value is negative, let the intermediate variable... If intermediate variables ,but The value is 1, otherwise, The value is 0;

[0055] when When it is a positive number, let the intermediate variable... If intermediate variables ,but The value is 1, otherwise, The value is 0.

[0056] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0057] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that the extraction of the received symbol vector... The pilot information in the image is used to calculate the distance and velocity of the sensed target using the extracted pilot information and the maximum likelihood estimation method; the specific process is as follows:

[0058] Step 61: Set the time delay dispersion parameters , , Represent the set of natural numbers, using Extracting fractional time delay dispersion features in the equivalent channel matrix The corresponding part , Only the equivalent channel matrix Part of the column, namely Only including formula (4) Corresponding columns:

[0059] (4)

[0060] in, The function represents taking the closest value to... Integers;

[0061] Step 62, according to Extracting fractional delay and fractional Doppler frequency offset features in the equivalent channel matrix The corresponding part is used to obtain the equivalent channel matrix. Equivalent channel matrix The corresponding image is shown in Figure 4(a), and the obtained equivalent channel matrix is ​​shown in Figure 4(a). The corresponding image is shown in Figure 4(b);

[0062] (5)

[0063] in, Representing the equivalent channel matrix The Middle Line number Column elements;

[0064] Step 63: Place the pilot symbol P in the transmit symbol vector The position in is denoted as Then, in receiving the symbol vector In, with symbol vector The set of elements related to the pilot symbol P in the middle for:

[0065] (6)

[0066] That is, the received symbol vector Only the middle The elements up to the first element and symbol vector The pilot symbol P is related to the first... The elements up to the first The element is Figure 3 middle Location;

[0067] According to the set Obtain the row-truncated identity matrix , That is, only the set is retained. The elements in 3D identity matrix Take the corresponding row from the matrix, delete the other rows, and obtain matrix T. Use the matrix... For the equivalent channel matrix Perform cropping to obtain the cropped matrix. ,matrix The corresponding image is shown in Figure 4(c);

[0068] Step 64: Based on the clipped matrix The distance and velocity of the perceived target are calculated using the maximum likelihood estimation method.

[0069] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0070] The implementation process of step six of this invention is shown in Table 1:

[0071] Table 1

[0072]

[0073] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that it utilizes a matrix. For the equivalent channel matrix Perform cropping to obtain the cropped matrix. Specifically:

[0074] (7)

[0075] The superscript H indicates the conjugate transpose.

[0076] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0077] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that the specific process of step six-four is as follows:

[0078] Step 641: Establish the log-likelihood function :

[0079] (8)

[0080] in, Represented by symbol vector The first in The elements up to the first A vector consisting of n elements; Represents the received symbol vector The first in The elements up to the first A vector consisting of n elements; Represents the 2-norm;

[0081] Step 642: Establish the estimated intermediate variables according to equation (8) Objective function:

[0082] (9)

[0083] in, , Represents the integer delay of the L paths to be estimated. The vector formed This represents the fractional delay of the L paths to be estimated. The vector formed Represents the integer Doppler frequency offset of the L paths to be estimated. The vector formed This represents the fractional Doppler frequency shift of the L paths to be estimated. The vector formed The range is indicated in The set of real numbers, express The estimated value, , express The estimated value, express The estimated value, express The estimated value, express The estimated value;

[0084] Step 643: Place the pilot symbol P in The position in is denoted as Then, according to equation (9), we get:

[0085] (10)

[0086] in, This indicates the value of the pilot symbol P. express conjugate, This indicates taking the absolute value. Representation matrix The conjugate transpose of;

[0087] intermediate variable matrix for:

[0088] (11)

[0089] in, Indicates according to For the identity matrix The row vector obtained by truncating rows. express An identity matrix of dimension 1, i.e. , identity matrix The first in OK;

[0090] Step 644: Solve equation (10) to obtain the estimation result. Based on the estimation results, the target's distance and velocity estimation parameters are calculated. :

[0091] (12)

[0092] in, The speed of light, with a value of , For carrier frequency, This represents a vector consisting of distance estimates for L targets, with the distance in meters (m). This represents a vector consisting of velocity estimates for L targets, with the velocity measured in m / s.

[0093] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0094] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that the solution formula (10) yields the estimation result. Specifically:

[0095] For delay range Perform mesh generation with a step size of . , For the Doppler frequency offset range Perform mesh generation with a step size of . , ;

[0096] A search is performed on the divided time delay grid and Doppler shift grid to find... The corresponding L extreme points, substitute the L extreme points into It is possible to estimate .

[0097] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0098] To verify the effectiveness of the method proposed in this invention, simulation verification was performed using the parameters shown in Table 2:

[0099] Table 2 Simulation Parameter Settings

[0100]

[0101] Simulation results are as follows Figure 5 As shown, (a) is the simulation graph of distance RMSE, which shows that when When the equivalent channel matrix is ​​sparsified, the fractional delay characteristic is lost, resulting in poor performance. At that time, its RMSE curve is similar to that of a traditional pilot RMSE curve, but because it ignores the characteristics of a partial fractional delay ( The larger the value, the less it is ignored, so the final convergence accuracy is slightly worse than that of the traditional pilot scheme. Meanwhile, by adjusting the parameters... Adjustment can achieve accuracy approaching that of traditional pilot schemes (increasing accuracy). (Prioritizing accuracy) or reducing perceptual complexity with a lower loss of accuracy (reducing...) (a) Prioritizes complexity to achieve a trade-off between perception accuracy and complexity; (b) shows the speed RMSE simulation diagram, due to For distance sensing corresponding to time delay dispersion parameters, For speed sensing corresponding to frequency extension parameters, and It has already been set by the sender, so it is set by the receiver. Adjusting the speed measurement will hardly affect the accuracy of speed perception, but sparsifying the equivalent channel matrix will also reduce the complexity of speed perception.

[0102] Table 3. Complexity Comparison

[0103]

[0104] Table 3 shows a comparison of the complexity of the low-complexity sensing method described in this invention with that of traditional pilot sensing. It can be seen that the method of this invention has two advantages:

[0105] Compared to traditional pilot schemes, the length Pilot length A portion of it (as shown in Figure 4(c)), namely Furthermore, the absence of quadratic terms greatly reduces perceptual complexity.

[0106] parameter The settings are already configured on the sending end and cannot be changed, while on the receiving end we can configure and adjust them. Achieving a balance between perceptual complexity and accuracy.

[0107] 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. A monostatic AFDM-ISAC sensing method based on fractional delay-Doppler feature extraction and pilot optimization ML estimation, characterized in that, The method specifically includes the following steps: At the launch end Step 1: Perform serial-to-parallel conversion, constellation mapping, and pilot insertion on the original bitstream sequentially to generate a symbol vector. ; The pilot insertion process specifically includes: Step 11: Insert a single pilot symbol P at any position in the constellation mapping result; Step 1 and 2: Insert 0s on both sides of the pilot symbol as pilot protection intervals; Step 13: Insert 0s on both sides of the pilot protection interval as data protection intervals; Step 2: For the symbol vector Perform inverse discrete affine Fourier transform to generate a time-domain AFDM signal; Step 3: Add a chirped cyclic prefix to the time-domain AFDM signal, then perform parallel-to-serial conversion and digital-to-analog conversion on the signal after adding the chirped cyclic prefix, and then send the digital-to-analog converted signal to the channel through the radio frequency antenna of the transmitter. At the sensing receiver Step 4: Receive analog signals from the channel using the radio frequency antenna of the sensing receiver, and then convert the received analog signals into digital signals through analog-to-digital conversion. Step 5: Perform serial-to-parallel conversion, chirped cyclic prefix removal, and discrete affine Fourier transform on the digital signal obtained in Step 4 to generate the received symbol vector. ; (1) in, Indicates by The target reflection produced One wireless link; Indicates the first Gain of each path Indicates the first The equivalent channel matrix of each path; It is a length of AFDM transmit symbol vector, The superscript T indicates transpose. They represent The first in One AFDM transmission symbol; , They represent The first in One AFDM received symbol, It is Gaussian white noise; The equivalent channel matrix is: (2) in, Represents the emission symbol vector element index, Represents the received symbol vector element index, Representing the equivalent channel matrix The Middle Line 1 Column elements; The base of the natural logarithm. Represents the imaginary unit; and They represent the first The integer and fractional parts of the fractional delay for each path; As an intermediate variable; , For any irrational number or less rational numbers; Step 6: Extract the received symbol vector The distance and velocity of the sensed target are calculated based on the extracted pilot information and the maximum likelihood estimation method.

2. The monostatic AFDM-ISAC sensing method based on fractional delay-Doppler feature extraction and pilot optimization ML estimation according to claim 1, characterized in that, The number of zero elements on both sides of a single pilot symbol as a guard interval is equal; The number of zero elements on each side of a single pilot symbol serving as a guard interval is: ; in, Indicates the maximum integer delay. , For the maximum physical delay, The sampling interval is... Indicates rounding up; For the maximum Doppler frequency shift, , For the duration of an AFDM transmitted symbol, The maximum physical Doppler shift; The Doppler frequency shift dispersion parameter, This indicates the number of zero elements on each side of a single pilot symbol that serve as a guard interval.

3. The monostatic AFDM-ISAC sensing method based on fractional delay-Doppler feature extraction and pilot optimization ML estimation according to claim 2, characterized in that, The intermediate variable for: (3) in, Indicates the first The equivalent delay of the path, , and They represent the first The integer and fractional parts of the fractional Doppler frequency offset of each path; Indicates indicator functions, sets ,gather elements in intermediate variables , , Indicates rounding down; when When the value is negative, let the intermediate variable... If intermediate variables ,but The value is 1, otherwise, The value is 0; when When it is a positive number, let the intermediate variable... If intermediate variables ,but The value is 1, otherwise, The value is 0.

4. The monostatic AFDM-ISAC sensing method based on fractional delay-Doppler feature extraction and pilot optimization ML estimation according to claim 3, characterized in that, The extracted received symbol vector The pilot information in the image is used to calculate the distance and velocity of the sensed target using the extracted pilot information and the maximum likelihood estimation method; the specific process is as follows: Step 61: Set the time delay dispersion parameters ,use Extracting fractional time delay dispersion features in the equivalent channel matrix The corresponding part : (4) in, The function represents taking the closest value to... Integers; Step 62, according to Extracting fractional delay and fractional Doppler frequency offset features in the equivalent channel matrix The corresponding part is used to obtain the equivalent channel matrix. ; (5) in, Representing the equivalent channel matrix The Middle Line 1 Column elements; Step 63: Place the pilot symbol P in the transmit symbol vector The position in is denoted as Then, in receiving the symbol vector In, with symbol vector The set of elements related to the pilot symbol P in the middle for: (6) According to the set Obtain the row-truncated identity matrix Using matrices For the equivalent channel matrix Perform cropping to obtain the cropped matrix. ; Step 64: Based on the clipped matrix The distance and velocity of the perceived target are calculated using the maximum likelihood estimation method.

5. The monostatic AFDM-ISAC sensing method based on fractional delay-Doppler feature extraction and pilot optimization ML estimation according to claim 4, characterized in that, The use of matrix For the equivalent channel matrix Perform cropping to obtain the cropped matrix. Specifically: (7) The superscript H indicates the conjugate transpose.

6. The monostatic AFDM-ISAC sensing method based on fractional delay-Doppler feature extraction and pilot optimization ML estimation according to claim 5, characterized in that, The specific process of step six-four is as follows: Step 641: Establish the log-likelihood function : (8) in, Represented by symbol vector The first in The elements up to the first A vector consisting of n elements; Represents the received symbol vector The first in The elements up to the first A vector consisting of n elements; Represents the 2-norm; Step 642: Establish the estimated intermediate variables according to equation (8) Objective function: (9) in, , Represents the integer delay of the L paths to be estimated. The vector formed This represents the fractional delay of the L paths to be estimated. The vector formed Represents the integer Doppler frequency offset of the L paths to be estimated. The vector formed This represents the fractional Doppler frequency shift of the L paths to be estimated. The vector formed The range is indicated in The set of real numbers; express The estimated value; , express The estimated value, express The estimated value, express The estimated value, express The estimated value; Step 643: Place the pilot symbol P in The position in is denoted as Then, according to equation (9), we get: (10) in, Indicates taking the absolute value; Representation matrix The conjugate transpose of; intermediate variable matrix for: (11) in, Indicates according to For the identity matrix The row vector obtained by truncating rows. express An identity matrix of dimensionality; Step 644: Solve equation (10) to obtain the estimation result. Based on the estimation results, the target's distance and velocity estimation parameters are calculated. : (12) in, At the speed of light, For carrier frequency; This represents a vector consisting of distance estimates for L targets; This represents a vector consisting of velocity estimates for L targets.

7. The monostatic AFDM-ISAC sensing method based on fractional delay-Doppler feature extraction and pilot optimization ML estimation according to claim 6, characterized in that, The solution to equation (10) yields the estimation result. Specifically: For delay range Perform mesh generation with a step size of . For the Doppler frequency offset range Perform mesh generation with a step size of . ; A search is performed on the divided time delay grid and Doppler shift grid to find... There are L corresponding extreme points.

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