A fractional parameter estimation method for an OTFS-based ISAC system

Abstract

This invention discloses a fractional parameter estimation method for an ISAC system based on OTFS, belonging to the field of wireless communication technology. The method includes performing time-delay-Doppler domain channel estimation on the radar received signal, establishing initial parameter estimates for fractional time delay and fractional Doppler using the atomic correlation of the dictionary matrix, refining the GDR algorithm using gradient descent, and iteratively optimizing parameters by maximizing the atomic correlation function of the relevant dictionary. During the iteration, multipath parameters are separated using the Path Decoupling Interference Elimination (PDIC) mechanism, and residual interference is eliminated using the Residual Minimization Interference Elimination (RMIC) mechanism. Once the residual error reaches the convergence condition, a high-precision parameter estimation result is output. This invention employs the above-mentioned fractional parameter estimation method for an ISAC system based on OTFS, solving the problems of traditional methods' difficulty in accurately estimating fractional time delay and fractional Doppler, the significant impact of multipath interference, and high computational complexity, achieving high-precision parameter estimation, strong anti-interference capability, and efficient resource utilization.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a fractional parameter estimation method for an ISAC system based on OTFS. Background Technology

[0002] In high-mobility wireless communication scenarios, traditional Orthogonal Frequency Division Multiplexing (OFDM) systems face severe Doppler shift challenges. The difficulty in maintaining orthogonality between subcarriers leads to inter-carrier interference, significantly degrading system performance. Orthogonal Time-Frequency Space (OTFS) technology, by modulating data in the delay-Doppler domain rather than the traditional time-frequency domain, exhibits strong robustness to Doppler shift and time delay in highly dynamic and complex environments. This characteristic makes OTFS a highly promising signal waveform for Integrated Sensing and Communication (ISAC) systems. ISAC systems aim to simultaneously achieve communication and sensing functions using the same hardware and spectrum resources, thereby improving resource utilization efficiency and reducing system complexity. The advantages of OTFS modulation in the delay-Doppler domain enable it to effectively separate paths with different delays and Doppler frequencies, which is crucial for parameter estimation in target sensing.

[0003] Accurate estimation of target echo parameters, such as time delay and Doppler shift, is crucial for target sensing in OTFS systems. However, when the target's time delay or Doppler shift is not an integer multiple of the system resolution, the received signal energy diffuses into adjacent time-delay-Doppler grid cells, leading to fractional time delay and fractional Doppler shift problems. Existing parameter estimation methods, such as threshold-based channel estimation methods, typically only estimate parameter values ​​as integer multiples, failing to meet the requirements of high-precision sensing. To address the inter-carrier interference problem caused by fractional Doppler shift, some research has proposed efficient fractional Doppler shift estimation algorithms, but these methods generally still estimate the time delay as an integer value.

[0004] To more accurately estimate fractional time delay (OTFS) and fractional Doppler shift (FDoP) frequency shift, numerous studies have explored this topic in depth. Some studies employ pulse-based channel estimation methods, but these typically require high signal-to-noise ratio (SNR) pilot signals, increasing the system's peak-to-average power ratio (PAPR), which is disadvantageous in practical applications. Other studies utilize the sparsity of the time delay-Doppler domain, transforming the parameter estimation problem into a sparse signal recovery problem and applying compressed sensing algorithms for solution. However, these methods often neglect the correlations between atoms in the dictionary matrix when constructing it. In fact, the OTFS channel estimation problem is not entirely equivalent to the general sparse signal recovery problem because the correlations between atoms in the dictionary matrix are not fully utilized, leading to high algorithmic complexity. Furthermore, some algorithms based on Orthogonal Matching Pursuit (OMP), such as the two-step Orthogonal Matching Pursuit with Fractional Refinement (OMPFR) algorithm, while attempting to reduce computational complexity, suffer from performance limitations due to the greedy nature of the OMP algorithm itself. Therefore, it is necessary to develop a fractional parameter estimation method that can effectively utilize the time-delay-Doppler domain characteristics, consider the correlation between atoms in the dictionary matrix, and overcome the limitations of traditional methods, thereby achieving low complexity and high accuracy. Summary of the Invention

[0005] The purpose of this invention is to provide a fractional parameter estimation method for an ISAC system based on OTFS, in order to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, this invention provides a method for estimating the fractional parameters of an ISAC system based on OTFS, comprising the following steps:

[0007] S1. The OTFS modulated signal is transmitted through the transmitter of the ISAC system, the radar receiver receives the reflected radar signal of the target channel, and the communication receiver receives the communication signal. The radar receiver and the communication receiver share the spectrum resources of the OTFS modulated signal.

[0008] S2. Perform time-delay-Doppler domain channel estimation on the signal received by the radar receiver, and establish the initial parameter estimates of fractional time delay and fractional Doppler frequency shift by the correlation between atoms of the dictionary matrix;

[0009] S3. The initial parameter estimation is optimized by refining the GDR algorithm based on gradient descent. The parameters are iteratively adjusted until convergence is achieved by maximizing the correlation function between dictionary atoms related to the initial parameters.

[0010] S4. During the iterative optimization process, the interference cancellation mechanism is dynamically selected based on the actual interference characteristics. If it is necessary to eliminate multipath interference and separate the target parameters of different propagation paths, the path decoupling interference cancellation PDIC mechanism is activated. If it is necessary to further eliminate residual interference to improve signal quality, the residual minimization interference cancellation RMIC mechanism is activated to minimize the residual error through iterative optimization.

[0011] S5. When the residual error meets the preset convergence condition, output the high-precision parameter estimation result.

[0012] Preferably, the specific steps of the gradient descent refinement GDR algorithm in S3 are as follows:

[0013] S31. Convert the reflected radar signal r0 received by the radar receiver into vector form r vec , as the initial residual;

[0014] S32, Based on the integer dictionary matrix Ψ I The time delay and Doppler shift of each propagation path in the target channel are estimated by integer multiple approximations.

[0015] S33. Construct the correlation function between dictionary atoms related to the initial parameter estimation, and adjust the above parameters through the gradient descent iterative algorithm to maximize the value of the correlation function;

[0016] S34. Update the fraction dictionary matrix Ψ based on the parameters obtained from the iteration. f And adjust the residual r based on this. s , where r s The residual obtained in the s-th iteration;

[0017] S35. Repeat steps S32-S34 until the number of iterations exceeds the maximum number of iterations or the residual r. s If the value is less than the threshold ε, stop the iteration and obtain the optimized fractional parameter estimation result.

[0018] Preferably, the correlation function of S33 is denoted as C(l e ,k e Specifically, it is expressed as:

[0019]

[0020] Among them, l e For normalized time delay estimation, k e For normalized Doppler estimation, Γ MN Let be a time-delay shift diagonal matrix, (·) H This indicates the conjugate transpose operation. Let F be the power transformation matrix for time delay shift. MN Let be a normalized Fourier transform matrix of size MN. For the matrix associated with the Doppler shift, s vec Let M be the vector form of the time-domain symbol matrix s after column expansion, where M is the number of time delay units and N is the number of Doppler units.

[0021] Preferably, the derivation process of the gradient expression of the gradient descent iterative algorithm in S33 is as follows:

[0022] a. Define an intermediate variable z to simplify the correlation function;

[0023]

[0024] b. Using the chain rule for complex differentiation, solve for the correlation function with respect to l. e and k e The partial derivative;

[0025]

[0026] c. Solve for the intermediate variable z with respect to l e and k e The partial derivative;

[0027]

[0028] Where Λ is a diagonal matrix, defined as:

[0029]

[0030] Here, diag{·} is the operation for constructing a diagonal matrix, j is the imaginary unit, and Arg(·) is the principal value operation.

[0031] Preferably, the specific steps of the path decoupling interference elimination PDIC mechanism in S4 are as follows:

[0032] S411. Obtain the fractional parameter estimation results of the gradient descent refined GDR algorithm, identify the number P of propagation paths in the target channel, and extract the initial normalized delay l of each path. p and normalized Doppler k p ;

[0033] S412. For each path p, perform the decoupling interference iteration;

[0034] S413. After completing the decoupling of all paths, obtain the fractional parameter estimation results after the decoupling interference of each path, update the residuals. If the residual interference suppression effect does not reach the preset, the preset convergence condition is that the residual norm is less than the threshold, the parameter adjustment amount is less than the minimum step size or the maximum number of iterations is reached. Repeat S412 and S413. Otherwise, perform the residual minimization interference elimination RMIC mechanism.

[0035] Preferably, the specific steps of S412 are as follows:

[0036] a. Use the estimated initial score parameters of the path obtained by the GDR algorithm as the initial estimate;

[0037] b. Transform the fraction dictionary matrix Ψ f Set the p-th column corresponding to the p-th path in the matrix to zero, and construct a temporary score dictionary matrix Ψ. f,temp ;

[0038] c. Based on the current estimate and the temporary score dictionary matrix Ψ f,temp Recalculate the residual r after removing path p interference. p ;

[0039] d. Perform gradient descent iterations again on the p-th path to refine the estimates of the fractional delay and fractional Doppler for that path;

[0040] e. Update the fraction dictionary matrix Ψ based on the refined estimates. f .

[0041] Preferably, the specific steps of the residual minimization interference elimination (RMIC) mechanism in S4 are as follows:

[0042] S421. Based on the parameter estimation results and updated residuals of the GDR algorithm refined by gradient descent, the residual norm is defined as the objective function.

[0043]

[0044] Where ||·||2 is the L2 norm, and r is the current residual vector, which satisfies the following formula;

[0045]

[0046] Where, r vec The received signal is in vectorized form, where P is the number of propagation paths and h is the vectorized form. p Let p be the complex gain of the p-th path. For path p-based normalized delay l p The time delay shift matrix, For path p-based normalized Doppler k p Shift matrix;

[0047] S422. For each propagation path, calculate the partial derivatives of the residual norm objective function with respect to the normalized delay and normalized Doppler for that path.

[0048]

[0049] Wherein, the residual r is normalized to the path p with respect to the delay l p and normalized Doppler k p The partial derivatives satisfy:

[0050]

[0051] S423. Use the gradient descent iterative algorithm to adjust the parameter estimates of each path based on the partial derivative results;

[0052] S424. After each parameter adjustment, update the fraction dictionary matrix and residuals, and recalculate the residual norm objective function value.

[0053] S425. If the residuals meet the preset convergence conditions, stop the iteration and output the optimized parameter estimation results; otherwise, return to S422 and repeat the parameter adjustment until the convergence conditions are met.

[0054] Therefore, the present invention employs the above-mentioned fractional parameter estimation method for an ISAC system based on OTFS, which has the following beneficial effects:

[0055] (1) The GDR algorithm combines dictionary atomic correlation iterative optimization and PDIC mechanism to decouple multipath interference, breaking through the accuracy bottleneck of traditional methods, separating multipath parameters in complex scenarios, and realizing high-precision estimation of fractional delay and Doppler.

[0056] (2) The RMIC mechanism eliminates residual interference and improves the system's ability to resist multipath and fractional Doppler interference. At the same time, it reduces computational complexity and pilot resource dependence through algorithm optimization, taking into account both efficient computation and spectrum / energy resource utilization.

[0057] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0058] Figure 1 This is a flowchart of a fraction parameter estimation method for an ISAC system based on OTFS according to the present invention;

[0059] Figure 2 This is a structural diagram of the OTFS-ISAC system device of the present invention;

[0060] Figure 3 This is the iterative process of the gradient descent refinement technique of the present invention, where the dots represent the true values ​​and the broken lines represent the iterative process;

[0061] Figure 4 This is the iterative process of the path decoupling interference elimination technique after gradient descent refinement in this invention, where the dots represent the true values ​​and the broken lines represent the iterative process.

[0062] Figure 5 This is a comparison curve of the estimation accuracy of the normalized time delay of this invention;

[0063] Figure 6This is a comparison curve of the estimation accuracy of the normalized Doppler of the present invention;

[0064] Figure 7 This is a comparison curve of the estimation accuracy of the real part of the path gain in this invention;

[0065] Figure 8 This is a comparison curve of the estimation accuracy of the imaginary part of the path gain in this invention;

[0066] Figure 9 This is a probability density function curve of the time resource consumption of this invention. Detailed Implementation

[0067] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0068] Example

[0069] like Figure 1 As shown, this invention provides a method for estimating the fractional parameters of an ISAC system based on OTFS, comprising the following steps:

[0070] This embodiment presents a radar parameter estimation technique based on an Integrated Sensing and Communication System (ISAC) device using Orthogonal Time-Frequency Spatial (OTFS) modulation. The system mainly comprises three devices: a transmitter, a radar receiver, and a communication receiver. Figure 2 As shown in the diagram, the radar receiver and transmitter are located in the same position, sharing the same transmit and receive antenna. The radar receiver possesses all information about the transmitted symbols. After receiving the signal and performing a Wigner transform and a symplectic finite Fourier transform, the time delay and Doppler parameters of the target in the channel can be estimated. The communication receiver possesses the pilot information of the transmitted symbols. The received symbols are also transformed using a Wigner transform and a symplectic finite Fourier transform. Based on the pilot information, the channel is estimated and equalized, thereby performing symbol detection to obtain communication information.

[0071] The main technology in this embodiment lies in the parameter estimation method in the radar receiver. The communication receiver is consistent with a typical OTFS-based system. The OTFS system model is described below.

[0072] OTFS models the channel as a linear time-varying channel, taking into account multipath propagation and the Doppler effect. The transmitted symbols are modulated in the time-delay-Doppler domain, where the time-delay-Doppler plane is discretized into an information grid Ω, defined as:

[0073]

[0074] in, and Let Δf represent the resolution in the time delay dimension and the Doppler dimension, respectively. Δf is the frequency spacing between adjacent carriers, and T is the duration of a single time slot, satisfying... Therefore, MΔf represents the total bandwidth occupied by the system, and NT represents the duration of an OTFS frame.

[0075] The time-delay-Doppler domain symbol matrix is ​​obtained through inverse symplectic finite Fourier transform (ISFFT). It can be mapped to a time-frequency domain symbol matrix. Right now:

[0076]

[0077] Among them, F M It is a normalized discrete Fourier transform (DFT) matrix of size M, (·) H This indicates the conjugate transpose.

[0078] By applying the Heisenberg transform and combining it with the pulse shaping filter at the transmitting end, the time-frequency domain symbol matrix X... TF Converted to a time-domain symbol matrix Its expression is:

[0079]

[0080] in, The matrix form of the transmitting pulse shaping filter has the following diagonal elements:

[0081]

[0082] Send symbol vector s vec It is the vector form of the time-domain symbolic matrix s after column expansion, i.e.:

[0083] s vec =vec(s) (19)

[0084] Suppose there are P propagation paths in the channel, and the complex gain, time delay, and Doppler shift of each path are h, ... p τ p and ν p The normalized delay and normalized Doppler of the path are defined as follows:

[0085] l p =τ p MΔf (20)

[0086] k p =ν p NT (21)

[0087] Considering fractional delay and fractional Doppler, the matrix form of the time-domain channel impulse response. It can be represented as:

[0088]

[0089] in, It is a diagonal matrix with the following form:

[0090]

[0091] It is also a diagonal matrix, with the following form:

[0092]

[0093] Received time-domain OTFS signal vector r vec It can be represented as:

[0094] r vec =H TD s vec +w (25)

[0095] in, It is a complex Gaussian white noise vector.

[0096] After receiving a signal, the radar receiver can estimate the time delay and Doppler parameters of the target in the channel based on the symbol information transmitted by the transmitter. After receiving a signal, the communication receiver can estimate and equalize the channel based on the pilot information, and then perform symbol detection to obtain communication information.

[0097] S1. The OTFS modulated signal is transmitted through the transmitter of the ISAC system. The radar receiver receives the reflected radar signal from the target channel, and the communication receiver receives the communication signal. The radar receiver and the communication receiver share the spectrum resources of the OTFS modulated signal.

[0098] S2. Perform time-delay-Doppler domain channel estimation on the signal received by the radar receiver, and establish the initial parameter estimates of fractional time delay and fractional Doppler frequency shift through the correlation between atoms of the dictionary matrix.

[0099] To improve the accuracy of radar receiver estimation of fractional delay and fractional Doppler frequency shift parameters, this embodiment provides the following three techniques: Gradient descent refinement of the GDR algorithm can achieve good radar parameter estimation accuracy and low computational complexity in scenarios with a small number of paths in the channel. If further improvement in parameter estimation accuracy is required or the number of paths in the channel is large, a small amount of additional time resources can be consumed to use the Path Decoupling Interference Cancellation (PDIC) mechanism or the Residual Minimization Interference Cancellation (RMIC) mechanism to achieve better results.

[0100] S3. The initial parameter estimation is optimized by refining the GDR algorithm based on gradient descent. The parameters are iteratively adjusted until convergence by maximizing the correlation function between dictionary atoms related to the initial parameters.

[0101] The specific steps of refining the GDR algorithm using gradient descent are as follows:

[0102] S31. Convert the reflected radar signal r0 received by the radar receiver into vector form r vec , as the initial residual;

[0103] S32, Based on the integer dictionary matrix Ψ I The time delay and Doppler shift of each propagation path in the target channel are estimated by integer multiple approximations.

[0104] S33. Construct the correlation function between dictionary atoms related to the initial parameter estimation, and adjust the above parameters through the gradient descent iterative algorithm to maximize the value of the correlation function;

[0105] Unlike general sparse signal recovery problems where the correlation between column vectors of the dictionary matrix is ​​random, the dictionary vectors in the OTFS parameter estimation problem exhibit specific correlations. This correlation manifests in the time-delay-Doppler domain as follows: dictionary vectors corresponding to adjacent points in the time-delay-Doppler neighborhood are more strongly correlated. In other words, in the dictionary matrix, if the estimated vector corresponds to a slightly offset time delay or Doppler value, it is likely to be replaced by a vector from a nearby point.

[0106] When using the orthogonal matching pursuit algorithm to estimate the target parameters, let r s Let represent the residual obtained in the s-th iteration. Represents the dictionary matrix Ψ f Each column vector and the residual r s The correlation; denoted as C(l) e ,k e It is a normalized time delay estimate. e With normalized Doppler estimation k e Functions:

[0107]

[0108] Among them, l e For normalized time delay estimation, k e For normalized Doppler estimation, Γ MN Let be a time-delay shift diagonal matrix, (·) H This indicates the conjugate transpose operation. Let F be the power transformation matrix for time delay shift. MN Let be a normalized Fourier transform matrix of size MN. For the matrix associated with the Doppler shift, svec Let M be the vector form of the time-domain symbol matrix s after column expansion, where M is the number of time delay units and N is the number of Doppler units.

[0109] At this point, estimating the time delay and Doppler of a certain path can be transformed into maximizing C(l) e ,k e The problem is that, through experimental verification, within the neighborhood of the target point on the time-delay-Doppler plane, C(l) e ,k e Since is a locally convex function, it can be solved using the gradient descent iterative algorithm. The gradient expression is derived below.

[0110] a. Define an intermediate variable z to simplify the correlation function;

[0111]

[0112] b. Using the chain rule for complex differentiation, solve for the correlation function with respect to l. e and k e The partial derivative;

[0113]

[0114] c. Solve for the intermediate variable z with respect to l e and k e The partial derivative;

[0115]

[0116] Where Λ is a diagonal matrix with elements in the range j[-π,π), defined as:

[0117]

[0118] Here, diag{·} is the operation for constructing a diagonal matrix, j is the imaginary unit, and Arg(·) is the principal value operation.

[0119] S34. Update the fraction dictionary matrix Ψ based on the parameters obtained from the iteration. f And adjust the residual r based on this. s , where r s The residual obtained in the s-th iteration;

[0120] S35. Repeat steps S32-S34 until the number of iterations exceeds the maximum number of iterations or the residual r. s If the value is less than the threshold ε, stop the iteration and obtain the optimized fractional parameter estimation result.

[0121] S4. During the iterative optimization process, the interference cancellation mechanism is dynamically selected based on the actual interference characteristics. If it is necessary to eliminate multipath interference and separate the target parameters of different propagation paths, the path decoupling interference cancellation PDIC mechanism is activated. If it is necessary to further eliminate residual interference to improve signal quality, the residual minimization interference cancellation RMIC mechanism is activated, and the residual error is minimized through iterative optimization.

[0122] When there are P paths in the channel (P>1), the receiver will receive P copies of each transmitted symbol. The superposition of signals from each path will cause the objective function C(l) to... e ,k e The peak position of the signal shifts, especially when the delay-Doppler interval of each path is small, the shift will be more severe.

[0123] One approach is to decouple the individual path to be estimated from other paths, i.e., the Path Decoupling Interference Cancellation (PDIC) mechanism, similar to the orthogonalization operation in the OMP algorithm. Specifically, each path is re-estimated individually; when re-estimating a path, existing information from other paths is used to cancel its interference with the received signal, and then gradient descent iterations are performed to refine the fractional parameter estimation of that path.

[0124] The specific steps of the path decoupling interference elimination PDIC mechanism are as follows:

[0125] S411. Obtain the fractional parameter estimation results of the gradient descent refined GDR algorithm, identify the number P of propagation paths in the target channel, and extract the initial normalized delay l of each path. p and normalized Doppler k p ;

[0126] S412. For each path p, perform the decoupling interference iteration;

[0127] a. Use the estimated initial score parameters of the path obtained by the GDR algorithm as the initial estimate;

[0128] b. Transform the fraction dictionary matrix Ψ f Set the p-th column corresponding to the p-th path in the matrix to zero, and construct a temporary score dictionary matrix Ψ. f,temp ;

[0129] c. Based on the current estimate and the temporary score dictionary matrix Ψ f,temp Recalculate the residual r after removing path p interference. p ;

[0130] d. Perform gradient descent iterations again on the p-th path to refine the estimates of the fractional delay and fractional Doppler for that path;

[0131] e. Update the fraction dictionary matrix Ψ based on the refined estimates.f .

[0132] S413. After completing the decoupling of all paths, obtain the fractional parameter estimation results after the decoupling interference of each path, update the residuals. If the residual interference suppression effect does not reach the preset, the preset convergence condition is that the residual norm is less than the threshold, the parameter adjustment amount is less than the minimum step size or the maximum number of iterations is reached. Repeat S412 and S413. Otherwise, perform the residual minimization interference elimination RMIC mechanism.

[0133] Both Gradient Descent Refinement (GDR) and Path Decoupling Interference Cancellation (PDIC) aim to maximize the objective function C(l) during iteration. e ,k e Both of these techniques are greedy and can only achieve local optima. If we directly use "residual minimization" as the objective function, we can achieve the global optimum. However, since we need to optimize 2P variables simultaneously, convergence is a significant challenge. Therefore, we can first use gradient descent to refine the solution to obtain an approximate solution, and then optimize it using the residual minimization criterion to obtain a more accurate result.

[0134] The specific steps of the residual minimization interference cancellation (RMIC) mechanism are as follows:

[0135] S421. Based on the parameter estimation results and updated residuals of the GDR algorithm refined by gradient descent, the residual norm is defined as the objective function.

[0136]

[0137] Where ||·||2 is the L2 norm, and r is the current residual vector, which satisfies the following formula;

[0138]

[0139] Where, r vec The received signal is in vectorized form, where P is the number of propagation paths and h is the vectorized form. p Let p be the complex gain of the p-th path. For path p-based normalized delay l p The time delay shift matrix, For path p-based normalized Doppler k p Shift matrix;

[0140] S422. For each propagation path, calculate the partial derivatives of the residual norm objective function with respect to the normalized delay and normalized Doppler for that path.

[0141]

[0142] Wherein, the residual r is normalized to the path p with respect to the delay l p and normalized Doppler kp The partial derivatives satisfy:

[0143]

[0144] S423. Use the gradient descent iterative algorithm to adjust the parameter estimates of each path based on the partial derivative results;

[0145] S424. After each parameter adjustment, update the fraction dictionary matrix and residuals, and recalculate the residual norm objective function value.

[0146] S425. If the residuals meet the preset convergence conditions, stop the iteration and output the optimized parameter estimation results; otherwise, return to S422 and repeat the parameter adjustment until the convergence conditions are met.

[0147] S5. When the residual error meets the preset convergence condition, output the high-precision parameter estimation result.

[0148] In the implementation, simulation tests were conducted on the fractional parameter estimation of the OTFS-ISAC system, and Table 1 shows the parameters of each reflection path in the channel. To better demonstrate the difference between the effect of gradient descent refinement technology and the interference cancellation effect of path decoupling interference cancellation technology, strong interference conditions were configured to make the inter-path interference particularly significant.

[0149] Table 1 Simulation parameters under strong interference conditions

[0150] path p <![CDATA[Normalized delay l p > <![CDATA[Normalized Doppler k p > <![CDATA[Gain h p > 1 6.4 9.4 1 2 7.4 7.6 1 3 8.4 8.6 1

[0151] Figure 3 and Figure 4 The iterative process of gradient descent refinement and the iterative process after interference elimination using path decoupling and interference cancellation techniques are illustrated separately. The background of the figure is a correlation contour plot calculated based on the objective function formula, the broken line represents the iterative path of gradient descent, and the blue dots represent the true values ​​of the path parameters. Figure 3 This shows that the gradient descent refinement technique can quickly converge to the vicinity of the true parameter values ​​with only a few iterations without densely sampling the entire time-delay-Doppler domain. Figure 4 This indicates that the interference from paths 1 and 3 was effectively suppressed when estimating the parameters of path 2.

[0152] Assume the channel contains 5 reflection paths, whose corresponding time delays and Doppler offsets are random values ​​uniformly distributed within the maximum range. The path gain is a complex number, with its magnitude uniformly distributed between 0 and 1, and its argument uniformly distributed between [0, 2π). The parameters used in the simulation are detailed in Table 2. The algorithms compared include: Integer parameter estimation based on the Orthogonal Matching Pursuit algorithm (Integral), Orthogonal Matching Pursuit Fractional Refinement Algorithm (OMPFR), Gradient Descent Refinement (GDR), Path Decoupling Interference Cancellation (PDIC), and Residual Minimization Interference Cancellation (RMIC). Furthermore, the estimation accuracy of the techniques in this embodiment is compared with the Cramero Lower Bound (CRLB) of this system.

[0153] Table 2 Algorithm Performance Comparison Experimental Simulation Parameters

[0154] Parameter name Parameter value Frame size M*N=16*16 Modulation method 4QAM Channel bandwidth 10MHz Frame duration 25.6us Adjacent carrier frequency spacing 625kHz carrier frequency 30GHz Number of paths in the channel 5

[0155] The OMPFR algorithm aims to reduce the dimensionality of the dictionary matrix to decrease computational complexity. However, the algorithm has certain limitations: its computational complexity remains high when high parameter estimation accuracy is required; furthermore, in channels with multiple propagation paths, the OMPFR algorithm's performance degrades significantly due to its greedy nature.

[0156] from Figures 5-8 The root mean square errors (RMSEs) of the five algorithms for estimating normalized delay, normalized Doppler, the real part of path gain, and the imaginary part of path gain are presented. It can be seen that, compared to GDR, the performance of OMPFR is limited by the finite number of fractional sampling points in the delay-Doppler plane, resulting in lower estimation accuracy. GDR, even with fewer sampling points, achieves better estimation accuracy by implementing smaller sampling intervals. Introducing inter-path interference cancellation (PDIC) and RMIC mechanisms into GDR can further improve estimation accuracy, with RMIC's performance approaching the Cramer-Rao lower bound.

[0157] Figure 9 The probability density function of time resource consumption for different algorithms is shown. It can be seen that the OMP-based integer parameter estimation algorithm (Integral) has the least time consumption because it does not require calculating a small dictionary matrix. The GDR algorithm adopts a strategy of calculating the sampling point positions first and then constructing the dictionary matrix, which greatly reduces the matrix size, thus its time consumption is significantly lower than the OMPFR algorithm. The PDIC and RMIC algorithms add inter-path interference cancellation modules to the GDR algorithm, which slightly increases the time consumption, but the overall time consumption is still much lower than OMPFR.

[0158] Therefore, this invention adopts the above-mentioned fractional parameter estimation method for an ISAC system based on OTFS. The GDR technology utilizes the correlation of atoms in the dictionary matrix in the time-delay-Doppler domain to achieve better parameter estimation accuracy and lower computational complexity compared to conventional methods. The PDIC and RMIC technologies can consume a small amount of additional computational resources to combat inter-path interference, thereby achieving higher estimation accuracy.

[0159] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A fractional parameter estimation method for an ISAC system based on OTFS, characterized in that, Includes the following steps: S1. The OTFS modulated signal is transmitted through the transmitter of the ISAC system, the radar receiver receives the reflected radar signal of the target channel, and the communication receiver receives the communication signal. The radar receiver and the communication receiver share the spectrum resources of the OTFS modulated signal. S2. Perform time-delay-Doppler domain channel estimation on the signal received by the radar receiver, and establish the initial parameter estimates of fractional time delay and fractional Doppler frequency shift by the correlation between the atoms of the dictionary matrix; S3. The initial parameter estimation is optimized by refining the GDR algorithm based on gradient descent. The parameters are iteratively adjusted until convergence is achieved by maximizing the correlation function between dictionary atoms related to the initial parameters. S4. During the iterative optimization process, the interference cancellation mechanism is dynamically selected based on the actual interference characteristics. If it is necessary to eliminate multipath interference and separate the target parameters of different propagation paths, the path decoupling interference cancellation PDIC mechanism is activated. If it is necessary to further eliminate residual interference to improve signal quality, the residual minimization interference cancellation RMIC mechanism is activated to minimize the residual error through iterative optimization. S5. When the residual error meets the preset convergence condition, output the high-precision parameter estimation result.

2. The fractional parameter estimation method for an ISAC system based on OTFS according to claim 1, characterized in that, The specific steps of refining the GDR algorithm using gradient descent in S3 are as follows: S31, converting the reflected radar signal r0 received by the radar receiver into a vector form r vec as an initial residual; S32, estimating an integer multiple approximation value of the time delay and the Doppler shift of each propagation path in the target channel according to the integer dictionary matrix Ψ I , estimating an integer multiple approximation value of the time delay and the Doppler shift of each propagation path in the target channel according to the integer dictionary matrix Ψ S33. Construct the correlation function between dictionary atoms related to the initial parameter estimation, and adjust the above parameters through the gradient descent iterative algorithm to maximize the value of the correlation function; S34, update the sub-dictionary matrix Ψ based on the obtained parameters in iteration f and adjust the residual r based on this s where r s is the residual obtained in the s-th iteration; S35. Repeat steps S32-S34 until the number of iterations exceeds the maximum number of iterations or the residual r. s If the value is less than the threshold ε, stop the iteration and obtain the optimized fractional parameter estimation result.

3. The fractional parameter estimation method for an ISAC system based on OTFS according to claim 2, characterized in that, The correlation function of S33 is denoted as C(l e ,k e Specifically, it is expressed as: Among them, l e For normalized time delay estimation, k e For normalized Doppler estimation, Γ MN Let be a time-delay shift diagonal matrix, (·) H This indicates the conjugate transpose operation. Let F be the power transformation matrix for time delay shift. MN Let be a normalized Fourier transform matrix of size MN. For the matrix associated with the Doppler shift, s vec Let M be the vector form of the time-domain symbol matrix s after column expansion, where M is the number of time delay units and N is the number of Doppler units.

4. The fractional parameter estimation method for an ISAC system based on OTFS according to claim 3, characterized in that, The derivation of the gradient expression for the gradient descent iterative algorithm in S33 is as follows: a. Define an intermediate variable z to simplify the correlation function; b. Using the chain rule for complex differentiation, solve for the correlation function with respect to l. e and k e The partial derivative; c. Solve for the intermediate variable z with respect to l e and k e The partial derivative; Where Λ is a diagonal matrix, defined as: Here, diag{·} is the operation for constructing a diagonal matrix, j is the imaginary unit, and Arg(·) is the principal value operation.

5. The fractional parameter estimation method for an ISAC system based on OTFS according to claim 1, characterized in that, The specific steps of the path decoupling interference elimination PDIC mechanism in S4 are as follows: S411. Obtain the fractional parameter estimation results of the gradient descent refined GDR algorithm, identify the number P of propagation paths in the target channel, and extract the initial normalized delay l of each path. p and normalized Doppler k p ; S412. For each path p, perform the decoupling interference iteration; S413. After completing the decoupling of all paths, obtain the fractional parameter estimation results after the decoupling interference of each path, update the residuals. If the residual interference suppression effect does not reach the preset level, repeat S412 and S413. Otherwise, perform the residual minimization interference elimination RMIC mechanism.

6. The fractional parameter estimation method for an ISAC system based on OTFS according to claim 1, characterized in that, The specific steps of S412 are as follows: a. Use the estimated initial score parameters of the path obtained by the GDR algorithm as the initial estimate; b. Transform the fraction dictionary matrix Ψ f Set the p-th column corresponding to the p-th path in the matrix to zero, and construct a temporary score dictionary matrix Ψ. f,temp ; c. Based on the current estimate and the temporary score dictionary matrix Ψ f,temp Recalculate the residual r after removing path p interference. p ; d. Perform gradient descent iterations again on the p-th path to refine the estimates of the fractional delay and fractional Doppler for that path; e. Update the fraction dictionary matrix Ψ based on the refined estimates. f .

7. The fractional parameter estimation method for an ISAC system based on OTFS according to claim 3, characterized in that, The specific steps of the residual minimization interference cancellation (RMIC) mechanism in S4 are as follows: S421. Based on the parameter estimation results and updated residuals of the GDR algorithm refined by gradient descent, the residual norm is defined as the objective function. Where ||·||2 is the L2 norm, and r is the current residual vector, which satisfies the following formula; Where, r vec The received signal is in vectorized form, where P is the number of propagation paths and h is the vectorized form. p Let p be the complex gain of the p-th path. For path p-based normalized delay l p The time delay shift matrix, For path p-based normalized Doppler k p Shift matrix; S422. For each propagation path, calculate the partial derivatives of the residual norm objective function with respect to the normalized delay and normalized Doppler for that path. Wherein, the residual r is normalized to the path p with respect to the delay l p and normalized Doppler k p The partial derivatives satisfy: S423. Use the gradient descent iterative algorithm to adjust the parameter estimates of each path based on the partial derivative results; S424. After each parameter adjustment, update the fraction dictionary matrix and residuals, and recalculate the residual norm objective function value. S425. If the residuals meet the preset convergence conditions, stop the iteration and output the optimized parameter estimation results; otherwise, return to S422 and repeat the parameter adjustment until the convergence conditions are met.

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