Fractional parameter estimation method of ISAC system based on OTFS

Abstract

The invention discloses a fractional parameter estimation method of an ISAC system based on OTFS, and belongs to the technical field of wireless communication, and the method comprises the steps: carrying out the time delay-Doppler domain channel estimation of a radar receiving signal, and building the fractional time delay and fractional Doppler initial parameter estimation through dictionary matrix atom correlation; the GDR algorithm is refined through gradient descent, and parameters are iteratively optimized by maximizing the atom correlation function of the correlation dictionary; in iteration, multipath parameters are separated by a path decoupling interference elimination PDIC mechanism, and residual interference is eliminated by a residual error minimization interference elimination RMIC mechanism; after the residual error reaches a convergence condition, outputting a high-precision parameter estimation result; according to the fractional parameter estimation method of the ISAC system based on the OTFS, the problems that a traditional method is difficult to accurately estimate fractional delay and fractional Doppler, the multi-path interference influence is large, and the calculation complexity is high are solved, and high-precision parameter estimation, high anti-interference capacity and efficient resource utilization are achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, and particularly relates to a fractional parameter estimation method of an OTFS-based ISAC system. BACKGROUND

[0002] In high-mobility wireless communication scenarios, traditional Orthogonal Frequency Division Multiplexing (OFDM) systems face serious challenges of Doppler shift. Due to the difficulty in maintaining the orthogonality between subcarriers, inter-carrier interference occurs, and the system performance is significantly degraded. 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 delay in high dynamic and complex environments. This feature makes OTFS a highly potential signal waveform for Integrated Sensing and Communication (ISAC) systems. ISAC systems aim to realize communication and sensing functions simultaneously using the same set of hardware and spectrum resources, thereby improving resource utilization efficiency and reducing system complexity. The advantage of OTFS modulation in the delay-Doppler domain enables it to effectively separate paths with different delays and Dopplers, which is crucial for parameter estimation in target sensing.

[0003] When performing target sensing in an OTFS system, it is crucial to accurately estimate the echo parameters of the target, such as delay and Doppler shift. However, when the delay or Doppler shift of the target is not an integer multiple of the system resolution, the received signal energy will spread to adjacent delay-Doppler grid cells, leading to the problem of fractional delay and fractional Doppler shift. Existing parameter estimation methods, such as threshold-based channel estimation methods, can usually only estimate integer multiple parameter values, which cannot meet the demand of high-precision sensing. In order to solve the problem of inter-carrier interference caused by fractional Doppler shift, some research works have proposed effective fractional Doppler shift estimation algorithms, but these methods still estimate the delay as an integer value.

[0004] To estimate fractional delay and fractional Doppler shift more accurately, many research works have been carried out. Some researches adopt pulse-based channel estimation method, but this usually requires high signal-to-noise ratio pilot signals, thereby increasing the peak-to-average power ratio of the system, which is not conducive to practical application. Some other research works utilize the sparsity of the delay-Doppler domain, convert the parameter estimation problem into a sparse signal recovery problem, and apply a compressive sensing algorithm to solve it. However, when constructing the dictionary matrix, these methods often ignore the correlation between the atoms in the dictionary matrix. In fact, the OTFS channel estimation problem is not completely equivalent to the general sparse signal recovery problem, because the correlation between the atoms in the dictionary matrix is not fully utilized, which leads to a higher algorithm complexity. In addition, some algorithms based on orthogonal matching pursuit (OMP), such as two-step orthogonal matching pursuit with fractional refinement (OMPFR) algorithm, although attempt to reduce the computational complexity, but its performance is limited by the greedy nature of the OMP algorithm itself. Therefore, it is necessary to develop a fractional parameter estimation method for OTFS-based ISAC system, which can effectively utilize the characteristics of delay-Doppler domain, consider the correlation between the atoms in the dictionary matrix, and overcome the limitations of traditional methods, and realize low complexity and high precision. SUMMARY

[0005] The purpose of the present application is to provide a fractional parameter estimation method for OTFS-based ISAC system to solve the problems raised in the background art.

[0006] To achieve the above purpose, the present application provides a fractional parameter estimation method for OTFS-based ISAC system, comprising the following steps:

[0007] S1, sending an OTFS modulated signal through the transmitter of the ISAC system, receiving a reflected radar signal of the target channel by the radar receiver, receiving a communication signal by the communication receiver, and sharing the spectrum resource of the OTFS modulated signal by the radar receiver and the communication receiver;

[0008] S2, performing delay-Doppler domain channel estimation on the signal received by the radar receiver, and establishing initial parameter estimation of fractional delay and fractional Doppler shift through the correlation between the atoms in the dictionary matrix;

[0009] S3, optimizing the initial parameter estimation based on the gradient descent refinement (GDR) algorithm, and iteratively adjusting the parameters until convergence by maximizing the correlation function between the dictionary atoms related to the initial parameters;

[0010] S4, in the iterative optimization process, dynamically selecting interference cancellation mechanism according to actual interference characteristics; if it is needed to cancel multipath interference and separate target parameters of different propagation paths, starting path decoupling interference cancellation (PDIC) mechanism; if it is needed to further cancel residual interference to improve signal quality, enabling residual minimization interference cancellation (RMIC) mechanism, and minimizing residual error through iterative optimization;

[0011] S5, outputting high-precision parameter estimation result when residual error meets preset convergence condition.

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

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

[0014] S32, performing integer multiple approximation value estimation on the time delay and Doppler shift of each propagation path in the target channel according to the integer dictionary matrix Ψ I ;

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

[0016] S34, updating the fractional dictionary matrix Ψ f according to the parameters obtained through iteration, and adjusting the residual r s based on the same, wherein r s is the residual obtained through the s-th iteration;

[0017] S35, repeating steps S32-S34 until the iteration number is greater than the maximum iteration number or the residual r s is less than the threshold value ε, stopping iteration, and obtaining the optimized fractional parameter estimation result.

[0018] Preferably, the correlation function of S33 is denoted as C(l e ,k e ), and specifically represented as:

[0019]

[0020] wherein l e is a normalized time delay estimation, k e is a normalized Doppler estimation, Γ MN is a time delay shift diagonal matrix, (·) H denotes a conjugate transpose operation, is a time delay shift power transformation matrix, F MN is a normalized Fourier transformation matrix with a size of MN, The matrix associated with Doppler shift, s vec The vector form after column expansion of the time domain symbol matrix s, 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 iteration algorithm in S33 is as follows:

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

[0023]

[0024] b. According to the chain rule of complex derivative, the partial derivatives of the correlation function with respect to l e and k e are solved;

[0025]

[0026] c. The partial derivatives of the intermediate variable z with respect to l e and k e are solved;

[0027]

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

[0029]

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

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

[0032] S411, obtaining the fractional parameter estimation result output by the gradient descent refinement GDR algorithm, identifying the number P of propagation paths in the target channel, and extracting the initial normalized time delay l p and the normalized Doppler k p of each path;

[0033] S412, for each path p, performing decoupling interference iteration;

[0034] S413, after completing the decoupling of all paths, obtaining the fractional parameter estimation result after decoupling interference of each path, updating the residual error, and if the residual error interference suppression effect does not reach the preset, the preset convergence condition is that the residual error norm is less than a threshold value, the parameter adjustment amount is less than a minimum step or the maximum iteration number is reached, repeat S412 and S413, otherwise, residual minimization interference cancellation RMIC mechanism is performed.

[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, adopt gradient descent iterative algorithm, adjust parameter estimation value of each path according to partial derivative result;

[0052] S424, after each parameter adjustment, update digital dictionary matrix and residual error, and recalculate residual error norm target function value;

[0053] S425, if residual error meets preset convergence condition, stop iteration, and output optimized parameter estimation result;Otherwise, return S422 and repeatedly execute parameter adjustment until the convergence condition is met.

[0054] Therefore, the present application adopts the fractional parameter estimation method of the OTFS-based ISAC system, which has the following beneficial effects:

[0055] (1) GDR algorithm combines dictionary atom correlation iterative optimization, PDIC mechanism decouples multipath interference, breaks through the precision bottleneck of traditional method, separates multipath parameters in complex scene, and realizes high-precision estimation of fractional delay and Doppler.

[0056] (2) RMIC mechanism eliminates residual interference, improves system anti-multipath and fractional Doppler interference ability;At the same time, through algorithm optimization, the calculation complexity is reduced, the dependence on pilot resource is reduced, and efficient calculation and spectrum / energy resource utilization are considered.

[0057] The technical solutions of the present application will be further described in detail below through the drawings and examples. DETAILED DESCRIPTION

[0058] Figure 1 It is a flow chart of the fractional parameter estimation method of the OTFS-based ISAC system of the present application;

[0059] Figure 2 It is a structure diagram of the OTFS-ISAC system device of the present application;

[0060] Figure 3 It is the iteration process of the gradient descent refinement technology of the present application, wherein the circle point is the true value, and the broken line is the iteration process;

[0061] Figure 4 It is the iteration process of the path decoupling interference cancellation technology after the gradient descent refinement of the present application, wherein the circle point is the true value, and the broken line is the iteration process;

[0062] Figure 5 It is a comparison curve diagram of the estimation precision of the normalized delay of the present application;

[0063] Figure 6A comparison chart of estimation accuracy of path gain real part of the present application;

[0064] Figure 7 A comparison chart of estimation accuracy of path gain imaginary part of the present application;

[0065] Figure 8 A comparison chart of estimation accuracy of path gain imaginary part of the present application;

[0066] Figure 9 A comparison chart of estimation accuracy of path gain imaginary part of the present application. DETAILED DESCRIPTION

[0067] The following detailed description of embodiments of the application provided in the accompanying drawings is not intended to limit the scope of the application as claimed, but merely represents selected embodiments of the application. Based upon the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work are within the scope of protection of the present application.

[0068] EMBODIMENT

[0069] As shown in the figure, the present application provides a fractional parameter estimation method of OTFS-based ISAC system, including the following steps: Figure 1

[0070] The present embodiment is a radar parameter estimation technology based on an integrated sensing and communication system (ISAC) device of orthogonal time frequency space (OTFS) modulation, which mainly includes a transmitter, a radar receiver and a communication receiver, as shown in the figure. The radar receiver and the transmitter are in the same position, share the same transceiver antenna, and the radar receiver has all the information of the transmitter transmitted symbols. After the received signal is subjected to Wigner transform and symplectic finite Fourier transform, the time delay and Doppler parameters of the target in the channel can be estimated. The communication receiver has pilot information of the transmitted symbols. The received symbols are also subjected to Wigner transform and symplectic finite Fourier transform. According to the pilot information, the channel is estimated and equalized, so as to perform symbol detection to obtain communication information. Figure 2

[0071] The technology of the present embodiment mainly lies in the parameter estimation method in the radar receiver. The communication receiver is consistent with the general OTFS-based system. The OTFS system model is introduced as follows.

[0072] OTFS models the channel as a linear time-varying channel, considering multipath propagation and 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, which is defined as:

[0073] ​​

[0074] where, and denote the resolution in delay dimension and Doppler dimension, respectively. Δf is the frequency interval between adjacent carriers, 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 one OTFS frame.

[0075] By inverse symplectic finite Fourier transform (ISFFT), the delay-Doppler domain symbol matrix can be mapped to the time-frequency domain symbol matrix i.e.,

[0076]

[0077] where, F M is a normalized discrete Fourier transform (DFT) matrix of size M, (·) H denotes the conjugate transpose.

[0078] By applying the Heisenberg transform and combining with the transmit-end pulse-shaping filter, the time-frequency domain symbol matrix X TF is converted to the time-domain symbol matrix which is expressed as:

[0079]

[0080] where, denotes the matrix form of the transmit-end pulse-shaping filter, whose diagonal elements are:

[0081]

[0082] The transmit symbol vector s vec is the vector form obtained by unfolding the time-domain symbol matrix s column by column, i.e.,

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

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

[0085] l p = τ p MΔf (20)

[0086] k p = v p NT (21)

[0087] Considering fractional delay and fractional Doppler, the matrix form of the time-domain channel impulse response may be expressed as:

[0088]

[0089] wherein, is a diagonal matrix, which has the form:

[0090]

[0091] is also a diagonal matrix, which has the form:

[0092]

[0093] The received time-domain OTFS signal vector r vec may be expressed as:

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

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

[0096] After the radar receiver receives the signal, the time delay and Doppler parameters of the target in the channel can be estimated according to the symbol information transmitted by the transmitter, and the communication receiver can estimate and equalize the channel according to the pilot information after receiving the signal, so as to detect the symbol to obtain the communication information.

[0097] S1, the transmitter of the ISAC system transmits an OTFS modulated signal, the radar receiver receives the reflected radar signal of the target channel, the communication receiver receives the communication signal, and the radar receiver and the communication receiver share the spectrum resource of the OTFS modulated signal.

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

[0099] In order to improve the accuracy of the parameter estimation of the fractional delay and the fractional Doppler frequency shift by the radar receiver, the following three technologies are provided in the embodiment, the gradient descent refinement GDR algorithm can achieve better radar parameter estimation accuracy and lower calculation complexity in the scene with fewer paths in the channel, if it is necessary to further improve the accuracy of the parameter estimation or the number of paths in the channel is larger, a small amount of time resource can be additionally consumed, and the path decoupling interference cancellation PDIC mechanism or the residual minimization interference cancellation RMIC mechanism is used to achieve better effect.

[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 Compared 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 is the vector form after column expansion of time-domain symbol matrix s, M is the number of time-delay units, and N is the number of Doppler units.

[0109] At this time, estimating the time delay and Doppler of a path can be converted into a problem of maximizing C(l e ,k e ) through experiments. It is verified that, in the neighborhood of the target point on the time-delay-Doppler plane, C(l e ,k e ) is a locally convex function, and therefore a gradient descent iterative algorithm can be used for solving. The gradient expression is derived as follows.

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

[0111]

[0112] b. According to the chain rule for derivation of complex numbers, the partial derivatives of the correlation function with respect to l e and k e are solved;

[0113]

[0114] c. The partial derivatives of the intermediate variable z with respect to l e and k e are solved;

[0115]

[0116] wherein Λ is a diagonal matrix, the elements of which are in the range of j[-π, π), and is defined as:

[0117]

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

[0119] S34, update the sub-dictionary matrix Ψ f according to the parameters obtained through iteration, and adjust the residual r s based on this, wherein r s is the residual obtained through the s-th iteration;

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

[0121] S4, in the iterative optimization process, dynamically select the interference cancellation mechanism according to 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 started; if it is necessary to further eliminate residual interference to improve signal quality, the residual minimization interference cancellation (RMIC) mechanism is enabled, and the residual error is minimized through iterative optimization.

[0122] When there are P paths (P > 1) in the channel, the receiving end will receive P copies of each transmitted symbol. After the superposition of the path signals, the peak position of the target function C (l e ,k e ) will shift, especially when the time delay - Doppler interval of each path is small, the shift phenomenon will be more serious.

[0123] One idea is to decouple the single path to be estimated from other paths, that is, the path decoupling interference cancellation (PDIC) mechanism, similar to the orthogonalization operation in the OMP algorithm. Specifically, each path is re-estimated separately; when re-estimating a path, the interference of the path to the received signal is cancelled using the existing information of other paths, and then gradient descent iteration is performed to refine the fractional parameter estimation of the path.

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

[0125] S411, obtain the fractional parameter estimation result output by the gradient descent refinement (GDR) algorithm, identify the number P of propagation paths in the target channel, and extract the initial normalized time delay l p and the normalized Doppler k p of each path;

[0126] S412, for each path p, perform decoupling interference iteration;

[0127] a. the initial fractional parameter estimation value of the path obtained by the GDR algorithm is used as the initial estimation value;

[0128] b. set the pth column corresponding to the pth path in the dictionary matrix Ψ f to zero, and construct a temporary dictionary matrix Ψ f,temp ;

[0129] c. recalculate the residual r f,temp after removing the interference of path p according to the current estimation value and the temporary dictionary matrix Ψ p ;

[0130] d. perform gradient descent iteration again for the pth path to refine the estimation value of the fractional time delay and the fractional Doppler of the path;

[0131] e. update the dictionary matrix Ψf .

[0132] S413, after all path decoupling is completed, the fractional parameter estimation result after each path decoupling interference is obtained, the residual error is updated, if the residual error interference suppression effect does not reach the preset, the preset convergence condition is that the residual error norm is less than the threshold value, the parameter adjustment amount is less than the minimum step or the maximum iteration number is reached, S412 and S413 are repeated, otherwise the residual error minimization interference cancellation RMIC mechanism is performed.

[0133] Gradient descent refinement technique (GDR) and path decoupling interference cancellation technique (PDIC) maximize the objective function C(l e ,k e ) in iteration, both of which belong to greedy and can only achieve local optimization. If the "residual error minimization" is directly taken as the objective function, the global optimization can be achieved. However, since 2P variables need to be optimized at the same time, there is a great challenge in convergence. Therefore, the gradient descent refinement technique can be used to obtain an approximate solution first, and then the residual error minimization criterion is used to optimize it to obtain a more accurate result.

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

[0135] S421, based on the parameter estimation result output by the gradient descent refinement GDR algorithm and the updated residual error, the residual error norm is defined as the objective function;

[0136]

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

[0138]

[0139] Where r vec is the received signal vector, P is the number of propagation paths, h p is the complex gain of the pth path, is the delay shift matrix based on the path p normalized delay l p , is the shift matrix based on the path p normalized Doppler k p ;

[0140] S422, for each propagation path, the partial derivative of the residual error norm objective function with respect to the path normalized delay and normalized Doppler is calculated;

[0141]

[0142] Where the residual error r is the partial derivative of the path p normalized delay l p and the 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 Normalized latency l p ]]> Normalized Doppler k p ]]> 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] Suppose there are 5 paths in the channel, and the corresponding time delay and Doppler shift are random values uniformly distributed in the maximum range. The path gain is a complex number, whose modulus is uniformly distributed between 0 and 1, and the amplitude angle is uniformly distributed between [0, 2π). The parameters used in the simulation are shown in Table 2. The algorithms compared include: integral parameter estimation technology based on orthogonal matching pursuit algorithm (Integral), orthogonal matching pursuit fractional refinement algorithm (OMPFR), gradient descent refinement technology (GDR), path decoupling interference cancellation technology (PDIC), and residual minimization interference cancellation technology (RMIC). In addition, the estimation accuracy of the technology in the system is compared with the Cramer-Rao lower bound (CRLB) of the system.

[0153] Table 2 Simulation parameters for performance comparison of algorithms

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

[0155] The OMPFR algorithm aims to reduce the dimension of the dictionary matrix to reduce the computational complexity. However, this algorithm has certain limitations: when the parameter estimation accuracy is required to be high, the computational complexity is still high; in addition, in a channel with multiple propagation paths, the performance of the OMPFR algorithm will be greatly reduced due to its greedy nature.

[0156] From Figure 5-Figure 8 The root mean square error of the estimation of the normalized delay, normalized Doppler, real part of the path gain, and imaginary part of the path gain by the five algorithms is shown. It can be seen that, compared with GDR, the performance of the OMPFR technology is limited by the limited number of fractional sampling points in the time delay-Doppler plane, resulting in low estimation accuracy. The GDR technology can achieve a smaller sampling interval and thus better estimation accuracy even with fewer sampling points. If the PDIC and RMIC mechanisms are introduced based on the GDR technology, the estimation accuracy can be further improved, and the performance of the RMIC is very close to the Cramer-Rao lower bound.

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

[0158] Therefore, the application adopts the fractional parameter estimation method of the OTFS-based ISAC system, and the GDR technology realizes better parameter estimation accuracy and lower calculation complexity compared with conventional methods by utilizing the correlation of atoms in the dictionary matrix in the time delay-Doppler domain; the PDIC technology and the RMIC technology can additionally consume a small amount of calculation resources to resist inter-path interference, thereby realizing higher estimation accuracy.

[0159] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application but not to limit them, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can still be modified or replaced by equivalents, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A method for fractional parameter estimation of an OTFS-based ISAC system, characterized in that, The method comprises the following steps: S1, transmitting an OTFS modulated signal through a transmitter of an ISAC system, receiving a reflected radar signal of a target channel by a radar receiver, receiving a communication signal by a communication receiver, and sharing spectrum resources of the OTFS modulated signal by the radar receiver and the communication receiver; S2, performing time-delay-Doppler domain channel estimation on the signal received by the radar receiver, and establishing initial parameter estimation of fractional time delay and fractional Doppler shift through correlation between atoms in a dictionary matrix; S3, optimizing the initial parameter estimation based on a gradient descent refinement GDR algorithm, and iteratively adjusting parameters until convergence by maximizing a correlation function between dictionary atoms related to the initial parameters; S4, dynamically selecting an interference cancellation mechanism according to actual interference characteristics during the iterative optimization process; if it is necessary to cancel multipath interference and separate target parameters of different propagation paths, a path decoupling interference cancellation PDIC mechanism is started; if it is necessary to further cancel residual interference to improve signal quality, a residual minimization interference cancellation RMIC mechanism is enabled, and residual error is minimized through iterative optimization; S5, outputting high-precision parameter estimation results when the residual error meets a preset convergence condition.

2. The fractional parameter estimation method for an OTFS-based ISAC system according to claim 1, characterized in that, The specific steps of the gradient descent refinement GDR algorithm 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, constructing a correlation function between dictionary atoms related to the initial parameter estimation, and adjusting the above parameters by a 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 iteration number is greater than the maximum iteration number or the residual r s is less than the threshold value ε, stop iteration, and obtain the optimized score parameter estimation result.

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

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

5. The fractional parameter estimation method for an OTFS-based ISAC system according to claim 1, characterized in that, The specific steps of the path decoupling interference cancellation PDIC mechanism in S4 are as follows: S411、Obtain the score parameter estimation result output by the gradient descent refinement 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, performing decoupling interference iteration for each path p; S413, obtaining fractional parameter estimation results after path decoupling interference is completed, updating residual error, and repeating S412 and S413 if residual error interference suppression effect does not meet a preset, or performing residual minimization interference cancellation RMIC mechanism.

6. The fractional parameter estimation method for an OTFS-based ISAC system according to claim 1, characterized in that, The specific steps of S412 are as follows: a. taking the initial fractional parameter estimation value of the path obtained by the GDR algorithm as an initial estimation value; b. Set the p-th column corresponding to the p-th path in the matrix Ψ f to zero, and construct a temporary matrix Ψ f,temp ; c. According to the current estimate and the temporary fractional number dictionary matrix Ψ f,temp Recalculating the residual r after removing the path p interference p ; d. performing gradient descent iteration again for the pth path to refine the estimation value of the fractional time delay and the fractional Doppler of the path; e. updating the sparse dictionary matrix Ψ according to the refined estimates f .

7. The fractional parameter estimation method for an OTFS-based ISAC system according to claim 3, characterized in that, The specific steps of the residual minimization interference cancellation RMIC mechanism in S4 are as follows: S421, defining a residual norm as an objective function based on the parameter estimation results output by the gradient descent refinement GDR algorithm and the updated residual error; wherein ||·||2 is an L2 norm, r is a current residual vector, and satisfies the following formula; where r vec is the received signal, P is the number of propagation paths, h p is the complex gain of the p-th path, is the delay shift matrix based on the normalized delay l p of the p-th path, is the Doppler shift matrix based on the normalized Doppler k p of the p-th path; S422, calculating the partial derivative of the residual norm objective function with respect to the normalized time delay and the normalized Doppler of each propagation path; where the partial derivative of the residual r with respect to the path p normalized delay l p and normalized Doppler k p satisfies: S423, adjusting the parameter estimation value of each path according to the partial derivative result by using a gradient descent iterative algorithm; S424, updating the fractional dictionary matrix and the residual error after each parameter adjustment, and recalculating the residual norm objective function value. S425, if the residual satisfies a preset convergence condition, stopping iteration and outputting an optimized parameter estimation result; otherwise, returning to S422 to repeatedly perform parameter adjustment until the convergence condition is satisfied.

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