Multi-target parameter estimation method and system based on OTFS common sense sharing waveform

Abstract

The application discloses a multi-target parameter estimation method and system based on an OTFS sensing shared waveform, relates to the technical field of communication and sensing integration, and first jointly adopts two representation methods of a discrete DD domain sensing channel and a continuous DD domain sensing channel and corresponding DD domain echo signal modes, and describes a problem model suitable for multi-target sensing and fractional delay Doppler estimation; when a target is sensed, a BCS-ML algorithm in the application estimates target parameters in two stages, estimates integer delay Doppler in the first stage, and estimates fractional delay Doppler in the second stage, the model adopted by the application and the algorithm proposed by the application realize low-complexity parameter estimation and high-precision parameter estimation of multi-target, and break through the limitations of a traditional OTFS sensing parameter estimation algorithm.

Description

Technical Field

[0001] This invention relates to the field of integrated communication and sensing technology, specifically to a multi-objective parameter estimation method and system based on OTFS sensing shared waveform. Background Technology

[0002] In recent years, with the development of integrated communication and sensing technologies, the need to simultaneously perform functions such as sensing target parameter estimation on base stations with communication capabilities using shared sensing waveforms has become increasingly urgent. Traditional shared sensing waveforms mainly include Linear Frequency Modulation (LFM) signals and Orthogonal Frequency Division Multiplexing (OFDM) signals. However, LFM signals have low communication rates, and OFDM suffers from severe inter-carrier interference in high-speed (600 km / h) scenarios. These inherent limitations restrict the further development of LFM and OFDM. Against this backdrop, Orthogonal Time Frequency Space (OTFS) signals, due to their unique advantages in time-frequency dual-selection channels, have gained increasing attention in the research and application of shared sensing waveforms.

[0003] Currently, sensing algorithms based on OTFS-based synesthetic shared waveforms mainly include matched filter (MF) algorithm, two-dimensional correlation algorithm, and maximum likelihood (ML) estimation algorithm.

[0004] The MF algorithm designs a matched filter matrix using the known Delay Doppler (DD) domain transmitted symbol matrix, and performs matched filtering on the received DD domain echo signal to achieve delay Doppler estimation of the sensed target. The advantage of the MF algorithm is its ability to sense multiple targets. However, its disadvantages include high computational complexity due to the high-dimensional matched filter matrix and matrix inversion operations, and its limitation to estimating only the integer delay Doppler of the target, resulting in lower sensing accuracy.

[0005] The two-dimensional correlation algorithm estimates the delay and Doppler of a target by performing a two-dimensional correlation operation between the received DD-domain echo signal and the transmitted DD-domain symbol. Similar to the MF algorithm, this algorithm can estimate the parameters of multiple sensed targets, but it has high computational complexity and low sensing accuracy.

[0006] The ML estimation algorithm constructs a maximization problem based on the linear relationship between the DD domain echo signal, DD domain channel, DD domain transmitted signal, and noise, and performs on-network or off-network searches based on the DD domain grid. The ML estimation algorithm can be used to estimate integer and fractional delay Doppler signals, achieving high sensing accuracy. However, when there are many targets or significant interference between targets, accurately estimating the parameters of each sensed target using the ML estimation algorithm becomes quite difficult.

[0007] Bayesian Compressed Sensing (BCS) algorithms are widely used in communication channel estimation problems. By constructing a reasonable sensing channel model and utilizing the sparsity of the sensing channel in the DD domain, the BCS algorithm can also be used to estimate channel parameters related to the sensing target. Within the BCS algorithm framework, applying the Generalized Approximate Message Passing (GAMP) algorithm can effectively reduce the computational complexity of the BCS algorithm.

[0008] Therefore, there is currently a lack of a multi-target parameter estimation scheme that can comprehensively consider factors such as computational complexity, accuracy of perception parameter estimation, and multi-target perception. Summary of the Invention

[0009] In view of this, the present invention provides a multi-target parameter estimation method and system based on OTFS sensing shared waveforms. It can comprehensively consider factors such as computational complexity, sensing parameter estimation accuracy and multi-target sensing, and estimate the distance and velocity of the sensing target in two stages in the discrete DD domain and the continuous DD domain respectively, thus realizing low-complexity parameter estimation and high-precision parameter estimation for multiple sensing targets.

[0010] To achieve the above objectives, the technical solution of the present invention includes the following steps:

[0011] Step 1: For the integrated communication and sensing scenario based on OTFS, construct the base station received echo model based on the discrete DD domain channel representation, denoted as Model A; construct the base station received echo model based on the continuous DD domain channel representation, denoted as Model B.

[0012] Step 2: Randomly select R rows from the received echo vector signal to construct a BCS linear model, where, The value is a positive integer; the sensing channel h is estimated iteratively using the GAMP algorithm to obtain the integer delay Doppler estimate of the target, and the approximate echo signal of each target is reconstructed based on the estimation results and model A.

[0013] Step 3: Based on Model B, use the approximate echo signal of each reconstructed target to perform interference cancellation and construct a problem model for ML estimation of each target; construct a two-dimensional function based on the problem model of ML estimation of each target; use the Coordinate Descent (CD) algorithm to iteratively estimate the fractional delay Doppler of the target.

[0014] Step 4: Output the target's distance and velocity estimates.

[0015] Furthermore, the integrated communication and sensing scenario based on OTFS specifically involves: the user communicating with the integrated sensing base station and the target being actively sensed are the same individual; the base station transmits OTFS integrated sensing signals and receives the echo reflected by the target; the base station uses the DD domain signal from the transmitter... DD domain signal at the receiving end The relative distance *r* and relative radial velocity *v* between the target and the base station are obtained, thereby estimating the target's physical parameters *r* and *v*; where, This represents an MN×1 dimensional complex field, where M and N represent the number of subcarriers and the number of time slots, respectively.

[0016] The physical parameters r and v correspond to the sensing channel, respectively. The two parameters in the equation are the delay τ = 2r / c and the Doppler ν = 2f. c v / c; where P is the number of targets; ξ p , τ p v p These represent the reflection coefficient, delay, and Doppler amplitude of target p, respectively; f c denoted as carrier frequency, c as speed of light, and δ(·) as the Dirac delta function.

[0017] Furthermore, a base station received echo model is constructed based on the discrete DD domain channel representation, specifically as follows:

[0018] In the discrete DD domain channel representation, τ and v are integer multiples of the delay resolution 1 / MΔf and the Doppler resolution 1 / NT, respectively, i.e., τ=l / MΔf, l=0,…,M-1, ν=k / NT, k=0,…,N-1; where Δf is the subcarrier spacing, T is the time slot length, TΔf=1, and the delay tap l and Doppler tap k are both integers;

[0019] make At the tap p and k p If there exists a target p at a certain location, then h(l) p ,k p ξ is the reflection coefficient of the target. pIf there are no targets at taps l and k, then h(l,k) is 0. When there are P targets, the discrete DD domain channel contains P non-zero reflection coefficients, denoted as...

[0020] Let Y = vec -1 (y DD ), X = vec -1 (x DD ), h(kM+l)=h(l,k), h=[h(0),h(1),…,h(MN-1)] T , Among them, vec -1 (·) denotes the matrix representation of a vector;

[0021] In this representation mode, the elements of the m-th row and n-th column of the received DD domain signal matrix Y under noise-free conditions are: Where 0 ≤ m ≤ M-1, 0 ≤ n ≤ N-1; [·] M Indicates the modulus M;

[0022]

[0023] make

[0024]

[0025] ⊙ denotes the matrix inner product, (·) H Represents the conjugate transpose of a matrix;

[0026] make

[0027] Let o nM+m =o m,n O H =[o0,o1,…,o MN-1 ], y DD =Oh;

[0028] Considering noise, y DD =Oh+ω, ω represents additive white Gaussian noise; matrix O is based on the transmitted signal x. DD With phase ρ m,n Perform a unique design.

[0029] Furthermore, a base station received echo model is constructed based on the continuous DD domain channel representation, specifically as follows:

[0030] In the continuous DD-domain channel representation, τ and v respectively contain the fractional delay resolution of 1 / MΔf and the fractional Doppler resolution of 1 / NT;

[0031] In this representation mode, the received DD-domain signal vector is expressed as where, Ω is the continuous DD-domain sensing channel matrix, is the additive white Gaussian noise, denotes the Kronecker product, and I MN denotes the MN-dimensional identity matrix; is defined as is the continuous DD-domain sensing channel matrix related to the target p, defined as where, F N is the N-dimensional FFT matrix, and F M is the M-dimensional FFT matrix, Π MN is the MN-dimensional forward circulant matrix, is the M-dimensional IFFT matrix, is the N-dimensional IFFT matrix,

[0032] Furthermore, step 2 specifically includes the following steps:

[0033] Before iteratively estimating the sensing channel h, randomly select R rows from the received vector y DD = Oh + ω, where P < R < S and S = MN, to obtain where, y is the observed data randomly sampled according to the received signal y DD Φ is the observation matrix designed according to the transmitted signal x DD and the generation information of the observed data y, is the additive white Gaussian noise after random sampling;

[0034] For the linear model use the GAMP-BCS algorithm to estimate the vector h containing the target delay l p and Doppler k p information; it is considered that the latent variable h = [h(0), h(1),..., h(S - 1)] T obeys the Gaussian prior distribution with a mean of 0 S×1 and a variance of α = [α0, α1,..., α S-1 T The hyperparameter α obeys the gamma hyperprior distribution. At the same time, the noise ​The variance t is unknown and follows a gamma hyperprior distribution.

[0035] Furthermore, the GAMP-BCS algorithm has a nested iterative form, where the superscript {t} represents the t-th outer iteration and the superscript (i) represents the i-th inner iteration.

[0036] Before the outer iteration begins, initialize the hyperparameters, α. {0} =1 S×1 , ζ {0} =0.2;

[0037] For a given α {t} , ζ {t} t≥0, before the inner iteration begins, let i=0; initialize the mean and variance of the channel h to be estimated, μ h (0) =Φ H y, σ h (0) =1 S×1 Initialization factor

[0038] The inner iteration repeats the following steps:

[0039] 1) Noise-free observation Noise-free observation The variance τ of the Gaussian prior distribution u (i) =(Φ⊙Φ)σ h (i) mean

[0040] 2) Posterior mean of noise-free observations Posterior variance of noiseless observations factor factor in This indicates that corresponding elements of the matrix are divided.

[0041] 3) Factors factor

[0042] 4) The posterior mean of h posterior variance of h

[0043] 5) When or i≥i max The inner iteration ends, and the result of the last iteration is output. in, It is the inner iteration threshold, i max It is the maximum number of internal iterations;

[0044] In the outer iteration, repeat the following steps:

[0045] 1) Hyperparameters hyperparameters Where a and b are the parameters in the gamma distribution of α, and c and d are the parameters in the gamma distribution of ζ;

[0046] 2) When or t≥t max The outer iteration ends, and the result of the last iteration is output.

[0047] make Γ is a discrete delayed Doppler grid.

[0048] Furthermore, step 3 specifically includes the following steps:

[0049] The rough estimate obtained in step 2 Based on this, use representation patterns Further refine the estimation results; for P targets, the ML algorithm needs to perform P estimations, estimating one target at a time.

[0050] The sensing channel estimated in step 2 This can be considered as the sum of the sensing channel estimation results corresponding to P targets, i.e. in It is the sensing channel estimation of target p′ in the first stage;

[0051] make The DD domain received echo from target p′ is represented as an approximate reconstruction for interference cancellation. After interference cancellation, the ML model is used to estimate the received signal from target p. It is additive white Gaussian noise related to the target p;

[0052] For the target p, let Γ p It is the continuous delayed Doppler grid corresponding to target p;

[0053] for The ML estimate of the continuous-delay Doppler of target p is Transform the two-dimensional minimization problem into a two-dimensional maximization problem, i.e. Then, the CD algorithm is used to iteratively solve the two-dimensional maximization problem.

[0054] Furthermore, the CD algorithm is used iteratively to solve the two-dimensional maximization problem. The specific process is as follows:

[0055] definition Its domain is Γ p Given initial coordinates Repeat the following steps in each iteration:

[0056] 1) Fixed

[0057] 2) Fixed

[0058] 3) When or j≥j max The iteration ends, and the result of the last iteration is output. in, It is the threshold, j max It is the maximum number of iterations;

[0059] Final distance estimation of target p c is the speed of light; final velocity estimate

[0060] Another embodiment of the present invention provides a multi-target parameter estimation system based on OTFS sensing shared waveforms, including a sensing channel model construction module, an integer delay Doppler estimation module, and a fractional delay Doppler estimation module.

[0061] The sensing channel model construction module is used to construct a base station received echo model based on the discrete DD domain channel representation for the OTFS-based integrated communication sensing scenario, denoted as Model A; and to construct a base station received echo model based on the continuous DD domain channel representation, denoted as Model B.

[0062] The integer delay Doppler estimation module is used to randomly select R rows in the received echo vector signal to construct a BCS linear model; the GAMP algorithm is used to iteratively estimate the sensing channel h to obtain the integer delay Doppler estimate of the target; and the approximate echo signal of each target is reconstructed based on the estimation results and model A.

[0063] The fractional delay Doppler estimation module, based on model B, utilizes the approximate echo signal of each reconstructed target for interference cancellation and constructs a problem model for ML estimation of each target; it constructs a two-dimensional function based on the problem model of ML estimation of each target; it iteratively estimates the fractional delay Doppler of the target using the CD algorithm; and outputs the target's range and velocity estimation results.

[0064] Preferably, in the OTFS-based integrated communication and sensing scenario, the user communicating with the integrated sensing base station and the target being actively sensed are the same individual; the base station transmits OTFS integrated sensing signals and receives the echo reflected by the target; the base station transmits DD domain signals from the transmitter. DD domain signal at the receiving end The relative distance *r* and relative radial velocity *v* between the target and the base station are obtained, thereby estimating the target's physical parameters *r* and *v*; where, Let M represent the MN×1 dimensional complex field, where M and N represent the number of subcarriers and the number of time slots, respectively.

[0065] The physical parameters r and v correspond to the sensing channel, respectively. The two parameters in the equation are the delay τ = 2r / c and the Doppler ν = 2f. c v / c; where P is the number of targets; ξ p , τ p v p These represent the reflection coefficient, delay, and Doppler amplitude of target p, respectively; f c denoted as carrier frequency, c as speed of light, and δ(·) as the Dirac delta function.

[0066] The base station receive echo model is constructed based on the discrete DD domain channel representation, specifically as follows:

[0067] In the discrete DD domain channel representation, τ and ν are integer multiples of the delay resolution 1 / MΔf and the Doppler resolution 1 / NT, respectively, i.e., τ=l / MΔf, l=0,…,M-1, ν=k / NT, k=0,…,N-1; where Δf is the subcarrier spacing, T is the time slot length, TΔf=1, and the delay tap l and Doppler tap k are both integers.

[0068] make At the tap p and k p If there exists a target p at a certain location, then h(l) p ,k p ξ is the reflection coefficient of the target. p If there are no targets at taps l and k, then h(l,k) is 0; when there are P targets, the discrete DD domain channel contains P non-zero reflection coefficients, denoted as...

[0069] Let Y = vec -1 (y DD ), X = vec -1 (x DD ), h(kM+l)=h(l,k), h=[h(0),h(1),…,h(MN-1)] T , Among them, vec -1 (·) denotes the matrix representation of a vector.

[0070] In this representation mode, the elements of the m-th row and n-th column of the received DD domain signal matrix Y under noise-free conditions are: Where 0 ≤ m ≤ M-1, 0 ≤ n ≤ N-1; [·] M M represents the modulus.

[0071]

[0072] make

[0073]

[0074] ⊙ denotes the matrix inner product, (·) H Represents the conjugate transpose of a matrix;

[0075] make

[0076] Let o nM+m =o m,n O H =[o0,o1,…,o MN-1 ], y DD =Oh;

[0077] Considering noise, y DD =Oh+ω, ω represents additive white Gaussian noise; matrix O is based on the transmitted signal x. DD With phase ρ m,n Perform a unique design.

[0078] The base station received echo model is constructed based on the continuous DD domain channel representation, specifically as follows:

[0079] In the continuous DD domain channel representation, τ and v respectively contain fractional times the delay resolution 1 / MΔf and fractional times the Doppler resolution 1 / NT.

[0080] In this representation mode, the received DD domain signal vector is represented as in, Ω is the continuous DD domain sensing channel matrix. It is additive white Gaussian noise. I represents the Kronecker product. MN Represents the MN-dimensional identity matrix; Defined as is the continuous DD domain sensing channel matrix related to the target p, defined as where F N is an N-dimensional FFT matrix, and F M is an M-dimensional FFT matrix, Π MN is an MN-dimensional forward circulant matrix, is an M-dimensional IFFT matrix, is an N-dimensional IFFT matrix,

[0081] The integer delay Doppler estimation module specifically performs the following steps:

[0082] Before iteratively estimating the sensing channel h, randomly select R rows from the received vector y DD = Oh + ω, where P < R < S, S = MN, to obtain where y is the observed data generated by randomly sampling the received signal y DD , Φ is the observation matrix designed according to the transmitted signal x DD and the generation information of the observed data y, is the additive Gaussian noise after random sampling.

[0083] For the linear model use the GAMP-BCS algorithm to estimate the vector h containing the target delay l p and Doppler k p information; assume that the latent variable h = [h(0), h(1),..., h(S-1)] T obeys a Gaussian prior distribution with a mean of 0 S×1 and a variance of α = [α0, α1,..., α S-1 T , and the hyperparameter α obeys a gamma hyperprior distribution. At the same time, the variance ζ of the noise is unknown and obeys a gamma hyperprior distribution.

[0084] The GAMP-BCS algorithm has a form of inner and outer nested iterations. Define the superscript {t} to represent the t-th outer iteration and the superscript (i) to represent the i-th inner iteration.

[0085] Before the start of the outer iteration, initialize the hyperparameters, α {0} = 1 S×1 , ζ {0} = 0.2;

[0086] For a given α {t} , ζ {t} ​t≥0, before the inner iteration begins, let i=0; initialize the mean and variance of the channel h to be estimated, μ h (0) =Φ H y, σ h (0) =1 S×1 Initialization factor

[0087] The inner iteration repeats the following steps:

[0088] 1) Noise-free observation Noise-free observation The variance τ of the Gaussian prior distribution u (i) =(Φ⊙Φ)σ h (i) mean

[0089] 2) Posterior mean of noise-free observations Posterior variance of noiseless observations factor factor in This indicates that corresponding elements of the matrix are divided.

[0090] 3) Factors factor

[0091] 4) The posterior mean of h posterior variance of h

[0092] 5) When or i≥i max The inner iteration ends, and the result of the last iteration is output. in, It is the inner iteration threshold, i max It is the maximum number of internal iterations.

[0093] In the outer iteration, repeat the following steps:

[0094] 1) Hyperparameters hyperparameters Where a and b are the parameters in the gamma distribution of α, and c and d are the parameters in the gamma distribution of ζ.

[0095] 2) When or t≥t max The outer iteration ends, and the result of the last iteration is output.

[0096] make Γ is a discrete delayed Doppler grid.

[0097] The fractional-delay Doppler estimation module performs the following steps:

[0098] The coarse estimate obtained from the integer delay Doppler estimation module Based on this, use representation patterns Further refine the estimation results; for P targets, the ML algorithm needs to perform P estimations, estimating one target at a time.

[0099] The sensing channel estimated by the integer delay Doppler estimation module This can be considered as the sum of the sensing channel estimation results corresponding to P targets, i.e. in It is the sensing channel estimation of target p′ in the first stage.

[0100] make The DD domain received echo from target p′ is represented as an approximate reconstruction for interference cancellation. After interference cancellation, the ML model is used to estimate the received signal from target p. It is additive white Gaussian noise related to the target p.

[0101] For the target p, let Γ p It is the continuous delayed Doppler grid corresponding to target p.

[0102] for The ML estimate of the continuous-delay Doppler of target p is Transform the two-dimensional minimization problem into a two-dimensional maximization problem, i.e.

[0103] Preferably, the CD algorithm is used to iteratively solve the two-dimensional maximization problem, and the specific process is as follows:

[0104] definition Its domain is Γ p Given initial coordinates Repeat the following steps in each iteration:

[0105] 1) Fixed

[0106] 2) Fixed

[0107] 3) When or j≥jmax The iteration ends, and the result of the last iteration is output. in, It is the threshold, j max It is the maximum number of iterations;

[0108] Final distance estimation of target p c is the speed of light; final velocity estimate

[0109] Beneficial effects:

[0110] This invention provides a multi-target parameter estimation method based on OTFS sensing shared waveforms. It adopts two DD domain sensing channel representation methods that can be approximately switched in real-world scenarios, and estimates the distance and velocity of the sensing target in two stages based on the corresponding DD domain echo representation mode. This avoids the limitations of traditional OTFS sensing algorithms caused by fractional Doppler problems or multi-target scenarios, making the sensing method more applicable and practical.

[0111] Based on the sparsity of the sensing channel in the DD domain, this invention describes the estimation of the first stage as a sparse sensing channel reconstruction process within the framework of the BCS algorithm. It utilizes the GAMP-BCS algorithm to estimate the integer delay and Doppler of the target, effectively reducing computational complexity.

[0112] Based on the estimation in the first stage, this invention approximately reconstructs the echo signal of each target, solving the interference problem between different targets. The estimation in the second stage is described as an ML problem. The fractional delay and Doppler of the target are estimated by the ML-CD algorithm, which effectively improves the accuracy of the perception of the target distance and velocity.

[0113] Based on the above results, it can be seen that this invention comprehensively considers factors such as computational complexity, accuracy of sensing parameter estimation, and multi-target sensing. It estimates the distance and velocity of the sensing targets in two stages, in the discrete DD domain and the continuous DD domain, respectively, thus achieving low-complexity parameter estimation and high-precision parameter estimation for multiple sensing targets. Attached Figure Description

[0114] Figure 1 This is a schematic diagram of the integrated communication and sensing scenario based on OTFS in this invention;

[0115] Figure 2 This is a flowchart of the modeling and algorithm in this invention;

[0116] Figure 3 This is a diagram showing the distance estimation results in this invention;

[0117] Figure 4 This is a diagram showing the velocity estimation results in this invention. Detailed Implementation

[0118] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0119] The present invention provides a multi-objective parameter estimation method based on OTFS inductively shared waveforms, the basic implementation process of which is as follows:

[0120] Step 1: Target-aware description and channel modeling based on OTFS sensing shared waveforms

[0121] like Figure 1 As shown, in the OTFS-based integrated communication and sensing scenario, it is assumed that the user communicating with the integrated sensing base station and the target being actively sensed are the same individual. The base station transmits the OTFS integrated sensing signal and receives the echo reflected from the target. The base station uses the DD domain signal at the transmitting end... DD domain signal at the receiving end The relative distance *r* and relative radial velocity *c* between the target and the base station are obtained, thereby estimating the target's physical parameters *r* and *c*. Let M represent the MN×1 dimensional complex field, where M and N represent the number of subcarriers and the number of time slots, respectively.

[0122] The physical parameters r and v correspond to the sensing channel, respectively. The two parameters in the equation are the delay τ = 2r / c and the Doppler ν = 2f. c v / c. Where P is the number of targets; ξ p , τ p v p These represent the reflection coefficient, delay, and Doppler amplitude of target p, respectively; f c denoted as carrier frequency, c as speed of light, and δ(·) as the Dirac delta function.

[0123] like Figure 2 As shown, this invention uses two representation methods: discrete DD domain channel and continuous DD domain channel, which correspond to two DD domain received signal representation modes, respectively.

[0124] In the discrete DD domain channel representation, τ and v are integer multiples of the delay resolution 1 / MΔf and the Doppler resolution 1 / NT, respectively. That is, τ = l / MΔf, l = 0,…,M-1, v = k / NT, k = 0,…,N-1. Here, Δf is the subcarrier spacing, T is the time slot length, TΔf = 1, and the delay tap l and Doppler tap k are both integers.

[0125] make Assuming at tap l p and k p If there exists a target p at a certain location, then h(l) p ,k pξ is the reflection coefficient of the target. p If there are no targets at taps l and k, then h(l,k) is 0. When there are P targets, the discrete DD domain channel contains P non-zero reflection coefficients, denoted as...

[0126] Let Y = vec -1 (y DD ), X = vec -1 (x DD ), h(kM+l)=h(l,k), h=[h(0),h(1),…,h(MN-1)] T , Among them, vec -1 (·) denotes the matrix representation of a vector.

[0127] In this representation mode, the elements of the m-th row and n-th column of the received DD domain signal matrix Y under noise-free conditions are: Where 0 ≤ m ≤ N-1, 0 ≤ n ≤ N-1. [·] M Indicates the modulus M;

[0128] make

[0129]

[0130] ⊙ denotes the matrix inner product, (·) H This represents the conjugate transpose of a matrix.

[0131] make

[0132] Let o nM+m =o m,n O H =[O0,O1,…,o MN-1 ], y DD =Oh. Considering noise, y DD =Oh+ω, ω represents additive white Gaussian noise. It is easy to see that matrix O can be determined based on the transmitted signal x. DD With phase ρ m,n Perform a unique design.

[0133] In the continuous DD domain channel representation, τ and v respectively contain fractional times the delay resolution 1 / MΔf and fractional times the Doppler resolution 1 / NT.

[0134] In this representation mode, the received DD domain signal vector can be represented as Among them, Ω is the continuous DD domain sensing channel matrix, is additive white Gaussian noise, represents the Kronecker product, and I MN represents the MN-dimensional identity matrix. is defined as is the continuous DD domain sensing channel matrix related to the target p, defined as Among them, F N is the N-dimensional FFT matrix, and F M is the M-dimensional FFT matrix, Π MN is the MN-dimensional forward circulant matrix, is the M-dimensional IFFT matrix, is the N-dimensional IFFT matrix,

[0135] In the present invention, when the delay resolution 1 / MΔf and the Doppler resolution 1 / NT reach a certain value, it can be considered that the above two DD domain channel representation methods and the corresponding receiving-end DD domain echo signal representation modes are approximately equivalent. In the following steps, we will use the known transmitted signal x DD and the received echo signal y DD , and respectively use the two representation modes to efficiently estimate the parameters (τ, v) of the sensed target. The designed method has the advantages of low computational complexity and high estimation accuracy.

[0136] Step 2: Use the BCS-ML algorithm to achieve multi-target parameter estimation in two stages

[0137] In the first stage, based on the discrete DD domain channel representation method, we designed a GAMP-BCS algorithm to estimate the integer delay tap l p of the target and the integer Doppler tap k p .

[0138] Before iteratively estimating the sensing channel h, randomly select R rows from the received vector y DD = Oh + ω, where P < R < S and S = MN. We get Among them, y is the observed data randomly sampled according to the received signal y DD , Φ is the observation matrix designed according to the transmitted signal x DD and the generation information of the observed data y, is the additive white Gaussian noise after random sampling.

[0139] For linear models The GAMP-BCS algorithm is used to estimate the target delay l. p and Doppler K p The information vector h. We assume the latent variable h = [h(0), h(1), ..., h(S-1)] T Obey the mean of 0 S×1 , the variance is α=[α0,α1,…,α S-1 ] T The Gaussian prior distribution is given, and the hyperparameter α follows a gamma hyperprior distribution. Meanwhile, noise... The variance ζ is unknown and follows a gamma hyperprior distribution.

[0140] The GAMP-BCS algorithm of this invention has a nested iterative form. The superscript {t} represents the t-th outer iteration, and the superscript (i) represents the i-th inner iteration.

[0141] Before the outer iteration begins, initialize the hyperparameters, α. {0} =1 S×1 , ζ {0} =0.2.

[0142] For a given α {t} , ζ {t} t≥0, before the inner iteration begins, let i=0; initialize the mean and variance of the channel h to be estimated, μ h (0) =Φ H y, σ h (0) =1 S×1 Initialization factor

[0143] The inner iteration repeats the following steps:

[0144] 1) Noise-free observation Noise-free observation The variance τ of the Gaussian prior distribution u (i) =(Φ⊙Φ)σ h (i) mean

[0145] 2) Posterior mean of noise-free observations Posterior variance of noiseless observations factor factor in This indicates that corresponding elements of the matrix are divided.

[0146] 3) Factors factor

[0147] 4) The posterior mean of h posterior variance of h

[0148] 5) When or i≥i max The inner iteration ends, and the result of the last iteration is output. in, It is the inner iteration threshold, i max It is the maximum number of internal iterations;

[0149] In the outer iteration, repeat the following steps:

[0150] 1) Hyperparameters hyperparameters Where a and b are the parameters in the gamma distribution of α, and c and d are the parameters in the gamma distribution of ζ;

[0151] 2) When or t≥t max The outer iteration ends, and the result of the last iteration is output.

[0152] make Γ is a discrete delayed Doppler grid.

[0153] In the second stage, based on the continuous DD domain channel representation method, we designed an ML-CD algorithm to estimate the target's delay tap τ, which includes fractional-fold resolution. p And Doppler tap v p .

[0154] The rough estimate obtained in the first stage Based on this, we use representation patterns Further refine the estimation results. For P targets, the ML algorithm needs to perform P estimations, estimating one target at a time.

[0155] For traditional machine learning algorithms, accurately estimating the parameters of each target is extremely difficult due to interference among multiple targets. In this invention, before performing maximum likelihood estimation on target p, the parameters are estimated in the first stage... The echoes of the other P-1 targets can be approximately reconstructed, thereby eliminating interference to a considerable extent.

[0156] The sensing channel estimated in the first stage This can be considered as the sum of the sensing channel estimation results corresponding to P targets, i.e. in It is the sensing channel estimation of target p′ in the first stage.

[0157] make This represents the approximately reconstructed DD-domain received echo from target p′, used for interference cancellation. (Reconstruction process)

[0158] After interference cancellation, the ML model is used to estimate the received signal of target p. It is additive white Gaussian noise related to the target p.

[0159] For the target p, let Γ p It is the continuous delayed Doppler grid corresponding to target p.

[0160] for The ML estimate of the continuous-delay Doppler of target p is This two-dimensional minimization problem can be transformed into a two-dimensional maximization problem, that is... We use the CD algorithm to solve this problem iteratively.

[0161] definition Its domain is Γ p Given initial coordinates Repeat the following steps in each iteration:

[0162] 1) Fixed

[0163] 2) Fixed

[0164] 3) When or j≥j max The iteration ends, and the result of the last iteration is output. in, It is the threshold, j max It represents the maximum number of iterations.

[0165] Final distance estimation of target p c is the speed of light; final velocity estimate

[0166] The computational complexity of the BCS-ML algorithm proposed in this invention is... Computational complexity lower than algorithms such as MF

[0167] Another embodiment of the present invention provides a multi-target parameter estimation system based on OTFS sensing shared waveforms, including a sensing channel model construction module, an integer delay Doppler estimation module, and a fractional delay Doppler estimation module.

[0168] The sensing channel model construction module is used to construct a base station received echo model based on the discrete DD domain channel representation for the OTFS-based integrated communication sensing scenario, denoted as Model A; and to construct a base station received echo model based on the continuous DD domain channel representation, denoted as Model B.

[0169] The integer delay Doppler estimation module is used to randomly select R rows in the received echo vector signal to construct a BCS linear model; the GAMP algorithm is used to iteratively estimate the sensing channel h to obtain the integer delay Doppler estimate of the target; and the approximate echo signal of each target is reconstructed based on the estimation results and model A.

[0170] The fractional delay Doppler estimation module, based on model B, utilizes the approximate echo signal of each reconstructed target for interference cancellation and constructs a problem model for ML estimation of each target; it constructs a two-dimensional function based on the problem model of ML estimation of each target; it iteratively estimates the fractional delay Doppler of the target using the CD algorithm; and outputs the target's range and velocity estimation results.

[0171] Preferably, in the OTFS-based integrated communication and sensing scenario, the user communicating with the integrated sensing base station and the target being actively sensed are the same individual; the base station transmits OTFS integrated sensing signals and receives the echo reflected by the target; the base station transmits DD domain signals from the transmitter. DD domain signal at the receiving end The relative distance *r* and relative radial velocity *v* between the target and the base station are obtained, thereby estimating the target's physical parameters *r* and *v*; where, Let M represent the MN×1 dimensional complex field, where M and N represent the number of subcarriers and the number of time slots, respectively.

[0172] The physical parameters r and v correspond to the sensing channel, respectively. The two parameters in the equation are the delay τ = 2r / c and the Doppler ν = 2f. c v / c; where P is the number of targets; ξ p , τ p ,ν p These represent the reflection coefficient, delay, and Doppler amplitude of target p, respectively; f c denoted as carrier frequency, c as speed of light, and δ(·) as the Dirac delta function.

[0173] The base station receive echo model is constructed based on the discrete DD domain channel representation, specifically as follows:

[0174] In the discrete DD domain channel representation, τ and ν are integer multiples of the delay resolution 1 / MΔf and the Doppler resolution 1 / NT, respectively, i.e., τ=l / MΔf, l=0,…,M-1, v=k / NT, k=0,…,N-1; where Δf is the subcarrier spacing, T is the time slot length, TΔf=1, and the delay tap l and Doppler tap k are both integers.

[0175] make At the tap p and k p If there exists a target p at a certain location, then h(l) p ,k p ξ is the reflection coefficient of the target. p If there are no targets at taps l and k, then h(l,k) is 0; when there are P targets, the discrete DD domain channel contains P non-zero reflection coefficients, denoted as...

[0176] Let Y = vec -1 (y DD ), X = vec -1 (x DD ), h(kM+l)=h(l,k), h=[h(0),h(1),…,h(MN-1)] T , Among them, vec -1 (·) denotes the matrix representation of a vector.

[0177] In this representation mode, the elements of the m-th row and n-th column of the received DD domain signal matrix Y under noise-free conditions are: Where 0 ≤ m ≤ M-1, 0 ≤ n ≤ N-1; [·] M M represents the modulus.

[0178]

[0179] make

[0180]

[0181] ⊙ denotes the matrix inner product, (·) H Represents the conjugate transpose of a matrix;

[0182] make

[0183] Let o nM+m =o m,n O H =[o0,o1,…,o MN-1 ], yDD = Oh;

[0184] Considering noise, y DD = Oh + ω, where ω is additive white Gaussian noise; the matrix O is uniquely designed according to the transmitted signal x DD and the phase ρ m,n Then, a base station received echo model is constructed based on the discrete DD domain channel representation.

[0185] Constructing a base station received echo model based on the continuous DD domain channel representation, specifically:

[0186] In the continuous DD domain channel representation, τ and ν respectively include the fractional delay resolution 1 / MΔf and the fractional Doppler resolution 1 / NT.

[0187] In this representation mode, the received DD domain signal vector is expressed as where Ω is the continuous DD domain sensing channel matrix, is the additive white Gaussian noise, denotes the Kronecker product, and I MN denotes the MN-dimensional identity matrix; is defined as is the continuous DD domain sensing channel matrix related to the target p, defined as where F N is the N-dimensional FFT matrix, and F M is the M-dimensional FFT matrix, Π MN is the MN-dimensional forward circulant matrix, is the M-dimensional IFFT matrix, is the N-dimensional IFFT matrix,

[0188] The integer delay Doppler estimation module specifically performs the following steps:

[0189] Before iteratively estimating the sensing channel h, randomly select R rows from the received vector y DD = Oh + ω, where R < S, S = MN, to obtain where y is the observed data randomly sampled from the received signal y DD Φ is the observation matrix designed according to the transmitted signal x DD and the generation information of the observed data y, is the additive white Gaussian noise after random sampling.

[0190] For linear models The GAMP-BCS algorithm is used to estimate the target delay l. p and Doppler K p The information vector h; the latent variable is considered to be h = [h(0), h(1), ..., h(S-1)]. T Obey the mean of 0 S×1 , the variance is α=[α0,α1,…,α S-1 ] T The Gaussian prior distribution is given, and the hyperparameter α follows a gamma hyperprior distribution. Meanwhile, noise... The variance ζ is unknown and follows a gamma hyperprior distribution.

[0191] The GAMP-BCS algorithm has a nested iterative form, where the superscript {t} represents the t-th outer iteration and the superscript (i) represents the i-th inner iteration.

[0192] Before the outer iteration begins, initialize the hyperparameters, α. {0} =1 S×1 , ζ {0} =0.2;

[0193] For a given α {t} , ζ {t} t≥0, before the inner iteration begins, let i=0; initialize the mean and variance of the channel h to be estimated, μ h (0) =Φ H y, τ h (0) =1 S×1 Initialization factor

[0194] The inner iteration repeats the following steps:

[0195] 1) Noise-free observation Noise-free observation The variance τ of the Gaussian prior distribution u (i) =(Φ⊙Φ)σ h (i) mean

[0196] 2) Posterior mean of noise-free observations Posterior variance of noiseless observations factor factor in This indicates that corresponding elements of the matrix are divided.

[0197] 3) Factors factor

[0198] 4) The posterior mean of h posterior variance of h

[0199] 5) When or i≥i max The inner iteration ends, and the result of the last iteration is output. in, It is the inner iteration threshold, i max It is the maximum number of internal iterations.

[0200] In the outer iteration, repeat the following steps:

[0201] 1) Hyperparameters hyperparameters Where a and b are the parameters in the gamma distribution of α, and c and d are the parameters in the gamma distribution of ζ.

[0202] 2) When or t≥t max The outer iteration ends, and the result of the last iteration is output.

[0203] make Γ is a discrete delayed Doppler grid.

[0204] The fractional-delay Doppler estimation module performs the following steps:

[0205] The coarse estimate obtained from the integer delay Doppler estimation module Based on this, use representation patterns Further refine the estimation results; for P targets, the ML algorithm needs to perform P estimations, estimating one target at a time.

[0206] The sensing channel estimated by the integer delay Doppler estimation module This can be considered as the sum of the sensing channel estimation results corresponding to P targets, i.e. in It is the sensing channel estimation of target p′ in the first stage.

[0207] make The DD domain received echo from target p′ is represented as an approximate reconstruction for interference cancellation. After interference cancellation, the ML model is used to estimate the received signal from target p. It is additive white Gaussian noise related to the target p.

[0208] For the target p, let Γ p It is the continuous delayed Doppler grid corresponding to target p.

[0209] for The ML estimate of the continuous-delay Doppler of target p is Transform the two-dimensional minimization problem into a two-dimensional maximization problem, i.e.

[0210] Preferably, the CD algorithm is used to iteratively solve the two-dimensional maximization problem, and the specific process is as follows:

[0211] definition Its domain is Γ p Given initial coordinates Repeat the following steps in each iteration:

[0212] 1) Fixed

[0213] 2) Fixed

[0214] 3) When or j≥j max The iteration ends, and the result of the last iteration is output. in, It is the threshold, j max It is the maximum number of iterations;

[0215] Final distance estimation of target p c is the speed of light; final velocity estimate

[0216] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-target parameter estimation method based on OTFS omnistatic sharing waveform, characterized in that, Comprising the following steps: Step 1: For the OTFS-based communication and perception integrated scene, a base station received echo model is constructed based on a discrete DD domain channel representation, denoted as model A; a base station received echo model is constructed based on a continuous DD domain channel representation, denoted as model B; The OTFS-based communication and perception integrated scenario is specifically: the user of the communication of the base station and the target of the active perception are the same individual; the base station transmits the OTFS communication and perception integrated signal, and receives the echo reflected by the target; the base station obtains the relative distance between the target and the base station and the relative radial velocity by transmitting the DD domain signal of the transmitting end and receiving the DD domain signal of the receiving end ​​​​​​​​​​ Physical parameters and correspond to two parameters in the sensing channel , i.e., delay and Doppler , respectively; where is the number of targets; , , are the reflection coefficient, delay and Doppler of the target , respectively; is the carrier frequency, is the speed of light; is the Dirac function; The base station received echo model constructed based on the discrete DD domain channel representation is specifically: In a discrete DD domain channel representation, and are integer multiples of the delay resolution and the Doppler resolution respectively, i.e., , , , ; wherein is the subcarrier spacing, is the slot length, delay taps and Doppler taps are integers; Let , there is a target at tap , and , then is the reflection coefficient for this target , if there is no target at tap and , then is ; when there are targets, the discrete DD-domain channel contains non-zero reflection coefficients, denoted as ;​ Let , , , , , ; wherein, denotes the matrixization of a vector. In this representation mode, the received DD domain signal matrix without noise is the element in the first row, first column wherein , ; represents a module ; ， ； Let ； , denotes the matrix inner product, denotes the conjugate transpose of a matrix; Let , ; ; Let , , , ; considering noise, , , is an additive white Gaussian noise; matrix according to the transmitted signal with the phase unique design; The base station received echo model constructed based on the continuous DD domain channel representation is specifically: In a continuous DD domain channel representation, and respectively contain fractional multiples of delay resolution and fractional multiples of Doppler resolution ; In this representation mode, the received DD domain signal vector is represented as ;in, , , For a continuous DD domain sensing channel matrix, , It is additive white Gaussian noise. Indicates the Kronecker product. express An identity matrix of 3D; Defined as ; It is related to the goal The relevant continuous DD domain sensing channel matrix is ​​defined as follows: ;in, yes A 3D FFT matrix, It is an M-dimensional FFT matrix. , , yes A forward circular matrix of dimension, yes 1D IFFT matrix, yes 1D IFFT matrix, , ; Step 2: Randomly select in the received echo vector signal Row, construct the BCS linear model; use the GAMP algorithm to iteratively estimate the perception channel h, obtain the integer delay Doppler estimation of the target, and according to the estimation result, reconstruct the approximate echo signal of each target with model A; Step 3: Based on model B, interference cancellation is performed using the reconstructed approximate echo signal of each target to construct a problem model for ML estimation of each target; a two-dimensional function is constructed according to the problem model for ML estimation of each target; the fractional delay Doppler of the target is iteratively estimated using the coordinate CD algorithm; Step 4: Output the distance estimation and velocity estimation results of the target.

2. The OTFS sensing sharing waveform based multi-target parameter estimation method of claim 1, wherein, The step 2 specifically comprises the following steps: Before performing iterative estimation on the sensing channel , randomly select a row from the received vector , , to obtain , , , ; wherein is observation data generated according to random sampling of the received signal , is an observation matrix designed according to the transmitted signal and the generated information of the observation data , is additive Gaussian noise after random sampling; For linear models , the GAMP-BCS algorithm estimates the vector containing the target delays and Doppler information; it assumes that the latent variables follow Gaussian prior distributions with mean and variance , and that the hyperparameters follow Gamma hyperpriors; meanwhile, the variance of the noise is unknown and follows a Gamma hyperprior.

3. The OTFS sensing sharing waveform based multi-target parameter estimation method of claim 2, wherein, The GAMP-BCS algorithm has the form of inner and outer nested iterations, and the superscript denotes the th outer iteration, and the superscript denotes the th inner iteration; At the beginning of the outer iteration, the hyperparameters are initialized, ;​ For a given , , , let ; initialize the mean and variance of the channel to be estimated, , ; initialize the factor ; The following steps are repeated in the inner iteration: 1) noiseless observation noiseless observation variance of the Gaussian prior distribution mean ; 2) posterior mean of noiseless observation , Posterior variance of noiseless observation , Factor , Factor , wherein denotes division of the corresponding elements of the matrices; 3) Factor , Factor ; 4) posterior mean of , posterior variance ; 5) When , or , the inner iteration ends and the result of the last iteration is output , , , wherein, is the inner iteration threshold, is the maximum number of inner iterations; In the outer iteration, the following steps are repeated: 1) Hyperparameters Hyperparameters ; wherein is a parameter in the gamma distribution of is a parameter in the gamma distribution of 2) When , or , the outer iteration ends and the result of the last iteration is output ; Let , , , , is a discrete delay-Doppler grid.

4. The OTFS-based sensing and sharing waveform-based multi-target parameter estimation method of claim 2 or 3, wherein, The step 3 specifically comprises the following steps: The rough estimate obtained in step 2 Based on this, use representation patterns To further refine the estimation results; for For each objective, the ML algorithm needs to perform... Each estimation estimates one target at a time. ; the estimated sensing channel of step 2 are considered as the sum of the sensing channel estimation results corresponding to the targets respectively, i.e., wherein is the sensing channel estimation of the target in the first stage; Let , , denote the received echoes from the target 's DD domain for interference cancellation, after which the ML model is used to estimate the received signal for the target as ， ， is additive white Gaussian noise related to the target ​ For the target , let , is the target corresponding continuous delay-Doppler grid; For , Object The ML estimation of the continuous delay-Doppler for ， The two-dimensional minimization problem is converted into a two-dimensional maximization problem, That is ; Then the CD algorithm is used to iteratively solve the two-dimensional maximization problem.

5. The OTFS-based sensing sharing waveform based multi-target parameter estimation method of claim 4, wherein, The CD algorithm is used to iteratively solve the two-dimensional maximization problem, and the specific process is: Definitions , whose domain is ; given initial coordinates , , ; The following steps are repeated in each iteration: 1) fixed , ; 2) fixed , ; 3) When , or , the iteration ends and the result of the last iteration is output , where, is a threshold, is the maximum number of iterations; Target Final distance estimate = c , c is the speed of light; final velocity estimate = c .

6. A multi-target parameter estimation system based on OTFS comosense sharing waveform, characterized in that, Comprise a perception channel model construction module, an integer delay Doppler estimation module and a fractional delay Doppler estimation module; The perception channel model construction module is used to construct a base station received echo model based on a discrete DD domain channel representation for an OTFS-based communication and perception integrated scene, denoted as model A; A base station received echo model is constructed based on a continuous DD domain channel representation, denoted as model B; The integer delay Doppler estimation module is used to randomly select R rows in the received echo vector signal to construct a BCS linear model; the GAMP algorithm is used to iteratively estimate the perception channel h to obtain the integer delay Doppler estimation of the target, and the approximate echo signal of each target is reconstructed according to the estimation result and model A; The fractional delay Doppler estimation module uses the reconstructed approximate echo signal of each target to perform interference cancellation based on model B to construct a problem model for ML estimation of each target; a two-dimensional function is constructed according to the problem model for ML estimation of each target; the fractional delay Doppler of the target is iteratively estimated using the coordinate CD algorithm; and the distance estimation and velocity estimation results of the target are outputted; The OTFS-based communication and perception integrated scenario is specifically: the user of the communication of the base station and the target of the active perception are the same individual; the base station transmits an OTFS communication and perception integrated signal and receives a back wave reflected by the target; the base station obtains the relative distance between the target and the base station and the relative radial velocity by transmitting the DD domain signal of the transmitting end and receiving the DD domain signal of the receiving end ​​​​​​​​​​ Physical parameters and correspond to two parameters in the sensing channel , i.e., delay and Doppler , respectively; where is the number of targets; , , are the reflection coefficient, delay and Doppler of the target , respectively; is the carrier frequency, is the speed of light; is the Dirac function; The base station received echo model constructed based on the discrete DD domain channel representation is specifically: In a discrete DD domain channel representation, and are integer multiples of the delay resolution and the Doppler resolution respectively, i.e., , , , ; wherein is the subcarrier spacing, is the slot length, delay taps and Doppler taps are integers; Let , at tap and there is a target , then is the reflection coefficient for this target , if at tap and there is no target, then is ; when there are targets, the discrete DD-domain channel contains non-zero reflection coefficients, denoted as ; Let , , , , ， ； wherein denotes the matrixization of a vector; In this representation mode, the received DD domain signal matrix without noise is the element in the first row, first column wherein , ; denotes a module ; ， ； Let ； , denotes the matrix inner product, denotes the conjugate transpose of a matrix; Let , ; ; Let , , , ; considering noise, , , for additive white Gaussian noise; matrix according to the transmitted signal with phase unique design; The base station received echo model constructed based on the continuous DD domain channel representation is specifically: In a continuous DD domain channel representation, and comprise a fractional multiple of the delay resolution and a fractional multiple of the Doppler resolution ; In this representation mode, the received DD domain signal vector is represented as ; wherein , , is a continuous DD-domain sensing channel matrix, , is an additive white Gaussian noise, denotes the Kronecker product, denotes an identity matrix of dimension , is defined as ; is a continuous DD-domain sensing channel matrix related to the target , is defined as ； wherein is an M-dimensional FFT matrix, is an M-dimensional FFT matrix, , , is an M-dimensional forward circular matrix, is an M-dimensional IFFT matrix, is an M-dimensional IFFT matrix, ， 。 7. The OTFS sensing sharing waveform based multi-target parameter estimation system of claim 6, wherein, The integer delay Doppler estimation module specifically performs the following steps: Before performing iterative estimation on the sensing channel , randomly select a row from the received vector , , to obtain , , , ; wherein is observation data generated according to random sampling of the received signal , is an observation matrix designed according to the transmitted signal and the generated information of the observation data , is additive Gaussian noise after random sampling; To linear model , estimate the vector containing target delay and Doppler information using GAMP-BCS algorithm; assume that the latent variable obeys a Gaussian prior distribution with mean and variance , and the hyperparameters obeys a Gamma hyperprior distribution; meanwhile, the variance of the noise is unknown and obeys a Gamma hyperprior distribution; The GAMP-BCS algorithm has the form of inner and outer nested iterations, and the superscript denotes the th outer iteration, and the superscript denotes the th inner iteration; At the beginning of the outer iteration, the hyperparameters are initialized, ;​ For a given , , , let ; initialize the mean and variance of the channel to be estimated, , ; initialize the factor ; The following steps are repeated in the inner iteration: 1) noiseless observation noiseless observation variance of the Gaussian prior distribution mean ; 2) posterior mean of noiseless observation , Posterior variance of noiseless observation , Factor , Factor , wherein denotes division of the corresponding elements of the matrices. 3) Factor , Factor ; 4) posterior mean of , posterior variance of ; 5) When , or , the inner iteration ends and the result of the last iteration is output , , , wherein, is the inner iteration threshold, is the maximum number of inner iterations; In the outer iteration, the following steps are repeated: 1) Hyperparameters hyperparameters ; wherein, is a parameter in the gamma distribution of is a parameter in the gamma distribution of 2) When , or , the outer iteration ends and the result of the last iteration is output ; Let , , , ， is a discrete delay-Doppler grid.

8. The OTFS sensing sharing waveform based multi-target parameter estimation system of claim 7, wherein, The fractional delay Doppler estimation module specifically performs the following steps: The coarse estimate obtained from the integer delay Doppler estimation module Based on this, use representation patterns To further refine the estimation results; for For each objective, the ML algorithm needs to perform... Each estimation estimates one target at a time. ; the perceived channel estimated by the integer delay Doppler estimation module is considered as the sum of the perceived channel estimation results corresponding to the targets respectively, i.e., wherein is the perceived channel estimation of the target in the first stage; Let , , denote the received echoes from the target in the DD domain, which are approximated reconstructed, for interference cancellation. After interference cancellation, the ML model is used to estimate the received signal of the target as , , is the additive white Gaussian noise related to the target ; For the target , let , is the target corresponding continuous delay-Doppler grid; For , Target The ML estimate of the continuous delayed Doppler is The two-dimensional minimization problem is transformed into a two-dimensional maximization problem, that is... ; The CD algorithm is used to iteratively solve the two-dimensional maximization problem, and the specific process is: Definitions , the domain of which is ; Given initial coordinates , , ; repeat the following steps for each iteration: 1) fixed , ; 2) fixed , ; 3) When , or , the iteration ends and the result of the last iteration is output , where, is a threshold, is the maximum number of iterations; Target Final distance estimate = c , c is the speed of light; final velocity estimate = c .

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