A vehicle-mounted radar super-resolution time delay doppler estimation method based on orthogonal time-frequency-space modulation

Abstract

This invention proposes a super-resolution time delay Doppler estimation method for vehicle-mounted radar based on orthogonal time-frequency conditioning. Compared with previous algorithms, this method has super-resolution characteristics and can effectively address the basis mismatch problem in the discrete domain that traditional estimation algorithms cannot handle, thus achieving higher accuracy in time delay and Doppler estimation. To address the off-grid problem in the discrete domain, this method uses a two-dimensional atomic norm to establish the estimation problem in the continuous domain. A positive semidefinite programming problem for solving continuous frequencies is established using the two-dimensional atomic norm and analyzed. Based on this, the alternating multiplier direction method is proposed, and an iterative approach is used to quickly solve the optimization problem.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, and particularly relates to a super-resolution time delay Doppler estimation method for vehicle-mounted radar based on orthogonal time-frequency air conditioning. Background Technology

[0002] In recent years, communication-sensing integration has garnered widespread attention due to its advantages in sharing a single hardware platform and joint signal processing framework. As a promising waveform choice for next-generation wireless communication, Orthogonal Time-Frequency Scheme (OTFS) effectively utilizes signal diversity in the Doppler domain, thus ensuring reliable communication in high-speed mobility scenarios. Recent research has also revealed the potential of OTFS as a radar signal. To explore this potential, several target estimation algorithms, including matched filtering and compressed sensing-based algorithms, have been proposed in recent years; however, a series of problems remain regarding the accurate estimation of target parameters.

[0003] The closest existing technology to this invention is a radar target parameter estimation method based on sparse Bayesian learning. This method is also applied to target parameter estimation for OTFS-based radar and can estimate the target's range and velocity relatively accurately. Existing compressed sensing-based radar target parameter estimation methods share a common limitation: because these methods divide the time-delay-Doppler plane into discrete grid points, the estimation resolution depends on the density of the plane division. Therefore, for targets that do not fall exactly on the discrete grid points, the estimation accuracy is affected by the resolution. If the grid points are divided more finely, it leads to longer processing time and consumes more spectrum resources. These resources are not infinite in practical applications, thus limiting the algorithm's performance. Summary of the Invention

[0004] The purpose of this invention is to provide a super-resolution time delay Doppler estimation method for vehicle-mounted radar based on orthogonal time-frequency air conditioning, so as to solve the technical problem that existing methods divide the time delay-Doppler plane into discrete grid points, and therefore the estimated resolution depends on the density of the plane division.

[0005] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0006] A super-resolution time delay Doppler estimation method for vehicle-mounted radar based on orthogonal time-frequency air conditioning includes the following steps:

[0007] Step 1: Construct a radar system based on orthogonal time-frequency control communication signals;

[0008] In an OTFS modulation frame, the number of blocks is N and the number of subcarriers is M. These N×M information symbols are distributed on the time-delay Doppler plane. The N×M information symbols are randomly selected from the PSK or QAM modulation symbol table.

[0009] Additionally, the duration of the N×M information symbols is set to T, and the length of the cyclic prefix is ​​also set to T. CP Then the total length of an information symbol is T. s =T+T CP To ensure orthogonality between subcarriers, the subcarrier bandwidth is set to Δf = 1 / T; therefore, the duration of an OTFS modulation frame is calculated to be NT. s The bandwidth is B = MΔf; let x dd [k,l], k=0,1,...,N-1, l=0,1,...M-1 are the information symbols on the time-delay Doppler plane. First, the inverse symplectic finite Fourier transform (ISFFT) is applied to transform the information symbols to the time-frequency (TF) plane. The information symbols in the time-frequency plane are represented as x. tf [n,m], n=0,1,...,N-1,m=0,1,…M-1; The conversion process from the time-delay Doppler domain to the time-frequency domain is written as:

[0010]

[0011] Next, consider the transmitted signal in the continuous-time domain; the transmission of the nth symbol block is represented as the superposition of M subcarriers of different frequencies, and is therefore expressed as...

[0012]

[0013] Where s n (t) represents the nth symbol block; N blocks are combined in chronological order to form an OTFS transmission frame, represented as...

[0014]

[0015] Next, the echo signal of the target is modeled; it is assumed that there are K point targets within the detection area, which cannot be accurately located on the grid points of the two-dimensional time-delay Doppler plane, such as... Figure 1 As shown. They are continuously and randomly distributed within the detection area; the k-th target is set to be located at a distance R from the radar. k At this location, the moving speed is V. k Therefore, the round-trip delay is denoted as Doppler frequency shift is Where c is the speed of light, f c The carrier frequency; considering path loss, reflection coefficient, and receiver gain, denoted as H. k ;

[0016] The phase rotation within a block is set to be constant because ν k T s If << 1, then the received signal is the superposition of K paths, represented as:

[0017]

[0018] Where v(t) is additive noise, which follows a Gaussian distribution with a mean of 0 and a variance that depends on the noise power;

[0019] Step 2: Based on the radar system constructed in Step 1, derive a super-resolution time-delay Doppler two-dimensional estimation method based on the atomic norm;

[0020] Step 3: The estimation algorithm in Step 2 is optimized using the alternating direction multiplier method.

[0021] Furthermore, the specific steps of step 2 are as follows: After receiving an OTFS frame, the receiver performs a Fourier transform on each block to obtain the time-frequency domain signal, which is then written as...

[0022]

[0023] The received signal in the time-delay Doppler domain is calculated by the inverse process of formula (1); since the inverse symplectic finite Fourier transform (SFFT) is a discrete signal processing process, it interrupts the continuity of time delay and Doppler, therefore, the time delay and Doppler are estimated in the time-frequency domain.

[0024] To account for time delay and Doppler estimation in the continuous domain, the concept of the atomic norm needs to be introduced. To obtain a two-dimensional atom containing both time delay and Doppler frequency shift information for estimation, the input-output relationship in the time-frequency domain is considered. This input-output relationship is obtained through mathematical derivation.

[0025]

[0026] In the above formula, normalization is achieved. For the sake of brevity, h is defined. k =H k T s ;v tf [n,m] represents additive noise in the time-frequency domain; z[n,m] represents atoms containing two-dimensional time delay and Doppler information; the normalized time delay and Doppler values ​​are continuous; next, z[n,m] is written in matrix form, and the terms containing delay and Doppler are separated; the steering vector is defined. and For K different targets, the K steering vectors are combined into a matrix, defined as follows: and Let h = [h1, h2, ..., hK ] T Given a vector containing amplitude information, and based on the above definition, the input-output relationship in the time-frequency domain can be written in matrix form as follows:

[0027]

[0028] in These represent time-frequency domain matrices, and their (n, m)th elements are y and m respectively. tf [n,m],x tf [n,m], z[n,m], v tf [n,m]; where ⊙ represents the Hadamard product; for vectorization Y tf Define atomic vectors as follows

[0029]

[0030] in Let Kronecker product represent the product; therefore, the final estimation model can be written in the following form.

[0031] y = Xz + v (9)

[0032] in According to formula (9), the problem of estimating time delay and Doppler is transformed into the problem of estimating the atomic vector z; z is a linear combination of K elements, as shown in formula (8); in practical application scenarios, the number of targets is much smaller than NM, that is, because K << MN, the two-dimensional atomic norm of z is defined as follows

[0033]

[0034] Unlike traditional compressed sensing that uses l1 norm minimization, we use the atomic norm instead of the l1 norm; after defining the atomic norm, the estimation problems of time delay and Doppler are transformed into the following optimization problem.

[0035]

[0036] Where λ is the weighting coefficient; ||z|| is calculated using formula (10). A ;

[0037] The above problem is a typical SDP problem, which can be solved using the convex optimization toolbox; after solving this optimization problem, As input to the two-dimensional MUSIC algorithm, the normalized time delay and Doppler frequency shift are obtained, denoted as... and

[0038] Furthermore, an equivalent form is used to replace the calculation method in equation (10). The equivalent calculation method of equation (10) is given here.

[0039]

[0040] Where w is a scalar, z H This refers to the conjugate transpose of matrix U and vector z. It is a block Topulitz matrix, defined as follows:

[0041]

[0042] In the matrix above, u i =[u i (-N+1),u i (-N+2),…,u i (N-1)]' and U=[u -M+1 ,u -M ,…,u M-1 ]; Toep(·) represents the Toplitz matrix; Substituting formula (12) into formula (11), we obtain a new form of the optimization problem, which is a semidefinite programming problem (SDP), written in the following form.

[0043]

[0044]

[0045] Furthermore, step 3 includes the following steps:

[0046] The Alternating Direction Multiplier Method (ADMM) is presented to solve this SDP problem iteratively. The specific implementation flow of the ADMM algorithm is as follows: To construct the parameters for the alternating iteration, the augmented Lagrangian function is defined as follows:

[0047]

[0048] Where Θ represents the intermediate parameter and Υ represents the dual variable; ρ represents the penalty factor used to introduce the augmented Lagrange multiplier. Defined as the inner product between two matrices;

[0049] The variables in the augmented Lagrange function are updated alternately in three steps:

[0050] The specific update method is shown in the following formula.

[0051]

[0052]

[0053]

[0054] Next, we will further explain formula (16), first considering z. l U l ,w l The update, z l U l ,w l To update, the function L(z,U,w,Υ) needs to be computed. l-1 ,Θ l-1 The derivative of Θ; for clarity and ease of expression, Θ is... l and Υ l Divide into 4 sub-matrices, written as

[0055]

[0056]

[0057] Among them and It is an MN×MN matrix, θ l and γ l It is a scalar. and It is a vector; calculated by the function L(z,U,w,Υ) l-1 ,Θ l-1 For z l U l ,w l The derivative of z, and setting the derivative to 0, calculate the derivative with respect to z. l U l ,w l Iterative calculation formula:

[0058]

[0059]

[0060] w l =θ l-1 +(γ l-1 -λ / 2) / ρ

[0061] In the above formula, T * (·) represents the adjoint matrix of T(·); in z l U l ,w l After the update, for Θ l The update of Θ can be viewed as an eigenvalue decomposition problem; through mathematical derivation, Θ l Update writing

[0062]

[0063] The optimal solution to the above equation is the projection onto the positive semi-definite hyperplane. This projection is calculated by eigenvalue decomposition and setting all negative eigenvalues ​​to 0. Θ can be obtained through this calculation. l The update; the final step of the iteration is to update Υ. l After multiple iterations, the algorithm will gradually approach the optimal solution; then, based on the solution obtained by the algorithm... The estimated values ​​of time delay and Doppler are calculated; the maximum number of iterations is set to L, and the entire algorithm process is summarized as Algorithm 1-ADMM-AN; thus, the final solution of the super-resolution time delay Doppler two-dimensional estimation algorithm is obtained.

[0064] The super-resolution time delay Doppler estimation method for vehicle-mounted radar based on orthogonal time-frequency air conditioning in this invention has the following advantages:

[0065] The super-resolution algorithm proposed in this invention solves the basis mismatch problem inherent in compressed sensing algorithms used for radar target parameter estimation in the discrete domain during signal processing. This algorithm can perform super-resolution estimation of target range and velocity in the continuous domain, thus achieving higher accuracy in estimating target parameters for discrete grid points not falling within the detection area. To address the off-grid issue in the discrete domain, this method uses a two-dimensional atomic norm to establish the estimation problem in the continuous domain. A positive semidefinite programming problem for solving continuous frequencies is established using the two-dimensional atomic norm and analyzed. Based on this, the alternating direction method of multipliers is proposed, employing an iterative approach to quickly solve this optimization problem. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of the target distribution estimated by the radar in this invention.

[0067] Figure 2 This is a schematic diagram of the pseudocode for the ADMM-AN algorithm of this invention;

[0068] Figure 3 This is a comparison chart of the RMSE curve performance of the distance estimation method of this invention;

[0069] Figure 4 This is a performance comparison chart of the RMSE curves for speed estimation in this invention;

[0070] Figure 5 This is a comparison chart of the success rate curves for detecting the target distance in this invention;

[0071] Figure 6 This is a comparison chart of the success rate curves for detecting the target speed of this invention;

[0072] Figure 7 This is a flowchart of the super-resolution time delay Doppler estimation method for vehicle-mounted radar based on orthogonal time-frequency air conditioning according to the present invention. Detailed Implementation

[0073] To better understand the purpose, structure, and function of this invention, the following description, in conjunction with the accompanying drawings, provides a more detailed account of a super-resolution time delay Doppler estimation method for vehicle-mounted radar based on orthogonal time-frequency conditioning.

[0074] A super-resolution time delay Doppler estimation method for vehicle-mounted radar based on orthogonal time-frequency air conditioning includes the following steps:

[0075] Step 1: Construct a radar system based on orthogonal time-frequency control communication signals;

[0076] In an OTFS modulation frame, the number of blocks is N and the number of subcarriers is M. These N×M information symbols are distributed on the time-delay Doppler plane. The N×M information symbols are randomly selected from the PSK or QAM modulation symbol table.

[0077] Additionally, the duration of the N×M information symbols is set to T, and the length of the cyclic prefix is ​​also set to T. CP Then the total length of an N×M information symbol is T. s =T+T CP To ensure orthogonality between subcarriers, the subcarrier bandwidth is set to Δf = 1 / T; therefore, the duration of an OTFS modulation frame is calculated to be NT. s The bandwidth is B = MΔf; let x dd [k,l], k=0,1,...,N-1, l=0,1,...M-1 are the information symbols on the time-delay Doppler plane. First, the inverse symplectic finite Fourier transform (ISFFT) is applied to transform these symbols to the time-frequency (TF) plane. The information symbols in the time-frequency plane are represented as x. tf [n,m], n=0,1,...,N-1, m=0,1,...M-1; The conversion process from the time-delay Doppler domain to the time-frequency domain can be written as:

[0078]

[0079] Next, consider the transmitted signal in the continuous-time domain; the transmission of the nth symbol block is represented as the superposition of M subcarriers of different frequencies, and is therefore expressed as...

[0080]

[0081] Where s n (t) represents the nth symbol block; N blocks are combined in chronological order to form an OTFS transmission frame, represented as...

[0082]

[0083] Next, the echo signal of the target is modeled; it is assumed that there are K point targets within the detection area, which cannot be accurately located on the grid points of the two-dimensional time-delay-Doppler plane, such as... Figure 1 As shown. They are continuously and randomly distributed within the detection area; the k-th target is set to be located at a distance R from the radar. k At this location, the moving speed is V. k Therefore, the round-trip delay is denoted as Doppler frequency shift is Where c is the speed of light, f c The carrier frequency; considering path loss, reflection coefficient, and receiver gain, denoted as H. k ;

[0084] The phase rotation within a block is set to be constant because ν k T s If << 1, then the received signal is the superposition of K paths, represented as:

[0085]

[0086] Where v(t) is additive noise, which follows a Gaussian distribution with a mean of 0 and a variance that depends on the noise power;

[0087] Step 2: Based on the radar system constructed in Step 1, derive a super-resolution time-delay Doppler two-dimensional estimation method based on the atomic norm;

[0088] Step 3: The estimation algorithm in Step 2 is optimized using the alternating direction multiplier method.

[0089] Step 2 consists of the following steps: After receiving an OTFS frame, the receiver performs a Fourier transform on each block to obtain the time-frequency domain signal, which is then written as...

[0090]

[0091] The received signal in the time-delay-Doppler domain is calculated by the inverse process of formula (1); since the inverse symplectic finite Fourier transform (SFFT) is a discrete signal processing process, it interrupts the continuity of time delay and Doppler, therefore, the time delay and Doppler are estimated in the time-frequency domain.

[0092] To account for time delay and Doppler estimation in the continuous domain, the concept of the atomic norm needs to be introduced. To obtain a two-dimensional atom containing both time delay and Doppler frequency shift information for estimation, the input-output relationship in the time-frequency domain is considered. This input-output relationship is obtained through mathematical derivation.

[0093]

[0094] In the above formula, normalization is achieved. For the sake of brevity, h is defined.k =H k T s ;v tf [n,m] represents additive noise in the time-frequency domain; z[n,m] is an atom containing two-dimensional time delay and Doppler information; the normalized time delay and Doppler values ​​are continuous; next, this atom term is written in matrix form, and the terms containing delay and Doppler are separated; the steering vector is defined. and For K different targets, the K steering vectors are combined into a matrix, defined as follows: and Let h = [h1, h2, ..., h K ] T Given a vector containing amplitude information, and based on the above definition, the input-output relationship in the time-frequency domain can be written in matrix form as follows:

[0095]

[0096] in These represent time-frequency domain matrices, and their (n, m)th elements are y and m respectively. tf [n,m],x tf [n,m], z[n,m], v tf [n,m]; where ⊙ represents the Hadamard product; for vectorization Y tf Define atomic vectors as follows

[0097]

[0098] in Let Kronecker product represent the product; therefore, the final estimation model can be written in the following form.

[0099] y = Xz + v (9)

[0100] in According to formula (9), the problem of estimating time delay and Doppler is transformed into the problem of estimating the atomic vector z; z is a linear combination of K elements, as shown in formula (8); in practical application scenarios, the number of targets is much smaller than NM, that is, because K << MN, the two-dimensional atomic norm of z is defined as follows

[0101]

[0102] Unlike traditional compressed sensing that uses l1 norm minimization, we use the atomic norm instead of the l1 norm; after defining the atomic norm, the estimation problems of time delay and Doppler are transformed into the following optimization problem.

[0103]

[0104] Where λ is the weighting coefficient; ||z|| is calculated using formula (10). A ;

[0105] An equivalent form is used to replace the calculation method in equation (10). The equivalent calculation method of equation (10) is given here.

[0106]

[0107]

[0108] Where w is a scalar It is a block Topulitz matrix, defined as follows:

[0109]

[0110] In the matrix above, u i =[u i (-N+1),u i (-N+2),...,u i (N-1)]' and U=[u -M+1 ,u -M ,…,u M-1 ]; Toep(·) represents the Toplitz matrix; Substituting formula (12) into formula (11), we obtain a new form of the optimization problem, which is a semidefinite programming problem (SDP), written in the following form.

[0111]

[0112]

[0113] The above problem is a typical SDP problem, which can be solved using the convex optimization toolbox; after solving this optimization problem, As input to the two-dimensional MUSIC algorithm, the normalized time delay and Doppler frequency shift are obtained, denoted as... and

[0114] Step 3 includes the following steps:

[0115] The Alternating Direction Multiplier Method (ADMM) is presented to solve this SDP problem iteratively. The specific implementation flow of the ADMM algorithm is as follows: To construct the parameters for the alternating iteration, the augmented Lagrangian function is defined as follows:

[0116]

[0117] Where Θ represents the intermediate parameter and Υ represents the dual variable; ρ represents the penalty factor used to introduce the augmented Lagrange multiplier. Defined as the inner product between two matrices;

[0118] Next, the variables in the augmented Lagrange function are updated alternately in three steps, as shown in the following equation.

[0119]

[0120]

[0121]

[0122] Next, we will further explain formula (16), first considering z. l U l ,w l The update, z l U l ,w l To update, the function L(z,U,w,Υ) needs to be computed. l-1 ,Θ l-1 The differential of Θl; for clarity and ease of expression, Θl and Υ are used. l Divide into 4 sub-matrices, written as

[0123]

[0124]

[0125] Among them and It is an MN×MN matrix, θ l and γ l It is a scalar. and It is a vector; calculated by the function L(z,U,w,Υ) l-1 ,Θ l-1 For z l U l ,w l The derivative of z, and setting the derivative to 0, calculate the derivative with respect to z. l U l ,w l Iterative calculation formula:

[0126]

[0127]

[0128] w l =θ l-1 +(γ l-1 -λ / 2) / ρ

[0129] In the above formula, T *(·) represents the adjoint matrix of T(·); in z l U l ,t l After the update, for Θ l The update of Θ can be viewed as an eigenvalue decomposition problem; through mathematical derivation, Θ l Update writing

[0130]

[0131] The optimal solution to the above equation is the projection onto the positive semi-definite hyperplane. This projection is calculated by eigenvalue decomposition and setting all negative eigenvalues ​​to 0. Θ can be obtained through this calculation. l The update; the final step of the iteration is to update Υ. l After multiple iterations, the algorithm will gradually approach the optimal solution; then, based on the solution obtained by the algorithm... The estimated values ​​of time delay and Doppler are calculated; the maximum number of iterations is set to L, and the entire algorithm process is summarized as Algorithm 1-ADMM-AN; thus, the final solution of the super-resolution time delay Doppler two-dimensional estimation algorithm is obtained.

[0132] The ADMM-AN algorithm is explained as follows: the inputs are the radar transmitted signal, the echo signal, the maximum number of iterations, and two optimization parameters; the outputs are the estimated values ​​of time delay and Doppler. First, the parameters are initialized, and then z is calculated using equation (18) during the algorithm iteration process. l U l ,w l Then Θ is calculated using equation (19). l Dual variable Υ l The update is calculated through (16), and after L iterations, the final estimated value z is obtained. L Using this estimate as input, the time delay and Doppler values ​​can be obtained through the 2D-MUSIC algorithm.

[0133] This invention proposes a super-resolution time-delay Doppler two-dimensional estimation method. To verify the performance advantages of the algorithm, an example flow of this invention is given below.

[0134] The super-resolution algorithm proposed in this invention solves the basis mismatch problem in signal processing in the discrete domain of compressed sensing algorithms used for radar target parameter estimation. This algorithm can perform super-resolution estimation of target range and velocity in the continuous domain, thus achieving higher accuracy in estimating target parameters for discrete grid points not falling within the detection area. The following numerical simulation results demonstrate the superior performance of the proposed ADMM-AN algorithm. The simulation parameters are set as follows: an OTFS radar transceiver system with a carrier frequency of is used; the number of OTFS frame blocks is set to N = 16; the number of subcarriers is set to M = 64; the bandwidth is set to B = 320 kHz; the bandwidth of each subcarrier is set to Δf = 5 kHz; the symbol duration T is 0.2 ms; and the cyclic prefix length is set to 0.1 ms.

[0135] First, simulations were performed to evaluate the root mean square error (RMSE) of distance and velocity estimation using different methods. These algorithms include the proposed ADMM-AN algorithm and a Bayesian learning (SBL) algorithm based on sparse compressed sensing. The received signal-to-noise ratio (SNR) ranged from -40 dB to 40 dB. 500 Monte Carlo simulations were performed for each SNR. The distance and velocity of targets were randomly selected within the monitored area. Figure 3 As shown, the distance RMSE of the proposed ADMM-AN method begins to decrease rapidly at -20dB and remains at a low level at -12dB. In contrast, the distance RMSE of the SBL method begins to decrease rapidly at -10dB and remains at a low level at 8dB. Therefore, the ADMM-AN method exhibits better noise resistance and can estimate the target distance more accurately.

[0136] Similarly, the velocity RMSE of the ADMM-AN method begins to decrease rapidly at -20 dB and remains at a low level at 0 dB. In contrast, the velocity RMSE of the SBL method begins to decrease rapidly at -14 dB and remains stable at 8 dB. Because the value of N is relatively small, the velocity resolution is relatively high, so the SBL estimation of velocity is inaccurate, while the ADMM-AN method has super-resolution characteristics and therefore has better estimation accuracy. Figure 4 As shown.

[0137] Next, we calculated the probability of successful detection, with the criterion for successful detection being that the difference between the estimated value and the ground truth value does not exceed half the resolution. For the detection success probability of distance estimation, the ADMM-AN method outperforms the SBL method.

[0138] For ADMM-AN, with a signal-to-noise ratio of 4dB, the detection probability is close to 1; in contrast, SBL requires a signal-to-noise ratio of 10dB to achieve the same level. Similarly, for speed estimation, ADMM-AN also outperforms SBL in terms of successful detection rate. Figure 6As shown, ADMM-AN achieves a detection success rate of almost 1 at -4dB. In contrast, SBL's probability approaching 1 is very slow due to the aforementioned resolution issue. In conclusion, the ADMM-AN algorithm exhibits superior performance.

[0139] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A super-resolution time delay Doppler estimation method for vehicle-mounted radar based on orthogonal time-frequency air conditioning, characterized in that, Includes the following steps: Step 1: Construct a radar system based on orthogonal time-frequency control communication signals; The number of blocks in an OTFS modulation frame are set as follows: The number of subcarriers are respectively ,this The information symbols are distributed on the time-delay Doppler plane; Each information symbol is randomly selected from a PSK or QAM modulation symbol table; Additional settings The duration of each information symbol is The length of the cyclic prefix is Then the total length of an information symbol is To ensure orthogonality between subcarriers, the subcarrier bandwidth is set to... Therefore, the duration of an OTFS modulated frame is calculated to be... bandwidth is ;set up To represent the information symbols in the time-delay Doppler plane, firstly, the inverse symplectic finite Fourier transform (ISFFT) is applied to transform the information symbols to the time-frequency (TF) plane. The information symbols in the time-frequency plane are represented as follows: The conversion process from the time-delay Doppler domain to the time-frequency domain can be written as follows: （1）； Next, consider the transmitted signal in the continuous time domain; for the first... The transmission of a symbol block is represented as The superposition of subcarriers of different frequencies is therefore represented as: （2）； in Indicates the first A block of symbols; grouped in chronological order. Blocks are formed into OTFS transport frames, represented as: （3）； Next, the echo signal of the target is modeled; a detection range is set where the target's echo signal is present. There are several point targets, which cannot be precisely located on the grid points of the two-dimensional time-delay Doppler plane; they are continuously and randomly distributed within the detection area. The first... The target is located at the radar distance. At this location, the movement speed is Therefore, the round-trip delay is denoted as Doppler frequency shift is ,in At the speed of light, The carrier frequency is denoted as ; considering path loss, reflection coefficient, and receiver gain, it is denoted as . ; The phase rotation within a block is set to be constant because The received signal is The superposition of paths is represented as: （4）； in It is additive noise, which follows a Gaussian distribution with a mean of 0, and its variance depends on the noise power. Step 2: Based on the radar system constructed in Step 1, derive a super-resolution time-delay Doppler two-dimensional estimation method based on the atomic norm; Step 3: Optimize the estimation algorithm in Step 2 using the alternating direction multiplier method; Step 2 consists of the following steps: After receiving an OTFS frame, the receiver performs a Fourier transform on each block to obtain the time-frequency domain signal, which is written as: （5）； The received signal in the time-delay Doppler domain is calculated by the inverse process of formula (1); since the inverse symplectic finite Fourier transform (SFFT) is a discrete signal processing process, it interrupts the continuity of time delay and Doppler, therefore, the time delay and Doppler are estimated in the time-frequency domain. To account for time delay and Doppler estimation in the continuous domain, the concept of the atomic norm needs to be introduced. To obtain a two-dimensional atom containing both time delay and Doppler shift information for estimation, the input-output relationship in the time-frequency domain is considered. Through mathematical derivation, this input-output relationship is obtained: （6）； In the above formula, normalization is achieved. , For the sake of brevity, it is defined as follows: ; It is additive noise in the time-frequency domain; It contains atoms with two-dimensional time delay and Doppler information; the normalized time delay and Doppler values ​​are continuous; next, ... Write it in matrix form, separating the terms containing delay and Doppler; define the steering vector. and For different One goal, to The guide vectors are combined into a matrix, defined as follows: and ;set up Given a vector containing amplitude information, and based on the above definition, the input-output relationship in the time-frequency domain can be written in matrix form as follows: （7）； in , , , They represent time-frequency domain matrices, and their first and second... The elements are respectively , , , ;in Represents the Hadamard product; for vectorization Define atomic vectors as follows: （8）； in This represents the Kronecker product; therefore, the final estimation model can be written in the following form: （9）； in , , According to formula (9), the problem of estimating time delay and Doppler is transformed into estimating atomic vectors. The problem; yes A linear combination of elements, as shown in formula (8); because ,definition The two-dimensional atomic norms are as follows: （10）； Replace with atomic norm Norm; After defining the atomic norm, the problem of estimating time delay and Doppler is transformed into the following optimization problem: （11）； Among them These are weighting coefficients; calculated using formula (10). ; The above problem is a typical SDP problem, which can be solved using the convex optimization toolbox; after solving this optimization problem, As input to the two-dimensional MUSIC algorithm, the normalized time delay and Doppler frequency shift are obtained, denoted as... and .

2. The method for super-resolution time delay Doppler estimation of vehicle-mounted radar based on orthogonal time-frequency air conditioning as described in claim 1, characterized in that, An equivalent form is used to replace the calculation method in equation (10). The equivalent calculation method of equation (10) is given here: （12）； in It is a scalar. This refers to the conjugate transpose of matrix U and vector z. It is a block Topulitz matrix, defined as follows: （13）； In the matrix above, and ; Let represent the Tollitz matrix; substituting formula (12) into formula (11), we obtain a new form of the optimization problem, which is a semidefinite programming problem (SDP), written in the following form: （14）。 3. The method for super-resolution time delay Doppler estimation of vehicle-mounted radar based on orthogonal time-frequency air conditioning as described in claim 1, characterized in that, Step 3 Includes the following steps: The Alternating Direction Multiplier Method (ADMM) is given to solve this SDP problem iteratively. The specific implementation flow of the ADMM algorithm is as follows: To construct the parameters for the alternating iteration, the augmented Lagrangian function is defined as: （15）； in Represents intermediate parameters and Represents the dual variable; The representative penalty factor is used to introduce augmented Lagrange multipliers; Defined as the inner product between two matrices; The variables in the augmented Lagrange function are updated alternately in three steps: The specific update method is shown in the following formula: （16）； Next, we will further explain formula (16), first considering... Update To update, the function needs to be calculated. The differential; for clarity and ease of expression, and Divide into 4 sub-matrices, written as: （17）； Among them and yes The matrix, and It is a scalar. and It is a vector; it is calculated by a function. for The derivative of , and setting the derivative to 0, calculate the derivative with respect to . Iterative calculation formula: （18）； In the above formula, represent The adjoint matrix; in After the update, for The update can be viewed as an eigenvalue decomposition problem; Through mathematical derivation Updated writing: （19）； The optimal solution to the above equation is the projection onto the positive semi-definite hyperplane. This projection is calculated by eigenvalue decomposition and setting all negative eigenvalues ​​to 0. The calculation yields... The update; the final step of the iteration is the update. After multiple iterations, the algorithm will gradually approach the optimal solution; then, based on the solution obtained by the algorithm... Calculate the estimated values ​​for time delay and Doppler; Set the maximum number of iterations to The entire algorithm process is summarized as Algorithm 1 - ADMM-AN; thus, the final solution of the super-resolution time-delay Doppler two-dimensional estimation algorithm is obtained.

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