OTFS communication perception integrated multi-target detection method based on group sparsity

Abstract

The invention provides an OTFS communication perception integrated multi-target detection method based on group sparsity. The method comprises the following steps: initializing parameters; constructing a sparse signal recovery problem based on an OTFS communication perception integrated group sparse model; solving a sparse signal recovery problem; and obtaining a multi-target detection result. According to the method, the OTFS communication perception integrated group sparse model is constructed, the sparse signal recovery problem of N channels is constructed through the model, channel gain parameters and error terms are updated step by step in the process of performing iterative solution on the sparse signal recovery problem, the influence of forced convergence on a channel gain estimated value is avoided, and in addition, the method has the advantages that the robustness is high, and the robustness is high. The interference brought by other targets is gradually eliminated by using the previously estimated channel gain parameter, so that the interference among the multiple targets is remarkably reduced, the defect that the interference among the multiple targets is enhanced along with the increase of the number of the targets is avoided, and the target detection precision and robustness are further improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and relates to a multi-target detection method for OTFS communication sensing integration based on group sparsity. Background Art

[0002] The orthogonal time-frequency-space (OTFS) modulation technology is a signal modulation method based on the delay-Doppler domain. It uses the diversity in the time domain and the frequency domain to convert the time-varying channel experienced by the modulated signal into a channel independent of time, and has good adaptability to Doppler frequency offset and delay, and can provide reliable transmission for future 6G and high-speed mobile communications.

[0003] The multi-target detection for OTFS communication sensing integration includes two categories: based on the communication sensing integration radar waveform and based on the communication sensing integration communication waveform. Among them, the multi-target detection method based on the communication sensing integration communication waveform uses the existing communication signal as the radar detection waveform without the need to adjust or design the communication waveform. In order to improve the estimation accuracy of parameters such as target distance and speed and enhance the robustness of the detection algorithm, for example, Huang Yongming et al. from Southeast University published a paper "Low-complexity parameter learning for OTFS modulation based automotive radar" in ICASSP2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing in 2021, which disclosed a multi-target detection method for OTFS communication sensing integration based on Bayesian learning. This method first uses the prior information of the distance and speed between the target and the transmitter to reduce the dimension of the transmitted signal matrix, then adopts a two-dimensional mode-coupled hierarchical Gaussian structure model, uses the sparse Bayesian learning method to estimate the channel, and finally estimates the distance and speed between the target and the transmitter according to the estimated channel parameters. This method improves the accuracy of multi-target detection by using the characteristics of sparse Bayesian learning that conform to the sparse characteristics of the channel of the OTFS communication sensing integration system. Under low signal-to-noise ratio conditions, during the iterative process, due to the influence of interference between targets and the influence of the algorithm learning rate, some non-zero target values are forced to converge to 0, reducing the detection accuracy. In addition, when the number of targets is large, the interference between targets cannot be effectively suppressed, and the algorithm performance drops sharply, further affecting the detection accuracy and robustness. Summary of the Invention

[0004] The object of the present invention is to overcome the defects existing in the above-mentioned prior art, and propose a multi-target detection method for OTFS communication sensing integration based on group sparsity, which is used to solve the technical problems of low detection accuracy and robustness existing in the prior art.

[0005] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0006] (1) Initialize parameters:

[0007] Initialize the OTFS communication and sensing integrated system including N channels. The number of transmitted signals in the time-delay Doppler domain is K×L, and the number of targets to be detected is P. Among them, N = K×L, where K and L respectively represent the number of Doppler taps and time-delay taps, K≥2, L≥2, and P≥1;

[0008] (2) Construct a sparse signal recovery problem based on the OTFS communication and sensing integrated group sparse model:

[0009] Construct an OTFS communication and sensing integrated group sparse model including the relationship between the real-domain echo signal and the transmitted signal matrix and the real-domain grouping of channel gains, and construct a sparse signal recovery problem for N channels through this model;

[0010] (3) Solve the sparse signal recovery problem;

[0011] Solve the sparse signal recovery problem, and the estimated results of the channel gains of N channels are where the estimated result of the nth channel gain h n is represents the real number field;

[0012] (4) Obtain multi-target detection results:

[0013] Construct a channel gain matrix with dimensions of K×L through the solution result of step (3) and according to the corresponding relationship between the target distance and speed and the channel taps, through the Doppler indices corresponding to the P maximum values in and the time-delay indices calculate the speed and distance

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] (1) The present invention constructs a sparse signal recovery problem for N channels through an OTFS communication and sensing integrated group sparse model of the relationship between the real-domain echo signal and the transmitted signal matrix and the real-domain grouping of channel gains. The real-domain channel gains divided therein maintain the sparsity between channel groups and the non-sparsity within the group in the time-delay Doppler domain. During the iterative solution of the sparse signal recovery problem, the channel gain parameters and error terms are gradually updated, avoiding the influence of forced convergence on the gain estimation value and effectively improving the detection accuracy.

[0016] (2) In the process of solving the sparse signal recovery problem, the present invention uses previously estimated channel parameters to gradually eliminate the interference brought by the remaining targets, thereby significantly reducing the interference between targets, avoiding the defect that the interference between multiple targets increases as the number of targets increases, and further improving the accuracy and robustness of target detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a flowchart of the implementation of the present invention.

[0018] Figure 2 is a simulation comparison diagram of the detection accuracy between the present invention and the prior art.

[0019] Figure 3 is a simulation comparison diagram of the robustness between the present invention and the prior art. DETAILED DESCRIPTION OF THE INVENTION

[0020] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] Refer to Figure 1 , the present invention includes the following steps:

[0022] Step 1) Initialize parameters:

[0023] Initialize the OTFS communication and sensing integrated system including N channels, and the number of transmitted signals in the time-delay Doppler domain is K×L. Denote the transmitted signal matrix, and the transmitted signal of the kth Doppler tap and the lth time-delay tap is {x[k, l]|k = 1, 2,..., K; l = 1, 2,..., L}. The number of targets to be detected is P, and the OTFS communication and sensing integrated system includes N time-delay Doppler domain channels. N = K×L, which is used to transmit the transmitted signal and receive the echo signals reflected by P targets. Among them, K and L respectively represent the number of Doppler taps and time-delay taps, K≥2, L≥2, P≥1; in this embodiment, K = 16, L = 16, P = 3.

[0024] Step 2) Construct a sparse signal recovery problem based on the OTFS communication and sensing integrated group sparse model:

[0025] Construct an OTFS communication and sensing integrated group sparse model including the relationship between the real-domain echo signal and the transmitted signal matrix and the real-domain grouping of channel gains, and construct a sparse signal recovery problem for N channels through this model. The specific implementation steps are as follows:

[0026] (2a) Obtain the target reflection signal received at the transmitter Input-output relationship between the constructed OTFS communication-sensing integrated complex-domain echo signal and the transmitted signal:

[0027]

[0028] where y[k, l] represents the signal in the k-th row and l-th column of the echo signal matrix in the time-delay Doppler domain in, ∑· represents the summation symbol, and h[k', l'] represents the channel gain matrix in the time-delay Doppler domain in the channel in the k'-th row and l'-th column, 1 ≤ k′ ≤ K, 1 ≤ l' ≤ L, e represents the natural constant, [·] K and [·] L respectively represent modulo K and modulo L operations, x[[k - k′] K , [l - l′] L represents the transmitted signal in the [k - k′]-th K row and [l - l′]-th L column of the transmitted signal matrix x, and w[k, l] represents independent and identically distributed complex Gaussian white noise.

[0029] The input-output relationship between the complex-domain echo signal and the transmitted signal is constructed based on the transmitted signal matrix and the echo signal matrix The transmitted signal matrix x, the received signal matrix y, and the N channels are all grids of dimension K × L. The transmitted signal at the transmitter generates an echo signal after being superimposed by the channel, and then is further processed by the transmitter.

[0030] (2b) Construct the matrix form of the relationship between the echo signal and the transmitted signal through matrix-vector relationship transformation:

[0031]

[0032] where, represents the complex-domain echo signal vector, represents the complex-domain transmitted signal matrix, represents the complex-domain channel vector, represents the complex-domain noise vector, are respectively obtained by converting y[k, l], h[k, l], w[k, l] into vector form according to the matrix-vector correspondence , represents in the (k+K(l-1)) th echo signal corresponding to the echo signal in the k-th row and l-th column of y, represents in the (k+K(l-1)) th echo signal corresponding to the channel in the k-th row and l-th column of h, represents The (k+K(l-1)) th echo signal corresponds to the noise at the k-th row and l-th column in w. Denote as the [i, j]-th element of, where 1 ≤ i = k′ + K(l′ - 1) ≤ N, 1 ≤ k′ ≤ K', K' = K, 1 ≤ l' ≤ L', L' = L, 1 ≤ j = k″ + K(l″ - 1) ≤ N, 1 ≤ k” ≤ K”, K” = K, 1 ≤ l” ≤ L”, L” = L, x[[k'-k”] K ,[l'-l”] L represents the transmission signal at the [k'-k′'] K th row and [l'-l”] L th column in the transmission signal matrix x;

[0033] Construct the matrix form of the relationship between the echo signal and the transmission signal. Vectorize the echo signal and the channel, then the transmission signal matrix is transformed into which helps to further process the echo signal.

[0034] (2c) Convert the matrix form of the relationship between the echo signal and the transmission signal to the real number domain to obtain the relationship between the echo signal and the transmission signal matrix in the real number domain:

[0035]

[0036] where, represents the echo signal in the real number domain, represents the transmission signal matrix in the real number domain, represents the channel in the real number domain, represents the noise in the real number domain, which are vectors constructed by the real part and the imaginary part of respectively, is composed of the extension of the real part and the imaginary part of each element in , denotes as the [i, j]-th element of, denotes the extension of the complex domain signal to the real number domain form;

[0037] The relationship between the echo signal and the transmission signal matrix in the real number domain is obtained by matrix transformation and extension of the matrix form of the relationship between the echo signal and the transmission signal in the complex domain system.

[0038] (2d) Group the channels. The real number domain grouping form of the n-th channel gain h n can be expressed as:

[0039]

[0040] where, (h n ) realand (h n ) imag represent the real part and the imaginary part of h n respectively;

[0041] The n-th channel gain h n is in the complex domain. By taking its real part and imaginary part respectively, a real-domain grouped form h n is constructed. When there is a target in this group of channels, h n represents the complex channel gain, which is composed of the real part and the imaginary part of the complex channel gain of this group of channels. When there is no target in this group of channels, is a zero vector.

[0042] (2e) Construct the OTFS communication and sensing integrated group sparse model according to the relationship between the real-domain echo signal and the transmitted signal matrix and the grouped channels:

[0043]

[0044] where, represents the real-domain matrix of the transmitted signal for the n-th channel h n , represents the n-th channel, represents the n-th group of noise vectors, is composed of N groups of h n . When there is a target in the corresponding channel, h n represents the real part and the imaginary part of the channel gain. Otherwise, h n is a zero vector. There are P groups of non-zero values in , and the remaining N - P groups are all zero vectors. Therefore

[0045] Construct the OTFS communication and sensing integrated group sparse model according to the relationship between the real-domain echo signal and the transmitted signal matrix in step (2c) and the real-domain grouped form in step (2d), where each and is a group, and there are N groups in total. According to the positions of the delay taps and Doppler taps in the channels corresponding to the P groups of non-zero values, the relative velocities and distance parameters of the corresponding P targets and the transmitter can be solved.

[0046] (2f) Construct the sparse signal recovery problem for N channels:

[0047] For the OTFS communication-sensing integrated group sparse model constructed in step (2e), since the relative speed and distance parameters between the target and the transmitter are related to the delay taps and Doppler taps in the channel gain matrix, only N channel gains need to be estimated to construct the channel gain matrix. According to the corresponding relationship between the delay taps and Doppler taps and the relative speed and distance between the target and the transmitter, the distance and speed parameters between the target and the transmitter can be obtained. Therefore, a sparse signal recovery problem for N channels is constructed.

[0048] The sparse signal recovery problem for N channels means finding the objective function minimum value The problem is expressed as:

[0049]

[0050]

[0051] where ||·|| represents the operation of taking the two-norm, K represents the identity matrix of dimension 2×2, λ represents the hyperparameter, represents transpose.

[0052] Step 3) Solve the sparse signal recovery problem:

[0053] (3a) Initialize the number of iterations as m, the maximum number of iterations as M, and the hyperparameter as λ, and let m = 1; in this Example 1, let M = 10 and λ = 0.01;

[0054] (3b) Calculate the result of the objective function and calculate the nth channel gain through

[0055]

[0056] where, is the echo signal, represents the result of the error in the mth round of iteration, represents transpose,

[0057] represents the estimation result of the N - 1 channel gains in the (m - 1)th round of iteration. When m = 1, is a 0 vector of dimension 2N×1;

[0058] (3c) Update using the nth channel gain :

[0059] ​

[0060] Among them represents the estimation result of N - 1 channel gains in the m - th iteration, is a vector with a dimension of 2N×1. The first n - 1 groups, that is, the first 2(n - 1) elements, are composed of and the last N - n groups, that is, the last 2(N - n) elements, are composed of The n - th group, that is, the 2n - th and (2n + 1)-th elements, are 0. The purpose of doing this is to subtract the influence of the other N - 1 channel gains on the estimation of the channel gain of this group.

[0061] (3d) Judge whether m≥M holds. If so, the estimation result of N channel gains is Otherwise, let m = m + 1 and execute step (3b).

[0062] The n - th channel gain The final result can be expressed as:

[0063]

[0064] where G is an approximate identity matrix, and G n,n represents the element in the n - th row and n - th column of the matrix G, represents the true value of the i - th channel gain, represents the estimated value of the i - th channel gain in the m - th iteration.

[0065] The off - diagonal elements of G are close to 0. Due to these off - diagonal elements, interference between multiple targets exists. However, in the iterative process of solving the algorithm, when estimating the p - th target in the m - th iteration, the estimated values of the other P - 1 targets in the previous iteration are used to eliminate the interference between targets. As the iteration progresses it will gradually approach the true value so that the interference term and gradually decrease. This avoids the defect that the interference between multiple targets increases as the number of targets increases, and improves the detection accuracy and robustness.

[0066] In addition, the estimation result of N channel gains is Due to the existence of, S is gradually updated n , and the channel gains without targets will be set to zero, which makes h have group sparsity and further improves the accuracy of channel gain estimation.

[0067] Step 4) Obtain the multi - target detection result:

[0068] Through the estimation result n of each group of channel gains h the modulus value According to the correspondence between the matrix and the vector construct a channel gain matrix of K×L Its expression is as follows:

[0069]

[0070] Since the restored channel gain matrix has the same sparsity characteristic as the true channel gain matrix However, due to the existence of noise and interference, although the estimated channel gain matrix is sparse, there are still some positions with relatively small values. In order to estimate the distance and speed parameters of P targets from the transmitter, by obtaining the P maximum values in find the row indices and column indices corresponding to the P maximum values, that is, the Doppler indices and the delay indices calculate the relative speed of each target with respect to the transmitter

[0071]

[0072] where c represents the speed of light, f c represents the carrier frequency, Δf and T represent the subcarrier spacing and the transmission signal duration respectively.

[0073] Next, in combination with the simulation results, the technical effects of the present invention will be further described:

[0074] 1. Experimental conditions and content:

[0075] The hardware platform for the simulation experiment is: a central processing unit of AMD Ryzen 7 4800H CPU with a main frequency of 2.90GHz×8, 16GB of memory, and a graphics processing unit of NVIDIA GeForce RTX 2060 4GB. The software platform is: Windows10Pro 64-bit operating system. Use the simulation software MATLAB R2021b to simulate the mean square error performance of the present invention:

[0076] Simulation 1. Comparative simulation of the detection accuracy of the present invention and the prior art between signal-to-noise ratios of 5 to 20 dB, including the root mean square error of speed RMSE V and the root mean square error of distance RMSE R , and the results are as Figure 2 shown, and the calculation formulas for RMSE V and RMSE R are as follows:

[0077]

[0078] Among them, represents the estimated value of the distance between the target and the system transmitter, represents the estimated value of the relative velocity between the target and the system transmitter, V p represents the true value of the distance between the target and the system transmitter, R p represents the true value of the relative velocity between the target and the system transmitter.

[0079] Simulation 2. Robustness comparison simulation of the present invention and the prior art when the number of targets is between 2 and 6, including the root mean square error of velocity RMSE V and the root mean square error of distance RMSE R , and the results are as Figure 3 shown.

[0080] 2. Analysis of experimental results:

[0081] Referring to Figure 2 , the abscissa represents the signal-to-noise ratio, with a range of 5 dB to 20 dB, among which Figure 2 (a) The ordinate represents the root mean square error of the distance between the target and the transmitter, Figure 2 (b) The ordinate represents the root mean square error of the velocity between the target and the transmitter. It can be seen from Figure 2 that as the signal-to-noise ratio increases from 5 dB to 20 dB, the detection accuracy of both the present invention and the prior art increases with the increase of the signal-to-noise ratio. Among them, the root mean square error of distance of the present invention decreases from 80 to 18, and the root mean square error of velocity decreases from 3 to 0.5, while the root mean square error of distance of the prior art decreases from 130 to 102, and the root mean square error of velocity decreases from 5.2 to 4.3. The present invention always maintains a high detection accuracy.

[0082] Referring to Figure 3 , the abscissa represents the number of targets, with a range of 2 to 6, among which Figure 3 (a) The ordinate represents the root mean square error of the distance between the target and the transmitter, Figure 3 (b) The ordinate represents the root mean square error of the velocity between the target and the transmitter. It can be seen from Figure 3 that as the number of targets changes from 2 to 6, the detection accuracy of both the present invention and the prior art fluctuates to a certain extent. Among them, the root mean square error of distance of the present invention increases from 23 to 40, and the root mean square error of velocity increases from 1 to 1.2, while the root mean square error of distance of the prior art increases from 80 to 230, and the root mean square error of velocity increases from 3 to 6.5. The present invention can not only always maintain a high detection accuracy, but also is almost not affected by the number of targets and has excellent robustness.

Claims

1. A multi-target detection method based on group sparse OTFS communication perception integration, characterized in that: The steps include: (1) Initialization parameters: Initialization OTFS communication perception integrated system includes N channels, the number of transmitted signals in the delay-Doppler domain is K×L, and the number of targets to be detected is P, where N=K×L, K and L represent the number of Doppler taps and delay taps, respectively, K≥2, L≥2, P≥1; (2) Constructing a sparse signal recovery problem based on the OTFS communication-sensing integrated group sparse model: Construct an OTFS communication perception integrated group sparse model including the real domain echo signal and the transmission signal matrix relationship and the real domain grouping of the channel gain, and use this model to construct the sparse signal recovery problem of N channels; (3) Solve the sparse signal recovery problem; Solving the sparse signal recovery problem, we get the estimated results of N channel gains: The gain of the nth channel h n The estimated result is represents the field of real numbers; (4) Obtaining multi-target detection results: The channel gain matrix with dimension K×L is constructed by solving the result of step (3) The Doppler index corresponding to the P maximum values ​​in and latency index Calculate the velocity of each target relative to the launcher and distance 2. The method according to claim 1, characterized in that The relationship between the real domain echo signal and the transmitted signal matrix described in step (2) is obtained by: The complex echo signal matrix with dimension K×L is constructed by the echo signal y[k,l] of the transmitted signal x[k,l] with the kth Doppler and the lth delay in the delay-Doppler domain And convert it into a real echo signal Construct the matrix relationship between the real domain echo signal and the transmitted signal: in represents the complex domain, represents the real domain transmitted signal matrix, represents N real-domain channels, represents real-domain noise.

3. The method according to claim 2, characterized in that The real domain grouping of the channel gains described in step (2), where the nth channel gain h n The real number field grouping form is: Among them (h n ) real and (h n ) imag Respectively represent the nth channel gain h n The real and imaginary parts of .

4. The method according to claim 3, characterized in that: The OTFS communication-aware integrated group sparse model described in step (2) is expressed as: in, express The nth channel h in n The transmitted signal is a real-domain matrix, represents real-domain noise.

5. The method according to claim 4, characterized in that The sparse signal recovery problem of N channels described in step (2) is expressed as finding the objective function Minimum The problem is expressed as: Among them, ‖·‖ represents the two-norm operation, Σ· represents the summation operation, K represents the identity matrix of dimension 2×2, λ represents the hyperparameter, express The transposed result of .

6. The method according to claim 5, characterized in that The steps for solving the sparse signal recovery problem described in step (3) are as follows: (3a) Initialize the number of iterations to m, the maximum number of iterations to M, the hyperparameter to λ, and set m = 1; (3b) Calculate the objective function result and through Calculate the gain of the nth channel in, is the echo signal, represents the error result of the mth iteration, express The transposed result of represents the estimated result of the N-1 channel gains in the m-1th iteration. When m=1, is a 0 vector of dimension 2N×1; (3c) Through the nth channel gain right To update: (3d) Determine whether m ≥ M. If so, obtain the estimated results of N channels. Otherwise, let m=m+1 and execute step (3b).

7. The method according to claim 6, characterized in that The estimated results of the N channels described in step (3d) are Its expression is:

8. The method according to claim 5, characterized in that Construct the K×L channel gain matrix described in step (4) The implementation steps are: Through the correspondence between matrix and vector The estimated result for each channel The modulus value Convert and get the channel gain matrix in The element in row k and column l of The expression is:

9. The method according to claim 5, characterized in that The velocity of each target relative to the transmitter in step (4) and distance The calculation formulas are: Where c is the speed of light, f c represents the carrier frequency, Δf and T represent the subcarrier spacing and the duration of the transmitted signal respectively.

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