A multi-target detection method based on group-sparse OTFS communication and sensing integration

Abstract

This invention proposes a multi-target detection method based on group sparsity OTFS communication sensing integration. The implementation steps are as follows: initializing parameters; constructing a sparse signal recovery problem based on the OTFS communication sensing integrated group sparsity model; solving the sparse signal recovery problem; and obtaining multi-target detection results. This invention constructs an OTFS communication sensing integrated group sparsity model and uses this model to construct a sparse signal recovery problem for N channels. During the iterative solution of the sparse signal recovery problem, the channel gain parameters and error terms are gradually updated, avoiding the impact of forced convergence on the channel gain estimate. Furthermore, the previously estimated channel gain parameters are used to gradually eliminate interference from other targets, thereby significantly reducing interference between multiple targets and avoiding the defect that interference between multiple targets increases with the number of targets, further improving target detection accuracy and robustness.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology and relates to a multi-target detection method based on group sparsity OTFS communication and sensing integration. Background Technology

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

[0003] OTFS communication-sensing integrated multi-target detection includes two categories: communication-sensing integrated radar waveform and communication-sensing integrated communication waveform. The communication-sensing integrated communication waveform multi-target detection method uses existing communication signals as radar detection waveforms, without the need to adjust or design the communication waveform. To improve the estimation accuracy of target distance and velocity parameters and enhance the robustness of detection algorithms, for example, Huang Yongming et al. from Southeast University published a paper titled "Low-complexity parameter learning for OTFS modulation based automotive radar" at the ICASSP2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing. This paper disclosed a Bayesian learning-based OTFS communication-sensing integrated multi-target detection method. This method first uses prior information about the distance and velocity between the target and the transmitter to reduce the dimension of the transmitted signal matrix. Then, it adopts a two-dimensional mode-coupled hierarchical Gaussian structure model and uses sparse Bayesian learning to estimate the channel. Finally, it estimates the distance and velocity between the target and the transmitter based on the estimated channel parameters. This method improves the accuracy of multi-target detection by leveraging the characteristic that sparse Bayesian learning matches the sparse characteristics of the OTFS communication-sensing integrated system channel. Under low signal-to-noise ratio conditions, during the iteration process, some non-zero target values ​​are forced to converge to 0 due to the influence of inter-target interference and the algorithm's learning rate, which reduces the detection accuracy. In addition, when the number of targets is large, the interference between targets cannot be effectively suppressed, the algorithm performance drops sharply, and further affects the detection accuracy and robustness. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology and propose a multi-target detection method based on group sparsity OTFS communication and sensing integration, which is used to solve the technical problems of low detection accuracy and robustness in the existing technology.

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

[0006] (1) Initialize parameters:

[0007] The initialization of the OTFS integrated communication and sensing system includes N channels, the number of signals transmitted in the time-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 time-delay taps respectively, K≥2, L≥2, P≥1;

[0008] (2) Constructing a sparse signal recovery problem based on an OTFS-based integrated communication and sensing sparse model:

[0009] We construct a real-domain grouped sparse model of OTFS communication sensing integration, which includes the matrix relationship between real-domain echo signals and transmitted signals and channel gain, and use this model to construct the sparse signal recovery problem for N channels.

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

[0011] Solving the sparse signal recovery problem yields estimates of the gains of N channels. Where the nth channel gain h n The estimation result is Represents the real number field;

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

[0013] Construct a channel gain matrix of dimension K×L using the solution results from step (3). And based on the correspondence between target range velocity and channel taps, through Doppler indices corresponding to the P maximum values ​​in and delay index Calculate the velocity of each target relative to the launcher. and distance

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

[0015] (1) This invention constructs a sparse signal recovery problem for N channels by using the OTFS communication 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 the channel gain. The real domain channel gain of the partitioned channel maintains the sparsity between the time delay Doppler domain channel groups and the non-sparseness within the groups. In the process of iteratively solving the sparse signal recovery problem, the channel gain parameters and error terms are updated step by step, avoiding the influence of forced convergence on the gain estimate and effectively improving the detection accuracy.

[0016] (2) In the process of solving the sparse signal recovery problem, the present invention uses the previously estimated channel parameters to gradually eliminate the interference caused by other targets, thereby significantly reducing the interference between targets and avoiding the defect that the interference between multiple targets increases with the number of targets, further improving the accuracy and robustness of target detection. Attached Figure Description

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

[0018] Figure 2 This is a simulation comparison chart of the detection accuracy of the present invention and existing technologies.

[0019] Figure 3 This is a simulation comparison diagram showing the robustness of the present invention and the prior art. Detailed Implementation

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

[0021] Reference Figure 1 The present invention includes the following steps:

[0022] Step 1) Initialize parameters:

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

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

[0025] An OTFS communication sensing integrated group sparse model is constructed, which includes the matrix relationship between real-domain echo signals and transmitted signals and channel gain. This model is then used to construct a sparse signal recovery problem for N channels. The specific implementation steps are as follows:

[0026] (2a) Obtain the target reflection signal received by the transmitter The input-output relationship between the constructed OTFS integrated communication sensing complex domain echo signal and transmitted signal is as follows:

[0027]

[0028] Where y[k,l] represents the time-delayed Doppler domain echo signal matrix. The signal in the k-th row and l-th column is denoted by ∑·, where ∑· represents the summation symbol, and h[k',l'] represents the channel gain matrix in the time-delay Doppler domain. 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 Let x[[kk′] represent the modulo K and modulo L operations, respectively. K ,[ll′] L ] represents the [kk']th element in the transmitted signal matrix x. K Line [ll'] L The transmitted signal of the column, 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 based on the transmitted signal matrix. and echo signal matrix The system consists of a transmit signal matrix x, a receive signal matrix y, and N channels. All are K×L grids. The signals transmitted by the transmitter are superimposed through the channels to generate echo signals, which are then further processed by the transmitter.

[0030] (2b) Constructing the matrix form of the relationship between the echo signal and the transmitted signal by transforming the matrix and vector relationships:

[0031]

[0032] in, Represents the complex domain echo signal vector. Represents the complex field transmitted signal matrix. Represents the channel vector in the complex field. Represents a noise vector in the complex field. These are the matrix-vector correspondences of y[k,l], h[k,l], and w[k,l], respectively. Convert to vector form, express The Middle (k+K(l-1)) Each echo signal corresponds to the echo signal in the k-th row and l-th column of y. express The Middle (k+K(l-1)) Each echo signal corresponds to a channel in the k-th row and l-th column of h. express The Middle (k+K(l-1)) Each echo signal corresponds to the noise in the k-th row and l-th column of w. express The [i,j]th element, 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 [k'-k'']th element in the transmitted signal matrix x. K Line [l'-l”] L The column sends signals;

[0033] By constructing a matrix representation of the relationship between the echo signal and the transmitted signal, and vectorizing the echo signal and the channel, the transmitted signal matrix is ​​transformed into... This helps in further processing the echo signal.

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

[0035]

[0036] in, Represents the echo signal in the real number domain. This represents the transmitted signal matrix in the real number field. Represents the channel in the real number field. Representing noise in the real number domain, respectively, are... The vector constructed from the real and imaginary parts of the vector. It is by The real and imaginary parts of each element in the equation are expanded. express The [i,j]th element, This indicates that the complex field signal Extended to the form of the real number field;

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

[0038] (2d) Group the channels, and the gain h of the nth channel. n The grouping of the real number field can be expressed as:

[0039]

[0040] Among them, (h n ) realand (h) n ) imag They represent h respectively n The real and imaginary parts;

[0041] The nth channel gain h n It is in the complex field. By taking its real and imaginary parts respectively, we can construct the grouping form h of the real field. n When a target exists in this channel group, h n Indicates the channel complex gain. Composed of the real and imaginary parts of the complex gain of this channel group, when there is no target in this channel group, It is a zero vector.

[0042] (2e) Construct an OTFS communication sensing integrated group sparse model based on the relationship between the real domain echo signal and the transmitted signal matrix and the group channel:

[0043]

[0044] in, Represents the nth channel h n The real-field matrix of the transmitted signal. Indicates the nth channel. This represents the nth noise vector. From N groups h n Composition, when the corresponding channel has a target, h n Represents the real and imaginary parts of the channel gain; otherwise, h n It is a zero vector. There are P groups of non-zero values, and the remaining NP groups are all zero vectors. Therefore It is a sparse group.

[0045] Based on the matrix relationship between the real-domain echo signal and the transmitted signal from step (2c) and the real-domain grouping form from step (2d), an OTFS communication sensing integrated group sparse model is constructed, where each and There are N groups in total. Based on the positions of the time delay taps and Doppler taps in the channel corresponding to the non-zero values ​​of the P groups, the relative speed and distance parameters between the corresponding P targets and the transmitter can be solved.

[0046] (2f) Constructing a sparse signal recovery problem with N channels:

[0047] For the sparse model of the OTFS communication sensing integrated group constructed in step (2e), since the relative velocity and distance parameters between the target and the transmitter are related to the time delay taps and Doppler taps in the channel gain matrix, it is only necessary to estimate N channel gains and construct the channel gain matrix. Based on the correspondence between the time delay taps and Doppler taps and the relative velocity and distance between the target and the transmitter, the distance and velocity parameters between the target and the transmitter can be obtained. Therefore, the sparse signal recovery problem of N channels is constructed.

[0048] The problem of sparse signal recovery with N channels is represented by finding the objective function. Minimum value The problem is expressed as:

[0049]

[0050]

[0051] Where ||·|| denotes the L2 norm operation, K represents the 2×2 identity matrix, and λ represents the hyperparameter. express The transpose of .

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

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

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

[0055]

[0056] in, It is an echo signal. This represents the result of the error in the m-th iteration. express transpose,

[0057] This represents the estimated channel gain for the (m-1)th iteration, where m = 1. It is a 0 vector of dimension 2N×1;

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

[0059]

[0060] in This represents the estimated channel gain for the (N-1)th iteration in the m-th iteration. It is a vector of dimension 2N×1, whose first n-1 groups, that is, the first 2(n-1) elements, are... Composed of, the last Nn groups, that is, the last 2 (Nn) elements are composed of The nth group, which consists of the 2nth and 2n+1th elements, is 0. This is done to subtract the influence of the remaining N-1 channel gains on the channel gain estimation of this group.

[0061] (3d) Determine if m ≥ M holds true. If so, obtain the estimated results of N channel gains. Otherwise, let m = m + 1 and proceed to step (3b).

[0062] The nth channel gain The final result can be expressed as:

[0063]

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

[0065] The off-diagonal elements of G are close to 0. It is precisely because of these off-diagonal elements that interference exists between multiple targets. However, during the algorithm's iterative solution process, when estimating the p-th target in the m-th iteration, the estimated values ​​of the other P-1 targets from the previous iteration are used to eliminate the interference between targets. As the iteration progresses... It will gradually approach the true value. This makes the interference items and The interference between multiple targets is gradually reduced. This avoids the defect that the interference between multiple targets increases with the number of targets, thus improving the accuracy and robustness of detection.

[0066] Furthermore, the estimation results for the N channel gains are as follows: because The existence of S gradually updates n The channel gain without a target will be set to zero, which makes h have set sparsity, further improving the accuracy of channel gain estimation.

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

[0068] Through the channel gain h of each group n estimation results modulus And based on the correspondence between matrices and vectors Construct a K×L channel gain matrix Its expression is:

[0069]

[0070] Due to the recovered channel gain matrix Compared with the actual channel gain matrix While maintaining the same sparsity characteristics, the estimated channel gain matrix is ​​affected by noise and interference. Although sparse, there are still some locations with smaller values. To estimate the distance and velocity parameters between the P targets and the transmitter, we can obtain... Find the P maximum values ​​in the array, and then find the row and column indices corresponding to these P maximum values; this is known as the Doppler index. and delay index Calculate the relative velocity between each target and the launcher. and distance

[0071]

[0072] Where c represents the speed of light, f c The carrier frequency is represented by Δf, and the subcarrier spacing and the duration of the transmitted signal are represented by T, respectively.

[0073] The technical effects of the present invention will be further explained below with reference to simulation results:

[0074] 1. Experimental conditions and contents:

[0075] The hardware platform for the simulation experiment consisted of an AMD Ryzen 7 4800H CPU with a clock speed of 2.90GHz×8, 16GB of RAM, and an NVIDIA GeForce RTX 2060 4GB graphics processor. The software platform was Windows 10 Pro 64-bit operating system. The mean square error performance of the invention was simulated using MATLAB R2021b.

[0076] Simulation 1. A comparative simulation of the detection accuracy of the present invention and prior art in the signal-to-noise ratio range of 5 to 20 dB, including the mean square error of velocity (RMSE). V and the mean square error of distance RMSE R The result is as follows Figure 2 As shown, RMSE V and RMSE R The calculation formula is:

[0077]

[0078] in, This represents an estimated distance between the target and the system's transmitter. V represents an estimate of the relative velocity between the target and the system's transmitter. p R represents the true distance between the target and the system's transmitter. p This represents the true value of the relative velocity between the target and the system's transmitter.

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

[0080] 2. Analysis of experimental results:

[0081] Reference Figure 2 The horizontal axis represents the signal-to-noise ratio, ranging from 5dB to 20dB. Figure 2 The vertical axis of (a) represents the mean square error of the distance between the target and the transmitter. Figure 2 (b) The vertical axis represents the mean square error between the target and transmitter velocities. From Figure 2 As can be seen, as the signal-to-noise ratio increases from 5dB to 20dB, the detection accuracy of both the present invention and the prior art increases with the increase of the signal-to-noise ratio. Specifically, the mean square error of distance in the present invention decreases from 80 to 18, and the mean square error of velocity decreases from 3 to 0.5, while the mean square error of distance in the prior art decreases from 130 to 102, and the mean square error of velocity decreases from 5.2 to 4.3. The present invention maintains a high detection accuracy throughout.

[0082] Reference Figure 3 The horizontal axis represents the number of targets, ranging from 2 to 6. Figure 3 The vertical axis of (a) represents the mean square error of the distance between the target and the transmitter. Figure 3 (b) The vertical axis represents the mean square error between the target and transmitter velocities. From Figure 3 As can be seen, the detection accuracy of both the present invention and the prior art fluctuates to some extent as the number of targets changes from 2 to 6. Specifically, the mean square error of distance of the present invention increases from 23 to 40, and the mean square error of speed increases from 1 to 1.2, while the mean square error of distance of the prior art increases from 80 to 230, and the mean square error of speed increases from 3 to 6.5. The present invention can not only maintain a high detection accuracy at all times, but is also almost unaffected by the number of targets, and has excellent robustness.

Claims

1. A group sparse-based OTFS communication and perception integrated multi-target detection method, characterized in that, Includes the following steps: (1) Initialize parameters: Initializing the OTFS integrated communication and sensing system includes There are channels, and the number of signals transmitted in the time-delay Doppler domain is . The number of targets to be detected is ,in, , and These represent the number of Doppler taps and the number of time delay taps, respectively. , , ; (2) Constructing a sparse signal recovery problem based on an OTFS-based integrated communication and sensing sparse model: Construct a real-domain packet-sparse model of OTFS communication sensing integration, including the matrix relationship between real-domain echo signals and transmitted signals and channel gain, and build a sparse model based on this model. The problem of sparse signal recovery in one channel, The problem of sparse signal recovery in one channel is expressed as finding the objective function. Minimum value The problem is expressed as: ； ； in, This represents the 2-norm operation. This represents the summation operation. The dimension is The identity matrix, Indicates hyperparameters, Indicates the first Channel gain The transpose result, Represents a real echo signal. Represents the real-field transmitted signal matrix The Middle A real-field matrix of transmitted signals from each channel; (3) Solve the sparse signal recovery problem; Solving the sparse signal recovery problem yields the following results: The estimation results of the channel gain are as follows , of which Channel gain The estimation result is , Represents the real number field; (4) Obtain multi-target detection results: The dimension is constructed using the solution results of step (3). Channel gain matrix In Doppler index corresponding to the maximum value and delay 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 mentioned in step (2) is obtained by the following method: Through the time-delayed Doppler domain, the first Doppler A time-delayed transmission signal echo signal The construction dimension is Complex echo signal matrix 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 field of complex numbers. This represents the transmitted signal matrix in the real number field. express A real-number domain channel, This represents noise in the real number field.

3. The method according to claim 2, characterized in that, The real-domain grouping of the channel gain mentioned in step (2), wherein the first Channel gain The grouping form of the real number field is as follows: ； in and They represent the first Channel gain The real and imaginary parts.

4. The method according to claim 3, characterized in that, The OTFS communication-sensing integrated sparse model described in step (2) is expressed as follows: ； in, express The first in A real-field matrix of transmitted signals from each channel. This represents noise in the real number field.

5. The method according to claim 4, 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 be The maximum number of iterations is The hyperparameters are and order ; (3b) Calculate the objective function result and through Calculate the first Estimate of the current gain of each channel : ； ； in, It is an echo signal. Indicates the first The result of the error in the round of iteration. express The transpose result, Indicates the first Round iteration The estimation results of the channel gain, when hour, For dimension of vector; (3c) Through the first Channel gain right Update: ； (3d) Judgment Is it true? If so, obtain Estimation results for each channel Otherwise Then proceed with step (3b).

6. The method according to claim 5, characterized in that, The steps described in step (3d) Estimation results for each channel Its expression is: 。 7. The method according to claim 4, characterized in that, The construction described in step (4) Channel gain matrix The implementation steps are as follows: Through the correspondence between matrices and vectors For each channel estimation result modulus The channel gain matrix is ​​obtained by transformation. ,in The Middle Line number Column elements The expression is: 。 8. The method according to claim 4, characterized in that, The velocity of each target relative to the launcher as described in step (4) and distance The calculation formulas are as follows: ； ； in, Represents the speed of light. Indicates the carrier frequency. and These represent the subcarrier spacing and the duration of the transmitted signal, respectively.

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