Fast sparse estimation method and device for broadband target echo parameters

Abstract

The invention discloses a fast sparse estimation method and device for broadband target echo parameters, and the method comprises the steps: solving an unknown vector in a two-dimensional time delay-Doppler sparse representation model between a receiving end and a transmitting end through a fast matrix decomposition algorithm, and obtaining the position serial number of a non-zero element in the unknown vector, the two-dimensional time delay-Doppler sparse representation model is composed of an unknown vector and a measurement matrix, and the position sequence number of a non-zero element in the unknown vector is the same as the column sequence number of a corresponding time delay-Doppler parameter in the measurement matrix; and determining the time delay-Doppler parameter of each broadband target signal according to the corresponding relationship between the non-zero element and the time delay-Doppler parameter. The calculation amount can be reduced, and the calculation efficiency and stability are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater acoustic detection, and in particular relates to a method and a device for fast sparse estimation of broadband target echo parameters. Background Art

[0002] The complex time-frequency characteristics of the underwater acoustic channel make it one of the most challenging wireless channels. Since the propagation speed of sound waves in the underwater acoustic channel is relatively low, the relative motion between the target and the sonar will cause the Doppler effect to appear in the echo signal. Hyperbolic Frequency Modulated (HFM) is a broadband signal commonly used in active sonar, and the Doppler effect will cause the pulse width of the received HFM signal to be compressed or widened. For active sonar, by estimating the Doppler coefficient and time delay in the echo signal, the relative speed and distance of the detected target can be calculated.

[0003] As a traditional method for estimating the delay-Doppler parameters in HFM signals, the matched filter method estimates the parameters in the ambiguity plane by calculating the mutual ambiguity function between the transmitted signal and the received signal. However, the main disadvantage of this method is that it requires the transmitted signal to have a large time-bandwidth product in order to obtain a sharp correlation peak and low sidelobes in the ambiguity plane, which results in a low resolution limitation in practical applications.

[0004] If the delay-Doppler parameter estimation problem is converted into a sparse recovery problem in the delay-Doppler domain, the compressed sensing algorithm can be used to solve it, thereby obtaining higher estimation accuracy and resolution. However, the traditional orthogonal matching pursuit algorithm in the compressed sensing algorithm requires matrix inversion operations during the iteration process, which leads to low computational efficiency and poor stability.

[0005] Therefore, traditional delay-Doppler parameter estimation methods have problems such as limited application scenarios or low computational efficiency and poor stability. Summary of the invention

[0006] The embodiments of the present invention provide a method and device for fast sparse estimation of broadband target echo parameters, which can solve the problems of limited application scenarios, low computational efficiency and poor stability of traditional delay-Doppler parameter estimation methods.

[0007] In a first aspect, an embodiment of the present invention provides a method for fast sparse estimation of broadband target echo parameters, the method comprising:

[0008] The unknown vector in the two-dimensional delay-Doppler sparse representation model between the receiving end and the transmitting end is solved by a fast matrix decomposition algorithm to obtain the position sequence number of the non-zero element in the unknown vector, wherein the two-dimensional delay-Doppler sparse representation model is composed of the unknown vector and the measurement matrix, and the position sequence number of the non-zero element in the unknown vector is the same as the column sequence number of the corresponding delay-Doppler parameter in the measurement matrix;

[0009] The delay-Doppler parameters of each broadband target signal are determined according to the corresponding relationship between the non-zero elements and the delay-Doppler parameters.

[0010] In a second aspect, an embodiment of the present invention provides a fast sparse estimation device for broadband target echo parameters, comprising:

[0011] A first solving module, the first solving module is used to solve the unknown vector in the two-dimensional delay-Doppler sparse representation model between the receiving end and the transmitting end by a fast matrix decomposition algorithm, and obtain the position sequence number of the non-zero element in the unknown vector, wherein the two-dimensional delay-Doppler sparse representation model is composed of the unknown vector and the measurement matrix, and the position sequence number of the non-zero element in the unknown vector is the same as the column sequence number of the corresponding delay-Doppler parameter in the measurement matrix;

[0012] The second solution module is used to determine the delay-Doppler parameters of each broadband target signal according to the corresponding relationship between the non-zero elements and the delay-Doppler parameters.

[0013] Compared with the prior art, the embodiments of the present invention have the following beneficial effects: according to the method provided by the present invention, a sparse estimation is performed on an unknown vector through a fast matrix decomposition algorithm to determine the positions of non-zero elements therein, and vector operations can be used to replace the matrix inversion process in the traditional compressed sensing algorithm, thereby reducing the amount of calculation and improving calculation efficiency and stability; and this method obtained by improving the compressed sensing algorithm can avoid the problem of limited application scenarios of the matched filtering method due to the low resolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 A flowchart of a method for fast sparse estimation of broadband target echo parameters provided by an embodiment of the present invention;

[0015] Figure 2 A flowchart of a method for solving an unknown vector by a fast matrix decomposition algorithm provided by the present invention;

[0016] Figure 3 A schematic diagram of the structure of a fast sparse estimation device for broadband target echo parameters provided by an embodiment of the present invention;

[0017] Figure 4A schematic diagram for comparing the index set recovery rate and the running time provided by an embodiment of the present invention;

[0018] Figure 5 A schematic diagram for comparing estimation results provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0019] In the following description, specific details such as specific system structures, technologies, etc. are provided for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present invention. However, it should be clear to those skilled in the art that the present invention may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to prevent unnecessary details from obstructing the description of the present invention.

[0020] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or combinations thereof.

[0021] It should also be understood that the term "and / or" used in the present description and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.

[0022] As used in the present specification and the appended claims, the term "if" may be interpreted as "when" or "upon" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrase "if it is determined" or "if [described condition or event] is detected" may be interpreted as meaning "upon determination" or "in response to determining" or "upon detection of [described condition or event]" or "in response to detecting [described condition or event]", depending on the context.

[0023] In addition, in the description of the present specification and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0024] References to "one embodiment" or "some embodiments" etc. described in the present specification mean that one or more embodiments of the present invention include specific features, structures or characteristics described in conjunction with the embodiment. Therefore, the statements "in one embodiment", "in some embodiments", "in some other embodiments", "in some other embodiments", etc. that appear in different places in this specification do not necessarily refer to the same embodiment, but mean "one or more but not all embodiments", unless otherwise specifically emphasized in other ways. The terms "including", "comprising", "having" and their variations all mean "including but not limited to", unless otherwise specifically emphasized in other ways.

[0025] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0026] The fast sparse estimation method for broadband target echo parameters provided by the embodiment of the present invention can be applied to electronic devices such as mobile terminals, personal laptops, supercomputers, etc. The embodiment of the present invention does not impose any restrictions on the specific type of electronic devices.

[0027] Figure 1 The flowchart shown is an implementation flow of a method for fast sparse estimation of broadband target echo parameters provided by an embodiment of the present invention. As an example but not a limitation, the method may include steps S101-S104, and each step is described below.

[0028] S101, obtaining a received signal.

[0029] Exemplarily, if the broadband target echo signal has K targets, the received signal received by the receiving end may satisfy the following formula:

[0030]

[0031] Among them, s(t) is the HFM signal transmitted by the receiving end, a k ,d k and τ k They represent the amplitude, Doppler scale and delay parameters corresponding to the kth target respectively, and w(t) represents additive noise.

[0032] S102, establishing a two-dimensional delay-Doppler sparse representation model between the receiving end and the transmitting end through discretization processing.

[0033] Exemplarily, the two-dimensional delay-Doppler sparse representation model may satisfy the following formula:

[0034] y=Au+w

[0035] Where y and w represent the discretized received signal vector and noise vector respectively, A is the measurement matrix, and u is an unknown vector with sparsity K.

[0036] In a possible implementation, the sampling interval of the observation time, Doppler scale and delay can be set, and the observation time, Doppler scale and delay are discretized respectively, so as to obtain a discretized received signal vector and a discretized noise vector. After that, a measurement matrix can be constructed and the unknown vector to be solved can be defined; a two-dimensional delay-Doppler sparse representation model can be constructed according to the measurement matrix, the discretized received signal vector, the discretized noise vector and the unknown vector.

[0037] In one example, the discretized observation time can be t m =mΔt, m=0,…,M-1, M represents the length of the observation vector. Similarly, the discretized delay can be τ n =τ0+(n-1)Δτ, n=1,...,N, τ0 represents the reference delay, N represents the maximum delay sampling dimension; the discretized Doppler scale can be expressed as d l =d0+(l-1)Δd, l=1,...,L, d0 is the lower limit of the Doppler scale to be searched, and L represents the dimension of the Doppler scale space.

[0038] In one example, the measurement matrix can be expressed as A = [A1, ..., A L ], the i-th measurement matrix can satisfy the following formula:

[0039]

[0040] Exemplarily, each measurement matrix is ​​an M×N dimensional Toeplitz matrix and corresponds to the Doppler parameter d i If the reference delay τ0 = 0, then the matrix A i The delay parameter corresponding to the j-th column of is (j-1)Δτ.

[0041] In one example, the unknown vector u can be defined as u=[u1,...,u L ] T For each u j There is j =[u j (1),...,u j (N)] T ,j=1,...,L, at this time, each non-zero element in the unknown vector u corresponds to a set of multipath delay-Doppler parameters in the measurement matrix A.

[0042] S103, solving the unknown vectors in the two-dimensional delay-Doppler sparse representation model between the receiving end and the transmitting end by using a fast matrix decomposition algorithm, and obtaining the position sequence numbers of the non-zero elements in the unknown vectors.

[0043] Exemplarily, the position number of the non-zero element in the unknown vector is the same as the column number of its corresponding delay-Doppler parameter in the measurement matrix.

[0044] In one example, the two-dimensional delay-Doppler sparse representation model can be iteratively solved by a fast matrix decomposition algorithm. In each iteration, the column number of the column vector in the measurement matrix that is most correlated with the residual vector of the previous round is used as the position number of a non-zero element obtained in this iteration.

[0045] Exemplarily, the iterative solution method provided by the present invention may also be referred to as a fast orthogonal matching pursuit algorithm.

[0046] S104, determining the delay-Doppler parameters of each broadband target signal according to the corresponding relationship between the non-zero elements and the delay-Doppler parameters.

[0047] According to the method provided by the present invention, a fast matrix decomposition algorithm is used to perform sparse estimation on an unknown vector to determine the positions of non-zero elements therein, and vector operations can be used to replace the matrix inversion process in a traditional compressed sensing algorithm, thereby reducing the amount of calculation and improving calculation efficiency and stability; and this method obtained by improving the compressed sensing algorithm can avoid the problem of limited application scenarios of the matched filtering method due to its low resolution.

[0048] Figure 2 The flowchart of the method for solving an unknown vector by a fast matrix decomposition algorithm provided by the present invention is shown. As an example but not a limitation, the method is a specific possible implementation of step S103 in the above estimation method, and the method may include steps S201-S205, and each step is described below.

[0049] S201, taking the column number of the column vector most correlated with the k-1th residual vector in the measurement matrix as the position number of the kth non-zero element.

[0050] In one example, before the first iteration, the input measurement matrix A of M×LN dimensions and the received signal vector y of M×1 dimensions can be initialized, and the 0th residual vector r0=y and the index set Orthogonal Set

[0051] In one example, the position number of the kth non-zero element may satisfy the following formula:

[0052]

[0053] Among them, λ k is the position number of the kth non-zero element, a j is the jth column vector of the measurement matrix, j is a positive integer less than or equal to L×N, r k-1 is the k-1th residual vector.

[0054] Exemplarily, k is a positive integer less than or equal to K, and the 0th residual vector is a discretized received signal vector.

[0055] Optionally, after obtaining the position number of the kth non-zero element, the index set can be updated to Λ k =Λ k-1 ∪{λ k}.

[0056] S202: Determine whether k is greater than or equal to K.

[0057] In one example, if k is less than K, steps S203 and S204 may be performed in sequence, and the orthogonal set and the residual vector may be updated according to the column vector most relevant to the k-1th residual vector in the measurement matrix; and then k=k+1 may be set for the next iteration.

[0058] In another example, if k is greater than or equal to K, step S205 may be performed to output the index set and end the iteration.

[0059] S203, updating the orthogonal set according to the column vector in the measurement matrix that is most correlated with the k-1th residual vector to obtain the kth orthogonal set.

[0060] Exemplarily, the kth orthogonal set may satisfy the following formula:

[0061] Q k =[Q k-1 |q k ]

[0062] Q k is the kth orthogonal set, Q k-1 is the k-1th orthogonal set, q k Q k The kth column vector in ;

[0063] in:

[0064]

[0065] a λk is the column vector in the measurement matrix most correlated with the kth residual vector, λ k is the position index of the kth non-zero element.

[0066] S204, updating the residual vector according to the kth orthogonal set to obtain the kth residual vector.

[0067] Exemplarily, the kth residual vector may satisfy the following formula:

[0068]

[0069] Among them, r k is the kth residual vector, r k-1 is the k-1th residual vector, and y is the discretized received signal vector.

[0070] S205, output the position numbers of all non-zero elements in the unknown vector.

[0071] For example, after K iterations, the best matching K atoms can be selected from the measurement matrix. If the index set is updated synchronously during the iteration, the Kth updated index set Λ including the position numbers of all non-zero elements can be directly used. K Output.

[0072] The present invention simplifies the matrix inversion operation required to update the residual in the iterative process of the traditional compressed sensing algorithm into a low-complexity vector operation, which can reduce the computational complexity and improve the computational efficiency and stability. In addition, in the application scenario where only the delay-Doppler parameters of the broadband target need to be solved, only the index set needs to be calculated by this method without calculating the final sparse solution, which can further save computing resources.

[0073] Figure 3 The structure diagram of a fast sparse estimation device for broadband target echo parameters provided by an embodiment of the present invention is shown. As an example but not a limitation, the device 300 may include a first solution module 310 and a second solution module 320 .

[0074] Exemplarily, the first solution module 310 is used to solve the unknown vector in the two-dimensional delay-Doppler sparse representation model between the receiving end and the transmitting end through a fast matrix decomposition algorithm to obtain the position number of the non-zero elements in the unknown vector, wherein the two-dimensional delay-Doppler sparse representation model is composed of an unknown vector and a measurement matrix, and the position number of the non-zero element in the unknown vector is the same as the column number of the corresponding delay-Doppler parameter in the measurement matrix; the second solution module 320 is used to determine the delay-Doppler parameters of each broadband target signal according to the corresponding relationship.

[0075] In one example, the first solution module 310 can be specifically used to iteratively solve the two-dimensional delay-Doppler sparse representation model through a fast matrix decomposition algorithm, and in each round of iteration, the column number of the column vector in the measurement matrix that is most correlated with the residual vector of the previous round is used as the position number of a non-zero element obtained in this round of iteration.

[0076] In one example, during the k-th round of iterative solution of a two-dimensional delay-Doppler sparse representation model using a fast matrix decomposition algorithm, the first solution module can be specifically used to: use the column number of the column vector in the measurement matrix that is most correlated with the k-1th residual vector as the position number of the k-th non-zero element, where k is a positive integer less than or equal to the sparsity K of the unknown vector, and the 0th residual vector is a discretized received signal vector; determine whether k is greater than or equal to K; if k is less than K, update the orthogonal set according to the column vector in the measurement matrix that is most correlated with the k-1th residual vector to obtain the k-th orthogonal set; and update the residual vector according to the k-th orthogonal set to obtain the k-th residual vector.

[0077] In one example, the kth orthogonal set may satisfy the following formula:

[0078] Q k =[Q k-1 |q k ]

[0079] Q k is the kth orthogonal set, Q k-1 is the k-1th orthogonal set, q k Q k The kth column vector in ;

[0080] in:

[0081]

[0082] is the column vector in the measurement matrix most correlated with the kth residual vector, λ k is the position index of the kth non-zero element.

[0083] In one example, the kth residual vector may satisfy the following formula:

[0084]

[0085] Among them, r k is the kth residual vector, r k-1 is the k-1th residual vector, and y is the discretized received signal vector.

[0086] In order to better illustrate the beneficial effects of the present invention, the following simulation experiments were conducted:

[0087] Figure 4 The figure shows a comparison diagram of index set recovery rate and running time provided by an embodiment of the present invention.

[0088] Since the key to sparse estimation of broadband target echo parameters is to accurately establish the index set in the matching pursuit process, the index set recovery rate can be used to measure the matching pursuit performance of the algorithm.

[0089] For example, M c The response rate of the index set obtained after the Monte Carlo experiment can satisfy the following formula:

[0090]

[0091] in, represents the index set estimated by the mth independent experiment, Λ represents the true index set, is the set intersection symbol, and |·| represents the number of sets.

[0092] Exemplarily, a simulation experiment may be performed under the conditions that the Gaussian sparse signal length is set to 256, the observation vector length is set to 64, the received signal-to-noise ratio is set to 25 dB, the sparsity K=6:3:24, and the number of Monte Carlo independent trials is set to 500.

[0093] Specifically, see Figure 4 , wherein the relevant parameters of the traditional compressed sensing algorithm are represented in black, and the relevant parameters of the present invention are represented in red. Figure 4 (a) is a schematic diagram comparing the index set recovery rate of the method provided by the present invention and the traditional compressed sensing algorithm. Figure 4 (b) is a schematic diagram comparing the operation time of the method provided by the present invention and the traditional compressed sensing algorithm. Figure 4 It can be seen that the method provided by the present invention has the same matching pursuit capability as the traditional compressed sensing algorithm, and the computational efficiency is significantly higher than that of the traditional algorithm. Moreover, the greater the sparsity, the more obvious the improvement in computational efficiency of the method provided by the present invention.

[0094] Figure 5 A schematic diagram showing a comparison of estimation results provided by an embodiment of the present invention is shown.

[0095] For example, the transmitted signal may be an HFM signal, and in the simulation, it is assumed that there are four broadband targets and the delay search interval is Δτ=1 / f s =0.25ms, the delay search range is [0, 20]ms, that is, τ n =0+0.25(n-1), n=1,...,81; the Doppler scale search interval is Δd=0.005, and the search range is [0.85, 1.15], that is, d l =0.85+0.005(l-1), l=1,...,61; the observation vector length is set to M=0.8f s*T=3200, that is, under the condition that the size of the measurement matrix A is 3200×4800, comparative experiments are conducted according to the method provided by the present invention and the traditional mutual ambiguity function method based on matched filtering to solve the delay-Doppler parameters of each broadband target signal.

[0096] For example, the parameters of the transmission signal may be: pulse width T=1s, frequency range f L =1200Hz, f H =1600Hz, bandwidth B = 400Hz, receiving sampling rate f s =4000Hz, signal-to-noise ratio is 10dB.

[0097] Exemplarily, the delay-Doppler scale parameters corresponding to each target are shown in the following Table 1:

[0098] Table 1

[0099] k 1 2 3 4 <![CDATA[τ k ]]> 3ms 6ms 12ms 17ms <![CDATA[d k ]]> 1.06 0.95 1.00 0.92

[0100] Specifically, see Figure 5 , Figure 5 (a) is the estimation result obtained by the traditional mutual fuzzy function method. Figure 5 (b) in FIG. 1 is the estimation result obtained by the method provided by the present invention. Figure 5 It can be seen that the resolution of the mutual fuzzy function method is low and it is difficult to directly give the estimated delay-Doppler result; while the present invention can obtain a high-resolution and accurate estimation result. At the same time, the relevant simulation results show that the average word running time of the method provided by the present invention is only half of that of the mutual fuzzy function method.

[0101] Therefore, the above simulation experiments can prove that according to the method provided by the present invention, a fast matrix decomposition algorithm is used to perform sparse estimation on an unknown vector to determine the position of non-zero elements therein, and vector operations can be used to replace the matrix inversion process in the traditional compressed sensing algorithm, thereby reducing the amount of calculation and improving calculation efficiency and stability; and this method obtained by improving the compressed sensing algorithm can avoid the problem of limited application scenarios of the matched filtering method due to the low resolution.

[0102] In the above embodiments, the description of each embodiment has its own emphasis. For the part that is not described or recorded in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

Claims

1. A fast sparse estimation method for broadband target echo parameters, characterized in that: include: Solving an unknown vector in a two-dimensional delay-Doppler sparse representation model between a receiving end and a transmitting end by a fast matrix decomposition algorithm, and obtaining a position number of a non-zero element in the unknown vector, wherein the two-dimensional delay-Doppler sparse representation model is composed of the unknown vector and a measurement matrix, and the position number of the non-zero element in the unknown vector is the same as the column number of the delay-Doppler parameter corresponding to the non-zero element in the measurement matrix; The delay-Doppler parameter of each broadband target signal is determined according to the corresponding relationship between the non-zero elements and the delay-Doppler parameter.

2. The method according to claim 1, characterized in that The method of solving the unknown vector in the two-dimensional delay-Doppler sparse representation model between the receiving end and the transmitting end by using a fast matrix decomposition algorithm to obtain the position sequence number of the non-zero element in the unknown vector includes: The two-dimensional delay-Doppler sparse representation model is iteratively solved by a fast matrix decomposition algorithm. In each iteration, the column number of the column vector in the measurement matrix that is most correlated with the residual vector of the previous round is used as the position number of the non-zero element obtained in this iteration.

3. The method according to claim 2, characterized in that The process of performing the k-th round of iterative solution of the two-dimensional delay-Doppler sparse representation model by using a fast matrix decomposition algorithm includes: The column number of the column vector most correlated with the k-1th residual vector in the measurement matrix is ​​used as the position number of the kth non-zero element, where k is a positive integer less than or equal to the sparsity K of the unknown vector, and the 0th residual vector is a discretized received signal vector; Determine whether k is greater than or equal to K; If k is less than K, the orthogonal set is updated according to the column vector most correlated with the k-1th residual vector in the measurement matrix to obtain the kth orthogonal set; and the residual vector is updated according to the kth orthogonal set to obtain the kth residual vector.

4. The method according to claim 3, characterized in that The kth orthogonal set satisfies the following formula: Q k =[Q k-1 |q k ] Q k is the kth orthogonal set, Q k-1 is the k-1th orthogonal set, q k Q k The kth column vector in ; in: is the column vector in the measurement matrix most relevant to the k-th residual vector, λ k is the position number of the kth non-zero element.

5. The method according to claim 4, characterized in that The kth residual vector satisfies the following formula: Among them, r k is the kth residual vector, r k-1 is the k-1th residual vector, and y is the discretized received signal vector.

6. A fast sparse estimation device for broadband target echo parameters, characterized in that: include: A first solving module, wherein the first solving module is used to solve an unknown vector in a two-dimensional delay-Doppler sparse representation model between a receiving end and a transmitting end by a fast matrix decomposition algorithm, and obtain a position number of a non-zero element in the unknown vector, wherein the two-dimensional delay-Doppler sparse representation model is composed of the unknown vector and a measurement matrix, and the position number of the non-zero element in the unknown vector is the same as the column number of the delay-Doppler parameter corresponding to the non-zero element in the measurement matrix; The second solution module is used to determine the delay-Doppler parameters of each broadband target signal according to the corresponding relationship between the non-zero elements and the delay-Doppler parameters.

7. The device according to claim 6, characterized in that The first solution module is specifically used for: The two-dimensional delay-Doppler sparse representation model is iteratively solved by a fast matrix decomposition algorithm. In each iteration, the column number of the column vector in the measurement matrix that is most correlated with the residual vector of the previous round is used as the position number of the non-zero element obtained in this iteration.

8. The device according to claim 7, characterized in that In the process of performing the k-th round of iterative solution of the two-dimensional delay-Doppler sparse representation model by using the fast matrix decomposition algorithm, the first solution module is specifically used for: The column number of the column vector most correlated with the k-1th residual vector in the measurement matrix is ​​used as the position number of the kth non-zero element, where k is a positive integer less than or equal to the sparsity K of the unknown vector, and the 0th residual vector is a discretized received signal vector; Determine whether k is greater than or equal to K; If k is less than K, the orthogonal set is updated according to the column vector most correlated with the k-1th residual vector in the measurement matrix to obtain the kth orthogonal set; and the residual vector is updated according to the kth orthogonal set to obtain the kth residual vector.

9. The device according to claim 8, characterized in that The kth orthogonal set satisfies the following formula: Q k =[Q k-1 |q k ] Q k is the kth orthogonal set, Q k-1 is the k-1th orthogonal set, q k Q k The kth column vector in ; in: is the column vector in the measurement matrix most relevant to the k-th residual vector, λ k is the position number of the kth non-zero element.

10. The device according to claim 9, characterized in that The kth residual vector satisfies the following formula: Among them, r k is the kth residual vector, r k-1 is the k-1th residual vector, and y is the discretized received signal vector.

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