DRM signal external radiation source radar echo processing method adopting compressed sensing algorithm

Abstract

The invention discloses a DRM signal external radiation source radar echo processing method adopting a compressed sensing algorithm. The DRM signal external radiation source radar echo processing method comprises the following steps: step 1, establishing a mathematical model of a problem to be solved; step 2, obtaining a received signal sequence; step 3, constructing a replica signal dictionary matrix; step 5, solving an L1 norm constraint problem by adopting a near-end gradient algorithm; step 6, calculating a gradient vector; step 7, calculating a near-end operator; step 8, updating a solution; step 9, judging whether the solution is finished or not; step 10, converting the final solution into an RD diagram. The method disclosed by the invention is moderate in calculation amount, has the advantages of high calculation precision and stable performance, and has positive effects on subsequent target detection and other processing.

Description

Technical Field

[0001] The invention belongs to the field of radar signal processing, and in particular relates to a method for processing radar echoes of external radiation sources of DRM (Digital Radio Mondiale, global digital broadcasting) signals in the field. Background Art

[0002] The article "Super-Resolution Delay-Doppler Estimation for OFDM Passive Radar" discloses a method for processing OFDM (Orthogonal Frequency Division Multiplexing) signal external radiation source radar echo using a compressed sensing (Compressed Sensing, CS) algorithm with an atomic norm (Atomic Norm, AN). The method is to construct a frequency domain model of the external radiation source radar echo signal, use the atomic norm to solve the compressed sensing equation, and thus obtain the RD map (Range Doppler Map, RDM) of the radar echo signal. The disadvantage is that the echo signal model is approximated in the frequency domain, and the solution calculation is very large.

[0003] The article "Exogenous Radar Target Detection Based on Compressed Sensing" discloses an exogenous radar target detection method using a compressed sensing algorithm using the OMP (Orthogonal Matching Pursuit) algorithm. The method constructs a time domain mutual ambiguity function model of the exogenous radar echo signal, uses the OMP algorithm to solve the compressed sensing equation, and thus obtains the RD diagram of the radar echo signal. The disadvantage is that the calculation accuracy is not high and the performance is unstable. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a method for processing radar echoes of external radiation sources of DRM signals with moderate computational complexity, high computational accuracy and stable performance.

[0005] The present invention adopts the following technical solution:

[0006] A method for processing radar echoes from external radiation sources of DRM signals using a compressed sensing algorithm, the improvement of which is that it comprises the following steps:

[0007] Step 1: Establish a mathematical model of the problem to be solved:

[0008]

[0009] In the above formula, is the estimation result, α is a sparse vector, r is the received signal sequence, X is the replica signal dictionary matrix, is the square of the 2-norm, γ is a constant, ||·||1 represents the L1 norm of the vector, for a K-dimensional vector x=[x0,x1,…,x K-1 ] T , its L1 norm is defined as:

[0010]

[0011] Step 2: Get the received signal sequence:

[0012] Get the received signal sequence r and write it in the form of a K×1 vector;

[0013] Step 3, construct the replica signal dictionary matrix:

[0014] Construct the replica signal dictionary matrix X, X is a K×M D N R The matrix, M D is the number of search points in the Doppler-frequency dimension, N R is the number of search points in the distance-delay dimension, and each column has the following form:

[0015]

[0016] In the above formula, s is a K×1 vector consisting of a time domain transmission signal sequence, k = 0, 1, ..., K-1, s(kn) is a replica signal sequence of s delayed by n sampling points, n = 0, 1, ..., N R -1,f m To search for Doppler frequency deviation, m = 0, 1, ..., M D -1, T s is the sampling interval, F s is the sampling frequency;

[0017] Step 4, setting the weighting factor γ;

[0018] Step 5: Use the proximal gradient algorithm to solve the L1 norm constraint problem:

[0019] Let the initial solution be α 0 =0, and set the update step size η;

[0020] Step 6, calculate the gradient vector:

[0021]

[0022] Then the gradient vector of the lth iteration is:

[0023]

[0024] Step 7, calculate the proximal operator:

[0025] Let prox(·) represent the proximal operator, which is defined as:

[0026] prox(x)=(|x|-μ)sign(x)(|x|>μ)

[0027]

[0028] So there is another form of prox(x):

[0029]

[0030] In the above formula, μ is the update step length η, (|x|>μ) is an indicator expression, which is 1 when the conditions in the brackets are met, and 0 when the conditions in the brackets are not met;

[0031] make: μ=η,calculate prox(x l ):

[0032] prox(x l )=(|x l |-μ)sign(x l )(|x l |>μ)

[0033]

[0034] Step 8, update the solution α:

[0035] α l+1 =prox(x l )

[0036] Step 9, determine whether the solution is completed:

[0037] Set the iteration stop condition. When the iteration stop condition is met, the iteration process ends and the solution ends. When the iteration stop condition is not met, go to step 6 and continue the iteration process.

[0038] Step 10, convert the final solution into RD diagram:

[0039] According to the one-to-one correspondence between each element in the final solution α and the distance dimension and Doppler dimension coordinates on the RD map, the equivalent conversion between α and the RD map is realized.

[0040] Furthermore, in step 9, the iteration stopping condition is that the difference between the results of the previous and next two iterations is less than a certain threshold value.

[0041] The beneficial effects of the present invention are:

[0042] The method disclosed in the present invention has the advantages of moderate computational complexity, high computational accuracy and stable performance, and has a positive effect on subsequent target detection and other processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic flow diagram of the method of the present invention;

[0044] Figure 2 is the RD diagram of the transformation of Example 1;

[0045] Figure 3 This is the RD diagram of the transformation of Example 2. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0047] Embodiment 1, this embodiment discloses a method for processing radar echoes of external radiation sources of DRM signals using a compressed sensing algorithm, such as Figure 1 As shown, the following steps are included:

[0048] Step 1: Establish a mathematical model of the problem to be solved:

[0049] The mathematical model of the problem to be solved can be described as a convex optimization problem with L1 norm constraints:

[0050]

[0051] In the above formula, is the estimation result, α is a sparse vector, r is the received signal sequence, X is the replica signal dictionary matrix, is the square of the 2-norm, γ is a constant, ||·||1 represents the L1 norm of the vector, for a K-dimensional vector x=[x0,x1,…,x K-1 ] T , its L1 norm is defined as:

[0052]

[0053] Step 2: Get the received signal sequence:

[0054] Get the received signal sequence r and write it in the form of a K×1 vector; where K=9*15*1280=172800;

[0055] Step 3, construct the replica signal dictionary matrix:

[0056] Construct the replica signal dictionary matrix X, X is a K×MD N R The matrix, M D =375, is the number of search points in the Doppler-frequency dimension, N R =1024 is the number of search points in the distance-delay dimension, and each column has the following form:

[0057]

[0058] In the above formula, s is a K×1 vector consisting of a time domain transmitted signal sequence (known or reconstructed reference signal), k = 0, 1, ..., K-1, s(kn) is a replica signal sequence of s delayed by n sampling points, n = 0, 1, ..., N R -1,f m To search for Doppler frequency deviation, the unit is Hz, m = 0, 1, ..., M D -1, T s is the sampling interval, F s is the sampling frequency, F s =48kHz;

[0059] Step 4, set the weighting factor γ = 0.18905; γ determines the estimation result The larger the value of γ, the greater the weight of the sparsity of the target variable in the solution process, and the higher the sparsity of the result.

[0060] Step 5: Use the Proximal Gradient (PG) algorithm to solve the L1 norm constraint problem:

[0061] The proximal gradient algorithm is an iterative solution process, which first requires parameter initialization.

[0062] Let the initial solution be α 0 =0. To ensure convergence, the update step size η is usually very small. Here, the update step size η is set to 1.0×10 -4 =0.0001;

[0063] Step 6, calculate the gradient vector:

[0064]

[0065] Then the gradient vector of the lth iteration is:

[0066]

[0067] Step 7, calculate the proximal operator:

[0068] Let prox(·) represent the proximal operator, which is defined as:

[0069] prox(x)=(|x|-μ)sign(x)(|x|>μ)

[0070]

[0071] So there is another form of prox(x):

[0072]

[0073] In the above formula, μ is the update step length η, (|x|>μ) is an indicator expression, which is 1 when the conditions in the brackets are met, and 0 when the conditions in the brackets are not met;

[0074] make: μ=η,calculate prox(x l ):

[0075] prox(x l )=(|x l |-μ)sign(x l )(|x l |>μ)

[0076]

[0077] Step 8, update the solution α:

[0078] α l+1 =prox(x l )

[0079] Step 9, determine whether the solution is completed:

[0080] Set the iteration stop condition to be that the difference between the results of the previous and next two iterations is less than a certain threshold value. When the iteration stop condition is met, it is considered that the iteration process has converged, the iteration process and the solution are terminated and the process goes to step 10; when the iteration stop condition is not met, go to step 6 and continue the iteration process;

[0081] Step 10, convert the final solution into RD diagram:

[0082] According to the one-to-one correspondence between each element in the final solution α and the range dimension (Range dimension) and Doppler dimension coordinates on the RD map, the equivalent conversion between α and the RD map is realized. The converted RD map is as follows Figure 2 shown.

[0083] Embodiment 2: This embodiment discloses a method for processing radar echoes of external radiation sources of DRM signals using a compressed sensing algorithm, comprising the following steps:

[0084] Step 1: Establish a mathematical model of the problem to be solved:

[0085]

[0086] In the above formula, is the estimation result, r is the received signal sequence, X is the replica signal dictionary matrix, γ is a constant, and ||·||1 represents the L1 norm of the vector. For a K-dimensional vector x=[x0,x1,…,x K-1 ] T , its L1 norm is defined as:

[0087]

[0088] Step 2: Get the received signal sequence:

[0089] Get the received signal sequence r and write it in the form of a K×1 vector; where K=9*15*1280=172800;

[0090] Step 3, construct the replica signal dictionary matrix:

[0091] Construct the replica signal dictionary matrix X, X is a K×M D N R The matrix, M D =375, is the number of search points in the Doppler-frequency dimension, N R =1024 is the number of search points in the distance-delay dimension, and each column has the following form:

[0092]

[0093] In the above formula, s is a K×1 vector consisting of a time domain transmitted signal sequence (known or reconstructed reference signal), k = 0, 1, ..., K-1, s(kn) is a replica signal sequence of s delayed by n sampling points, n = 0, 1, ..., N R -1,f m To search for Doppler frequency deviation, the unit is Hz, m = 0, 1, ..., M D -1, T s is the sampling interval, F s is the sampling frequency, F s =48kHz;

[0094] Step 4, set the weighting factor γ = 0.094525;

[0095] Step 5: Use the Proximal Gradient (PG) algorithm to solve the L1 norm constraint problem:

[0096] The proximal gradient algorithm is an iterative solution process, which first requires parameter initialization.

[0097] Let the initial solution be α 0 =0, and set the update step size η = 1.0×10 -4 =0.0001;

[0098] Step 6, calculate the gradient vector:

[0099]

[0100] Then the gradient vector of the lth iteration is:

[0101]

[0102] Step 7, calculate the proximal operator:

[0103] Let prox(·) represent the proximal operator, which is defined as:

[0104] prox(x)=(|x|-μ)sign(x)(|x|>μ)

[0105]

[0106] So there is another form of prox(x):

[0107]

[0108] In the above formula, μ is the update step length η, (|x|>μ) is an indicator expression, which is 1 when the conditions in the brackets are met, and 0 when the conditions in the brackets are not met;

[0109] make: μ=η,calculate prox(x l ):

[0110] prox(x l )=(|x l |-μ)sign(x l )(|x l |>μ)

[0111]

[0112] Step 8, update the solution α:

[0113] α l+1 =prox(x l )

[0114] Step 9, determine whether the solution is completed:

[0115] Set the iteration stop condition to be that the difference between the results of the previous and next two iterations is less than a certain threshold value. When the iteration stop condition is met, it is considered that the iteration process has converged, the iteration process and the solution are terminated and the process goes to step 10; when the iteration stop condition is not met, go to step 6 and continue the iteration process;

[0116] Step 10, convert the final solution into RD diagram:

[0117] According to the one-to-one correspondence between each element in the final solution α and the Range dimension and Doppler dimension coordinates on the RD map, the equivalent conversion between α and the RD map is realized. The converted RD map is as follows: Figure 3 shown.

Claims

1. A method for processing radar echoes from external radiation sources of DRM signals using a compressed sensing algorithm, characterized in that: The steps include: Step 1: Establish a mathematical model of the problem to be solved: In the above formula, is the estimation result, α is a sparse vector, r is the received signal sequence, X is the replica signal dictionary matrix, is the square of the 2-norm, γ is a constant, ||·||1 represents the L1 norm of the vector, for a K-dimensional vector x=[x0,x1,…,x K-1 ] T , its L1 norm is defined as: Step 2: Get the received signal sequence: Get the received signal sequence r and write it in the form of a K×1 vector; Step 3, construct the replica signal dictionary matrix: Construct the replica signal dictionary matrix X, X is a K×M D N R The matrix, M D is the number of search points in the Doppler-frequency dimension, N R is the number of search points in the distance-delay dimension, and each column has the following form: In the above formula, s is a K×1 vector consisting of a time domain transmission signal sequence, k = 0, 1, ..., K-1, s(kn) is a replica signal sequence of s delayed by n sampling points, n = 0, 1, ..., N R -1,f m To search for Doppler frequency deviation, m = 0, 1, ..., M D -1, T s is the sampling interval, F s is the sampling frequency; Step 4, setting the weighting factor γ; Step 5: Use the proximal gradient algorithm to solve the L1 norm constraint problem: Let the initial solution be α 0 =0, and set the update step size η; Step 6, calculate the gradient vector: Then the gradient vector of the lth iteration is: Step 7, calculate the proximal operator: Let prox(·) represent the proximal operator, which is defined as: prox(x)=(|x|-μ)sign(x)(|x|>μ) So there is another form of prox(x): In the above formula, μ is the update step length η, (|x|>μ) is an indicator expression, which is 1 when the conditions in the brackets are met, and 0 when the conditions in the brackets are not met; make: μ=η,calculate prox(x l ): prox(x l )=(|x l |-μ)sign(x l )(|x l |>μ) Step 8, update the solution α: α l+1 =prox(x l ) Step 9, determine whether the solution is completed: Set the iteration stop condition. When the iteration stop condition is met, the iteration process ends and the solution ends. When the iteration stop condition is not met, go to step 6 and continue the iteration process. Step 10, convert the final solution into RD diagram: According to the one-to-one correspondence between each element in the final solution α and the distance dimension and Doppler dimension coordinates on the RD map, the equivalent conversion between α and the RD map is realized.

2. The method for processing radar echoes from external radiation sources of DRM signals using a compressed sensing algorithm according to claim 1, characterized in that: In step 9, the iteration stopping condition is that the difference between the results of the previous and next two iterations is less than a certain threshold value.

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