CN111046329A - Frequency hopping signal block sparse Bayesian reconstruction method based on edge maximum likelihood - Google Patents

Frequency hopping signal block sparse Bayesian reconstruction method based on edge maximum likelihood Download PDF

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CN111046329A
CN111046329A CN201911257576.5A CN201911257576A CN111046329A CN 111046329 A CN111046329 A CN 111046329A CN 201911257576 A CN201911257576 A CN 201911257576A CN 111046329 A CN111046329 A CN 111046329A
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刘乃安
王赐
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Xidian University
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Abstract

The invention provides a frequency hopping signal block sparse Bayesian reconstruction method based on edge maximum likelihood, belongs to the field of signal processing, and is used for solving the problem of high time complexity of the existing frequency hopping signal block sparse Bayesian reconstruction method, and the realization steps are as follows: compressing the frequency hopping signal X; initializing the segmentation number g; acquiring a frequency hopping signal X and a compressed frequency hopping signal y represented by a signal block; constructing a covariance matrix gamma B of the frequency hopping signal X; constructing an identity matrix I and a {0,1} Bernoulli matrix phi and splitting; construction of a cost function L (A) based on edge maximum likelihoodi) (ii) a And acquiring a block sparse Bayesian reconstruction result of the frequency hopping signal X. The invention optimizes the cost function of the block sparse Bayesian reconstruction method by the edge maximum likelihood method, thereby reducing the time complexity.

Description

Frequency hopping signal block sparse Bayesian reconstruction method based on edge maximum likelihood
Technical Field
The invention belongs to the technical field of signal processing, relates to a frequency hopping signal compressed sensing reconstruction method, and particularly relates to a frequency hopping signal block sparse Bayesian reconstruction method based on edge maximum likelihood, which can be used for compressed sensing reconstruction of frequency hopping signals in a Gaussian white noise environment.
Background
The frequency hopping signal is a non-stationary signal whose carrier frequency is controlled by pseudo-random sequence, and has the advantages of low interception, anti-interference and easy networking, etc., and can be extensively used. The working bandwidth of the frequency hopping signal is wide, the frequency hopping signal is sampled by using the traditional Nyquist sampling frequency, the problems of high sampling frequency and massive data processing are caused, and the frequency hopping signal is a signal with sparse frequency domain, so that the compressed sensing technology can be applied to the sampling and processing of the frequency hopping signal. The compressed sensing reconstruction of the frequency hopping signal is a key link of the compressed sensing technology of the frequency hopping signal, so that the research on the compressed sensing reconstruction method of the frequency hopping signal is of great significance.
At present, the frequency hopping signal compression sensing reconstruction methods researched at home and abroad mainly comprise 3 types: convex relaxation, greedy, non-convex relaxation. The convex relaxation algorithm can convert a non-convex problem into a convex optimization problem to solve, and has high computational complexity, wherein the most common convex relaxation algorithm is a basis tracking algorithm. The greedy algorithm core idea is that atoms most relevant to a received signal are selected one by one to form an original subset of the received signal, so that the received signal is represented as a linear combination of the atom set, including an OMP algorithm, a CoSaMP algorithm, an ROMP algorithm and the like, the calculation complexity is low, but prior information such as sparsity K of the signal to be reconstructed needs to be known, the prior information cannot be obtained in advance, and the reconstruction accuracy is poor generally. The third non-convex algorithm is divided into two parts, one is a reconstruction algorithm based on a Bayesian framework, and the other is a combination algorithm. The reconstruction algorithm based on the Bayesian framework has the advantages that the relevant knowledge of signal processing is introduced, and the prior information of the signals is considered, so that the reconstruction accuracy is higher, but the defect of higher algorithm complexity exists. The combination algorithm is currently applied in a small amount of research. A typical algorithm in the bayesian framework based reconstruction algorithm is a sparse bayesian reconstruction algorithm. The compression reconstruction precision and the calculation efficiency of the frequency hopping signal are equally important.
The sparse Bayesian reconstruction algorithm is one of signal reconstruction algorithms based on Bayesian frameworks, the idea of the sparse Bayesian reconstruction algorithm can be traced back to the early work of MacKay and Williams at the earliest, the algorithm is summarized and analyzed by Michel tilting, and the concept of sparse Bayesian reconstruction is put forward for the first time. The block sparse Bayesian reconstruction algorithm is developed based on a sparse Bayesian reconstruction algorithm, is originally proposed in 2012 by Zhang Chilean, and is innovative in that the block sparsity and correlation structure information of signals are utilized, and the block sparse Bayesian reconstruction algorithm has the defects of low calculation efficiency and difficulty in reconstructing signals with larger dimensions.
A typical improvement for block sparse bayesian reconstruction algorithms is an iterative update to obtain the hyperparametric vector using an expectation-maximization criterion, such as: the application publication number is CN 107703477A, the name is a patent application of a quasi-stationary broadband array signal direction of arrival estimation method based on block sparse Bayesian learning, and discloses a quasi-stationary broadband array signal direction of arrival estimation method based on block sparse Bayesian learning. However, the method has the disadvantage that the iterative updating formula for obtaining the hyperparameter vector by using the expectation maximization criterion has the characteristic of poor calculation efficiency, and is equally important for the compression reconstruction precision and the calculation efficiency of the frequency hopping signal.
Disclosure of Invention
The invention aims to provide a frequency hopping signal block sparse Bayesian reconstruction method based on edge maximum likelihood aiming at overcoming the defects of the prior art, and aims to improve the reconstruction speed while ensuring the same reconstruction precision of the frequency hopping signal after compressed sensing reconstruction.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:
(1) compressing the frequency hopping signal X:
compressing the frequency hopping signal X with the dimension of W based on a compressed sensing method to obtain a compressed frequency hopping signal y with the dimension of M, wherein W is more than 200, and W is more than M and more than 50;
(2) initializing segmentation number g:
initializing the segmentation number g, wherein 10> g >1, and g can be divided by M;
(3) acquiring a frequency hopping signal X and a compressed frequency hopping signal y represented by a signal block:
the compressed frequency hopping signal y is segmented into g frequency hopping signal blocks with equal length, and the compressed frequency hopping signal y is expressed as y ═ y1,y2,...,yi,...,ygDenotes the frequency hopping signal X as X ═ X at the same time1,X2,...,Xi,...,XgIn which yiFor the ith compressed frequency-hopping signal block, XiIs yiA corresponding frequency hopping signal block;
(4) constructing a covariance matrix gamma B of the frequency hopping signal X:
(4a) constructing a correlation coefficient matrix gamma of the frequency hopping signal X, wherein gamma is [ gamma ═ gamma [ [ gamma ]1,γ2,...,γi,...,γg]，γiFor the ith frequency hopping signal block XiCorrelation structure information of (1);
(4b) by gammaiAnd the ith frequency hopping signal block XiInner correlation structure matrix BiConstructing the ith frequency hopping signal block XiOf the covariance matrix gammaiBiObtaining the covariance matrix gamma B ═ gamma of the frequency hopping signal X1B1,γ2B2,...,γiBi,...,γgBg]；
(5) Constructing an identity matrix I and a {0,1} Bernoulli matrix phi and splitting:
dividing an identity matrix I with dimension W into g identity matrix blocks by columns, wherein I is [ I ═ I1,I2,...,Ii,...,Ig]Simultaneously, the {0,1} Bernoulli matrix phi with dimension of M multiplied by W is divided into g {0,1} Bernoulli matrix blocks according to columns, phi [ [ phi ] ]1,Φ2,...,Φi,...,Φg]Wherein, IiFor the ith identity matrix block, phiiIs the ith {0,1} Bernoulli matrix block;
(6) construction of a cost function L (A) based on edge maximum likelihoodi)：
Figure BDA0002310709900000031
Wherein A isiRepresenting the ith hop signal block XiThe log (-) represents the logarithm operation of the base 2, and the parameter
Figure BDA0002310709900000032
Parameter(s)
Figure BDA0002310709900000033
Figure BDA0002310709900000034
Is phiiTranspose of (2), β-1In order to observe the variance of the noise,
Figure BDA0002310709900000035
is qiTransposing;
(7) obtaining a block sparse Bayesian reconstruction result of a frequency hopping signal X:
(7a) let the iteration number be T, the maximum iteration number be T, T is 10, and the correlation coefficient matrix reconstruction error be η is 10-4And let t be 0, gamma be 2]，
Figure BDA0002310709900000036
Wherein | · | purple sweet2L of y2A norm;
(7b) calculating a cost function L (A)i) Parameter s iniAnd q isiThe value of (c):
Figure BDA0002310709900000037
Figure BDA0002310709900000038
(7c) according to siAnd q isiValue of (a) to calculate a frequency hopping signal Xith frequency hopping signal block XiRelated structural constraint of AiObtaining the relevant structural constraint A of X:
Figure BDA0002310709900000041
A＝[A1,A2,...,Ai,...,Ag]；
(7d) computing the average correlation structure constraint of X
Figure BDA0002310709900000042
(7e) According to AiAnd
Figure BDA0002310709900000043
calculating a cost function difference value delta L (i) to obtain a cost function difference value set delta L, wherein:
Figure BDA0002310709900000044
ΔL＝{ΔL(1),ΔL(2),...,ΔL(i),...,ΔL(g)}；
(7f) obtaining a sequence number j in the delta L (j) by selecting a cost function difference value delta L (j) min delta L with the minimum value in the delta L;
(7g) according to the sequence number j, at γnewIn selection
Figure BDA0002310709900000045
And selecting B from BjAnd then obtain
Figure BDA0002310709900000046
According to
Figure BDA0002310709900000047
Updating the covariance matrix γ B of the hopping signal X:
Figure BDA0002310709900000048
(7h) calculating and reconstructing a frequency hopping signal f according to the gamma B, and judging t<10 or
Figure BDA0002310709900000049
If yes, taking f as a block sparse Bayesian reconstruction result of the frequency hopping signal X, otherwise, executing the step (7 i);
(7i) according to gammai newAnd BiCalculating a cost function L (A)i) Parameter s iniAnd q isiLet t be t +1 and γ be γnewAnd step (7c) is performed.
Compared with the prior art, the invention has the following advantages:
the invention reconstructs the cost function of a block sparse Bayes reconstruction method based on an edge maximum likelihood method, so that the cost function is only related to the related structure constraint of a corresponding frequency hopping signal block, obtains a cost function difference value set by calculating the related structure constraint and the average related structure constraint of a frequency hopping signal, selects the minimum one from the cost function difference value set, updates the covariance matrix of the frequency hopping signal according to the selected subscript, updates only the selected subscript by the covariance matrix of the frequency hopping signal, does not completely update, and greatly improves the calculation efficiency when the updated covariance matrix is used for calculating the reconstructed frequency hopping signal and calculating the related structure constraint of the frequency hopping signal block.
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FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a simulation comparison graph of reconstruction accuracy and reconstruction efficiency after compression reconstruction of a frequency hopping signal using the present invention and the existing sparse Bayesian reconstruction algorithm for frequency hopping signal blocks based on the expectation-maximization criterion;
detailed description of the invention
The invention is described in detail below with reference to the following figures and specific examples:
referring to fig. 1, a multi-channel compression reconstruction method based on the bayesian reconstruction principle includes the following steps:
step 1) compressing the frequency hopping signal X:
compressing the frequency hopping signal X with the dimension of W based on a compressed sensing method to obtain a compressed frequency hopping signal y with the dimension of M, wherein W is more than 200, and W is more than M and more than 50;
step 2), initializing the segmentation number g:
initializing the segmentation number g, wherein 10> g >1, and g can be divided by M;
step 3) acquiring the frequency hopping signal X and the compressed frequency hopping signal y represented by the signal block:
the compressed frequency hopping signal y is segmented into g frequency hopping signal blocks with equal length, and the compressed frequency hopping signal y is expressed as y ═ y1,y2,...,yi,...,ygDenotes the frequency hopping signal X as X ═ X at the same time1,X2,...,Xi,...,XgIn which yiFor the ith compressed frequency-hopping signal block, XiIs yiA corresponding frequency hopping signal block;
step 4), constructing a covariance matrix gamma B of the frequency hopping signal X:
step 4a) constructing a correlation coefficient matrix gamma of the frequency hopping signal X, wherein gamma is [ gamma ═ gamma [ [ gamma ]1,γ2,...,γi,...,γg]，γiFor the ith frequency hopping signal block XiCorrelation structure information of (1);
step 4b) by gammaiAnd the ith frequency hopping signal block XiInner correlation structure matrix BiConstructing the ith frequency hopping signal block XiOf the covariance matrix gammaiBiObtaining the covariance matrix gamma B ═ gamma of the frequency hopping signal X1B1,γ2B2,...,γiBi,...,γgBg]；
Step 5), constructing an identity matrix I and a {0,1} Bernoulli matrix phi and segmenting:
dividing an identity matrix I with dimension W into g identity matrix blocks by columns, wherein I is [ I ═ I1,I2,...,Ii,...,Ig]Simultaneously, the {0,1} Bernoulli matrix phi with dimension of M multiplied by W is divided into g {0,1} Bernoulli matrix blocks according to columns, phi [ [ phi ] ]1,Φ2,...,Φi,...,Φg]Wherein, IiFor the ith identity matrix block, phiiIs the ith {0,1} Bernoulli matrix block;
step 6)Construction of a cost function L (A) based on edge maximum likelihoodi)：
Figure BDA0002310709900000062
Wherein A isiRepresenting the ith hop signal block XiThe log (-) represents the logarithm operation of the base 2, and the parameter
Figure BDA0002310709900000063
Parameter(s)
Figure BDA0002310709900000064
Figure BDA0002310709900000065
Is phiiTranspose of (2), β-1In order to observe the variance of the noise,
Figure BDA0002310709900000066
is qiTransposing;
step 7), acquiring a block sparse Bayesian reconstruction result of the frequency hopping signal X:
step 7a) sets the iteration number as T, the maximum iteration number as T, T is 10, and the reconstruction error of the correlation coefficient matrix is η is 10-4And let t be 0, gamma be 2]，
Figure BDA0002310709900000067
Wherein | · | purple sweet2L of y2A norm;
step 7b) calculating a cost function L (A)i) Parameter s iniAnd q isiThe value of (c):
Figure BDA0002310709900000068
Figure BDA0002310709900000069
step 7c) according to siAnd q isiValue of (a) to calculate a frequency hopping signal Xith frequency hopping signal block XiRelated structural constraint of AiObtaining the relevant structural constraint A of X:
Figure BDA00023107099000000610
A＝[A1,A2,...,Ai,...,Ag]；
step 7d) calculating the average correlation structure constraint of X
Figure BDA00023107099000000611
Step 7d1) according to AiCalculating the ith frequency hopping signal block X of the frequency hopping signal XiNovel correlation structure information gammai newObtaining a new phase relation number matrix gamma of Xnew：
Figure BDA0002310709900000061
γnew＝[γ1 new,γ2 new,...,γi new,...,γg new]
Wherein, Tr (A)i) Representation pair matrix AiSumming all the characteristic values;
step 7d2) according to γi newCalculating the ith frequency hopping signal block X of the frequency hopping signal XiInner correlation structure matrix BiObtaining a correlation structure matrix B of X:
Figure BDA0002310709900000071
B＝[B1,B2,...,Bi,...,Bg]；
step 7d3) according to BiCalculating the ith frequency hopping signal block X of the frequency hopping signal XiAverage correlation structure constraint of
Figure BDA0002310709900000074
Obtaining an average correlation structure constraint of X
Figure BDA0002310709900000075
Figure BDA0002310709900000072
Figure BDA0002310709900000073
Wherein, Tr (B)i) Representation pair matrix BiIs summed up.
Step 7e) according to AiAnd
Figure BDA0002310709900000076
calculating a cost function difference value delta L (i) to obtain a cost function difference value set delta L, wherein:
Figure BDA0002310709900000077
ΔL＝{ΔL(1),ΔL(2),...,ΔL(i),...,ΔL(g)}；
step 7f), selecting a cost function difference value Δ L (j) min Δ L with the minimum value in Δ L to obtain a sequence number j in Δ L (j);
step 7g) according to the sequence number j, at γnewIn selection
Figure BDA0002310709900000078
And selecting B from BjAnd then obtain
Figure BDA0002310709900000079
According to
Figure BDA00023107099000000710
Updating the covariance matrix γ B of the hopping signal X:
Figure BDA00023107099000000711
step 7h) calculating and reconstructing a frequency hopping signal f according to gamma B, and judging t<10 or
Figure BDA00023107099000000712
And if so, taking f as a block sparse Bayesian reconstruction result of the frequency hopping signal X, otherwise, executing the step 7 i):
f＝((γB)-1+ΦTβΦ)-1ΦTβy
step 7i) according to γi newAnd BiCalculating a cost function L (A)i) Parameter s iniAnd q isiLet t be t +1 and γ be γnewAnd performing step 7 c):
Figure BDA0002310709900000082
Figure BDA0002310709900000083
the technical effects of the present invention will be described below with reference to simulation experiments.
1. Simulation conditions and contents:
in the simulation experiment, the signal-to-interference ratio is taken as a technical index of the precision of a weighing algorithm, and the mathematical definition of the signal-to-interference ratio is as follows:
Figure BDA0002310709900000081
where x represents a frequency hopping signal and where,
Figure BDA0002310709900000084
representing the reconstructed signal in the time domain.
The simulation parameters are set as follows: the method comprises the steps that frequency hopping signals with frequency sets of {1.8,1.4,2.1,2.4,2.7,3.0 and 3.3} MHz, hopping speed of 2000 hops/s, code speed of 50Kbit/s and length of 30000 points are subjected to compression sampling to serve as input signals, a random demodulation sampling structure is adopted in a compression sampling method, a measurement matrix is a {0,1} Bernoulli matrix, a sparse basis is a Fourier basis, a compression ratio is 5, and Matlab is used for carrying out simulation comparison on reconstruction accuracy and reconstruction efficiency after compressed frequency hopping signals are reconstructed by using the method and an existing sparse Bayesian reconstruction algorithm based on an expectation-maximization criterion frequency hopping signal block, and the result is shown in figure 2;
2. and (3) simulation result analysis:
referring to fig. 2(a), this embodiment compares the signal-to-interference ratio of the present invention with the signal-to-noise ratio of the existing prior art frequency hopping signal block sparse bayesian reconstruction algorithm based on the expectation-maximization criterion. The abscissa in fig. 2(a) represents the signal-to-noise ratio and the ordinate represents the signal-to-interference ratio. In fig. 2(a), the curve with x-dots represents the variation curve of the signal-to-interference ratio with the signal-to-noise ratio of the present invention, and the curve with x-dots represents the variation curve of the signal-to-interference ratio with the signal-to-noise ratio of the sparse bayesian reconstruction algorithm for the frequency hopping signal block based on the expectation-maximization criterion.
As can be seen from fig. 2 (a): with the increase of the signal-to-noise ratio, the signal-to-interference ratio of the two algorithms is gradually increased, and the reconstruction accuracy of the signal is better and better. Under the condition of the same signal-to-noise ratio, the signal-to-interference ratio of the method is not much different from a sparse Bayesian reconstruction algorithm of a frequency hopping signal block based on an expectation maximization criterion.
Referring to fig. 2(b), this embodiment compares the variation of the single simulation time with the signal-to-noise ratio of the present invention with the existing sparse bayesian reconstruction algorithm based on the expectation-maximization criterion for the frequency hopping signal block. The abscissa in fig. 2(b) represents the signal-to-noise ratio, and the ordinate represents the single simulation time. In fig. 2(b), the curve connected by o represents the variation curve of the one-shot simulation time with the signal-to-noise ratio of the present invention, and the curve connected by + represents the variation curve of the one-shot simulation time with the signal-to-noise ratio of the sparse bayesian reconstruction algorithm of the frequency hopping signal block based on the expectation-maximization criterion.
As can be seen from fig. 2 (b): the single simulation time of the invention is greatly superior to the single simulation time of the sparse Bayesian reconstruction algorithm of the frequency hopping signal block based on the expectation maximization criterion, the time complexity is reduced, and the reconstruction efficiency is improved.
The 2 results obtained from two simulation experiments show that the frequency hopping signal can be reconstructed with low time complexity and high reconstruction accuracy by using the method of the invention.

Claims (4)

1. A frequency hopping signal block sparse Bayesian reconstruction method based on edge maximum likelihood is characterized by comprising the following steps:
(1) compressing the frequency hopping signal X:
compressing the frequency hopping signal X with the dimension of W based on a compressed sensing method to obtain a compressed frequency hopping signal y with the dimension of M, wherein W is more than 200, and W is more than M and more than 50;
(2) initializing segmentation number g:
initializing the segmentation number g, wherein 10> g >1, and g can be divided by M;
(3) acquiring a frequency hopping signal X and a compressed frequency hopping signal y represented by a signal block:
the compressed frequency hopping signal y is segmented into g frequency hopping signal blocks with equal length, and the compressed frequency hopping signal y is expressed as y ═ y1,y2,...,yi,...,ygDenotes the frequency hopping signal X as X ═ X at the same time1,X2,...,Xi,...,XgIn which yiFor the ith compressed frequency-hopping signal block, XiIs yiA corresponding frequency hopping signal block;
(4) constructing a covariance matrix gamma B of the frequency hopping signal X:
(4a) constructing a correlation coefficient matrix gamma of the frequency hopping signal X, wherein gamma is [ gamma ═ gamma [ [ gamma ]1,γ2,...,γi,...,γg]，γiFor the ith frequency hopping signal block XiCorrelation structure information of (1);
(4b) by gammaiAnd the ith frequency hopping signal block XiInner correlation structure matrix BiConstructing the ith frequency hopping signal block XiOf the covariance matrix gammaiBiObtaining the covariance matrix gamma B ═ gamma of the frequency hopping signal X1B1,γ2B2,...,γiBi,...,γgBg]；
(5) Constructing an identity matrix I and a {0,1} Bernoulli matrix phi and splitting:
dividing an identity matrix I with dimension W into g by columnsUnit matrix block, I ═ I1,I2,...,Ii,...,Ig]Simultaneously, the {0,1} Bernoulli matrix phi with dimension of M multiplied by W is divided into g {0,1} Bernoulli matrix blocks according to columns, phi [ [ phi ] ]1,Φ2,...,Φi,...,Φg]Wherein, IiFor the ith identity matrix block, phiiIs the ith {0,1} Bernoulli matrix block;
(6) construction of a cost function L (A) based on edge maximum likelihoodi)：
Figure FDA0002310709890000027
Wherein A isiRepresenting the ith hop signal block XiThe log (-) represents the logarithm operation of the base 2, and the parameter si＝Φi T(β-1Ii+ΦiγiBiΦi T)-1ΦiParameter qi＝Φi T(β-1Ii+ΦiγiBiΦi T)-1y，Φi TIs phiiTranspose of (2), β-1In order to observe the variance of the noise,
Figure FDA0002310709890000021
is qiTransposing;
(7) obtaining a block sparse Bayesian reconstruction result of a frequency hopping signal X:
(7a) let the iteration number be T, the maximum iteration number be T, T is 10, and the correlation coefficient matrix reconstruction error be η is 10-4And let t be 0, gamma be 2]，
Figure FDA0002310709890000022
Wherein | · | purple sweet2L of y2A norm;
(7b) calculating a cost function L (A)i) Parameter s iniAnd q isiThe value of (c):
si＝Φi Tβ-1IiΦi
qi＝Φi Tβ-1Iiy；
(7c) according to siAnd q isiValue of (a) to calculate a frequency hopping signal Xith frequency hopping signal block XiRelated structural constraint of AiObtaining the relevant structural constraint A of X:
Figure FDA0002310709890000023
A＝[A1,A2,...,Ai,...,Ag]；
(7d) computing the average correlation structure constraint of X
Figure FDA0002310709890000024
(7e) According to AiAnd
Figure FDA0002310709890000025
calculating a cost function difference value delta L (i) to obtain a cost function difference value set delta L, wherein:
Figure FDA0002310709890000026
ΔL＝{ΔL(1),ΔL(2),...,ΔL(i),...,ΔL(g)}；
(7f) obtaining a sequence number j in the delta L (j) by selecting a cost function difference value delta L (j) min delta L with the minimum value in the delta L;
(7g) according to the sequence number j, at γnewIn selection
Figure FDA0002310709890000031
And selecting B from BjAnd then obtain
Figure FDA0002310709890000032
According to
Figure FDA0002310709890000033
Updating the covariance matrix γ B of the hopping signal X:
Figure FDA0002310709890000034
(7h) calculating and reconstructing a frequency hopping signal f according to the gamma B, and judging t<10 or
Figure FDA0002310709890000035
If yes, taking f as a block sparse Bayesian reconstruction result of the frequency hopping signal X, otherwise, executing the step (7 i);
(7i) according to gammai newAnd BiCalculating a cost function L (A)i) Parameter s iniAnd q isiLet t be t +1 and γ be γnewAnd step (7c) is performed.
2. The sparse Bayesian reconstruction method for frequency-hopping signal blocks based on edge maximum likelihood as claimed in claim 1, wherein the average correlation structure constraint of X in step (7d) is calculated
Figure FDA0002310709890000038
The method comprises the following implementation steps of,
(7d1) according to AiCalculating the ith frequency hopping signal block X of the frequency hopping signal XiNovel correlation structure information gammai newObtaining a new phase relation number matrix gamma of Xnew：
Figure FDA0002310709890000036
γnew＝[γ1 new,γ2 new,...,γi new,...,γg new]
Wherein, Tr (A)i) Representation pair matrix AiSumming all the characteristic values;
(7d2) according to gammai newCalculating the ith frequency hopping signal block X of the frequency hopping signal XiInner correlation structure matrix BiObtaining a correlation structure matrix B of X:
Figure FDA0002310709890000037
B＝[B1,B2,...,Bi,...,Bg]；
(7d3) according to BiCalculating the ith frequency hopping signal block X of the frequency hopping signal XiAverage correlation structure constraint of
Figure FDA0002310709890000041
Obtaining an average correlation structure constraint of X
Figure FDA0002310709890000042
Figure FDA0002310709890000043
Figure FDA0002310709890000044
Wherein, Tr (B)i) Representation pair matrix BiIs summed up.
3. The sparse Bayesian reconstruction method for frequency hopping signal blocks based on edge maximum likelihood as recited in claim 1, wherein the step (7h) is to compute the reconstructed frequency hopping signal f according to γ B by the following formula:
f＝((γB)-1+ΦTβΦ)-1ΦTβy。
4. the sparse Bayesian reconstruction method for frequency hopping signal blocks based on edge maximum likelihood (MLML) as claimed in claim 1, wherein said step (7i) is based on γi newAnd BiComputing generationPrice function L (A)i) Parameter s iniAnd q isiThe calculation formula is as follows:
si＝Φi T(β-1Ii+ΦiγiBiΦi T)-1Φi
qi＝Φi T(β-1Ii+ΦiγiBiΦi T)-1y。
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