CN103886207A - Nest multiple-input and multiple-output radar DOA estimating method based on compressed sensing - Google Patents

Nest multiple-input and multiple-output radar DOA estimating method based on compressed sensing Download PDF

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CN103886207A
CN103886207A CN201410119377.9A CN201410119377A CN103886207A CN 103886207 A CN103886207 A CN 103886207A CN 201410119377 A CN201410119377 A CN 201410119377A CN 103886207 A CN103886207 A CN 103886207A
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廖桂生
杨杰
黄岩
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Xidian University
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Abstract

The invention discloses a nest multiple-input and multiple-output radar DOA estimating method based on compressed sensing. The implementing process includes the steps that (1), an emitting array and a receiving array of a nest multiple-input and multiple-output radar are determined by using an array element layout form of a nest array; (2), each pulse repetition period of the radar is matched with a filtering echo signal; (3), a covariance matrix matched with filtering output data is vectorized; (4), a matrix reconstruction method and singular value decomposition are adopted for obtaining noise subspace; (5), an L1norm bound term and an L2 norm bound term in a sparse recovery problem are constructed; (6), the target DOA is determined by solving the sparse recovery problem. The freedom degree expansion characteristic and the high resolution characteristic of compressed sensing of the nest array are used at the same time, and the estimating method can be used for accurately positioning targets with the number larger than the total number of virtual array elements through the radar.

Description

Based on the nested MIMO radar DOA method of estimation of compressed sensing
Technical field
The invention belongs to communication technical field, further relate to a kind of nested MIMO radar direction of arrival (Direction-of-Arrival DOA) method of estimation based on compressed sensing in Radar Technology field.The present invention can be used for realization number is accurately located more than the target of MIMO radar Virtual array sum.
Background technology
MIMO radar, owing to adopting Orthogonal injection signal formation space diversity, is therefore compared phased-array radar, and degree of freedom is improved in effectively array extending aperture, is conducive to survey multiple goal.The existing technology designing about MIMO radar formation mainly concentrates on evenly and structures the formation, and launch battle array and the next virtual multiple equidistant array element of little spacing reception battle array, thereby the parameter of raising system can identification by large spacing.In the direction of arrival DOA of MIMO radar estimation problem, because compressed sensing is as the efficient sparse signal reconfiguring method of one, can effectively solve the functional limitation that conventional subspace class methods (as MUSIC method, ESPRIT method) exist under fast umber of beats, low signal-to-noise ratio situation less, therefore the direction of arrival DOA method of estimation based on compressed sensing (as JLZA method, SPICE method) is widely used.
Piya Pal and P P Vaidyanathan are at paper " Nested arrays:a novel approach to array processing with enhanced degrees of freedom " (IEEE Transactions on Signal Processing, 2010,58 (8): 4167-4181) a kind of formation method for designing-nested battle array of effectively array extending degree of freedom in system is proposed in.The method is designed one group of nested element position coordinate with accurate closed solutions, utilizes the reception signal covariance matrix of the long-pending form of KR to solve the Parameter Estimation Problem of information source number to be differentiated more than array element number simultaneously, in engineering application, is convenient to realize.The deficiency that the method exists is, only relate to the formation optimization of generic array system, nested formation is not applied in multi-input multi-output radar system, thereby cannot further expand the virtual aperture of multi-input multi-output radar system, and then can not differentiate the target more than MIMO radar Virtual array number.
Beijing University of Post & Telecommunication discloses a kind of reconstructing method of compressed sensing signal in the patent " a kind of reconstructing method of compressed sensing signal " (number of patent application 201210090845.5, publication number CN102624399A) of its application.The method is designed the iterative algorithm that a kind of computational complexity is lower and is carried out Exact recovery sparse signal vector.The concrete steps of the method are: first, calculate through the signal of compressed sensing processing and the inner product of each row of sensing matrix, as the inner product result of iteration for the first time, then judge whether to stop iteration according to the inner product result of this iteration, if do not stop, from the inner product result of this iteration, finding the index value corresponding to element of absolute value maximum, index value is added to index set, calculate the inner product result of next iteration, and enter next iterative process; If stop, the row of the sensing matrix that in current index set, each mutually different index value is corresponding are formed to matrix, and according to the matrix and the described signal reconstruction compressed sensing signal that form.The deficiency that the method exists is, do not make full use of the potential degree of freedom extended attribute of Sparse Array (as minimal redundancy battle array, nested battle array etc.), therefore can not be applied to and owe to determine direction of arrival DOA estimation problem.
Nan Hu, Zhongfu Ye, Xu Xu and Ming Bao are at paper " DOA estimation for sparse array via sparse signal reconstruction " (IEEE Transactions on Aerospace and Electronic Systems, 2013,49 (2): 760-773) a kind of compressed sensing direction of arrival DOA method of estimation that is applicable to nested battle array is proposed in.The method utilizes the reception signal covariance matrix of the long-pending form of Khatri-Rao to construct single vector Sparse Problems of measuring that computational complexity is lower, and solves this problem by associating L1, L2 norm.The method (hereinafter to be referred as L1-L2 method) is applicable to owe to determine direction of arrival DOA estimation problem, and the deficiency of existence is that solving result is prone to pseudo-peak, gives and determines that target true bearing causes difficulty.
Summary of the invention
The object of the invention is to overcome the deficiency of above-mentioned prior art, propose a kind of nested MIMO radar direction of arrival DOA method of estimation based on compressed sensing.
The basic ideas that realize the object of the invention are: utilize the covariance matrix of Khatri-Rao product representation vectorization, obtain the degree of freedom extended attribute of nested battle array; Use the high-resolution characteristic of compression sensing method simultaneously, by the sparse recovery problem of rational structure, accurately estimate the direction of arrival DOA of number more than the target of MIMO radar Virtual array number.
For achieving the above object, specific implementation step of the present invention comprises as follows:
(1) determine transmitting-receiving formation:
(1a) according to the computing formula of nested element position coordinate set, calculate the position coordinates set of nested array element, obtain nested formation;
(1b), according to the computing formula of Virtual array position coordinates set, to the MIMO radar of many groups of different transmitting-receiving formation, the Virtual array position coordinates set of calculating respectively each group of radar, obtains the set of many group Virtual array position coordinateses;
(1c), from the set of many groups Virtual array position coordinates, choose the Virtual array position coordinates set that comprises all nested formation element position coordinates, by the nested transmitting-receiving battle array of the many groups of transmitting-receiving formation composition set corresponding selected multiple virtual battle array;
(1d), from many groups of nested transmitting-receivings gust set, choose the minimum formation of transmitting-receiving array element sum, the transmitting formation using this formation as nested MIMO radar and reception formation.
(2) matched filtering echoed signal:
Within each transponder pulse repetition period of radar, the echoed signal in all reception array element of the nested MIMO radar of matched filtering, obtains matched filtering output vector.
(3) covariance matrix vectorization:
(3a) the matched filtering output vector of each radar transmitted pulse repetition period and its conjugate transpose are multiplied each other, obtain the autocorrelation matrix of each transponder pulse repetition period;
(3b) get the mean value of the autocorrelation matrix of multiple radar transmitted pulse repetition periods, obtain covariance matrix;
(3c) utilize the long-pending distortion of the covariance matrix to vectorization of Khatri-Rao, obtain Khatri-Rao vector;
(3d) remove the redundant row in Khatri-Rao vector, obtain standard K hatri-Rao vector.
(4) burbling noise subspace:
(4a) adopt matrix regrouping method, ask the level and smooth correlation matrix of standard K hatri-Rao vector;
(4b) level and smooth correlation matrix is carried out to svd, obtain the noise subspace being formed by all little eigenwert characteristic of correspondence vectors.
(5) construct sparse recovery problem:
(5a) evaluated error of Khatri-Rao vector is retrained, construct the L2 norm constraint item in sparse recovery problem;
(5b) utilize noise subspace to the weighting of sparse signal vector, construct the L1 norm constraint item in sparse recovery problem;
(5c) meeting under the condition of L2 norm constraint item, minimizing L1 norm constraint item, obtaining sparse recovery problem.
(6) solve target direction of arrival DOA:
The sparse recovery problem of utilizing protruding Optimization Software bag to solve to construct, determines target direction of arrival DOA.
The present invention compared with prior art has the following advantages:
First, the present invention is in to the design process of nested MIMO radar transmitting-receiving formation, use the degree of freedom extended attribute of nested battle array, overcome prior art and cannot differentiate the shortcoming of number more than the target of Virtual array number, the present invention can be differentiated than the more target of traditional MIMO radar.
Second, the present invention has adopted compression sensing method in the estimation procedure of the direction of arrival DOA to target, can make full use of the high-resolution characteristic of sparse signal reconfiguring method, overcome the functional limitation that prior art exists under fast umber of beats, low signal-to-noise ratio situation less, made the present invention can to improve the estimated accuracy of target direction of arrival DOA.
Accompanying drawing explanation
Fig. 1 is process flow diagram of the present invention;
Fig. 2 is the space spectrogram that the present invention estimates 15 target direction of arrival DOA;
Fig. 3 is that the present invention and prior art root-mean-square error that 3 target direction of arrival DOA are estimated is with signal to noise ratio (S/N ratio) change curve.
Embodiment
Below in conjunction with accompanying drawing, the present invention will be further described.
With reference to accompanying drawing 1, concrete steps of the present invention are as follows.
Step 1, determines transmitting-receiving formation.
According to the computing formula of following nested element position coordinate set, calculate the position coordinates set of nested array element, obtain nested formation:
{ x i } = { id } , ( i = 1 , · · · , 0.5 Q ) { ( i - 0.5 Q ) ( 0.5 Q + 1 ) d } , ( i = 1 + 0.5 Q , · · · , Q )
Wherein, x ithe position coordinates that represents i nested array element, d represents the half wavelength of radar emission signal, and Q represents nested array element sum, and { } represents set operation.
According to the computing formula of following Virtual array position coordinates set, to the MIMO radar of many groups of different transmitting-receiving formation, calculate respectively the Virtual array position coordinates of each group of radar, obtain the set of many group Virtual array position coordinateses:
{x m+x n},(m＝1,…,M,n＝1,…,N)
Wherein, x mrepresent the position coordinates of m radar emission array element, x nrepresent that n radar receives the position coordinates of array element, M represents radar emission array element sum, and N represents that radar receives array element sum, and { } represents set operation.
From the set of many groups Virtual array position coordinates, choose the Virtual array position coordinates set that comprises all nested formation element position coordinates, by the nested transmitting-receiving battle array of the many groups of transmitting-receiving formation composition set corresponding selected multiple virtual battle array.
From many groups of nested transmitting-receivings gust set, choose the minimum formation of transmitting-receiving array element sum, the transmitting formation using this formation as nested MIMO radar and reception formation.
Step 2, matched filtering echoed signal.
Within each transponder pulse repetition period of radar, the echoed signal in all reception array element of the nested MIMO radar of matched filtering according to the following formula, obtains matched filtering output vector:
∫ y n ( t ) s m * ( t ) dt
Wherein, y n(t) represent that n radar receives the echoed signal of array element at moment t, n=1,2 ..., N, N represents that radar receives array element sum,
Figure BDA0000483183300000052
represent to m radar emission array element the transmitted waveform complex envelope at moment t, do the conjugation obtaining after complex conjugate operation and transmit, m=1,2 ..., M, M represents radar emission array element sum.
Step 3, covariance matrix vectorization.
The matched filtering output vector of each radar transmitted pulse repetition period and its conjugate transpose are multiplied each other, obtain the autocorrelation matrix of each transponder pulse repetition period.
The mean value of getting the autocorrelation matrix of multiple radar transmitted pulse repetition periods, obtains covariance matrix.
Utilize the long-pending distortion of the covariance matrix to vectorization of Khatri-Rao, obtain according to the following formula Khatri-Rao vector:
Figure BDA0000483183300000053
Wherein, A *represent the array manifold matrix of nested MIMO radar to do complex conjugate operation, the conjugation array manifold matrix obtaining, ⊙ represents to ask the long-pending operation of Khatri-Rao, and g represents target reflection factor vector,
Figure BDA0000483183300000054
represent that radar receives array element noise variance,
Figure BDA0000483183300000055
represent the unit matrix of vectorization.
Remove the redundant row in Khatri-Rao vector, obtain standard K hatri-Rao vector.
Step 4, burbling noise subspace.
Adopt matrix regrouping method, ask the level and smooth correlation matrix of standard K hatri-Rao vector, its concrete steps are:
The first step, using central element as axis of symmetry, is divided into two subvectors by standard K hatri-Rao vector;
Second step, using the central element of standard K hatri-Rao vector as the elements in a main diagonal, using the element in two subvectors adjacent with central element respectively as+1 and-1 diagonal line on element, the rest may be inferred, obtain (N+1) × (N+1) the level and smooth correlation matrix of dimension, wherein, N represents the element number in each subvector.
Level and smooth correlation matrix is carried out to svd, obtain the noise subspace being formed by all little eigenwert characteristic of correspondence vectors.
Step 5, constructs sparse recovery problem.
Error of calculation matrix according to the following formula:
1 P L * ⊗L
Wherein, P represents total number of radar transmitted pulse repetition period, L *represent to decompose the lower triangle battle array obtaining and do complex conjugate operation carried out Cholesky by covariance matrix, triangle battle array under the conjugation obtaining,
Figure BDA0000483183300000066
represent to ask the long-pending operation of Kronecker.
Calculate according to the following formula complete array extending stream shape matrix:
Figure BDA0000483183300000061
Wherein,
Figure BDA0000483183300000062
represent the array extending stream shape matrix of nested MIMO radar to do complex conjugate operation, the Conjugate extended array manifold matrix obtaining, Θ represents to cover the likely discrete angle collection in spatial domain of target azimuth of institute, and ⊙ represents to ask that Khatri-Rao is long-pending operates.
Evaluated error to Khatri-Rao vector retrains, and constructs according to the following formula the L2 norm constraint item in sparse recovery problem:
| | W - 1 ( y - σ v 2 1 → v ) - ( W - 1 A ~ Θ ) g Θ | | 2 ≤ γ
Wherein, W -1represent error matrix to invert and operate the weighting matrix obtaining, y represents Khatri-Rao vector,
Figure BDA0000483183300000064
represent that radar receives array element noise variance,
Figure BDA0000483183300000065
represent the unit matrix of vectorization, represent the complete array extending stream shape matrix of nested MIMO radar, Θ represent to cover the discrete angle collection in spatial domain of target azimuth likely, g Θrepresent sparse signal vector, || || 2represent to get 2 norm operations, γ represents the upper limit threshold of L2 norm constraint item.
Utilize noise subspace to the weighting of sparse signal vector, construct according to the following formula the L1 norm constraint item in sparse recovery problem:
||diag(w)g Θ|| 1
Wherein, diag () represents to ask diagonal matrix operation, and w represents noise subspace weighting matrix, the matrix being obtained as inner product operation by complete array extending stream shape matrix and noise subspace, the weighing vector of asking line by line 2 norms to obtain, g Θrepresent sparse signal vector, Θ represent to cover the discrete angle collection in spatial domain of target azimuth likely, || || 1represent to get 1 norm operation.
Meeting under the condition of L2 norm constraint item, minimizing L1 norm constraint item, obtaining sparse recovery problem.
Step 6, solves target direction of arrival DOA.
The sparse recovery problem of utilizing protruding Optimization Software bag to solve to construct, determines target direction of arrival DOA.
Below by emulation, effect of the present invention is described further.
1. simulated conditions:
Emulation of the present invention is to carry out under the software environment of MATLAB R2010a.
2. emulation content:
The position coordinates of 3 transmitting array elements of nested MIMO radar is respectively: 0,1.5d, and 6.5d, 4 position coordinateses that receive array element are respectively: 0,0.5d, d, 3d.D is the half wavelength of radar emission signal.Total number of radar pulse repetition period is that 300, Monte Carlo experiment number is 300.The direction of arrival DOA that supposes 3 pinpoint targets is respectively :-10.3 °, and 3.2 °, 5.4 °.Direction of arrival DOA estimated performance represents by root-mean-square error, definition root-mean-square error
Figure BDA0000483183300000073
for extraction of square root operation, E is for asking expectation value operation, θ with
Figure BDA0000483183300000072
be respectively direction of arrival DOA actual value and estimated value.
3. simulated effect analysis:
Fig. 2 has provided 15 spatial spectrum curves that pinpoint target direction of arrival DOA estimates.Horizontal ordinate in Fig. 2 represents direction of arrival, ordinate representation space spectral amplitude.In Fig. 2, solid line represents the spatial spectrum curve that direction of arrival DOA method of estimation of the present invention obtains.In Fig. 2, indicate the true direction of arrival DOA that dashdotted curve represents all targets.From Fig. 2,15 of space spectral curve spectrum peaks can be found out, nested MIMO radar can accurately estimate the direction of arrival DOA of number more than the target of Virtual array number.In identical transmitting array number and reception array number situation, tradition MIMO radar distinguishable 11 pinpoint targets at most, and the nested MIMO radar of the present invention's design can improve the degree of freedom of MIMO radar, improve the parameter identifiability of target.
Fig. 3 has provided the change curve of 3 pinpoint target direction of arrival DOA root-mean-square errors with signal to noise ratio (S/N ratio).Horizontal ordinate in Fig. 3 represents signal to noise ratio (S/N ratio), and ordinate represents root-mean-square error.In Fig. 3, represent with the curve of circle the curve that the present invention obtains the estimation root-mean-square error of target direction of arrival DOA.In Fig. 3, represent with square curve the curve that MUSIC method obtains the estimation root-mean-square error of target direction of arrival DOA.In Fig. 3, represent with the curve of plus sige the curve that JLZA method obtains the estimation root-mean-square error of target direction of arrival DOA.In Fig. 3, represent with leg-of-mutton curve the curve that SPICE method obtains the estimation root-mean-square error of target direction of arrival DOA.In Fig. 3, represent with the curve of star the curve that carat Metro lower bound changes with signal to noise ratio (S/N ratio).Five curves in comparison diagram 3 can be found out, under identical state of signal-to-noise, the root-mean-square error that the method for the invention is estimated target direction of arrival DOA is less than existing method, therefore method of the present invention is better than existing method to the estimated performance of target direction of arrival DOA.

Claims (8)

1. the nested MIMO radar DOA method of estimation based on compressed sensing, comprises the steps:
(1) determine transmitting-receiving formation:
(1a) according to the computing formula of nested element position coordinate set, calculate the position coordinates set of nested array element, obtain nested formation;
(1b), according to the computing formula of Virtual array position coordinates set, to the MIMO radar of many groups of different transmitting-receiving formation, the Virtual array position coordinates set of calculating respectively each group of radar, obtains the set of many group Virtual array position coordinateses;
(1c), from the set of many groups Virtual array position coordinates, choose the Virtual array position coordinates set that comprises all nested formation element position coordinates, by the nested transmitting-receiving battle array of the many groups of transmitting-receiving formation composition set corresponding selected multiple virtual battle array;
(1d), from many groups of nested transmitting-receivings gust set, choose the minimum formation of transmitting-receiving array element sum, the transmitting formation using this formation as nested MIMO radar and reception formation;
(2) matched filtering echoed signal:
Within each transponder pulse repetition period of radar, the echoed signal in all reception array element of the nested MIMO radar of matched filtering, obtains matched filtering output vector;
(3) covariance matrix vectorization:
(3a) the matched filtering output vector of each radar transmitted pulse repetition period and its conjugate transpose are multiplied each other, obtain the autocorrelation matrix of each transponder pulse repetition period;
(3b) get the mean value of the autocorrelation matrix of multiple radar transmitted pulse repetition periods, obtain covariance matrix;
(3c) utilize the long-pending distortion of the covariance matrix to vectorization of Khatri-Rao, obtain Khatri-Rao vector;
(3d) remove the redundant row in Khatri-Rao vector, obtain standard K hatri-Rao vector;
(4) burbling noise subspace:
(4a) adopt matrix regrouping method, ask the level and smooth correlation matrix of standard K hatri-Rao vector;
(4b) level and smooth correlation matrix is carried out to svd, obtain the noise subspace being formed by all little eigenwert characteristic of correspondence vectors;
(5) construct sparse recovery problem:
(5a) evaluated error of Khatri-Rao vector is retrained, construct the L2 norm constraint item in sparse recovery problem;
(5b) utilize noise subspace to the weighting of sparse signal vector, construct the L1 norm constraint item in sparse recovery problem;
(5c) meeting under the condition of L2 norm constraint item, minimizing L1 norm constraint item, obtaining sparse recovery problem;
(6) solve target direction of arrival DOA:
Solve the sparse recovery problem constructing, determine target direction of arrival DOA.
2. the nested MIMO radar DOA method of estimation based on compressed sensing according to claim 1, is characterized in that: the computing formula of the described nested element position coordinate set of step (1a) is as follows:
{ x i } = { id } , ( i = 1 , · · · , 0.5 Q ) { ( i - 0.5 Q ) ( 0.5 Q + 1 ) d } , ( i = 1 + 0.5 Q , · · · , Q )
Wherein, x ithe position coordinates that represents i nested array element, d represents the half wavelength of radar emission signal, and Q represents nested array element sum, and { } represents set operation.
3. the nested MIMO radar DOA method of estimation based on compressed sensing according to claim 1, is characterized in that: the computing formula of the described Virtual array position coordinates of step (1b) set is as follows:
{x m+x n},(m＝1,…,M,n＝1,…,N)
Wherein, x mrepresent the position coordinates of m radar emission array element, x nrepresent that n radar receives the position coordinates of array element, M represents radar emission array element sum, and N represents that radar receives array element sum, and { } represents set operation.
4. the nested MIMO radar DOA method of estimation based on compressed sensing according to claim 1, is characterized in that: the described matched filtering of step (2) is carried out according to the following formula:
∫ y n ( t ) s m * ( t ) dt
Wherein, y n(t) represent that n radar receives the echoed signal of array element at moment t, n=1,2 ..., N, N represents that radar receives array element sum,
Figure FDA0000483183290000031
represent to m radar emission array element the transmitted waveform complex envelope at moment t, do the conjugation obtaining after complex conjugate operation and transmit, m=1,2 ..., M, M represents radar emission array element sum.
5. the nested MIMO radar DOA method of estimation based on compressed sensing according to claim 1, is characterized in that: the computing formula of the described Khatri-Rao vector of step (3c) is as follows:
Figure FDA0000483183290000032
Wherein, A *represent the array manifold matrix of nested MIMO radar to do complex conjugate operation, the conjugation array manifold matrix obtaining, ⊙ represents to ask the long-pending operation of Khatri-Rao, and g represents target reflection factor vector,
Figure FDA0000483183290000033
represent that radar receives array element noise variance,
Figure FDA0000483183290000034
represent the unit matrix of vectorization.
6. the nested MIMO radar DOA method of estimation based on compressed sensing according to claim 1, is characterized in that: the concrete steps of the described matrix regrouping method of step (4a) are as follows:
The first step, using central element as axis of symmetry, is divided into two subvectors by standard K hatri-Rao vector;
Second step, using the central element of standard K hatri-Rao vector as the elements in a main diagonal, using the element in two subvectors adjacent with central element respectively as+1 and-1 diagonal line on element, the rest may be inferred, obtain (N+1) × (N+1) the level and smooth correlation matrix of dimension, wherein, N represents the element number in each subvector.
7. the nested MIMO radar DOA method of estimation based on compressed sensing according to claim 1, is characterized in that: the described L2 norm constraint of step (5a) item is expressed as follows:
| | W - 1 ( y - σ v 2 1 → v ) - ( W - 1 A ~ Θ ) g Θ | | 2 ≤ γ
Wherein, W -1represent error matrix to invert and operate the weighting matrix obtaining, y represents Khatri-Rao vector,
Figure FDA0000483183290000036
represent that radar receives array element noise variance, represent the unit matrix of vectorization,
Figure FDA0000483183290000038
represent the complete array extending stream shape matrix of nested MIMO radar, Θ represent to cover the discrete angle collection in spatial domain of target azimuth likely, g Θrepresent sparse signal vector, || || 2represent to get 2 norm operations, γ represents the upper limit threshold of L2 norm constraint item.
8. the nested MIMO radar DOA method of estimation based on compressed sensing according to claim 1, is characterized in that: the described L1 norm constraint of step (5b) item is expressed as follows:
||diag(w)g Θ|| 1
Wherein, diag () represents to ask diagonal matrix operation, and w represents noise subspace weighting matrix, the weighing vector of asking line by line 2 norms to obtain, g Θrepresent sparse signal vector, Θ represent to cover the discrete angle collection in spatial domain of target azimuth likely, || || 1represent to get 1 norm operation.
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