Known waveform source direction-of-arrival estimation method based on distributed array
阅读说明：本技术 基于分布式阵列的已知波形信源波达方向估计方法 (Known waveform source direction-of-arrival estimation method based on distributed array ) 是由 蔡晶晶 甘峰明 武斌 李盼盼 王亚宁 于 2021-08-19 设计创作，主要内容包括：本发明提出了一种基于分布式阵列的已知波形信源波达方向估计方法,实现步骤为：构建分布式阵列U；获取子阵输出信号X(t)；构造子阵输出信号X(t)的测量向量构造分布式阵列U的阵列流型字典基于压缩感知获取已知波形信源的波达方向估计值本发明在已知波形信源波达方向估计的基础上,利用分布式阵列接收信号,分布式阵列不仅能够对干扰、噪声等进行有效抑制,而且拥有较大的阵列孔径,使得分布式阵列对信号具有更高的角度分辨力,从而拥有较好的波达方向估计精度。(The invention provides a known waveform information source direction of arrival estimation method based on a distributed array, which comprises the following steps: constructing a distributed array U; acquiring a subarray output signal X (t); constructing a measurement vector of the subarray output signal X (t) Array flow pattern dictionary for constructing distributed array U Obtaining direction-of-arrival estimated value of known waveform information source based on compressed sensing The invention utilizes the distributed array to receive signals on the basis of the estimation of the direction of arrival of the known waveform signal source, and the distributed array not only can effectively inhibit interference, noise and the like, but also has larger array aperture, so that the distributed array has signal receiving functionThe method has higher angle resolution, thereby having better estimation precision of the direction of arrival.)
1. A known waveform source direction-of-arrival estimation method based on a distributed array is characterized by comprising the following steps:
(1) constructing a distributed array U:
constructing a distributed array comprising M uniform linear arrays, U ═ U1,U2,...,Um,...,UM}, each uniform linear array UmFrom NmThe antenna is composed of an antenna array element,and will Um0As a reference array element, uniform linear array UmThe distance between every two antenna elements is d, wherein M is more than or equal to 2, and U ismThe mth uniform linear array, N, representing a distributed array Um≥2，UmnTo represent uniform linear array UmD is not more than lambda/2, and lambda is the wavelength of the narrow-band signal incident to the array;
(2) obtaining a subarray output signal x (t):
(2a) selecting each uniform linear arrayIn a group of consecutive PmThe array elements form a subarray to obtain a matrix including Rm＝Lm-PmSet of +1 subarrays Wherein, 1 is less than or equal to Pm≤Nm，Rm＝Nm-Pm+1，umrRepresents UmR +1 th subarray, Um(r+p)To represent uniform linear array UmThe (r + p + 1) th antenna array element;
(2b) subarraysEach antenna element in the array pair space transmits far-field narrow-band signals y (t) { y ═ y) from K known waveform sources1(t),y2(t),...,yk(t),...,yK(t) sampling and filtering in sequence to obtain a sub-array umrOutput signal ofWherein the content of the first and second substances,yk(t) represents a far-field narrow-band signal of a kth known waveform, t represents discrete time, t is more than or equal to 1 and less than or equal to L, L represents the number of sampling points of the signal in a time domain, and xm(r+p)(t) denotes an antenna element Um(r+p)Output signal of [ ·]TRepresenting a matrix transposition operation;
(2c) by Xmr(t) construction of Uniform Linear array UmOutput signals of all sub-arrays
(2d) By Xm(t) constructing subarray output signals X (t) ═ X of all subarrays in distributed array U1(t),...,Xm(t),...,XM(t)}；
(3) Constructing a measurement vector of the subarray output signal X (t)
(3a) By outputting X in signal X (t) from subarraysmEach X of (t)mr(t) and far-field narrowband signal yk(t) calculating the cross-correlation vectorThen pass throughConstructing a cross-correlation matrixWherein [ ·]HRepresents a conjugate transpose operation;
(3b) to WmkPerforming conjugate transpose by WmkAnd WmkConjugate transpose W ofmk HCalculating to obtain a subarray signal matrix R'mk＝WmkWmk H；
(3c) To R'mkVectorizing to obtain a column vector Zmk＝vec{R′mkIs then passed through ZmkConstructing X in the subarray output signal X (t)m(t) measurement vectorAnd pass throughConstructing a measurement vector of the subarray output signal X (t)Wherein vec {. is } indicative of a column-wise straightening operation,andof [;]representing a line feed operation;
(4) array flow pattern dictionary for constructing distributed array U
(4a) Adopting space grid division method, and according to the space domain sparse characteristics of signal source observing space domain [ -90 deg. and 90 deg. °]Angle divided into V fixed values at equal intervalsWherein, V > K,represents the v-th fixed angle value;
(4b) by subarrays umrAnd a fixed angle valueConstruction of corresponding subarrays umrGuide vector ofWherein the content of the first and second substances, represents UmThe angular offset value of (a) is,
(4c) by passingConstructing a set of subarraysGuide vector of
(4d) To pairPerforming conjugate transposition, and passingAndconjugate transpose ofCalculating subarray dictionary matrix
(4e) To pairVectorizing to obtain column vectorThen pass throughConstruct uniform linear array UmArray flow pattern dictionary of all submatrices inThen the array flow pattern dictionary of all sub-arrays in the distributed array U is
(5) Obtaining direction-of-arrival estimated value of known waveform information source based on compressed sensing
(5a) Using the formula of the convex optimization problem and by measuring the vectorAnd array flow pattern dictionaryCalculating target vector s ═ s1,...,sv,...,sV]T；
(5b) To be provided withIs the x-axis coordinate, with the target vector s ═ s1,...,sv,...,sV]TThe value of (a) is a y-axis coordinate, and an amplitude spectrogram is drawnSearching the first K spectral peaks with larger amplitude values from the amplitude spectrogram in a sequence from high to low, wherein the x-axis coordinates corresponding to the peak points of the spectral peaks are the estimated values of the directions of arrival of the K known waveform information sources
2. The method of claim 1, wherein the formula of the convex optimization problem in step (5a) is expressed as:
min||s||1
where s denotes an object vector having one dimension of V × 1, and s ═ s1,...,sv,...,sV]T，Represents a vector of dimension (MV) × 1,Sm＝[sm1,...,smv,...,smV]Tand vector s and vectorHas a relationship of sv＝||[s1v,...,smv,...,sMv]T||2，||·||1Representing the 1-norm of the solved vector, | | · |. non-woven phosphor2The 2-norm of the vector is solved, min is used for solving the minimum value, s.t. is used for representing the constraint relation, and epsilon represents the allowable value of the error.
Technical Field
The invention belongs to the technical field of signal processing, relates to an information source direction of arrival estimation method, and particularly relates to a known waveform information source direction of arrival estimation method based on a distributed array.
Background
The array signal processing is an important subject content in the field of signal processing, and has wide application prospects in the fields of parameter estimation, military electronic countermeasure, signal identification, mobile communication, medical diagnosis and the like. The array signal processing is to place a plurality of antenna arrays in a certain arrangement mode in space to form an antenna array, and detect and process incoming wave signals by using the antenna array to realize the estimation of the number of signal sources, the direction of arrival and the accurate frequency. Direction-of-arrival (DOA) refers to the Direction of arrival of the spatial signals, i.e. the Direction angle at which each signal arrives at the array reference array element. The direction of arrival is an important component in the field of array signal processing, the capability of a processing system of an array for accurately estimating the direction of arrival of a space signal is mainly researched, and the method has important application value in the fields of radar, sonar, wireless communication and the like.
The estimation of the direction of arrival generally processes signals with unknown waveforms, but in many fields, such as active radar, sonar, medical equipment, seismic reconnaissance and the like, the situation of known waveform information sources is very common, and the estimation performance of the direction of arrival can be effectively improved by introducing waveform prior information. For example, the patent application with the application publication number CN111381208A, entitled "a method for estimating direction of arrival of a known waveform signal source" discloses a method for estimating direction of arrival of a known waveform signal source, which includes obtaining an array received data matrix containing a known waveform signal of a known waveform signal source, obtaining an initial spatial feature matrix and the initial rotation invariant vector according to the array received data matrix, calculating a high-precision rotation invariant vector, and obtaining an angle estimation value of the known waveform signal according to the high-precision rotation invariant vector. The method effectively solves the problem of large angle estimation error under the condition of small snapshot number, but has the defects that the uniform linear array is used for receiving the incident signal, and the small aperture characteristic of the uniform linear array can cause the uniform linear array to have weak inhibition capability on interference, noise and the like, so that the estimation precision of the signal arrival direction is low.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a method for estimating the direction of arrival of a known signal based on a distributed array, and aims to improve the estimation precision of the direction of arrival.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:
(1) constructing a distributed array U:
constructing a distributed array comprising M uniform linear arrays, U ═ U1,U2,...,Um,...,UM}, each uniform linear array UmFrom NmThe antenna is composed of an antenna array element,and will Um0As a reference array element, uniform linear array UmThe distance between every two antenna elements is d, wherein M is more than or equal to 2, and U ismThe mth uniform linear array, N, representing a distributed array Um≥2，UmnTo represent uniform linear array UmD is not more than lambda/2, and lambda is the wavelength of the narrow-band signal incident to the array;
(2) obtaining a subarray output signal x (t):
(2a) selecting each uniform linear arrayIn a group of consecutive PmThe array elements form a subarray to obtain a matrix including Rm＝Lm-PmSet of +1 subarrays Wherein, 1 is less than or equal to Pm≤Nm，Rm＝Nm-Pm+1，umrRepresents UmR +1 th subarray, Um(r+p)To represent uniform linear array UmThe (r + p + 1) th antenna array element;
(2b) subarraysEach antenna element in the array pair space transmits far-field narrow-band signals y (t) { y ═ y) from K known waveform sources1(t),y2(t),...,yk(t),...,yK(t) sampling and filtering in sequence to obtain a sub-array umrOutput signal ofWherein the content of the first and second substances,yk(t) represents a far-field narrow-band signal of a kth known waveform, t represents discrete time, t is more than or equal to 1 and less than or equal to L, L represents the number of sampling points of the signal in a time domain, and xm(r+p)(t) denotes an antenna element Um(r+p)Output signal of [ ·]TRepresenting a matrix transposition operation;
(2c) by Xmr(t) construction of Uniform Linear array UmOutput signals of all sub-arrays
(2d) By Xm(t) constructing subarray output signals X (t) ═ X of all subarrays in distributed array U1(t),...,Xm(t),...,XM(t)}；
(3) Constructing a measurement vector of the subarray output signal X (t)
(3a) By outputting X in signal X (t) from subarraysmEach X of (t)mr(t) and far-field narrowband signal yk(t) calculating the cross-correlation vectorThen pass throughConstructing a cross-correlation matrixWherein [ ·]HRepresents a conjugate transpose operation;
(3b) to WmkPerforming conjugate transpose by WmkAnd WmkConjugate transpose W ofmk HCalculating to obtain a subarray signal matrix R'mk＝WmkWmk H；
(3c) To R'mkVectorizing to obtain a column vector Zmk＝vec{R′mkIs then passed through ZmkConstructing X in the subarray output signal X (t)m(t) measurement vectorAnd pass throughConstructing a measurement vector of the subarray output signal X (t)Wherein vec {. is } indicative of a column-wise straightening operation,andof [;]representing a line feed operation;
(4) array flow pattern dictionary for constructing distributed array U
(4a) Adopting space grid division method and according to the space of signal sourceThe domain sparsity characteristic is that the observation airspace is [ -90 DEG, 90 DEG °]Angle divided into V fixed values at equal intervalsWherein, V > K,represents the v-th fixed angle value;
(4b) by subarrays umrAnd a fixed angle valueConstruction of corresponding subarrays umrGuide vector ofWherein the content of the first and second substances, represents UmThe angular offset value of (a) is,
(4c) by passingConstructing a set of subarraysGuide vector of
(4d) To pairPerforming conjugate transposition, and passingAndconjugate transpose ofCalculating subarray dictionary matrix
(4e) To pairVectorizing to obtain column vectorThen pass throughConstruct uniform linear array UmArray flow pattern dictionary of all submatrices inThen the array flow pattern dictionary of all sub-arrays in the distributed array U is
(5) Obtaining direction-of-arrival estimated value of known waveform information source based on compressed sensing
(5a) Using the formula of the convex optimization problem and by measuring the vectorAnd array flow pattern dictionaryCalculating target vector s ═ s1,...,sv,...,sV]T；
(5b) To be provided withIs the x-axis coordinate, with the target vector s ═ s1,...,sv,...,sV]TThe value of the peak value is y-axis coordinate, an amplitude spectrogram is drawn, the first K spectral peaks with larger amplitude values are searched from the amplitude spectrogram in a sequence from high to low, and the x-axis coordinate corresponding to the peak value points of the spectral peaks is the estimated value of the direction of arrival of the K known waveform information sources
Compared with the prior art, the invention has the following advantages:
(1) the distributed array constructed by the invention comprises a plurality of uniform linear arrays, each uniform linear array can receive incident signals, and information of the incident signals received by the plurality of uniform linear arrays is fused together.
(2) According to the method, the estimation value of the direction of arrival of the known waveform information source is obtained based on compressed sensing, and a compressed sensing algorithm is introduced into the estimation of the direction of arrival, so that the estimation precision of the direction of arrival and the estimation performance under the condition of a lower signal-to-noise ratio can be improved.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a schematic structural diagram of a distributed array received signal model employed by an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a uniform linear array received signal model of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
Referring to fig. 1, the present invention includes the steps of:
step 1) constructing a distributed array U:
constructing a distributed array comprising M uniform linear arrays, U ═ U1,U2,...,Um,...,UM}, each uniform linear array UmFrom NmThe antenna is composed of an antenna array element,and will Um0As a reference array element, uniform linear array UmThe distance between every two antenna elements is d, wherein M is more than or equal to 2, and U ismThe mth uniform linear array, N, representing a distributed array Um≥2，UmnTo represent uniform linear array UmD is not more than lambda/2, and lambda is the wavelength of the narrow-band signal incident to the array;
the structure of the distributed array received signal model in this embodiment is shown in fig. 2, and a distributed array U ═ 2 uniform linear arrays includes M ═ 2 uniform linear arrays1,U2And each uniform linear array comprises 7 antenna array elements, the distributed array U is positioned in a plane rectangular coordinate system, and the uniform linear arrays U of the distributed array U1、U2The coordinates in the rectangular plane coordinate system are respectively (x)1,y1)、(x2,y2) Assume that distributed array U receives a signal transmitted by source X of known waveform.
The structure of the uniform linear array signal receiving model in this embodiment is shown in fig. 3, and includes L1Uniform linear array U of 7 antenna elements1＝{U10,U11,...,U16}，U1Reference array element U10Origin of coordinates in plane rectangular coordinates, except U10And the other array elements are sequentially placed in the plane rectangular coordinate system. Uniform linear array U1The included angle between the linear array U and the x axis of the rectangular coordinate system is uniform1Angle offset value ofAnd the reference array element receives the signal transmitted by the known waveform signal source X and the included angle of the y axis of the rectangular coordinate system is the direction of arrival theta of the signal source XX。
Step 2), obtaining a subarray output signal X (t):
(2a) selecting each uniform linear arrayIn a group of consecutive PmThe array elements form a subarray to obtain a matrix including Rm＝Lm-PmSet of +1 subarrays Wherein, 1 is less than or equal to Pm≤Nm，Rm＝Nm-Pm+1，umrRepresents UmR +1 th subarray, Um(r+p)To represent uniform linear array UmThe (r + p + 1) th antenna array element;
(2b) subarraysEach antenna element in the array pair space transmits far-field narrow-band signals y (t) { y ═ y) from K known waveform sources1(t),y2(t),...,yk(t),...,yK(t) sampling and filtering in sequence to obtain a sub-array umrOutput signal ofWherein the content of the first and second substances,yk(t) represents the far-field narrow-band signal of the kth known waveform, t represents discrete time, 1 ≦ t ≦ L,l represents the number of samples of the signal in the time domain, xm(r+p)(t) denotes an antenna element Um(r+p)Output signal of [ ·]TRepresenting a matrix transposition operation;
(2c) by Xmr(t) construction of Uniform Linear array UmOutput signals of all sub-arrays
(2d) By Xm(t) constructing subarray output signals X (t) ═ X of all subarrays in distributed array U1(t),...,Xm(t),...,XM(t)}；
Step 3) constructing a measurement vector of a subarray output signal X (t)
(3a) By outputting X in signal X (t) from subarraysmEach X of (t)mr(t) and far-field narrowband signal yk(t) calculating the cross-correlation vectorThen pass throughConstructing a cross-correlation matrixWherein [ ·]HRepresents a conjugate transpose operation;
cross correlation vectorIs a far-field narrow-band signal y whose waveform is knownk(t) and Xmr(t) obtaining a mixture of (a) and (b),contains waveform information of a far-field narrowband signal whose waveform is known.
(3b) To WmkPerforming conjugate transpose by WmkAnd WmkConjugate transpose W ofmk HCalculating to obtain a subarray signal matrix R'mk＝WmkWmk H；
(3c) To R'mkVectorizing to obtain a column vector Zmk＝vec{R′mkIs then passed through ZmkConstructing X in the subarray output signal X (t)m(t) measurement vectorAnd pass throughConstructing a measurement vector of the subarray output signal X (t)Wherein vec {. is } indicative of a column-wise straightening operation,andof [;]representing a line feed operation;
step 4) constructing an array flow pattern dictionary of the distributed array U
(4a) Adopting space grid division method, and according to the space domain sparse characteristics of signal source observing space domain [ -90 deg. and 90 deg. °]Angle divided into V fixed values at equal intervalsWherein, V > K,represents the v-th fixed angle value;
(4b) by subarrays umrAnd a fixed angle valueConstruction of corresponding subarrays umrGuide vector ofWherein the content of the first and second substances, represents UmThe angular offset value of (a) is,
(4c) by passingConstructing a set of subarraysGuide vector of
(4d) To pairPerforming conjugate transposition, and passingAndconjugate transpose ofCalculating subarray dictionary matrix
(4e) To pairVectorizing to obtain column vectorThen pass throughConstruct uniform linear array UmArray flow pattern dictionary of all submatrices inThen the array flow pattern dictionary of all sub-arrays in the distributed array U is
Step 5) obtaining the estimated value of the direction of arrival of the known waveform information source based on compressed sensing
(5a) Using the formula of the convex optimization problem and by measuring the vectorAnd array flow pattern dictionaryCalculating target vector s ═ s1,...,sv,...,sV]T：
min||s||1
Where s denotes an object vector having one dimension of V × 1, and s ═ s1,...,sv,...,sV]T，Represents a vector of dimension (MV) × 1,Sm＝[sm1,...,smv,...,smV]Tand vector s and vectorHas a relationship of sv＝||[s1v,...,smv,...,sMv]T||2，||·||1Representing the 1-norm of the solved vector, | | · |. non-woven phosphor2The 2-norm of the vector is solved, min is used for solving the minimum value, s.t. is used for representing the constraint relation, and epsilon represents the allowable value of the error.
(5b) To be provided withIs the x-axis coordinate, with the target vector s ═ s1,...,sv,...,sV]TThe value of the peak value is y-axis coordinate, an amplitude spectrogram is drawn, the first K spectral peaks with larger amplitude values are searched from the amplitude spectrogram in a sequence from high to low, and the x-axis coordinate corresponding to the peak value points of the spectral peaks is the estimated value of the direction of arrival of the K known waveform information sources
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