CN112711000B - Electromagnetic vector mutual mass array tensor power spectrum estimation method based on minimization criterion - Google Patents
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Abstract
The invention discloses an electromagnetic vector mutual mass array tensor power spectrum estimation method based on a minimization criterion, which mainly solves the problem of limited power spectrum estimation precision in the existing method and comprises the following implementation steps: constructing an electromagnetic vector mutual mass array; tensor modeling of electromagnetic vector mutual mass array receiving signals; structured tensor beam forming for a mutual mass sparse uniform sub-area array; calculating tensor beam power of the cross sparse uniform sub-area array; electromagnetic vector mutual mass area array tensor power spectrum estimation based on sub area array tensor wave beam power minimization processing. The invention starts from the principle of spatial filtering of the signal tensor received by the electromagnetic vector mutual mass area array, establishes the correlation between the mutual mass distribution characteristics and the virtual peak distribution characteristics of two sparse uniform sub-area arrays, and forms a minimized power processing technical framework based on the output signals of the mutual mass sparse uniform sub-area arrays on the basis of the correlation, thereby realizing accurate tensor power spectrum estimation and being applicable to target positioning and imaging.
Description
Technical Field
The invention belongs to the field of array signal processing, in particular relates to a statistical signal processing technology based on electromagnetic vector mutual mass area array multidimensional receiving signals, and particularly relates to an electromagnetic vector mutual mass area array tensor power spectrum estimation method based on a minimization criterion, which can be used for target positioning and imaging.
Background
The power spectrum estimation is widely applied to the fields of radar, communication, medical imaging, geological exploration and the like as a tool for describing signal energy distribution in space. With the development of science and technology, the requirements of increasingly complex application scenes on the power spectrum estimation performance are also continuously improved. Compared with the traditional uniform array, the intersubstance array is used as a typical sparse array architecture, can break through the limit of the Nyquist sampling rate, has the advantages of large aperture and high resolution, and can realize performance break-through on power spectrum estimation. Further, in order to meet the requirements of complex application scenes on the polarization direction of the space signals, the electromagnetic vector sensor array can sense the arrival direction and the polarization direction of the space signals simultaneously compared with the traditional scalar sensor array. The new morphological array architecture integrating the electromagnetic vector sensor and the mutual mass array is hopeful to realize power spectrum estimation on multidimensional parameter planes such as the direction of arrival and the polarization direction. However, in the prior art, the received signals are stacked into vectors for processing, and the power spectrum function is constructed only in the one-dimensional direction of arrival, and the mode of vectorization signal processing causes the loss of the original structural information of the received signals of the electromagnetic vector mutual mass area array because the received signals have a multidimensional space information structure. For this reason, how to utilize the structured information of the electromagnetic vector mutual mass array multi-dimensional received signal to achieve accurate power spectrum estimation on the multi-dimensional parameter plane remains a great challenge.
In consideration of retaining original structural information of the multidimensional received signals, a tensor model is introduced into the field of array signal processing and is applied to various technologies such as multidimensional signal modeling, parameter extraction, spatial filtering and the like. However, the existing method for the uniform area array is based on the premise that the array element arrangement meets the Nyquist sampling rate, and in an electromagnetic vector mutual mass area array scene, the sparse arrangement of the array elements causes a model mismatch problem, and the introduced virtual peaks cause serious loss on the accuracy performance of power spectrum estimation. Therefore, how to match the multi-dimensional receiving signal structure of the electromagnetic vector mutual mass array and the sparse arrangement characteristic of array elements and estimate tensor power spectrums on a direction-of-arrival plane and a polarization direction plane at the same time is still a hot spot and difficult problem to be solved urgently.
Disclosure of Invention
Aiming at the problem that the power spectrum estimation precision is limited in the existing method, the invention provides an electromagnetic vector mutual mass area array tensor power spectrum estimation method based on a minimization criterion, and provides a feasible thinking and effective solution for constructing the relation between electromagnetic vector mutual mass area array multidimensional receiving signals and tensor beam power and enhancing the tensor beam power corresponding to the signal source direction of arrival and the polarization direction under the condition of inhibiting a virtual peak so as to realize accurate tensor power spectrum estimation.
The aim of the invention is realized by the following technical scheme: an electromagnetic vector mutual mass array tensor power spectrum estimation method based on a minimization criterion comprises the following steps:
(1) Receiving end useEach electromagnetic vector antenna array element is constructed according to the structure of a mutual mass array, realizes the perception of electromagnetic field by utilizing three mutually orthogonal electric dipoles and three mutually orthogonal magnetic dipoles, and has six paths of output; wherein (1)> and /> Respectively a pair of prime integers; the electromagnetic vector mutual mass area array can be decomposed into two sparse uniform subarrays +.> and />
(2) Assume that there is one fromFar-field narrowband signal source of direction, wherein θ and +.>Respectively represent the azimuth angle and the pitch angle of the signal source, and theta epsilon [ -pi/2, pi/2]，/>Six outputs of each array element in the electromagnetic vector mutual mass array simultaneously contain the information of the direction of arrival +.>And polarization direction information->Wherein gamma is E [0,2 pi ]]And eta epsilon [ -pi, pi]Respectively representing polarization auxiliary angle and polarization phase difference, direction of arrival matrix +.>And the polarization direction vector g (γ, η) can be specifically defined as:
wherein ,correspondingly, the output of each array element in the electromagnetic vector mutual mass array can use a space response vector +.>Expressed as:
to preserve sparse uniform sub-area arrayReceiving three-dimensional space information of signals at time t, namely wave arrival of x-axis direction and y-axis directionThe direction information and the electromagnetic vector space response information are represented by adopting a three-dimensional tensor, and the three-dimensional signal tensors of the collected T sampling snapshots are overlapped on a fourth dimension (namely the time dimension) to form a sub-area array corresponding to sparse uniformity>Is>Expressed as:
wherein , and /> Signal source guiding vectors respectively representing electromagnetic vector mutual mass area array in x-axis and y-axis directions, and +.> For the signal waveform of the incident signal source, lambda represents the signal wavelength, and />Respectively indicate->The middle array element is in the x axis and the y axisPosition in direction, ++>Representing the vector outer product, (. Cndot.) T Representing a transpose operation->Is an independent and equidistributed additive Gaussian white noise tensor;
(3) In order to perform spatial filtering in the direction of arrival and the polarization direction of the corresponding signal source to measure the power of the signal source, the method aims at the mutual mass sparse uniform sub-area arrayThe tensor of the received signal at time t> Design of tensor beamformer matching its multidimensional structured information +.>By->For->Performing spatial filtering to obtain an output signal +.>Expressed as:
wherein,<·>representing tensor inner product, (. Cndot. * Representing a conjugation operation. Taking into account thatAnd->Corresponding to each space dimension information one by one, can be +.>Beamforming weight vector expressed as corresponding to x-axis direction of arrival information by means of CANDECOMP/PARAFAC decomposition>Beamforming weight vector for y-axis direction of arrival informationAnd beam forming weight vector of electromagnetic vector space response information +.>Is the outer product of (2):
thereby, a signal tensor is receivedCan be expressed as three beamforming weight vectorsAt->Structured weighting in three spatial information dimensions, output signal +.>Can be expressed as:
wherein ,×r Representing the inner product of the tensor and the matrix along the r-th dimension. To obtain two sparse uniform sub-arraysCorresponding respective three beamforming weight vectors +.> and />Needs to minimize sparse uniform sub-area arrayThe average power of the signal is output in each spatial information dimension, and the response of the signal source corresponding to each spatial information dimension is ensured to be undistorted, and the specific optimization problem can be expressed as follows:
wherein , representing sparse uniform subarray->In the output signal of the r-th dimension, the beam forming weight vector pairs of the other two dimensions except the r-th dimension can be utilized>The two-dimensional weighting is performed to obtain the two-dimensional weighting, which is expressed as:
wherein ,(·)H Representing the conjugate transpose operation. Sequentially solving corresponding sparse uniform sub-area arrays by utilizing Lagrangian multiplier method and />Three beamforming weight vectors each>Is solved in a closed form as follows:
(4) Based on the beamforming weight vectorReceived signal tensor for mutual mass sparse uniform sub-area arrayThe corresponding tensor beam power is structurally weighted as follows:
wherein ,the term "modulus" refers to the modulus of a complex number. In the direction of arrival and polarization of the corresponding signal source, i.e.)>When (I)>The tensor beam power value of (c) is the largest. However, since the array element spacing in the sparse uniform sub-area array is greater than half a wavelength, the Nyquist sampling rate is not satisfied, resulting in +.>A virtual peak exists; because the two sparse uniform sub-area arrays are distributed with each other, the arrival direction and the polarization direction corresponding to the virtual peak positions of the two sparse uniform sub-area arrays are different from each other;
(5) Based on the characteristic that the arrival direction and the polarization direction corresponding to the virtual peaks of the cross-mass sparse uniform sub-area array are different from each other, the tensor beam power comparison of the two sparse uniform sub-area arrays in each arrival direction and the polarization direction is selected to be the minimum value, and an electromagnetic vector cross-mass area array tensor power spectrum without the interference of the virtual peaks is formed, and is expressed as follows:
wherein, min (·) represents the minimum operation. Correspondingly, the output signal y of the electromagnetic vector mutual mass array min (t) by pairing and />Is obtained by taking the minimum value of the power of (2), expressed as:
further, the electromagnetic vector mutual mass array structure described in the step (1) may be specifically described as follows: constructing a pair of sparse uniform sub-area arrays on a plane coordinate system xoy and /> and />Respectively include-> and />Antenna array elements-> and />Respectively a pair of prime integers; sparse uniform sub-area array->The spacing of the antenna elements in the x-axis and y-axis directions is +.> and />Unit interval d=λ/2; similarly, sparse uniform sub-area array +.>The spacing of the antenna elements in the x-axis and y-axis directions is +.> and /> Middle->The positions of the antenna array elements in the directions of the x axis and the y axis are respectively +.>And wherein ,/> Similarly, a->Middle->The positions of the antenna array elements in the directions of the x axis and the y axis are respectively and /> wherein ,will-> and />According to the array element at the origin position of the coordinate systemSub-array combining in an overlapping manner to obtain a real inclusionElectromagnetic vector mutual mass array of each antenna array element.
Further, the characteristics of the cross sparse uniform sub-area array virtual peak in the step (4) that the direction of arrival and the polarization direction corresponding to the virtual peak are different from each other are specifically described as follows: when (when)When (I)>There is a virtual peak, and when->In the time-course of which the first and second contact surfaces,there is a virtual peak. For a scalar sensor mutual mass linear array, the virtual peaks of the two sparse uniform sub-linear arrays have regular intervals, and the interval meets the mutual mass characteristic; due to the nature of prime numbers, the virtual peak positions of the two sparse uniform sub-linear arrays do not overlap with each other. And so on, because on the xoy coordinate plane, the sparse uniform subarray of the electromagnetic vector mutual mass area array is +.> and />The array element arrangement along the x-axis direction and the y-axis direction meets the mutual quality characteristic, so that the sparse uniform subarray +.> and />The direction of arrival and the direction of polarization respectively corresponding to the virtual peaks of (a)Are different from each other, i.e
Further, in step (5), in the direction of arrival and the direction of polarizationOn the other hand, due to->Tensor beam power value corresponding to virtual peak +.>Greater thanCorresponding to tensor beam power value +.>By selecting the minimum of them, elimination of the false peaks can be achieved. Similarly, in->On account ofTensor beam power value corresponding to virtual peak +.>Greater thanCorresponding to tensor beam power value +.>By choosing the minimum of them, the elimination of the false peaks will also be achieved. Therefore, the electromagnetic vector mutual mass area array tensor power spectrum based on the minimization criterion is formed by selecting the minimum value for tensor beam power comparison of two sparse uniform sub-area arrays in each direction of arrival and polarization.
Further, in the step (5), the specific process of drawing the complete electromagnetic vector mutual mass area array tensor power spectrum on the multidimensional parameter plane is as follows: will be and />The values of (2) are respectively fixed to be-pi, 0 and-pi, and +.>Gradually increasing from-pi/2 to pi/2 at intervals of 0.1 ° (2pi/360 °); subsequently, will->The value of (2 pi/360) is increased by 0.1 DEG from-pi,/pi> and />The value of (2) is still fixed to 0 and-pi, and +.>The process is repeated from-pi/2 to pi/2 gradually at intervals of 0.1 DEG x (2 pi/360 DEG), until +.>Increasing the value of (2) to pi; and so on, will->The value of (2) is increased from 0 to 2 pi @>The value of (2) is increased from-pi to pi, in +.>Traversing all values within the respective value ranges of the four parameters is possible, based on a minimized power criterion, at eachSequentially obtaining corresponding tensor beam power +.>Thereby estimating the complete electromagnetic vector mutual mass array tensor power spectrum.
Compared with the prior art, the invention has the following advantages:
(1) The invention constructs the structured tensor beam forming representation matched with the multidimensional space information based on the electromagnetic vector mutual mass array received signal tensor, thereby realizing the airspace filtering in the corresponding signal source direction of arrival and the polarization direction while retaining the original structured information of the multidimensional received signal and providing a technical premise for constructing a tensor power spectrum;
(2) The invention fully matches the sparse characteristic of the electromagnetic vector mutual prime area array, reveals the connection between the mutual prime arrangement characteristic of the two sub-area arrays and the virtual peak distribution, designs a minimized power processing technical frame of the output signals of the mutual prime sparse uniform sub-array based on the connection, thereby avoiding the loss of the virtual peak caused by the array sparse characteristic to the power spectrum estimation precision performance;
(3) The invention constructs tensor power spectrum on the direction of arrival plane and the polarization direction at the same time, accurately describes the energy distribution in the direction of arrival and the polarization direction of the corresponding signal source, and overcomes the problem of polarization information deficiency of the traditional one-dimensional power spectrum estimation method facing the scalar sensor array.
Drawings
Fig. 1 is a general flow diagram of the present invention.
Fig. 2 is a schematic structural diagram of an electromagnetic vector mutual mass array in the present invention.
Fig. 3 is a block diagram of electromagnetic vector mutual mass array tensor beamforming output based on the minimization criteria according to the present invention.
Fig. 4 is a tensor power spectrum estimation result of the proposed method in the direction of arrival plane.
Fig. 5 is a tensor power spectrum estimation result of the proposed method in the plane of polarization direction.
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the accompanying drawings.
In order to solve the problem of limited power spectrum estimation precision existing in the existing method, the invention provides an electromagnetic vector mutual mass area array tensor power spectrum estimation method based on a minimization criterion, and the correlation between the mutual mass layout characteristics and virtual peak distribution of two sparse uniform sub-area arrays is established based on the principle of mutual mass sparse uniform sub-area array structured tensor beam forming, so that a minimized power processing technical framework based on the output signals of the mutual mass sparse uniform sub-area arrays is formed, and an accurate tensor power spectrum is realized in an electromagnetic vector mutual mass area array scene.
Referring to fig. 1, the implementation steps of the present invention are as follows:
step 1: and constructing an electromagnetic vector mutual mass area array. At the receiving endEach electromagnetic vector antenna array element constructs an electromagnetic vector mutual mass array, and each electromagnetic vector antenna array element realizes the perception of electromagnetic field by utilizing three mutually orthogonal electric dipoles and three mutually orthogonal magnetic dipoles, and has six paths of output, as shown in fig. 2: constructing a pair of sparse uniform subarrays on a plane coordinate system xoy> and /> and />Respectively include-> and />Antenna array elements-> and />Respectively a pair of prime integers; sparse uniform sub-area array->The spacing of the antenna elements in the x-axis and y-axis directions is +.> and />Unit interval d=λ/2, λ representing the signal wavelength; similarly, sparse uniform sub-area array +.>The spacing of the antenna elements in the x-axis and y-axis directions is +.> and /> Middle->The positions of the antenna array elements in the directions of the x axis and the y axis are respectively +.>And wherein ,/>In a similar manner to that described above,middle->The positions of the antenna array elements in the directions of the x axis and the y axis are respectively +.> and /> wherein ,/> Will-> and />According to the array element at the origin position of the coordinate system>Sub-array combining in an overlapping manner to obtain the actual inclusion +.>Electromagnetic vector mutual mass arrays of the antenna array elements;
step 2: tensor modeling of electromagnetic vector mutual mass array received signals. Assume that there is one fromFar-field narrowband signal source of direction, wherein θ and +.>Respectively represent the azimuth angle and the pitch angle of the signal source, and theta epsilon [ -pi/2, pi/2]，Six outputs of each array element in electromagnetic vector mutual mass array simultaneously contain direction-of-arrival informationAnd polarization state information->Wherein gamma is E [0,2 pi ]]And eta epsilon [ -pi, pi]Respectively representing polarization auxiliary angle and polarization phase difference, direction of arrival matrix +.>And the polarization state vector g (γ, η) can be specifically defined as:
wherein ,correspondingly, the output of each array element in the electromagnetic vector mutual mass array can use a space response vector +.>Expressed as:
to preserve sparse uniform sub-area arrayReceiving three-dimensional spatial information of the signal at time t, i.e. x-axis direction, y-axis directionThe direction of arrival information and electromagnetic vector space response information of the system are represented by adopting a three-dimensional tensor, and the three-dimensional signal tensors of the collected T sampling snapshots are overlapped on a fourth dimension (namely the time dimension) to form a sub-area array corresponding to sparse uniformity>Is>Expressed as:
wherein ,and representing the expected signal guiding vectors of the electromagnetic vector mutual mass area array in the x-axis and y-axis directions respectively, andsignal waveform as signal source, ++>Representing the vector outer product, (. Cndot.) T Representing a transpose operation->Is an independent and equidistributed additive Gaussian white noise tensor;
step 3: structured tensor beamforming for a mutual mass sparse uniform sub-area array. For spatial filtering in the direction of arrival and polarization of the corresponding signal source to measure the power of the signal source, needleSparse and uniform sub-area array for mutual qualityThe tensor of the received signal at time t>Design of tensor beamformer matching its multidimensional structured information +.>By->For->Performing spatial filtering to obtain an output signal +.>Expressed as:
wherein,<·>representing tensor inner product, (. Cndot. * Representing a conjugation operation. Taking into account thatAnd->Corresponding to each space dimension information one by one, can be +.>Beamforming weight vector expressed as corresponding to x-axis direction of arrival information by means of CANDECOMP/PARAFAC decomposition>Beamforming of y-axis direction of arrival informationWeight vectorAnd beam forming weight vector of electromagnetic vector space response information +.>Is the outer product of (2):
thereby, a signal tensor is receivedCan be expressed as three beamforming weight vectorsAt->Structured weighting in three spatial information dimensions, output signal +.>Can be expressed as:
wherein ,×r Representing the inner product of the tensor and the matrix along the r-th dimension.
To obtain two sparse uniform sub-arraysCorresponding three beam forming weight vectors and />Needs to minimize sparse uniform sub-area array +.>The average power of the signal is output in each spatial information dimension, and the response of the signal source corresponding to each spatial information dimension is ensured to be undistorted, and the specific optimization problem can be expressed as follows:
wherein , representing sparse uniform subarray->In the output signal of the r-th dimension, the beam forming weight vector pairs of the other two dimensions except the r-th dimension can be utilized>The two-dimensional weighting is performed to obtain the two-dimensional weighting, which is expressed as:
wherein ,(·)H Representing the conjugate transpose operation. Sequentially solving corresponding sparse uniform sub-area arrays by utilizing Lagrangian multiplier method and />Three beamforming weight vectors each>Is solved in a closed form as follows:
step 4: and calculating tensor beam power of the mutual mass sparse uniform sub-area array. Beamforming weight vector by constructionTensor of received signal for mutual mass sparse uniform sub-area array>Structural weighting is performed, and the corresponding tensor beam power is expressed as:
wherein ,the term "modulus" refers to the modulus of a complex number. In the direction of arrival and polarization of the corresponding signal source, i.e.)>When (I)>The tensor beam power value of (c) is the largest. However, since the array element spacing in the sparse uniform sub-area array is greater than half a wavelength, the nyquist sampling rate is not satisfied, resulting in thatWhen (I)>There is a virtual peak, and when->In the time-course of which the first and second contact surfaces,there is a virtual peak. For a scalar sensor mutual mass linear array, the virtual peaks of the two sparse uniform sub-linear arrays have regular intervals, and the interval meets the mutual mass characteristic; due to the nature of prime numbers, the virtual peak positions of the two sparse uniform sub-linear arrays do not overlap with each other. And so on, because on the xoy coordinate plane, the sparse uniform subarray of the electromagnetic vector mutual mass area array is +.> and />The array element arrangement along the x-axis direction and the y-axis direction meets the mutual quality characteristic, so that the sparse uniform subarray +.> and />The direction of arrival and the direction of polarization respectively corresponding to the virtual peaks of (a)Are different from each other, i.e
Step 5: electromagnetic vector mutual mass area array tensor power spectrum estimation based on sub area array tensor wave beam power minimization processing. Based on the characteristic that the arrival directions and the polarization directions corresponding to the virtual peaks of the cross-mass sparse uniform sub-area arrays are different from each other, the tensor beam power of the two sparse uniform sub-area arrays is subjected to minimization treatment so as to realize electromagnetic vector cross-mass area array tensor power spectrum estimation without virtual peak interference, and specifically: in the direction of arrival and the direction of polarizationOn the other hand, due to->Tensor beam power value corresponding to virtual peak +.>Greater thanCorresponding to tensor beam power value +.>By selecting the minimum of them, elimination of the false peaks can be achieved. Similarly, in->On account ofTensor beam power value corresponding to virtual peak +.>Greater thanCorresponding to tensor beam power value +.>By choosing the minimum of them, the elimination of the false peaks will also be achieved. As shown in fig. 3, the output signal y of the electromagnetic vector mutual mass array min (t) is p-> and />Is obtained by taking the minimum value of the power of (2), expressed as:
wherein, min (·) represents the minimum operation. Accordingly, the tensor power spectrum of the electromagnetic vector mutual mass array based on the minimization criterion is formed by selecting the minimum value for tensor beam power comparison of two sparse uniform subarrays in each direction of arrival and polarization, and is expressed as:
specifically, it will and />The values of (2) are respectively fixed to be-pi, 0 and-pi, and +.>Gradually increasing from-pi/2 to pi/2 at intervals of 0.1 ° (2pi/360 °); subsequently, will->The value of (2 pi/360) is increased by 0.1 DEG from-pi,/pi> and />The value of (2) is still fixed to 0 and-pi, and +.>The process is repeated from-pi/2 to pi/2 gradually at intervals of 0.1 DEG x (2 pi/360 DEG), until +.>Increasing the value of (2) to pi; and so on, will->The value of (2) is increased from 0 to 2 pi @>The value of (1) is increased from-pi to pi, inTraversing all the values within the respective value ranges of the four parameters, and according to the sparse uniform subarray based on the mutual qualityTensor beam power criterion, at each +.>Sequentially obtaining corresponding tensor beam power +.>Thereby estimating the complete electromagnetic vector mutual mass array tensor power spectrum.
The effects of the present invention are further described below in connection with simulation examples.
Simulation example: receiving incident signals by adopting electromagnetic vector mutual mass array, and selecting parameters asThat is, the mutual mass area array of the framework contains +.> And a plurality of physical array elements. Assume that the azimuth angle, pitch angle, polarization auxiliary angle, and polarization phase difference of the incident signal source are θ=45.5°, respectively>γ=35.5°, η=55.5°; and under the condition of a signal-to-noise ratio of-5 dB, performing simulation experiments by adopting T=300 sampling snapshots.
The power spectrum estimation results of the method on the direction of arrival plane and the polarization direction plane are shown in fig. 4 and 5 respectively, wherein the x-axis and the y-axis in fig. 4 respectively represent the azimuth angle and the pitch angle of an incident signal source, and the x-axis and the y-axis in fig. 5 respectively represent the polarization auxiliary angle and the polarization phase difference of the incident signal source. It can be seen that the method provided by the invention can generate electromagnetic vector mutual mass area array tensor power spectrum without virtual peak interference on the direction of arrival plane and the polarization direction plane at the same time, and the tensor power spectrum effectively reflects the direction of arrival and the polarization direction information corresponding to the incident signal source.
In summary, the invention fully considers the multidimensional structural characteristics and the array sparse layout characteristics of electromagnetic vector mutual mass area array receiving signals, and starts from the structural tensor beam forming principle of the mutual mass sparse uniform sub-area array, and constructs the correlation between the mutual mass layout characteristics of the two sub-area arrays and the virtual peak distribution; then, from the viewpoint of inhibiting the virtual peak, a minimized power processing strategy based on the mutual mass sparse uniform sub-area array output signal is provided, so that a tensor power spectrum without the virtual peak interference is constructed on a wave arrival direction plane and a polarization direction plane, and the energy distribution of a signal source on a multidimensional parameter plane is effectively described.
The foregoing is merely a preferred embodiment of the present invention, and the present invention has been disclosed in the above description of the preferred embodiment, but is not limited thereto. Any person skilled in the art can make many possible variations and modifications to the technical solution of the present invention or modifications to equivalent embodiments using the methods and technical contents disclosed above, without departing from the scope of the technical solution of the present invention. Therefore, any simple modification, equivalent variation and modification of the above embodiments according to the technical substance of the present invention still fall within the scope of the technical solution of the present invention.
Claims (5)
1. The electromagnetic vector mutual mass array tensor power spectrum estimation method based on the minimization criterion is characterized by comprising the following steps of:
(1) Receiving end useEach electromagnetic vector antenna array element is constructed according to the structure of a mutual mass array, realizes the perception of electromagnetic field by utilizing three mutually orthogonal electric dipoles and three mutually orthogonal magnetic dipoles, and has six paths of output; wherein (1)> and /> Respectively a pair of prime integers; the electromagnetic vector mutual mass area array can be decomposed into two sparse uniform subarrays +.> and />
(2) Assume that there is one fromFar-field narrowband signal source of direction, wherein θ and +.>Respectively represent the azimuth angle and the pitch angle of the signal source, and theta epsilon [ -pi/2, pi/2]，/>Six outputs of each array element in the electromagnetic vector mutual mass array simultaneously contain the information of the direction of arrival +.>And polarization direction information->Wherein gamma is E [0,2 pi ]]And eta epsilon [ -pi, pi]Respectively representing polarization auxiliary angle and polarization phase difference, direction of arrival matrix +.>And the polarization direction vector g (γ, η) is specifically defined as:
wherein ,correspondingly, the output of each array element in the electromagnetic vector mutual mass array uses a space response vectorExpressed as:
to preserve sparse uniform sub-area arrayThree-dimensional space information of signals, namely wave arrival direction information of x-axis direction, y-axis direction and electromagnetic vector space response information, is received at the moment T, a three-dimensional tensor is adopted to represent the three-dimensional space information, and the three-dimensional signal tensors of the acquired T sampling snapshots are overlapped in the fourth dimension, namely the time dimension, so as to form a sparse uniform sub-area array>Is>Expressed as:
wherein , and /> Signal source guiding vectors respectively representing electromagnetic vector mutual mass area array in x-axis and y-axis directions, and +.> For the signal waveform of the incident signal source, lambda represents the signal wavelength, and />Respectively indicate->The position of the middle array element in the directions of the x axis and the y axis is expressed as the outer product of vectors, (. Cndot. T Representing a transpose operation->Is an independent and equidistributed additive Gaussian white noise tensor;
(3) In order to perform spatial filtering in the direction of arrival and the polarization direction of the corresponding signal source to measure the power of the signal source, the method aims at the mutual mass sparse uniform sub-area arrayAt time tReceive signal tensor-> Design of tensor beamformer matching its multidimensional structured information +.>By->For->Performing spatial filtering to obtain an output signal +.>Expressed as:
wherein,<represent tensor inner product, (· * Representing a conjugation operation; taking into account thatAnd->Is one-to-one corresponding to the spatial dimension information of +.>Beamforming weight vector expressed as corresponding to x-axis direction of arrival information by means of CANDECOMP/PARAFAC decomposition>Beam forming weight vector of y-axis direction of arrival information +.>And beam forming weight vector of electromagnetic vector space response information +.>Is the outer product of (2):
thereby, a signal tensor is receivedIs represented as three beamforming weight vectorsAt->Structured weighting in three spatial information dimensions, output signal +.>Expressed as:
wherein ,×r Representing the inner product of the tensor and the matrix along the r-th dimension; to obtain two sparse uniform sub-arraysCorresponding respective three beamforming weight vectors +.> and />Needs to minimize sparse uniform sub-area array +.>The average power of the signal is output in each spatial information dimension, the response of the signal source corresponding to each spatial information dimension is ensured to be undistorted, and the specific optimization problem is expressed as follows:
wherein ,representing sparse uniform subarray->In the output signal of the r-th dimension, the beam forming weight vector pairs of the other two dimensions except the r-th dimension are utilized for +.>The two-dimensional weighting is performed to obtain the two-dimensional weighting, which is expressed as:
wherein ,(·H Representing a conjugate transpose operation; sequentially solving corresponding sparse uniform sub-area arrays by utilizing Lagrangian multiplier method and />Three beamforming weight vectors each>Is solved in a closed form as follows:
(4) Based on the beam formingShape weight vectorTensor of received signal for mutual mass sparse uniform sub-area array>Structural weighting is performed, and the corresponding tensor beam power is expressed as:
wherein ,I/I represents a complex modulo operation; in the direction of arrival and polarization of the corresponding signal source, i.e.)>In the time-course of which the first and second contact surfaces,the tensor beam power value of (2) is the largest; however, since the array element spacing in the sparse uniform sub-area array is greater than half a wavelength, the Nyquist sampling rate is not satisfied, resulting in +.>A virtual peak exists; because the two sparse uniform sub-area arrays are distributed with each other, the arrival direction and the polarization direction corresponding to the virtual peak positions of the two sparse uniform sub-area arrays are different from each other;
(5) Based on the characteristic that the arrival direction and the polarization direction corresponding to the virtual peaks of the cross-mass sparse uniform sub-area array are different from each other, the tensor beam power comparison of the two sparse uniform sub-area arrays in each arrival direction and the polarization direction is selected to be the minimum value, and an electromagnetic vector cross-mass area array tensor power spectrum without the interference of the virtual peaks is formed, and is expressed as follows:
wherein, min (·) represents the operation of taking the minimum value; correspondingly, the output signal y of the electromagnetic vector mutual mass array min (t) by pairing and />Is obtained by taking the minimum value of the power of (2), expressed as:
2. the method for estimating an electromagnetic vector mutual mass array tensor power spectrum based on the minimization criterion of claim 1, wherein the electromagnetic vector mutual mass array structure of step (1) is specifically described as: constructing a pair of sparse uniform sub-area arrays on a plane coordinate system xoy and /> and />Respectively include-> and />The number of the antenna array elements is one, and />Respectively a pair of prime integers; sparse uniform sub-area array->The spacing of the antenna elements in the x-axis and y-axis directions is +.> and />Unit interval d=λ/2; similarly, sparse uniform sub-area array +.>The spacing of the antenna elements in the x-axis and y-axis directions is +.> and />Middle->The positions of the antenna array elements in the directions of the x axis and the y axis are respectively +.>And wherein ,/> Similarly, a->Middle->The positions of the antenna array elements in the directions of the x axis and the y axis are respectively and /> wherein ,will-> and />According to the array element at the origin position of the coordinate systemSub-array combining in an overlapping manner to obtain a real inclusionElectromagnetic vector mutual mass array of each antenna array element.
3. The method for estimating the power spectrum of the electromagnetic vector mutual mass area array tensor based on the minimization criterion of claim 1, wherein the characteristics of different directions of arrival and polarization corresponding to the virtual peak of the mutual mass sparse uniform sub-area array in the step (4) are specifically described as follows: when (when)When (I)>There is a virtual peak, and when->In the time-course of which the first and second contact surfaces,a virtual peak exists; for a scalar sensor mutual mass linear array, the virtual peaks of the two sparse uniform sub-linear arrays have regular intervals, and the interval meets the mutual mass characteristic; because of the nature of prime numbers, the virtual peak positions of the two sparse uniform sub-linear arrays are not overlapped with each other; and so on, because on the xoy coordinate plane, the sparse uniform subarray of the electromagnetic vector mutual mass area array is +.> and />The array element arrangement along the x-axis direction and the y-axis direction meets the mutual quality characteristic, so that the sparse uniform subarray +.> and />The direction of arrival and the direction of polarization respectively corresponding to the virtual peaks of (a)Are different from each other, i.e
4. The method for estimating an electromagnetic vector mutual mass array tensor power spectrum based on a minimization criterion as claimed in claim 3, wherein in step (5), in the direction of arrival and the polarization directionOn account ofTensor beam power value corresponding to virtual peak +.>Greater thanCorresponding to tensor beam power value +.>The elimination of the virtual peak is realized by selecting the minimum value in the two; similarly, in->On account ofTensor beam power value corresponding to virtual peak +.>Greater thanCorresponding to tensor beam power value +.>By selecting the minimum value in them, the elimination of the virtual peak will be realized; thus, the baseThe tensor power spectrum of the electromagnetic vector mutual mass array in the minimization criterion is formed by selecting the minimum value for tensor beam power comparison of two sparse uniform sub-arrays in each direction of arrival and polarization.
5. The method for estimating the power spectrum of the electromagnetic vector mutual mass array tensor based on the minimization criterion as claimed in claim 1, wherein in the step (5), the specific process of drawing the complete power spectrum of the electromagnetic vector mutual mass array tensor on the multidimensional parameter plane is as follows: will be and />The values of (2) are respectively fixed to be-pi, 0 and-pi, and +.>Gradually increasing from-pi/2 to pi/2 at intervals of 0.1 ° (2pi/360 °); subsequently, will->The value of (2 pi/360) is increased by 0.1 DEG from-pi,/pi> and />The value of (2) is still fixed to 0 and-pi, and +.>The process is repeated from-pi/2 to pi/2 gradually at intervals of 0.1 DEG x (2 pi/360 DEG), until +.>Increasing the value of (2) to pi; and so on, will->The value of (2) is increased from 0 to 2 pi @>The value of (2) is increased from-pi to pi, in +.>All values are traversed within the respective value ranges of the four parameters, based on a minimized power criterion, at each +.>Sequentially obtaining corresponding tensor beam power +.>Thereby estimating the complete electromagnetic vector mutual mass array tensor power spectrum.
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