CN107576953A - Relevant and incoherent compound target DOA estimation method based on relatively prime MIMO array - Google Patents
Relevant and incoherent compound target DOA estimation method based on relatively prime MIMO array Download PDFInfo
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Abstract
The invention discloses a kind of relevant and incoherent compound target DOA estimation method based on relatively prime MIMO array, compared to the sparse relatively prime MIMO array of reality, the present invention constructs uniformly densely covered virtual MIMO array, transmitting array element comprising greater number and reception array element, DOA estimations are carried out using equivalent more snapshot datas of the virtual MIMO array of acquisition, can solve the problems, such as that relevant and incoherent compound target DOA estimates, and can enough breaks through limitation of the actual array element number of relatively prime MIMO array to maximum distinguishable target numbers.The present invention can also obtain virtual MIMO array of the different transmittings with receiving array element number, corresponding different maximum distinguishable Coherent Targets number and maximum distinguishable relevant and incoherent target sum, pass through the number flexibly chosen virtual MIMO array emitter with receive array element, meet the needs of different scenes are to relevant and incoherent target DOA estimation, improve the flexibility of DOA estimations.
Description
Technical Field
The invention relates to a signal processing method, in particular to a coherent and incoherent mixed object DOA estimation method based on a co-prime MIMO array.
Background
Based on space-time sampling of a sensor array, azimuth position information of a plurality of space targets can be determined by direction of arrival (DOA) estimation, the method has high resolution, and is widely applied to the fields of communication, radar, sonar, seismic sensing and the like. For a fully-received array with adjacent array elements evenly spaced at half-wavelength intervals, the maximum resolvable number of incoherent objects is limited by the number of actual array elements. In order to break through the limitation of resolution number, a sparse receiving array with the adjacent array element spacing larger than half wavelength is used for designing a non-coherent target DOA estimation method, and commonly used sparse receiving arrays comprise a minimum redundant array, a minimum hole array, a nested array and a co-prime array, wherein the co-prime array proposed in recent years has outstanding advantages in the aspects of array element position determination, adjacent array element coupling mutual interference and the like, and gradually becomes a focus. At present, a mutual-prime receiving array-based incoherent target DOA estimation method mainly utilizes the characteristic that corresponding 'difference synergistic array' virtual array elements are uniformly distributed at a half-wavelength interval, and related elements are rearranged to construct 'difference synergistic array' equivalent single snapshot data, so that the DOA estimation of an incoherent target is realized. Because the number of the virtual array elements of the 'difference cooperative array' is greater than the number of the actual array elements of the co-prime array, the DOA estimation of the incoherent target with more than the actual array elements can be realized by using the 'difference cooperative array'.
However, in the above DOA estimation method based on the "difference synergistic array", the equivalent single snapshot signal used is derived from the relevant elements obtained after the actual multi-snapshot signal is correlated, and if there are multiple coherent targets, cross terms between the targets will be generated when the correlation is solved, so that a false target exists in the DOA estimation result, and therefore, the above method is not suitable for the case where coherent targets exist, that is, the DOA estimation of the coherent targets cannot be realized. Considering a multiple-input multiple-output (MIMO) array, the DOA estimation of coherent and incoherent mixed targets is easy to implement, and the traditional method requires that a transmitting array and a receiving array are generally uniformly and densely distributed arrays, and the interval between adjacent array elements is half wavelength. At this time, the total number of the maximum resolvable coherent and incoherent objects is limited by the number of the receiving array elements, which is equal to the number of the receiving array elements minus 1, and the number of the coherent objects is limited by the number of the transmitting array elements, which is equal to the number of the transmitting array elements. The invention introduces sparse co-prime layout into the MIMO array, on one hand, the DOA estimation of coherent and non-coherent mixed targets is realized by using the characteristics of the MIMO array, on the other hand, the maximum resolvable target number is increased by using the sparse transmitting and receiving array layout, and the limitation of the receiving array element number and the transmitting array element number on the maximum resolvable target total number and the maximum resolvable coherent target number is broken through. The invention has important value for improving the target capturing capability of radar and sonar and improving the capacity of a communication channel.
Disclosure of Invention
The invention aims to provide a coherent and incoherent mixed target DOA estimation method based on a co-prime MIMO array, which solves the problem of coherent and incoherent mixed target DOA estimation on the one hand, and breaks through the limitation of the actual array element number of the MIMO array to the maximum distinguishable target number by utilizing the sparse characteristic of the co-prime layout and the uniform dense distribution characteristic of the 'and cooperative array' on the other hand.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows: a coherent and incoherent mixed object DOA estimation method based on a co-prime MIMO array comprises the following steps:
(1) Selecting an area, and arranging N transmitting array elements and 2M-1 receiving array elements according to a mutual-prime layout to form a mutual-prime MIMO array, wherein M is less than N, the transmitting array elements and the receiving array elements are positioned on the same straight line, and the positions of the N transmitting array elements are P t = { Mnd; n =0,1, …, N-1}, and the positions of 2M-1 receiving antennas are P r = { Nmd; m =1,2, …,2M-1}, d is the fundamental spacing of half wavelength;
(2) N transmitting array elements sequentially transmit electromagnetic wave signals with the frequency of c/2d to carry out far-field target detection, wherein c is the light speed, if a target is detected, the electromagnetic wave signals are scattered and then returned, the returned echo signals are simultaneously received by 2M-1 receiving array elements to obtain echo signals of (2M-1) multiplied by N receiving and transmitting channels, and the echo signals of each channel are respectively subjected to K times of sampling to generate K times of snapshot data;
(3) Adding the positions of N transmitting array elements and the positions of 2M-1 receiving array elements in sequence, obtaining a virtual array element once every addition, forming a virtual array formed by the virtual array elements, and recording the virtual array element as a co-prime MIMO array and a co-pilot array, wherein the positions of the virtual array elements are as follows:
S＝{Mnd+Nmd；n＝0,1,…,N-1；m＝1,2,…,2M-1} (1)
(4) Extracting middle uniformly distributed virtual array elements from the sum cooperative array to form a reference sum cooperative array, wherein the uniformly distributed virtual array elements are MN + M-1 virtual array elements which are uniformly distributed in the interval from (MN-M + 1) d to (2 MN-1) d at an interval d;
(5) Constructing a uniformly-densely-distributed virtual MIMO array comprising A virtual transmitting array elements and B virtual receiving array elements on the basis of a reference and cooperative array, wherein the positions of the A virtual transmitting array elements are P v,t ＝{(x t + i) d; i =1,2, …, a }, and the positions of the B virtual receiving array elements are P v,r ＝{(x r + j) d; j =1,2, …, B }, while satisfying:
wherein x t And x r Is an arbitrary real number, and x t -x r ＝MN-M-1；
(6) Sequentially forming a virtual transceiving channel by the ith virtual transmitting array element and the jth virtual receiving array element to obtain (x) t +i)+(x r + j) using the position and value as reference, searching a virtual array element corresponding to the value from the reference and cooperative array, searching a transceiving channel for generating the virtual array element from the co-prime MIMO array, and using K pieces of snapshot data of the transceiving channel as equivalent snapshot data of the virtual transceiving channel; finally forming a BxAxK three-dimensional data matrix XV;
(7) For Xv, a two-dimensional correlation matrix Rv with dimension B × B is obtained by averaging K pieces of snapshot data over time, that is:
wherein the superscript H represents the pair matrix X v Transpose conjugate operation of (k);
(8) And aiming at a correlation matrix Rv with dimension B multiplied by B, calculating a spatial spectrum containing a target DOA estimated value according to a MUSIC subspace DOA estimation algorithm.
Preferably, the method comprises the following steps: in the step (5), the number and the position of the virtual transceiving array elements can be determined by the following formula (4),
wherein, b is any real number, and the position of the virtual transceiving array element can be represented as:
preferably, the method comprises the following steps: in the step (5), A is less than B.
In the invention, N transmitting array elements and 2M-1 receiving array elements of the co-prime MIMO array in the first step are all sparsely arranged at a distance exceeding a half wavelength (basic distance d), while A transmitting array elements and B receiving array elements of the virtual MIMO array in the fifth step are all densely arranged at a distance equal to the half wavelength, and under the premise of 'being equivalent to a cooperative array', the total number of the virtual array elements is greater than the total number of the actual array elements, namely (A + B) > (N + 2M-1). Therefore, it is easy to obtain A > N and B >2M-1 simultaneously, i.e. the number of virtual transmitting array elements is larger than the number of actual transmitting array elements, while the number of virtual receiving array elements is larger than the number of actual receiving array elements. Since the number of virtual array elements determines the maximum number of resolvable targets, the use of virtual array elements more than the actual number of array elements can achieve the limitation that the total number of maximum resolvable coherent and incoherent targets exceeds the number of receiving array elements, wherein the maximum resolvable coherent target number breaks through the limitation of the actual number of transmitting array elements of the co-prime MIMO array.
The sum cooperative array corresponding to the co-prime MIMO array in the third step can be divided into three parts, wherein the middle uniform part comprises MN + M-1 virtual array elements which are uniformly distributed in the interval from (MN-M + 1) d to (2 MN-1) d at the interval d, and the two end non-uniform parts comprise relatively less MN-M-N +1 virtual array elements which are non-uniformly distributed in the interval from Nd to (MN-M-1) d, (2MN + 1) d to (3 MN-M-N) d. In order to construct the virtual MIMO array in the fifth step, only MN + M-1 virtual array elements in the middle uniform part are selected as a reference and cooperative array in the fourth step.
Based on the virtual MIMO array constructed in the fifth step, the maximum resolvable target number is limited by the virtual receiving array element number, namely the maximum resolvable B-1 coherent and incoherent mixed targets are resolved; of the B-1 targets, the maximum resolvable coherent target number is limited by the virtual transmit array element number, i.e., at most A coherent targets are resolvable. In order to ensure that the degrees of freedom provided by the virtual MIMO array can be fully used for DOA estimation of coherent and incoherent mixed targets, A < B is required to be satisfied.
And: in the fifth step, the number a of virtual transmitting array elements and the number B of virtual receiving array elements of the virtual MIMO array are any two positive integers satisfying a + B = MN + M, and there are a plurality of different combinations of values, that is, the virtual MIMO array with different numbers of transmitting and receiving array elements can be obtained, and the number of the corresponding different maximum resolvable coherent targets and the maximum resolvable coherent and incoherent target total numbers correspond to the different maximum resolvable coherent targets and the maximum resolvable coherent and incoherent target total numbers, where the larger the number B of the virtual receiving array elements is, the smaller the number a of the virtual transmitting array elements is, the larger the resolvable coherent and incoherent target total numbers at this time are, but the smaller the resolvable coherent target numbers are, conversely, the smaller the B is, the larger the a is, the smaller the resolvable coherent and incoherent target total numbers at this time are, but the larger the resolvable coherent target numbers are. Therefore, the number of the transmitting and receiving array elements of the virtual MIMO array can be flexibly selected to meet the requirements of different scenes on the DOA estimation of coherent and incoherent mixed targets.
On one hand, when the number of virtual transmitting array elements A =1, the number of virtual receiving array elements reaches the maximum value B = MN + M-1, and the DOA of a coherent target cannot be estimated at this moment, but the DOA estimation capability of a non-coherent target reaches the maximum value, and at most MN + M-2 non-coherent targets can be estimated (distinguished); on the other hand, when the number of virtual array elements MN + M-1 of the "reference and cooperative array" in step four is an even number and B = a +1, i.e., a = (MN + M-1)/2,B = (MN + M + 1)/2, the DOA estimation capability for coherent targets reaches the maximum value, but the total number of resolvable targets reaches the minimum value, i.e., the maximum number of resolvable targets is B-1, and the maximum number of B-1 coherent targets.
Compared with the prior art, the invention has the advantages that: the invention introduces the co-prime layout into the MIMO array, utilizes the sparse characteristic of the co-prime layout and the uniform dense distribution characteristic of the 'and cooperative array', constructs the uniformly dense virtual MIMO array which has the same 'and cooperative array' with the sparse co-prime MIMO array based on the basic idea of the 'and cooperative array', and compared with the actual co-prime MIMO array, the virtual MIMO array has more transmitting array elements and receiving array elements, therefore, the invention obtains the equivalent multi-snapshot data of the virtual MIMO array and carries out DOA estimation accordingly, thereby not only solving the DOA estimation problem of coherent and non-coherent mixed targets, but also breaking through the limitation of the actual array element number of the co-prime MIMO array on the maximum distinguishable target number, because the receiving array element number limits the maximum distinguishable coherent and non-coherent target total number, the transmitting array element number limits the maximum distinguishable number of coherent targets therein. In addition, the invention can obtain the virtual MIMO array with different numbers of transmitting and receiving array elements, and the virtual MIMO array corresponds to different maximum distinguishable coherent target numbers and maximum distinguishable coherent and incoherent target total numbers, therefore, the invention improves the DOA estimation flexibility, and can meet the requirements of different scenes on coherent and incoherent mixed target DOA estimation by flexibly selecting the number of the transmitting and receiving array elements of the virtual MIMO array.
Drawings
FIG. 1 is a schematic diagram of the test of the present invention;
fig. 2 is a schematic diagram of a co-prime MIMO array with M =3 and N =4, a "sum cooperative array" and a corresponding virtual MIMO array;
FIG. 3 is a DOA estimation result when the number of spatial objects is 9 and 5 coherent objects are included;
fig. 4 shows the DOA estimation results when the number of spatial objects is 8 and 6 coherent objects are included.
Detailed Description
The invention will be further explained with reference to the drawings.
Example 1:
referring to fig. 1, a coherent and incoherent mixed target DOA estimation method based on a co-prime MIMO array includes the following steps:
(1) Selecting an area, and arranging N transmitting array elements and 2M-1 receiving array elements according to a mutual-prime layout to form a mutual-prime MIMO array, wherein M is less than N, the transmitting array elements and the receiving array elements are positioned on the same straight line, and the positions of the N transmitting array elements are P t = { Mnd; n =0,1, …, N-1}, and the positions of 2M-1 receiving antennas are P r = { Nmd; m =1,2, …,2M-1}, d being the basic spacing of half wavelength;
(2) N transmitting array elements sequentially transmit electromagnetic wave signals with the frequency of c/2d to detect a target, if the target is detected, the electromagnetic wave signals are scattered and returned, returned echo signals are received by 2M-1 receiving array elements at the same time, echo signals of (2M-1) x N receiving and transmitting channels are obtained, and the echo signals of each channel are respectively subjected to K times of sampling to generate K pieces of snapshot data;
(3) Adding the positions of N transmitting array elements and the positions of 2M-1 receiving array elements in sequence, obtaining a virtual array element once every addition to form a virtual array consisting of the virtual array elements, and recording the virtual array elements as a sum cooperative array of a co-prime MIMO array, wherein the positions of the virtual array elements are recorded as:
S＝{Mnd+Nmd；n＝0,1,…,N-1；m＝1,2,…,2M-1} (1)
(4) Extracting middle uniformly distributed virtual array elements from the sum cooperative array to form a reference sum cooperative array, wherein the uniformly distributed virtual array elements are MN + M-1 virtual array elements which are uniformly distributed in the interval from (MN-M + 1) d to (2 MN-1) d at an interval d;
(5) Constructing a uniformly-densely distributed virtual MIMO array comprising A virtual transmitting array elements and B virtual receiving array elements based on a reference and cooperative array, wherein the positions of the A virtual transmitting array elements are P v,t ＝{(x t + i) d; i =1,2, …, a }, and the positions of the B virtual receiving array elements are P v,r ＝{(x r + j) d; j =1,2, …, B }, while satisfying:
wherein x t And x r Is an arbitrary real number, and x t -x r ＝MN-M-1；
(6) Sequentially forming a virtual transceiving channel by the ith virtual transmitting array element and the jth virtual receiving array element to obtain (x) t +i)+(x r + j) using the position and value as reference, searching a virtual array element corresponding to the value from the reference and cooperative array, searching a transceiving channel for generating the virtual array element from the co-prime MIMO array, and using K pieces of snapshot data of the transceiving channel as equivalent snapshot data of the virtual transceiving channel; finally forming a B multiplied by A multiplied by K three-dimensional data matrix XV;
(7) Obtaining a two-dimensional correlation matrix Rv with dimension B multiplied by B by solving a time average mode for the K snapshot data for the XV, namely:
wherein the superscript H represents the pair matrix X v Transpose conjugate operation of (k);
(8) And aiming at a correlation matrix Rv with dimension B multiplied by B, calculating a spatial spectrum containing a target DOA estimated value according to a MUSIC subspace DOA estimation algorithm. .
Wherein: in step (5), the number and position of the virtual transceiving array elements can be determined by the following formula (4),
wherein, b is any real number, and the position of the virtual transceiving array element can be represented as:
and in the step (5), A is less than B.
Example 2:
see fig. 2-4; in this embodiment, MATLAB simulation software is used to perform simulation, a coherent and incoherent mixed target to be measured is set in a far field, a co-prime MIMO array with M =3 and N =4 is used, the number of snapshots is 2000, the signal-to-noise ratio is 10dB, and the basic spacing d of half wavelengths is 1.
(1) Placing N =4 transmitting array elements and 2M-1=5 receiving array elements according to a co-prime layout to form a co-prime MIMO array, wherein the positions of the 4 transmitting array elements are P t =0,3,6,9, and the positions of the 5 receiving antennas are P r = {4,8,12,16,20}, as shown in fig. 2.
(2) 4 emission array elements transmit electromagnetic wave signals with the frequency of c/2d =150MHz in sequence, echo signals after reaching a target and scattering are received by 5 receiving array elements at the same time, so that echo signals of 5 multiplied by 4 receiving and transmitting channels are obtained, and the echo signals of each channel are respectively subjected to 2000 times of sampling to generate 2000 snapshot data.
(3) Adding the positions of 4 transmitting array elements and the positions of 5 receiving array elements in sequence to obtain the positions of virtual array elements in a 'co-array' corresponding to the co-prime MIMO array, and recording as:
S＝{3n+4m；n＝0,1,…,3；m＝1,2,…,5}
as shown in fig. 1, the sum cooperative array of the relatively prime MIMO array can be divided into three parts, where the middle uniform part includes (MN + M-1) =14 virtual array elements uniformly distributed in an interval (MN-M + 1) =10 to (2 MN-1) =23 with a distance d =1, and the two end non-uniform parts include (MN-M-N + 1) =6 virtual array elements relatively less non-uniformly distributed in two intervals (N =4 to (MN-M-1) =8, (2mn + 1) =25 to (3 MN-M-N) = 29).
(4) And (MN + M-1) =14 virtual array elements which are uniformly distributed in the interval of (MN-M + 1) =10 to (2 MN-1) =23 at the interval d =1 are extracted from the 'sum cooperative array' to form a reference sum cooperative array, and the whole formed array is taken as the 'reference sum cooperative array'.
(5) Based on this "reference and cooperative array", a plurality of virtual MIMO arrays with different number combinations of a and B can be constructed on the condition that the sum of the number of virtual transmit and receive array elements, a + B, satisfies a + B = MN + M. According to the method for determining the number and the positions of the virtual MIMO array elements given by the formula (5), if x is set t B =4 and a =5, then B =10 is easily obtained from equation (5), and the positions of a =5 virtual transmitting array elements are P v,t =5,6,7,8,9, and the positions of B =10 virtual receiving array elements are P v,r = {5,6,7,8,9,10,11,12,13,14}, such as virtual MIMO array 1 in fig. 2. If x is set t = B =4 and a =6, then, according to equation (5), it can be obtained that the position of the virtual MIMO array 2 containing a =6 virtual transmitting array elements and B =9 virtual receiving array elements as shown in fig. 2 is P for a =6 virtual transmitting array elements v,t =5,6,7,8,9,10, and the positions of B =10 virtual receiving array elements are P v,r =5,6,7,8,9,10,11,12,13. Obviously, the sum cooperative array of the two virtual MIMO arrays is the same as the reference sum cooperative array of the co-prime MIMO array, and the three are considered to be equivalent.
(6) Taking the virtual MIMO array 1 as an example, regarding a virtual transceiving channel composed of the ith virtual transmitting array element and the jth virtual receiving array element, with the value of the sum of the transceiving virtual array element positions (4+i) + (4+j) as a reference, the virtual array element at the reference position in the "reference and cooperative array" is identified, and 2000 pieces of snapshot data of the corresponding transceiving channel in the co-prime MIMO array of the virtual array element are generated as equivalent snapshot data of the virtual transceiving channel. For example, for the 2 nd virtual transmitting array element at position 6 and the 3 rd virtual receiving array element at position 7, the sum of the positions of the virtual transmitting and receiving array elements is 13, and the sum of the positions of the actual transmitting array element at position 9 and the actual receiving array element at position 4 in the co-prime MIMO array is also 13, then the actual transmitting and receiving array elements at positions 4 and 9 and the virtual transmitting and receiving array elements at positions 7 and 6 are considered to be equivalent to the "sum matrix" array element position 13, so that the 2000 snapshot data corresponding to the actual transmitting and receiving channels are regarded as the 2000 equivalent snapshot data of the "sum matrix" equivalent virtual transmitting and receiving channels.
The equivalent snapshot data of all the virtual transceiving channels are determined in sequence, and the equivalent snapshot data are arranged in sequence according to the numbers of the virtual transceiving array elements to form a three-dimensional data matrix Xv with the dimension of 10 multiplied by 5 multiplied by 2000, namely the line number sequentially corresponds to the 1 st to 10 th virtual receiving array elements, the column number sequentially corresponds to the 1 st to 5 th virtual transmitting units, and the page number sequentially corresponds to the 1 st to 2000 th snapshot data.
(7) For an equivalent three-dimensional data matrix of 10 × 5 × 2000 of the virtual MIMO array 1, a two-dimensional correlation matrix Rv with dimensions of 10 × 10 is obtained by averaging 2000 snapshot data over time, that is:
wherein the superscript H represents the pair matrix X v Transpose conjugate operation of (:, k).
Step eight: according to the MUSIC subspace DOA estimation algorithm, carrying out eigenvalue decomposition on the correlation matrix Rv with dimension of 10 multiplied by 10 obtained in the seventh step, and extracting a noise subspace matrix U N From this, the spatial spectrum function is calculated:
changing theta of the spatial spectrum function to discretely take 1000 values between-90 degrees and 90 degrees, and searching an angle corresponding to a peak value of the spatial spectrum function to be used as an estimated value of the target DOA. Wherein the content of the first and second substances,for the steering matrix of the virtual receive array, the superscript T represents the transpose operation on the steering matrix.
For a virtual MIMO array 1 comprising 5 virtual transmit elements and 10 virtual receive elements, the total number of maximum resolvable coherent and incoherent targets is theoretically 9 (the number of virtual receive elements minus 1), where the maximum resolvable coherent target number is 5 (the number of virtual transmit elements), which exceeds the number of actual receive elements minus 1 (i.e. 4) and the number of actual transmit elements (i.e. 4) of the co-prime MIMO array, respectively. To verify the conclusion, 9 spatial targets are set in the simulation, sine values sin θ of the actual directions θ are sequentially-0.8, -0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, and 0.8, the first 5 targets are coherent targets, the last 4 targets are incoherent targets, and the DOA estimation result is shown in fig. 3, which confirms the feasibility of implementing DOA estimation of 5 coherent targets and 4 incoherent targets by using the virtual MIMO array 1.
For the virtual MIMO array 2 comprising 6 virtual transmit elements and 9 virtual receive elements, the total number of maximum resolvable coherent and incoherent objects is theoretically 8, wherein the number of maximum resolvable coherent objects is 6, which also exceeds the number of actual receive elements of the co-prime MIMO array minus 1 (i.e. 4) and the number of actual transmit elements 4 (i.e. 4), respectively. To verify the conclusion, 8 spatial targets are set in the simulation, the sine values sin θ of the actual directions θ are sequentially-0.8, -0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, and 0.8, the first 6 targets are coherent targets, the last 2 targets are incoherent targets, and the DOA estimation result is shown in fig. 4, which confirms the feasibility of implementing DOA estimation of 6 coherent targets and 2 incoherent targets by using the virtual MIMO array 1.
The simulation results shown in fig. 3 and 4 verify three advantages of the present invention, one is that DOA estimation for a mixed target of coherent and non-coherent is achieved; the total number of coherent and incoherent targets breaks through the limit that the number of actual receiving array elements of the co-prime MIMO array is reduced by 1, wherein the number of coherent targets breaks through the limit of the number of actual transmitting array elements of the co-prime MIMO array; and thirdly, the virtual MIMO array with different virtual array element numbers can be obtained, DOA estimation of different numbers of targets can be realized, DOA estimation flexibility is improved, and the requirements of different scenes on coherent and incoherent mixed target DOA estimation can be met.
Claims (3)
1. A coherent and incoherent mixed object DOA estimation method based on a co-prime MIMO array is characterized in that: the method comprises the following steps:
(1) Selecting an area, and arranging N transmitting array elements and 2M-1 receiving array elements according to a mutual-prime layout to form a mutual-prime MIMO array, wherein M is less than N, the transmitting array elements and the receiving array elements are positioned on the same straight line, and the positions of the N transmitting array elements are P t = { Mnd; n =0,1, …, N-1}, and the positions of 2M-1 receiving antennas are P r = { Nmd; m =1,2, …,2M-1}, d being the basic spacing of half wavelength;
(2) N transmitting array elements sequentially transmit electromagnetic wave signals with the frequency of c/2d to carry out far-field target detection, wherein c is the light speed, if a target is detected, the electromagnetic wave signals are scattered and then returned, the returned echo signals are simultaneously received by 2M-1 receiving array elements to obtain echo signals of (2M-1) multiplied by N receiving and transmitting channels, and the echo signals of each channel are respectively subjected to K times of sampling to generate K times of snapshot data;
(3) Adding the positions of N transmitting array elements and the positions of 2M-1 receiving array elements in sequence, obtaining a virtual array element once each addition, forming a virtual array formed by the virtual array elements, recording the virtual array element as a co-ordinated array of a co-prime MIMO array, wherein the positions of the virtual array elements are as follows:
S＝{Mnd+Nmd；n＝0,1,…,N-1；m＝1,2,…,2M-1} (1)
(4) Extracting middle uniformly distributed virtual array elements from the sum cooperative array to form a reference sum cooperative array, wherein the uniformly distributed virtual array elements are MN + M-1 virtual array elements which are uniformly distributed in the interval from (MN-M + 1) d to (2 MN-1) d at an interval d;
(5) Constructing a uniformly-densely distributed virtual MIMO array comprising A virtual transmitting array elements and B virtual receiving array elements based on a reference and cooperative array, wherein the positions of the A virtual transmitting array elements are P v,t ＝{(x t + i) d; i =1,2, …, a }, and the positions of the B virtual receiving array elements are P v,r ＝{(x r + j) d; j =1,2, …, B }, while satisfying:
wherein x t And x r Is an arbitrary real number, and x t -x r ＝MN-M-1；
(6) Sequentially forming a virtual transceiving channel by the ith virtual transmitting array element and the jth virtual receiving array element to obtain (x) t +i)+(x r + j) using the position and value as reference, searching a virtual array element corresponding to the value from the reference and cooperative array, searching a transceiving channel for generating the virtual array element from the co-prime MIMO array, and using K pieces of snapshot data of the transceiving channel as equivalent snapshot data of the virtual transceiving channel; finally forming a B multiplied by A multiplied by K three-dimensional data matrix XV;
(7) Obtaining a two-dimensional correlation matrix Rv with dimension B multiplied by B by solving a time average mode for the K snapshot data for the XV, namely:
wherein the superscript H represents the pair matrix X v Transpose conjugate operation of (k);
(8) And aiming at a correlation matrix Rv with dimension B multiplied by B, calculating a spatial spectrum containing a target DOA estimated value according to a MUSIC subspace DOA estimation algorithm.
2. The coherent and non-coherent mixed target DOA estimation method based on the co-prime MIMO array according to claim 1, characterized in that: in the step (5), the number and the position of the virtual transceiving array elements can be determined by the following formula (4),
obedience: a + B = MN + M
Wherein, b is any real number, and the position of the virtual transceiving array element can be represented as:
3. the coherent and non-coherent mixed target DOA estimation method based on the co-prime MIMO array according to claim 1, characterized in that: in the step (5), A is less than B.
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