Phase interferometer design method based on multiple linearly polarized antennas

Abstract

The invention discloses a phase interferometer design method based on multiple linearly polarized antennas, and belongs to the technical field of array signal processing. According to the invention, the problems of polarization mismatch and low robustness and precision of polarization parameter measurement of an existing polarization interferometer are solved. The design criterion of the linear polarization antenna spacing is direction finding precision and phase difference error measurement. The design criterion of the polarization directional angle of the linearly polarized antenna is to receive the hyper-volume of a matrix formed by polarization parameters of the linearly polarized antenna. The polarization directional angles of the receiving linear polarization antenna are diversified, and the polarization of the incident signal and the receiving linear polarization antenna are not orthogonal, so that the problems that the polarization mismatch phenomenon occurs and DOA parameters cannot be estimated under extreme conditions are avoided, and meanwhile, the robustness and the precision of polarization parameter measurement are improved; and more excellent ambiguity resolution performance and DOA estimation precision can be obtained in a broadband range. The method can be applied to phase interferometer design.

Description

Technical Field

[0001] The invention belongs to the technical field of array signal processing, and in particular relates to a phase interferometer design method based on multiple linear polarization antennas. Background Art

[0002] Passive radar direction finding systems estimate the direction of arrival by receiving electromagnetic waves emitted or reflected by the target. In scalar interferometer direction finders, the polarization parameters of electromagnetic wave signals cannot be estimated because the polarization characteristics of their antennas are the same. Multi-polarization non-uniform interferometer direction finders composed of multiple linearly polarized antennas perform better in measuring the polarization parameters of electromagnetic wave signals and can effectively avoid polarization mismatch, thereby improving the robustness and accuracy of polarization parameter measurement.

[0003] Interferometers are widely used for their high direction-finding accuracy and easy engineering implementation. Interferometric direction-finding systems often use three or more antennas to determine the frequency, amplitude, and phase of the incident radiation at a fixed distance. When the shortest baseline is less than half the wavelength of the highest frequency signal, the unambiguous DOA of the radiation source can be obtained by comparing the phase measurement value. Scalar interferometer direction finders are generally composed of multiple polarized antennas with the same polarization characteristics, so they cannot measure the polarization parameters of electromagnetic waves and have poor robustness to signal polarization. In order to accurately measure polarization, two orthogonal polarization receiving antennas are usually required to form an antenna element, so the number of antennas in the interferometer antenna array is doubled. In response to the problem of requiring a set of common polarization orthogonal antennas to measure polarization, scholars proposed to add an antenna with a polarization orthogonal to the original antenna on the basis of the original interferometer antenna array to form a polarization interferometer. However, this method has two weaknesses. First, using antennas with the same polarization to estimate DOA is prone to polarization mismatch. Second, the existing polarization interferometer uses a group of antennas with the same polarization to measure the DOA parameters of the incident signal. However, when the polarization of the incident signal is orthogonal to the polarization of the receiving antenna, polarization mismatch occurs, which makes it impossible to estimate the DOA parameters. At the same time, it leads to low robustness and accuracy of polarization parameter measurement. Compared with scalar interferometers and polarization interferometers, multi-polarization non-uniform interferometers can sense the polarization characteristics of signals, avoid polarization mismatch, reduce mutual coupling effects, etc. The design of multi-polarization non-uniform interferometers involves three key aspects: antenna spacing design, antenna polarization type design, and antenna polarization pointing angle design. However, the design of linear polarization antenna spacing and linear polarization antenna polarization pointing angle design with a resolution probability of not less than 98% in a wide band (0.8GHz to 18GHz) and strong robustness to the measurement phase difference error is still insufficient.

[0004] In summary, in order to solve the problems of polarization mismatch, robustness and low precision of polarization parameter measurement in existing polarization interferometers, the design of multi-polarization non-uniform interferometers needs further research. Summary of the invention

[0005] The purpose of the present invention is to solve the problems of polarization mismatch, robustness and low precision of polarization parameter measurement of existing polarization interferometers, and to propose a phase interferometer design method based on multiple linearly polarized antennas.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: a phase interferometer design method based on multiple linearly polarized antennas, the method specifically comprising the following steps:

[0007] Step 1: construct a receiving data model, and then calculate the relationship between the signal power received by N linear polarization antennas and the polarization pointing angle of the linear polarization antenna according to the receiving data model, and then obtain the polarization pointing angle matrix of the linear polarization antenna according to the relationship between the signal power and the polarization pointing angle;

[0008] Step 2: Determine the spacing between adjacent linear polarization antennas based on DOA estimation accuracy, linear polarization antenna layout environment, and linear polarization antenna size restrictions;

[0009] Step 3: Calculate the polarization spacing between adjacent linear polarization antennas according to the polarization pointing angle matrix of the linear polarization antennas, that is, calculate the difference in polarization pointing angles of adjacent linear polarization antennas;

[0010] Step 4: Design a phase interferometer based on the spacing between adjacent linear polarization antennas and the polarization pointing angle difference between adjacent linear polarization antennas.

[0011] Furthermore, the specific process of step one is:

[0012] Step 1: Build a receiving data model

[0013] The number of linearly polarized antennas constituting the phase interferometer is recorded as N, the N linearly polarized antennas are all located on the yoz plane and the phase centers of the N linearly polarized antennas are all located on the positive half axis of the y axis. The position coordinate vector of the nth linearly polarized antenna is recorded as l n =[0,d n ,0] T , d n is the position of the phase center of the nth linearly polarized antenna in the y-axis direction;

[0014] Get the received data X(t) of N linear polarization antennas:

[0015] X(t)=AS(t)+N(t) (1)

[0016] Among them, the dimension of the received data X(t) is N×K, K is the number of electromagnetic wave signal sampling snapshots, S(t) is the spatial signal vector, N(t) is the noise data vector of N linear polarization antennas, and A is the steering vector of the incident electromagnetic wave signal;

[0017]

[0018] Among them, α n is the polarization pointing angle of the nth linearly polarized antenna, u n is the spatial phase shift factor between the nth linearly polarized antenna and the origin, θ is the incident azimuth of the incident electromagnetic wave signal, θ∈[-π / 3,π / 3], γ is the polarization auxiliary angle of the incident electromagnetic wave signal, γ∈[0,-π / 2], η is the polarization phase difference of the incident electromagnetic wave signal, η∈[-π,π], j is the imaginary unit, and e is the base of the natural logarithm;

[0019] Step 1 and 2: Obtain the signal power received by N linear polarization antennas according to the received data model, and then establish the relationship between the signal power received by the N linear polarization antennas and the polarization pointing angle of the linear polarization antennas:

[0020] p n ′=a+bcos2α n +CSIN2α n (3)

[0021] Among them, p′ n is the signal power received by the nth linearly polarized antenna, and a, b, and c are all power-polarization coefficients;

[0022] Step 13: Obtain the linear polarization antenna polarization angle matrix Q based on the relationship between signal power and polarization angle:

[0023]

[0024] in, It is a pseudo-inverse operation, P is the vector composed of the signal power received by all N linearly polarized antennas, P = [p1′,…,p n ′,…,p′ N ],p1′,…,p′ n ,…,p′ N are the signal powers received by the 1st,…,nth,…,Nth linearly polarized antennas respectively.

[0025] Furthermore, the spatial phase shift factor u between the nth linearly polarized antenna and the origin is n for:

[0026]

[0027] in, is the unit direction vector of the incident electromagnetic wave signal, the superscript T represents the transpose, and λ is the wavelength of the incident electromagnetic wave signal.

[0028] Furthermore, the electromagnetic wave signal incident unit direction vector for:

[0029]

[0030] Furthermore, the specific process of step 2 is as follows:

[0031] Step 21: The positions of each linear polarization antenna satisfy:

[0032] d N -d1=d max ,d i -d j ≥d min , r<d min (7)

[0033] Where i>j, d1 is the position of the phase center of the first linearly polarized antenna in the y-axis direction, d i is the position of the phase center of the i-th linearly polarized antenna in the y-axis direction, d j is the position of the phase center of the jth linearly polarized antenna in the y-axis direction, d N is the position of the phase center of the Nth linearly polarized antenna in the y-axis direction, d max is the distance between the phase center of the first linear polarization antenna and the phase center of the Nth linear polarization antenna, d min is the minimum spacing between the phase centers of adjacent linearly polarized antennas, and r is the size of the linearly polarized antenna;

[0034] Step 2: Calculate the root mean square error σ of the measured phase difference error according to the signal-to-noise ratio SNR Δf :

[0035]

[0036] And the spacing d max satisfy:

[0037]

[0038] Among them, σ θ′ is the theoretical RMS angle measurement error, θ′ is the arrival angle of the received signal;

[0039] Step 2: Calculate the uniform distance D between adjacent phase lines:

[0040]

[0041] Among them, p i+1 and p i are mutually prime numbers; and the uniform distance D between adjacent phase lines satisfies:

[0042] D / 2>σ Δf (11)

[0043] And the relationship between the position of the phase center of the linear polarization antenna and the coprime number satisfies:

[0044]

[0045] Among them, k i+1 is the fuzzy number corresponding to the i+1th linear polarization antenna, k i is the fuzzy number corresponding to the i-th linear polarization antenna, is d i+1 The phase difference in [-π, +π] is is d i Phase difference in [-π, +π];

[0046] Step 24: Determine the spacing between every two adjacent linear polarization antennas according to equations (7) to (12), that is, the spacing between the phase centers of every two adjacent linear polarization antennas.

[0047] Furthermore, the linear polarization antenna polarization pointing angle matrix Q satisfies rank(Q)=3, where rank(Q) is the rank of the matrix Q.

[0048] Furthermore, the specific process of step three is:

[0049] A hyperparallel polyhedron is formed according to the polarization directivity matrix of the linear polarization antenna. When the volume of the hyperparallel polyhedron formed by the polarization directivity matrix of the linear polarization antenna is the largest, the polarization spacing between adjacent linear polarization antennas is obtained.

[0050] Furthermore, the volume of the hyperparallel polyhedron is Among them, det(·) represents the value of the calculated determinant, Q T is the transpose of Q.

[0051] Furthermore, when the volume of the hyperparallel polyhedron formed by the polarization pointing angle matrix of the linear polarization antenna is the largest, the polarization spacing between adjacent linear polarization antennas is:

[0052]

[0053] Among them, Δ p (α m ,α n ) is the polarization spacing between the mth linear polarization antenna and the nth linear polarization antenna, n=m+1.

[0054] The beneficial effects of the present invention are:

[0055] The present invention proposes a phase interferometer design method based on multiple linearly polarized antennas, including the design of the spacing between linearly polarized antennas and the design of the polarization pointing angle of linearly polarized antennas. The design criteria for the spacing between linearly polarized antennas are direction finding accuracy and measurement phase difference error. In addition, it is proposed to use the value of the volume of a hyperparallel polyhedron formed by the matrix Q, that is, the hypervolume of the matrix composed of the polarization parameters of the receiving linearly polarized antenna as the design criterion for the polarization pointing angle of the linearly polarized antenna. At the same time, the polarization pointing angle of the receiving linearly polarized antenna of the present invention is diverse, and the polarization of the incident signal and the receiving linearly polarized antenna are not all orthogonal, which avoids the occurrence of polarization mismatch and the problem of being unable to estimate DOA parameters in extreme cases, and at the same time improves the robustness and accuracy of polarization parameter measurement. In addition, the present invention is particularly designed for the spacing between linearly polarized antennas and the polarization pointing angle of linearly polarized antennas, and can obtain more superior deambiguation performance and DOA estimation accuracy within a wide bandwidth. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flow chart of a phase interferometer design method based on multiple linear polarization antennas of the present invention;

[0057] Figure 2 A schematic diagram of the linear polarization antenna distribution and incident signal of the multi-polarization non-uniform interferometer of the present invention;

[0058] Figure 3 Schematic diagram of the volume of the hyperparallel polyhedron spanned by the matrix Q and the area of ​​four linearly polarized antennas on the Poincare sphere;

[0059] In the figure, W1-W5 represent the polarization states of antennas 1-5, and S1, S2, and S3 are coordinate axes;

[0060] Figure 4 This is the relationship between frequency and deambiguation probability under different linear polarization antenna spacings;

[0061] Figure 5 This is the relationship diagram between the frequency and the root mean square error of the DOA estimation result under different linear polarization antenna polarization pointing angles;

[0062] Figure 6 This is the relationship between frequency and deambiguation probability under different linear polarization antenna polarization pointing angles;

[0063] Figure 7 This is the relationship diagram between the frequency and the root mean square error of polarization parameter estimation under different linear polarization antenna polarization pointing angles. DETAILED DESCRIPTION

[0064] Specific implementation method 1: Combination Figure 1 The present embodiment describes a method for designing a phase interferometer based on multiple linearly polarized antennas, and the method specifically includes the following steps:

[0065] Step 1: construct a receiving data model, and then calculate the relationship between the signal power received by N linear polarization antennas and the polarization pointing angle of the linear polarization antenna according to the receiving data model, and then obtain the polarization pointing angle matrix of the linear polarization antenna according to the relationship between the signal power and the polarization pointing angle;

[0066] Step 2: Determine the spacing between adjacent linear polarization antennas based on DOA estimation accuracy, linear polarization antenna layout environment, and linear polarization antenna size restrictions;

[0067] Step 3: Calculate the polarization spacing between adjacent linear polarization antennas according to the polarization pointing angle matrix of the linear polarization antennas, that is, calculate the difference in polarization pointing angles of adjacent linear polarization antennas;

[0068] Step 4: Design a phase interferometer based on the spacing between adjacent linear polarization antennas and the polarization pointing angle difference between adjacent linear polarization antennas.

[0069] Specific implementation method 2: Combination Figure 2 This embodiment is different from the first embodiment in that the specific process of step 1 is as follows:

[0070] Step 1: Build a receiving data model

[0071] The number of linearly polarized antennas constituting the phase interferometer is recorded as N, the N linearly polarized antennas are all located on the yoz plane and the phase centers of the N linearly polarized antennas are all located on the positive half axis of the y axis (that is, the layout of the linearly polarized antennas is determined first), and the position coordinate vector of the nth linearly polarized antenna is recorded as l n =[0,d n ,0] T , d n is the position of the phase center of the nth linearly polarized antenna in the y-axis direction;

[0072] The planes and coordinate axes in the present invention are planes and coordinate axes in a spatial rectangular coordinate system;

[0073] Get the received data X(t) of N linear polarization antennas:

[0074] X(t)=AS(t)+N(t) (1)

[0075] Among them, the dimension of the received data X(t) is N×K, K is the number of electromagnetic wave signal sampling snapshots, S(t) is the spatial signal vector, N(t) is the noise data vector of N linear polarization antennas, and A is the steering vector of the incident electromagnetic wave signal;

[0076]

[0077] Among them, α nis the polarization pointing angle of the nth linear polarization antenna, that is, the angle between the right side of the front of the nth linear polarization antenna and the positive half axis of the y-axis (the protruding surface in the figure is the front), u n is the spatial phase shift factor between the nth linearly polarized antenna and the origin, θ is the incident azimuth of the incident electromagnetic wave signal, θ∈[-π / 3,π / 3], γ is the polarization auxiliary angle of the incident electromagnetic wave signal, γ∈[0,-π / 2], η is the polarization phase difference of the incident electromagnetic wave signal, η∈[-π,π], j is the imaginary unit, and e is the base of the natural logarithm;

[0078] Step 1 and 2: Obtain the signal power received by N linear polarization antennas according to the received data model, and then establish the relationship between the signal power received by the N linear polarization antennas and the polarization pointing angle of the linear polarization antennas:

[0079] p n ′=a+bcos2α n +CSIN2α n (3)

[0080] Among them, p′ n is the signal power received by the nth linearly polarized antenna, and a, b, and c are all power-polarization coefficients;

[0081] Step 13: Obtain the linear polarization antenna polarization angle matrix Q based on the relationship between signal power and polarization angle:

[0082]

[0083] in, It is a pseudo-inverse operation, P is the vector composed of the signal power received by all N linearly polarized antennas, P = [p1′,…,p n ′,…,p′ N ],p1′,…,p′ n ,…,p′ N are the signal powers received by the 1st,…,nth,…,Nth linearly polarized antennas respectively.

[0084] The other steps and parameters are the same as those in the first embodiment.

[0085] Specific implementation method three: This implementation method is different from specific implementation method one or two in that the spatial phase shift factor u between the nth linear polarization antenna and the origin is n for:

[0086]

[0087] in, is the unit direction vector of the incident electromagnetic wave signal, the superscript T represents the transpose, and λ is the wavelength of the incident electromagnetic wave signal.

[0088] The other steps and parameters are the same as those in the first or second embodiment.

[0089] Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 1 to 3 in that the electromagnetic wave signal incident unit direction vector for:

[0090]

[0091] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0092] Specific implementation method 5: This implementation method is different from the specific implementation methods 1 to 4 in that the specific process of step 2 is as follows:

[0093] Step 21: The positions of each linear polarization antenna satisfy:

[0094] d N -d1=d max ,d i -d j ≥d min , r<d min (7)

[0095] Where i>j, d1 is the position of the phase center of the first linearly polarized antenna in the y-axis direction, d i is the position of the phase center of the i-th linearly polarized antenna in the y-axis direction, d j is the position of the phase center of the jth linearly polarized antenna in the y-axis direction, d N is the position of the phase center of the Nth linearly polarized antenna in the y-axis direction, d max is the distance between the phase center of the first linear polarization antenna and the phase center of the Nth linear polarization antenna, d min is the minimum spacing between the phase centers of adjacent linearly polarized antennas, and r is the size of the linearly polarized antenna;

[0096] Step 2: Calculate the root mean square error σ of the measured phase difference error according to the signal-to-noise ratio SNR Δf :

[0097]

[0098] And the spacing d max satisfy:

[0099]

[0100] Among them, σ θ′ is the theoretical RMS angle measurement error (related to the DOA estimation accuracy), θ′ is the arrival angle of the received signal;

[0101] Step 2: Calculate the uniform distance D between adjacent phase lines:

[0102]

[0103] Among them, p i+1 and p i are mutually prime numbers; and the uniform distance D between adjacent phase lines satisfies:

[0104] D / 2>σ Δf (11)

[0105] The best condition for deambiguation is that the distance between each spectral line in the phase sample space should be as large as possible. Therefore, by choosing Δφ The linear polarization antenna spacing can minimize the DOA estimation error.

[0106] And the relationship between the position of the phase center of the linear polarization antenna and the coprime number satisfies:

[0107]

[0108] Among them, k i+1 is the fuzzy number corresponding to the i+1th linear polarization antenna, k i is the fuzzy number corresponding to the i-th linear polarization antenna, is d i+1 The phase difference in [-π, +π] is is d i Phase difference in [-π, +π];

[0109] Step 24: Determine the spacing between every two adjacent linear polarization antennas according to equations (7) to (12), that is, the spacing between the phase centers of every two adjacent linear polarization antennas.

[0110] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0111] Specific implementation example 6: This implementation example is different from any one of specific implementation examples 1 to 5 in that the linear polarization antenna polarization pointing angle matrix Q satisfies rank(Q)=3, where rank(Q) is the rank of the matrix Q.

[0112] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0113] Specific implementation method 7: This implementation method is different from the specific implementation methods 1 to 6 in that the specific process of step 3 is as follows:

[0114] A hyperparallel polyhedron is formed according to the polarization directivity matrix of the linear polarization antenna. When the volume of the hyperparallel polyhedron formed by the polarization directivity matrix of the linear polarization antenna is the largest, the polarization spacing between adjacent linear polarization antennas is obtained.

[0115] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0116] Specific implementation eight: This implementation differs from any one of specific implementations one to seven in that the volume of the superparallel polyhedron is Among them, det(·) represents the value of the calculated determinant, Q T is the transpose of Q.

[0117] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0118] In order to make the matrix form of equations in formula (4) have a solution, it is necessary to satisfy:

[0119] rank(Q)=3 (13)

[0120] That is, three linearly polarized antennas with inconsistent polarization pointing angles are required to form the matrix Q. Wherein, rank(·) represents the rank of the matrix, and det(·) represents the determinant of the matrix.

[0121] The volume of the hyperparallel polyhedron is formed by using the matrix Q The geometric meaning of is the essence of the scaled size of the directed volume of this space. The matrix Q can be regarded as a geometric body. The transpose of the matrix Q is as follows:

[0122]

[0123] Among them, (1, cos2α1, sin2α1) represents a vector, which can also be expressed as a line segment on the Poincare sphere. (cos2α1, sin2α1) represents a point on the equator with an angle of 2α1 on the Poincare sphere, which is the linear polarization of the linear polarization antenna with a polarization pointing angle of α1. In other words, (cos2α1, sin2α1) represents the polarization representation of a linear polarization antenna with a polarization pointing angle of α1 on the equator of the Poincare sphere (i.e., the S1OS2 plane).

[0124] The volume of the hyperparallel polyhedron spanned by the matrix Q The maximum value can be converted into the maximum shadow volume formed by the linear polarization antenna on the equator of the Poincare sphere and the top of the sphere. According to the knowledge of solid geometry, when the linear polarization antenna on the equator of the Poincare sphere is evenly distributed, the volume of the shadow part is the largest. When the matrix Q is stretched into the volume of a hyperparallel polyhedron When it is maximum, the error of the power output vector P has the least effect on the errors of the power-polarization coefficients a, b and c.

[0125] Specific implementation method 9: This implementation method is different from any one of specific implementation methods 1 to 8 in that when the volume of the hyperparallel polyhedron formed by the polarization pointing angle matrix of the linear polarization antenna is the largest, the polarization spacing between adjacent linear polarization antennas is:

[0126]

[0127] Among them, Δ p (α m ,α n ) is the polarization spacing between the mth linear polarization antenna and the nth linear polarization antenna, that is, the polarization pointing angle α of the mth linear polarization antenna m and the polarization pointing angle α of the nth linearly polarized antenna n The difference, n=m+1.

[0128] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0129] In order to verify the effect of the method of the present invention, the deambiguation probability is analyzed according to the linear polarization antenna spacing and the linear polarization antenna polarization pointing angle of the present invention:

[0130] Considering a multi-polarization non-uniform interferometer with five linearly polarized antennas, the longest baseline length of 821 mm is determined according to the DOA estimation accuracy requirement and the linearly polarized antenna layout. According to the existing linearly polarized antenna spacing design and the linearly polarized antenna spacing design method of the present invention, according to different p i+1 :p i Combination, six linear polarization antenna spacing designs are given, among which spacing configuration 6 is the linear polarization antenna spacing designed by the present invention, and the scheme is shown in Table 1:

[0131] Table 1 Linear polarization antenna spacing configuration

[0132]

[0133] Figure 3 It is a volume diagram of five antennas on the Poincare sphere. Similarly, according to the polarization pointing angles of existing linear polarization antennas and the design criteria of the polarization pointing angles of the linear polarization antennas of the present invention, Table 2 gives seven designs of polarization pointing angles of linear polarization antennas, and the polarization pointing angles of the five linear polarization antennas are distributed within -90° to 90°. Configuration 7 is designed by the present invention, and the polarization pointing angles of the two linear polarization antennas with the longest baseline are the same.

[0134] Table 2 Polarization pointing angle configuration of linear polarization antenna

[0135]

[0136] Experiment 1: The impact of the spacing between linearly polarized antennas on the probability of deambiguation. Assume that the azimuth angle θ of the incoming signal is randomly located at (-0.5°~0.5°). The corresponding polarization parameters are (45°, 90°), that is, the polarization state of the incident signal is circular polarization. The number of snapshots K is fixed to 64, and the SNR is set to 0dB. The frequency range of the incident signal is 0.8GHz~18GHz, with a step size of 1GHz. The polarization pointing angle configurations of the linearly polarized antennas are all {α1, α2, α3, α4, α5}={-67.5,-22.5,22.5,67.5,-67.5}. The DOA estimation method adopts the DOA estimation method based on multiple linearly polarized antennas.

[0137] from Figure 4 It can be seen that when the polarization pointing angle of the linear polarized antenna is consistent with the DOA estimation method, when the signal-to-noise ratio is 0dB, the deambiguation probability of the linear polarized antenna spacing designed by the present invention in the range of 0.8GHz to 18GHz is higher than the deambiguation probability corresponding to the other five linear polarized antenna spacings, and the deambiguation success probability exceeds 98%. Especially when the incident signal frequency is greater than 10GHz, the deambiguation advantage of the linear polarized antenna spacing designed by the present invention is more obvious.

[0138] Experiment 2: The influence of the polarization pointing angle of the linear polarization antenna on the probability of resolution and the accuracy of DOA estimation. The spacing configuration of the linear polarization antenna is 7{0,d1,d2,d3,d4}={0,7,13,169 / 7,1183 / 35}821 / 33.8mm. The rest of the experimental conditions are the same as those of Experiment 1.

[0139] from Figure 5 It can be seen that the root mean square error of DOA estimation corresponding to configuration 7 is the smallest, which is lower than the polarization pointing angle configurations of other linear polarization antennas. This is because the closer the polarizations of the two linear polarization antennas on the longest baseline are, the smaller the impact on DOA estimation. Figure 6 It can be seen that the deambiguation probabilities of configuration 7 and configuration 6 are close, and both are higher than other linear polarization antenna polarization angle configurations. Figure 7 It can be seen that the polarization parameter estimation errors of configuration 7 and configuration 6 are lower than those of other linear polarization antenna polarization angle configurations. Although the polarization parameter estimation accuracy of configuration 7 is slightly inferior to that of linear polarization antenna polarization angle configuration 6, which is consistent with the design criteria of the linear polarization antenna polarization angle of the present invention, the linear polarization antenna polarization angle configuration 7 has the best DOA estimation accuracy in the range of 0.8 GHz to 18 GHz, and the probability of successful resolution of ambiguity exceeds 98%.

[0140] In summary, the present invention proposes a phase interferometer design method based on multiple linearly polarized antennas. The design principle of the present invention according to the position of the multi-polarization interferometer is as follows:

[0141] 1) Determine the maximum interval d max length.

[0142] 2) Determine the interval ratio p according to the required signal-to-noise ratio and number of snapshots i+1 and p i .

[0143] The design principles of the polarization pointing angle of the linear polarization antenna of the multi-polarization interferometer are as follows:

[0144] 1) The linear polarization antenna pointing angle matrix Q is a column full rank matrix.

[0145] 2) When the polarization states of the linearly polarized antennas are evenly distributed within the Poincare polarization sphere, the overall polarization distance between the linearly polarized antennas is the largest, and the polarization estimation accuracy is higher.

[0146] The present invention develops a phase interferometer design method based on multiple linear polarizations, improves the accuracy and robustness of DOA parameter and polarization parameter estimation of a polarization interferometer direction finding system, and achieves a success rate of over 98% in deambiguation.

[0147] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A phase interferometer design method based on multiple linearly polarized antennas, characterized in that: The method specifically comprises the following steps: Step 1: construct a receiving data model, and then calculate the relationship between the signal power received by N linear polarization antennas and the polarization pointing angle of the linear polarization antenna according to the receiving data model, and then obtain the polarization pointing angle matrix of the linear polarization antenna according to the relationship between the signal power and the polarization pointing angle; Step 2: Determine the spacing between adjacent linear polarization antennas based on DOA estimation accuracy, linear polarization antenna layout environment, and linear polarization antenna size restrictions; Step 3: Calculate the polarization spacing between adjacent linear polarization antennas according to the polarization pointing angle matrix of the linear polarization antennas, that is, calculate the difference in polarization pointing angles of adjacent linear polarization antennas; Step 4: Design a phase interferometer based on the spacing between adjacent linear polarization antennas and the polarization pointing angle difference between adjacent linear polarization antennas.

2. The method for designing a phase interferometer based on multiple linearly polarized antennas according to claim 1, characterized in that: The specific process of step one is: Step 1: Build a receiving data model The number of linearly polarized antennas constituting the phase interferometer is recorded as N, the N linearly polarized antennas are all located on the yoz plane and the phase centers of the N linearly polarized antennas are all located on the positive half axis of the y axis. The position coordinate vector of the nth linearly polarized antenna is recorded as l n =[0,d n ,0] T , d n is the position of the phase center of the nth linearly polarized antenna in the y-axis direction; Get the received data X(t) of N linear polarization antennas: X(t)=AS(t)+N(t) (1) Among them, the dimension of the received data X(t) is N×K, K is the number of electromagnetic wave signal sampling snapshots, S(t) is the spatial signal vector, N(t) is the noise data vector of N linear polarization antennas, and A is the steering vector of the incident electromagnetic wave signal; Among them, α n is the polarization pointing angle of the nth linearly polarized antenna, u n is the spatial phase shift factor between the nth linearly polarized antenna and the origin, θ is the incident azimuth of the incident electromagnetic wave signal, θ∈[-π / 3,π / 3], γ is the polarization auxiliary angle of the incident electromagnetic wave signal, γ∈[0,-π / 2], η is the polarization phase difference of the incident electromagnetic wave signal, η∈[-π,π], j is the imaginary unit, and e is the base of the natural logarithm; Step 1 and 2: Obtain the signal power received by N linear polarization antennas according to the received data model, and then establish the relationship between the signal power received by the N linear polarization antennas and the polarization pointing angle of the linear polarization antennas: p n ′s+bcos2α n +csin2α n (3) Among them, p′ n is the signal power received by the nth linearly polarized antenna, and a, b, and c are all power-polarization coefficients; Step 13: Obtain the linear polarization antenna polarization angle matrix Q based on the relationship between signal power and polarization angle: in, It is a pseudo-inverse operation, P is the vector composed of the signal power received by all N linearly polarized antennas, P = [p1′,…,p n ′,…,p′ N ],p1′,…,p′ n ,…,p′ N are the signal powers received by the 1st,…,nth,…,Nth linearly polarized antennas respectively.

3. The method for designing a phase interferometer based on multiple linearly polarized antennas according to claim 2, characterized in that: The spatial phase shift factor u between the nth linearly polarized antenna and the origin n for: in, is the unit direction vector of the incident electromagnetic wave signal, the superscript T represents the transpose, and λ is the wavelength of the incident electromagnetic wave signal.

4. The method for designing a phase interferometer based on multiple linearly polarized antennas according to claim 3, characterized in that: The electromagnetic wave signal incident unit direction vector for:

5. The method for designing a phase interferometer based on multiple linearly polarized antennas according to claim 4, characterized in that: The specific process of step 2 is as follows: Step 21: The positions of each linear polarization antenna satisfy: d N -d1=d max ,d i -d j ≥d min ,r<d min (7) Where i>j, d1 is the position of the phase center of the first linearly polarized antenna in the y-axis direction, d i is the position of the phase center of the i-th linearly polarized antenna in the y-axis direction, d j is the position of the phase center of the jth linearly polarized antenna in the y-axis direction, d N is the position of the phase center of the Nth linearly polarized antenna in the y-axis direction, d max is the distance between the phase center of the first linear polarization antenna and the phase center of the Nth linear polarization antenna, d min is the minimum spacing between the phase centers of adjacent linearly polarized antennas, and r is the size of the linearly polarized antenna; Step 2: Calculate the root mean square error σ of the measured phase difference error according to the signal-to-noise ratio SNR Δf : And the spacing d max satisfy: Among them, σ θ′ is the theoretical RMS angle measurement error, θ′ is the arrival angle of the received signal; Step 2: Calculate the uniform distance D between adjacent phase lines: Among them, p i+1 and p i are mutually prime numbers; and the uniform distance D between adjacent phase lines satisfies: D / 2>s Δf (11) And the relationship between the position of the phase center of the linear polarization antenna and the coprime number satisfies: Among them, k i+1 is the fuzzy number corresponding to the i+1th linear polarization antenna, k i is the fuzzy number corresponding to the i-th linear polarization antenna, is d i+1 The phase difference in [-π, +π] is is d i Phase difference in [-π, +π]; Step 24: Determine the spacing between every two adjacent linear polarization antennas according to equations (7) to (12), that is, the spacing between the phase centers of every two adjacent linear polarization antennas.

6. The method for designing a phase interferometer based on multiple linearly polarized antennas according to claim 5, characterized in that: The linear polarization antenna polarization pointing angle matrix Q satisfies rank(Q)=3, where rank(Q) is the rank of the matrix Q.

7. The method for designing a phase interferometer based on multiple linearly polarized antennas according to claim 6, characterized in that: The specific process of step three is: A hyperparallel polyhedron is formed according to the polarization directivity matrix of the linear polarization antenna. When the volume of the hyperparallel polyhedron formed by the polarization directivity matrix of the linear polarization antenna is the largest, the polarization spacing between adjacent linear polarization antennas is obtained.

8. The method for designing a phase interferometer based on multiple linearly polarized antennas according to claim 7, characterized in that: The volume of the hyperparallel polyhedron is where det(·) represents the value of the calculated determinant, Q T is the transpose of Q.

9. The method for designing a phase interferometer based on multiple linearly polarized antennas according to claim 8, characterized in that: When the volume of the hyperparallel polyhedron formed by the polarization pointing angle matrix of the linear polarization antenna is the largest, the polarization spacing between adjacent linear polarization antennas is: Among them, Δ p (α m ,α n ) is the polarization spacing between the mth linear polarization antenna and the nth linear polarization antenna, n=m+1.

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