A method of designing a phase interferometer based on multiple linear polarized antennas

Abstract

The application relates to a design method of a phase interferometer based on multiple linear polarization antennas, and belongs to the technical field of array signal processing. The application solves the problems of polarization mismatch, low robustness and low precision of polarization parameter measurement of an existing polarization interferometer. The design criteria of the linear polarization antenna spacing of the application are the direction finding precision and the phase difference measurement error. The design criteria of the polarization pointing angle of the linear polarization antenna are the super volume of the polarization parameter matrix of the receiving linear polarization antenna. Since the polarization pointing angle of the receiving linear polarization antenna of the application is varied, the polarization of the incident signal and the receiving linear polarization antenna are not all orthogonal, the polarization mismatch phenomenon is avoided, the problem that the DOA parameter cannot be estimated in an extreme case is solved, the robustness and precision of the polarization parameter measurement are improved, and more superior unblurring performance and DOA estimation precision can be obtained in a wide frequency band range. The method of the application can be applied to the design of a phase interferometer.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing technology, specifically relating to a design method for a phase interferometer based on multiple linearly polarized antennas. Background Technology

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

[0003] Interferometers are widely used due to their high direction-finding accuracy and ease of engineering implementation. Interferometric direction-finding systems often use three or more antennas to determine the frequency, amplitude, and phase of incident radiation at fixed distances. 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 phase measurements. Scalar interferometer direction finders generally consist of multiple polarized antennas with the same polarization characteristics; therefore, they cannot measure the polarization parameters of electromagnetic waves and have poor robustness to signal polarization. To accurately measure polarization, two orthogonally polarized receiving antennas are usually required to form an antenna element, thus doubling the number of antennas in the interferometer antenna array. To address the problem of requiring a set of common-point orthogonal polarized antennas for polarization measurement, researchers have proposed adding an antenna orthogonal to the original interferometer antenna array to form a polarized interferometer. However, this method has two weaknesses. First, using antennas with the same polarization to estimate DOA easily leads to polarization mismatch. Second, existing polarization interferometers use a set of antennas with the same polarization to measure the DOA parameters of the incident signal; however, when the polarization of the incident signal and the polarization of the receiving antenna are orthogonal, polarization mismatch occurs, making it impossible to estimate the DOA parameters and resulting in 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 the signal, avoid polarization mismatch, and reduce mutual coupling effects. 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, research on linear polarization antenna spacing design and linear polarization antenna polarization pointing angle design with a deambiguity probability of no less than 98% and strong robustness to measurement phase difference errors within a wide bandwidth (0.8GHz~18GHz) is still insufficient.

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

[0005] The purpose of this invention is to solve the problems of polarization mismatch, low robustness and low accuracy of polarization parameter measurement in 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-mentioned technical problems is: a design method for a phase interferometer based on multiple linearly polarized antennas, the method specifically including the following steps:

[0007] Step 1: Construct a receiving data model, then calculate the relationship between the signal power received by N linearly polarized antennas and the polarization pointing angle of the linearly polarized antennas based on the receiving data model, and finally obtain the polarization pointing angle matrix of the linearly polarized antennas based on the relationship between signal power and polarization pointing angle.

[0008] Step 2: Determine the spacing between adjacent linearly polarized antennas based on the DOA estimation accuracy, the layout environment of the linearly polarized antennas, and the size limitations of the linearly polarized antennas;

[0009] Step 3: Calculate the polarization spacing between adjacent linearly polarized antennas based on the polarization pointing angle matrix of the linearly polarized antennas, that is, calculate the difference in polarization pointing angle between adjacent linearly polarized antennas;

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

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

[0012] Step 11: Constructing a Data Reception Model

[0013] Let N be the number of linearly polarized antennas that make up the phase interferometer. All N linearly polarized antennas are located on the yoz plane, and the phase centers of all N linearly polarized antennas are located on the positive half of the y-axis. Let l be the position coordinate vector of the nth linearly polarized antenna. n =[0,d n ,0] T d n It is the position of the phase center of the nth linearly polarized antenna along the y-axis;

[0014] Obtain the received data X(t) from N linearly polarized antennas:

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

[0016] Wherein, the dimension of the received data X(t) is N×K, K is the number of sampling snapshots of the electromagnetic wave signal, S(t) is the spatial signal vector, N(t) is the noise data vector of N linearly polarized antennas, and A is the steering vector of the incident electromagnetic wave signal.

[0017]

[0018] Where, α n It 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 angle 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] Steps 1 and 2: Obtain the signal power received by N linearly polarized antennas based on the received data model, and then establish the relationship between the signal power received by N linearly polarized antennas and the polarization pointing angle of the linearly polarized antennas:

[0020] p n ′=a+bcos2α n +csin2α n (3)

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

[0022] Step 13: Obtain the polarization pointing angle matrix Q of the linearly polarized antenna based on the relationship between signal power and polarization pointing angle.

[0023]

[0024] in, It is a pseudo-inverse operation, where P is a vector composed of the signal power received by all N linearly polarized antennas, P = [p1′, ..., p n ′,…,p′ N ],p1′,…,p′ n ,…,p′ N These represent the signal power 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... n for:

[0026]

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

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

[0029]

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

[0031] Step 21: The positions of each linearly polarized antenna satisfy the following:

[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, and d i d is the position of the phase center of the i-th linearly polarized antenna along the y-axis. j d is the position of the phase center of the j-th linearly polarized antenna along the y-axis. N d is the position of the phase center of the Nth linearly polarized antenna along the y-axis. max d is the distance between the phase center of the first linearly polarized antenna and the phase center of the Nth linearly polarized antenna. min It 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 variance σ of the measurement phase difference error based on the signal-to-noise ratio (SNR). Δf :

[0035]

[0036] And the spacing d max satisfy:

[0037]

[0038] Where, σ θ′ It is the theoretical root mean square angle measurement error, and θ′ is the angle of arrival of the received signal;

[0039] Steps 2 and 3: Calculate the uniform distance D between adjacent phase lines:

[0040]

[0041] Where, p i+1 and p i They are coprime; and the uniform distance D between adjacent phase lines satisfies:

[0042] D / 2>σ Δf (11)

[0043] Furthermore, the relationship between the position of the phase center of the linearly polarized antenna and the coprime number satisfies:

[0044]

[0045] Where, k i+1 Let k be the ambiguity number corresponding to the (i+1)th linearly polarized antenna. i Let i be the ambiguity number corresponding to the i-th linearly polarized antenna. For d i+1 The phase difference within [-π, +π] For d i Phase difference within [-π, +π];

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

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

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

[0049] The polarization spacing between adjacent linearly polarized antennas is obtained when the volume of the hyperparallel polyhedron spanned by the polarization pointing angle matrix of the linearly polarized antenna is maximized.

[0050] Furthermore, the volume of the hyperparallel polyhedron is Where det(·) represents calculating the value of the determinant, Q T It is the transpose of Q.

[0051] Furthermore, when the volume of the hyperparallel polyhedron spanned by the polarization pointing angle matrix of the linearly polarized antennas is maximized, the polarization spacing between adjacent linearly polarized antennas is:

[0052]

[0053] Where, Δ p (α m ,α n ) represents the polarization spacing between the m-th linearly polarized antenna and the n-th linearly polarized antenna, where n = m + 1.

[0054] The beneficial effects of this invention are:

[0055] This invention proposes a phase interferometer design method based on multiple linearly polarized antennas, including the design of the antenna spacing and polarization pointing angle. The design criteria for the antenna spacing are direction-finding accuracy and measurement phase difference error. Furthermore, it proposes using the volume of the hyperparallel polyhedron spanned by matrix Q, i.e., the hypervolume of the matrix composed of the polarization parameters of the receiving linearly polarized antennas, as the design criterion for the polarization pointing angle. Simultaneously, the polarization pointing angle of the receiving linearly polarized antenna in this invention is diverse; the polarization of the incident signal and the receiving linearly polarized antenna will not all be orthogonal, avoiding polarization mismatch and the inability to estimate DOA parameters in extreme cases, while improving the robustness and accuracy of polarization parameter measurement. Moreover, this invention specifically designs the antenna spacing and polarization pointing angle, achieving superior deambiguity performance and DOA estimation accuracy over a wide frequency range. Attached Figure Description

[0056] Figure 1 This is a flowchart of a phase interferometer design method based on multiple linearly polarized antennas according to the present invention;

[0057] Figure 2 This is a schematic diagram of the linearly polarized antenna distribution and incident signal of the multi-polarized non-uniform interferometer in this invention;

[0058] Figure 3 A schematic diagram showing the volume of the hyperparallel polyhedron spanned by matrix Q and the areas of the four linearly polarized antennas on the Poincaré sphere;

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

[0060] Figure 4 A graph showing the relationship between frequency and deambiguity probability for antenna spacing with different linear polarizations;

[0061] Figure 5 A graph showing the relationship between frequency and root mean square error of DOA estimation results at different linear polarization pointing angles of antennas;

[0062] Figure 6 A graph showing the relationship between frequency and deambiguity probability at different linear polarization pointing angles of antennas;

[0063] Figure 7 The graph shows the root mean square error relationship between frequency and polarization parameter estimation at different linear polarization pointing angles for antennas. Detailed Implementation

[0064] Specific implementation method one: Combining Figure 1 This embodiment describes a phase interferometer design method based on multiple linearly polarized antennas, which specifically includes the following steps:

[0065] Step 1: Construct a receiving data model, then calculate the relationship between the signal power received by N linearly polarized antennas and the polarization pointing angle of the linearly polarized antennas based on the receiving data model, and finally obtain the polarization pointing angle matrix of the linearly polarized antennas based on the relationship between signal power and polarization pointing angle.

[0066] Step 2: Determine the spacing between adjacent linearly polarized antennas based on the DOA estimation accuracy, the layout environment of the linearly polarized antennas, and the size limitations of the linearly polarized antennas;

[0067] Step 3: Calculate the polarization spacing between adjacent linearly polarized antennas based on the polarization pointing angle matrix of the linearly polarized antennas, that is, calculate the difference in polarization pointing angle between adjacent linearly polarized antennas;

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

[0069] Specific Implementation Method Two: Combining Figure 2 This embodiment is described below. The difference between this embodiment and specific embodiment one is that the specific process of step one is as follows:

[0070] Step 11: Constructing a Data Reception Model

[0071] Let N be the number of linearly polarized antennas that make up the phase interferometer. All N linearly polarized antennas are located on the yoz plane, and the phase centers of all N linearly polarized antennas are located on the positive half-axis of the y-axis (i.e., the layout of the linearly polarized antennas is determined first). Let l be the position coordinate vector of the nth linearly polarized antenna. n =[0,d n ,0] T d n It is the position of the phase center of the nth linearly polarized antenna along the y-axis;

[0072] In this invention, both the planes and coordinate axes are in a spatial rectangular coordinate system.

[0073] Obtain the received data X(t) from N linearly polarized antennas:

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

[0075] Wherein, the dimension of the received data X(t) is N×K, K is the number of sampling snapshots of the electromagnetic wave signal, S(t) is the spatial signal vector, N(t) is the noise data vector of N linearly polarized antennas, and A is the steering vector of the incident electromagnetic wave signal.

[0076]

[0077] Where, α nIt is the polarization pointing angle of the nth linearly polarized antenna, that is, the angle between the right side of the front of the nth linearly polarized antenna and the positive half-axis of the y-axis (the surface with the protrusion in the figure is the front). n is the spatial phase shift factor between the nth linearly polarized antenna and the origin, θ is the incident azimuth angle 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] Steps 1 and 2: Obtain the signal power received by N linearly polarized antennas based on the received data model, and then establish the relationship between the signal power received by N linearly polarized antennas and the polarization pointing angle of the linearly polarized antennas:

[0079] p n ′=a+bcos2α n +csin2α n (3)

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

[0081] Step 13: Obtain the polarization pointing angle matrix Q of the linearly polarized antenna based on the relationship between signal power and polarization pointing angle.

[0082]

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

[0084] The other steps and parameters are the same as in Specific Implementation Method 1.

[0085] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the spatial phase shift factor u between the nth linearly polarized antenna and the origin is... n for:

[0086]

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

[0088] Other steps and parameters are the same as in specific implementation method one or two.

[0089] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the incident unit direction vector of the electromagnetic wave signal... for:

[0090]

[0091] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0092] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the specific process of step two is as follows:

[0093] Step 21: The positions of each linearly polarized antenna satisfy the following:

[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, and d i d is the position of the phase center of the i-th linearly polarized antenna along the y-axis. j d is the position of the phase center of the j-th linearly polarized antenna along the y-axis. N d is the position of the phase center of the Nth linearly polarized antenna along the y-axis. max d is the distance between the phase center of the first linearly polarized antenna and the phase center of the Nth linearly polarized antenna. min It 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 variance σ of the measurement phase difference error based on the signal-to-noise ratio (SNR). Δf :

[0097]

[0098] And the spacing d max satisfy:

[0099]

[0100] Where, σ θ′ θ′ is the theoretical root mean square angle measurement error (related to the accuracy of DOA estimation), and θ′ is the angle of arrival of the received signal.

[0101] Steps 2 and 3: Calculate the uniform distance D between adjacent phase lines:

[0102]

[0103] Where, p i+1 and p i They are coprime; and the uniform distance D between adjacent phase lines satisfies:

[0104] D / 2>σ Δf (11)

[0105] The optimal condition for deblurring is that the distance between each spectral line in the phase sample space should be as large as possible. Therefore, by choosing a spectral line that satisfies D / 2 > σ... Δφ The spacing between linearly polarized antennas can minimize the DOA estimation error.

[0106] Furthermore, the relationship between the position of the phase center of the linearly polarized antenna and the coprime number satisfies:

[0107]

[0108] Where, k i+1 Let k be the ambiguity number corresponding to the (i+1)th linearly polarized antenna. i Let i be the ambiguity number corresponding to the i-th linearly polarized antenna. For d i+1 The phase difference within [-π, +π] For d i Phase difference within [-π, +π];

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

[0110] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0111] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the polarization pointing angle matrix Q of the linearly polarized antenna satisfies rank(Q) = 3, where rank(Q) is the rank of matrix Q.

[0112] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0113] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One to Six in that the specific process of step three is as follows:

[0114] The polarization spacing between adjacent linearly polarized antennas is obtained when the volume of the hyperparallel polyhedron spanned by the polarization pointing angle matrix of the linearly polarized antenna is maximized.

[0115] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0116] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that the volume of the hyperparallel polyhedron is... Where det(·) represents calculating the value of the determinant, Q T It is the transpose of Q.

[0117] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0118] For the system of equations (4) to have a solution in matrix form, the following must be satisfied:

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

[0120] This requires three linearly polarized antennas with different polarization pointing angles to form matrix Q. Here, rank(·) represents the rank of the matrix, and det(·) represents the determinant of the matrix.

[0121] Volume of a hyperparallel polyhedron spanned by matrix Q The geometric meaning of Q is essentially the scaling of the directed volume of this space; matrix Q can be viewed as a geometric solid. The transpose of matrix Q is as follows:

[0122]

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

[0124] Volume of matrix Q spanned into a hyperparallel polyhedron The maximum volume can be converted to the maximum volume of the shadow formed by the linearly polarized antenna on the equator of the Poincaré sphere and the sphere's dome. According to solid geometry, the shadow volume is largest when the linearly polarized antennas on the Poincaré sphere's equator are uniformly distributed. The volume of the shadowed region is also the maximum when matrix Q spans a hyperparallel polyhedron. At its maximum, the error in the power output vector P has the least impact on the errors in the power-polarization coefficients a, b, and c.

[0125] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that, when the volume of the hyperparallel polyhedron spanned by the polarization pointing angle matrix of the linearly polarized antennas is maximized, the polarization spacing between adjacent linearly polarized antennas is:

[0126]

[0127] Where, Δ p (α m ,α n ) represents the polarization spacing between the m-th and n-th linearly polarized antennas, i.e., the polarization pointing angle α of the m-th linearly polarized antenna. m and the polarization pointing angle α of the nth linearly polarized antenna n The difference is n = m + 1.

[0128] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0129] To verify the effectiveness of the method of the present invention, the following analysis is performed on the deambiguation probability based on the linear polarization antenna spacing and the linear polarization pointing angle of the present invention:

[0130] Considering a multipolar non-uniform interferometer with five linearly polarized antennas, the longest baseline length of 821 mm is determined based on the DOA estimation accuracy requirements and the linearly polarized antenna layout. Based on existing linearly polarized antenna spacing designs and the linearly polarized antenna spacing design method of this invention, and according to different p... i+1 :p i The invention presents six linear polarization antenna spacing designs, with spacing configuration 6 representing the linear polarization antenna spacing designed in this invention. The schemes are shown in Table 1.

[0131] Table 1. Linear Polarized Antenna Spacing Configuration

[0132]

[0133] Figure 3 This is a schematic diagram of the volume of a five-antenna array on a Poincaré sphere. Similarly, based on existing linearly polarized antenna polarization pointing angles and the design criteria for linearly polarized antenna polarization pointing angles of this invention, Table 2 presents seven designs for linearly polarized antenna polarization pointing angles, with five antennas having polarization pointing angles distributed within the range of -90° to 90°. Configuration 7 represents the design method of this invention, and the two linearly polarized antennas with the longest baseline have the same polarization pointing angle.

[0134] Table 2 Polarization pointing angle configuration of linearly polarized antennas

[0135]

[0136] Experiment 1: The Influence of Linearly Polarized Antenna Spacing on Deambiguity Probability. Assume the azimuth angle θ of the incoming signal is randomly located between -0.5° and 0.5°. The corresponding polarization parameters are (45°, 90°), meaning the incident signal is circularly polarized. The number of snapshots K is fixed at 64, and the SNR is set to 0dB. The incident signal frequency varies from 0.8GHz to 18GHz, with a step size of 1GHz. The polarization pointing angles of the linearly polarized antennas are configured as {α1, α2, α3, α4, α5} = {-67.5, -22.5, 22.5, 67.5, -67.5}. The DOA estimation method uses a method based on multiple linearly polarized antennas.

[0137] from Figure 4 As can be seen, when the polarization pointing angle and DOA estimation method of the linearly polarized antenna are consistent, and the signal-to-noise ratio is 0dB, the deambiguity probability of the linearly polarized antenna spacing designed in this invention in the range of 0.8GHz to 18GHz is higher than that of the other five linearly polarized antenna spacings, and the success rate of deambiguity exceeds 98%. In particular, when the incident signal frequency is greater than 10GHz, the deambiguity advantage of the linearly polarized antenna spacing designed in this invention is even more obvious.

[0138] Experiment 2: The effect of the polarization pointing angle of a linearly polarized antenna on the deambiguity probability and the accuracy of DOA estimation. The spacing of the linearly polarized antennas was configured as follows: 7{0,d1,d2,d3,d4}={0,7,13,169 / 7,1183 / 35}821 / 33.8mm. All other experimental conditions were the same as in Experiment 1.

[0139] from Figure 5 It can be seen that configuration 7 corresponds to the smallest root mean square error in DOA estimation, lower than the polarization pointing angle configurations of the other linearly polarized antennas. This is because the closer the polarizations of the two linearly polarized antennas with the longest baseline are, the smaller their impact on DOA estimation. Meanwhile, from... Figure 6 It can be seen that the deambiguity probabilities of configurations 7 and 6 are similar, and both are higher than the polarization pointing angle configurations of other linearly polarized antennas. Furthermore, from... Figure 7 It can be seen that the polarization parameter estimation errors of configurations 7 and 6 are lower than those of other linearly polarized antenna polarization pointing angle configurations. Although the polarization parameter estimation accuracy of configuration 7 is slightly inferior to that of configuration 6, which is consistent with the design criteria for linearly polarized antenna polarization pointing angles in this invention, configuration 7 has the best DOA estimation accuracy in the 0.8GHz to 18GHz range, with a deambiguity success probability exceeding 98%.

[0140] In summary, this invention proposes a design method for a phase interferometer based on multiple linearly polarized antennas. The design principles for the position of the multi-polarized interferometer are as follows:

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

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

[0143] The design principles for the polarization pointing angle of a linearly polarized antenna in a multipolar interferometer are as follows:

[0144] 1) The pointing angle matrix Q of the linearly polarized antenna is a full column rank matrix.

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

[0146] This invention proposes a design method for a phase interferometer based on multiple linear polarizations, which improves the accuracy and robustness of DOA parameter and polarization parameter estimation in the polarization interferometer direction finding system, and achieves a success rate of over 98% in unambiguity resolution.

[0147] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

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

2. The phase interferometer design method based on multiple linearly polarized antennas according to claim 1, characterized in that, The specific process of step one is as follows: Step 11: Constructing a Data Reception Model Let N be the number of linearly polarized antennas that make up the phase interferometer. All N linearly polarized antennas are located on the yoz plane, and the phase centers of all N linearly polarized antennas are located on the positive half of the y-axis. Let l be the position coordinate vector of the nth linearly polarized antenna. n =[0,d n ,0] T d n It is the position of the phase center of the nth linearly polarized antenna in the y-axis direction; Obtain the received data X(t) from N linearly polarized antennas: X(t)=AS(t)+N(t) (1) Wherein, the dimension of the received data X(t) is N×K, K is the number of sampling snapshots of the electromagnetic wave signal, S(t) is the spatial signal vector, N(t) is the noise data vector of N linearly polarized antennas, and A is the steering vector of the incident electromagnetic wave signal. Where, α n It 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 angle 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. Steps 1 and 2: Obtain the signal power received by N linearly polarized antennas based on the received data model, and then establish the relationship between the signal power received by N linearly polarized antennas and the polarization pointing angle of the linearly polarized antennas: p n ′s+bcos2α n +csin2α n (3) Where, p′ n is the signal power received by the nth linearly polarized antenna, where a, b, and c are all power-polarization coefficients; Step 13: Obtain the polarization pointing angle matrix Q of the linearly polarized antenna based on the relationship between signal power and polarization pointing angle. in, It is a pseudo-inverse operation, where P is a vector composed of the signal power received by all N linearly polarized antennas, P = [p1′, ..., p n ′,…,p′ N ],p1′,…,p′ n ,…,p′ N These represent the signal power received by the 1st, ..., nth, ..., Nth linearly polarized antennas, respectively.

3. The phase interferometer design method 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, It is the incident electromagnetic wave signal unit direction vector, the superscript T represents transpose, and λ is the wavelength of the incident electromagnetic wave signal.

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

5. The phase interferometer design method based on multiple linearly polarized antennas according to claim 4, characterized in that, The specific process of step two is as follows: Step 21: The positions of each linearly polarized antenna satisfy the following: 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, and d i d is the position of the phase center of the i-th linearly polarized antenna along the y-axis. j d is the position of the phase center of the j-th linearly polarized antenna along the y-axis. N d is the position of the phase center of the Nth linearly polarized antenna along the y-axis. max d is the distance between the phase center of the first linearly polarized antenna and the phase center of the Nth linearly polarized antenna. 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 variance σ of the measurement phase difference error based on the signal-to-noise ratio (SNR). Δf : And the spacing d max satisfy: Where, σ θ′ It is the theoretical root mean square angle measurement error, and θ′ is the angle of arrival of the received signal; Steps 2 and 3: Calculate the uniform distance D between adjacent phase lines: Where, p i+1 and p i They are coprime; and the uniform distance D between adjacent phase lines satisfies: D / 2>s Δf (11) Furthermore, the relationship between the position of the phase center of the linearly polarized antenna and the coprime number satisfies: Where, k i+1 Let k be the ambiguity number corresponding to the (i+1)th linearly polarized antenna. i Let be the ambiguity number corresponding to the i-th linearly polarized antenna. For d i+1 The phase difference within [-π, +π] For d i Phase difference within [-π, +π]; Step 24: Determine the spacing between every two adjacent linearly polarized antennas according to equations (7) to (12), that is, the spacing between the phase centers of every two adjacent linearly polarized antennas.

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

7. The phase interferometer design method based on multiple linearly polarized antennas according to claim 6, characterized in that, The specific process of step three is as follows: The polarization spacing between adjacent linearly polarized antennas is obtained when the volume of the hyperparallel polyhedron spanned by the polarization pointing angle matrix of the linearly polarized antenna is maximized.

8. The phase interferometer design method based on multiple linearly polarized antennas according to claim 7, characterized in that, The volume of the hyperparallel polyhedron is Where det(·) represents calculating the value of the determinant, Q T It is the transpose of Q.

9. The phase interferometer design method based on multiple linearly polarized antennas according to claim 8, characterized in that, When the volume of the hyperparallel polyhedron spanned by the polarization pointing angle matrix of the linearly polarized antennas is maximized, the polarization spacing between adjacent linearly polarized antennas is: Where, Δ p (α m ,α n ) represents the polarization spacing between the m-th linearly polarized antenna and the n-th linearly polarized antenna, where n = m + 1.

Images