Polarization-sensitive array direction finding method based on antenna spatial polarization characteristics

Abstract

A polarization-sensitive array direction-finding method based on the spatial polarization characteristics of antennas belongs to the technical field of array signal processing. The purpose of the present invention is to solve the problem of large errors in DOA and spatial polarization parameter estimation due to the inconsistent representation of antenna and electromagnetic wave polarization in existing methods and the failure to consider the spatial polarization characteristics of receiving antennas. The present invention describes the polarization definition of the transmitting antenna and the receiving antenna, the rotation of the receiving antenna, and the polarization state of the electromagnetic wave in a unified global rectangular coordinate system during the polarization-sensitive array direction-finding process, which can quantitatively describe the polarization of the antenna, making the description of the electromagnetic wave and antenna polarization more natural. At the same time, the direction-finding method of the present invention also considers the influence of the spatial polarization characteristics of the receiving antenna, thereby improving the accuracy of DOA and spatial polarization parameter estimation. The method of the present invention can be applied to polarization-sensitive array direction-finding.

Description

Technical Field

[0001] The invention belongs to the technical field of array signal processing, and in particular relates to a polarization-sensitive array direction finding method based on antenna spatial polarization characteristics. Background Art

[0002] The joint estimation of DOA and polarization parameters based on polarization-sensitive arrays has attracted extensive attention from scholars, especially in satellite-borne, missile-borne radars and various aircraft. Due to the irregularity of the attitude, the surface on which the receiving array is installed has a certain curvature, and it is difficult to ensure that the polarization selection characteristics of all receiving antennas are the same. Therefore, the use of polarization-sensitive array modeling is more reasonable and scientific. In addition, the use of polarization-sensitive array antennas that conform to the surface has the advantages of reducing aerodynamic drag, saving array space, and reducing radar cross-sectional area. Therefore, it is of great significance to study the direction-finding model of polarization-sensitive arrays.

[0003] The polarization characteristics and position of the receiving antenna will affect the response to the incident electromagnetic wave signal, and the construction of a suitable model is crucial for the joint estimation of DOA and polarization parameters. The current polarization-sensitive array direction-finding model has the following two problems: 1) The polarization representation of different fields such as antennas and electromagnetic waves is not unified; 2) The spatial polarization characteristics of the receiving antenna are ignored. In electromagnetics and antenna theory, various coordinate systems are used to describe the radiation source and the waves it emits. Usually the radiation source is described in a spatial rectangular coordinate system. On the other hand, a spherical coordinate system that is homologous to the spatial rectangular coordinate system is used to describe the far-field waves emitted by these radiation sources. However, since the origin is shared between the two coordinate systems, some ambiguity and confusion arise in the interpretation and application of the appropriate definitions of co-polarization and cross-polarization. In addition, due to different research focuses, it is generally believed that the polarization characteristics of the antenna are constant within the main lobe, and the polarization in the direction of maximum gain is the polarization of the antenna. However, due to antenna processing errors, loading platform limitations, the influence of other antennas in the array, etc., the polarization of the receiving antenna always deviates from the expected value to a certain extent. Moreover, when the observation point deviates from the boresight direction, the polarization purity of the antenna changes with the pitch angle. This change in the polarization of the antenna in space is called the spatial polarization characteristic of the antenna. However, most of the current polarization-sensitive array direction-finding models do not consider the influence of the spatial polarization characteristics of the antenna, that is, it is assumed that the polarization of the receiving antenna in space is stable (equal to the polarization in the direction of maximum gain). When performing direction finding within a wide boresight range, this assumption will inevitably lead to direction-finding errors. Moreover, the farther away from the boresight, the greater the deviation between the polarization of the receiving antenna and the polarization characteristics in the direction of maximum gain, and the greater the error in DOA and spatial polarization parameter estimation.

[0004] In summary, due to the inconsistent representation of antenna and electromagnetic wave polarization in the existing polarization-sensitive array direction-finding model, and the neglect of the spatial polarization characteristics of the receiving antenna, the existing polarization-sensitive array direction-finding method has large errors in estimating DOA and spatial polarization parameters. It is very necessary to propose a new method to solve the above problems. Summary of the invention

[0005] The purpose of the present invention is to solve the problem of large errors in DOA and spatial polarization parameter estimation caused by the inconsistent representation of antenna and electromagnetic wave polarization in existing methods and the failure to consider the spatial polarization characteristics of the receiving antenna, and to propose a polarization-sensitive array direction finding method based on the spatial polarization characteristics of the antenna.

[0006] The technical solution adopted by the present invention to solve the above technical problems is:

[0007] A polarization sensitive array direction finding method based on antenna spatial polarization characteristics, the method specifically comprising the following steps:

[0008] Step 1: define the local rectangular coordinate system of the receiving array as the global rectangular coordinate system, and obtain the representation relationship of two sets of polarization orthogonal bases of the receiving antenna and the representation relationship of two sets of polarization orthogonal bases of the transmitting antenna in the global rectangular coordinate system;

[0009] Step 2: In a global rectangular coordinate system, define the spatial polarization parameters of the transmitting antenna and the spatial polarization parameters of the receiving antenna;

[0010] Step 3: obtaining a spatial polarization vector of the transmitting antenna according to the spatial polarization parameters of the transmitting antenna; obtaining a spatial polarization vector of the receiving antenna according to the spatial polarization parameters of the receiving antenna, and then obtaining a spatial polarization characteristic matrix of the receiving antenna according to the spatial polarization vector of the receiving antenna;

[0011] Step 4: According to the characterization relationship in step 1, the spatial polarization characteristic matrix of the receiving antenna and the spatial polarization vector of the transmitting antenna, a polarization loss factor when the nth receiving antenna in the polarization sensitive array receives a signal is obtained;

[0012] Step 5: Calculate the received signal of the receiving antenna array according to the polarization loss factor;

[0013] Step 6: Estimate the DOA of the incident signal and the spatial polarization parameters of the transmitting antenna based on the received signal of the receiving antenna array.

[0014] Furthermore, the specific process of step one is:

[0015] Step 1: In a plane perpendicular to the propagation direction of the electromagnetic wave, place a set of polarization orthogonal basis It is expressed as:

[0016]

[0017] in, Parallel to the global rectangular coordinate system o r x r y r z r x r o r y r flat, Perpendicular to The origin o of the global rectangular coordinate system r is the center of the receiving array, z in the global rectangular coordinate system r The x-axis direction is the viewing axis direction of the receiving array, and the x-axis direction is the viewing axis direction of the global rectangular coordinate system. r The axis is parallel to the ground, y r Axis and x r Axis, z r The axes form a right-handed rectangular coordinate system; θ represents the azimuth of the incident direction of the electromagnetic wave in the global rectangular coordinate system, represents the pitch angle of the incident direction of the electromagnetic wave in the global rectangular coordinate system, and T represents the transposition;

[0018] The unit vector of the incident direction of the electromagnetic wave It is expressed as:

[0019]

[0020] Using another pair of polarization orthogonal basis in the plane perpendicular to the propagation direction of the electromagnetic wave represents the electromagnetic wave emitted by the receiving antenna, where is the principal polarization vector, is the cross-polarization vector, then in the global rectangular coordinate system, the two sets of polarization orthogonal basis of the receiving antenna and The representation relationship is:

[0021]

[0022] Among them, ζ is the global rectangular coordinate system and The rotation angle between for The Cartesian coordinate matrix in the global rectangular coordinate system, for The Cartesian coordinate matrix in the global rectangular coordinate system, for and The transformation matrix between

[0023] Step 1 and 2: In the local rectangular coordinate system of the transmitting antenna, the two sets of polarization orthogonal basis of the transmitting antenna and The representation relationship is:

[0024]

[0025]

[0026] Among them, Q is and The transformation matrix between them, ε is the local rectangular coordinate system o of the transmitting antenna t x t y t z t middle and The angle between the transmitting antenna and the origin of the local rectangular coordinate system is o t is the center of the transmitting antenna array, and the z coordinate of the local rectangular coordinate system of the transmitting antenna is t Axis and the z of the global rectangular coordinate system r The x axis of the local rectangular coordinate system of the transmitting antenna is opposite to the t Axis and the x of the global rectangular coordinate system r The y axis is in the opposite direction. t Axis and y r The axis direction is the same; θ x is the azimuth of the incident direction of the electromagnetic wave in the local rectangular coordinate system of the transmitting antenna, is the elevation angle of the incident direction of the electromagnetic wave in the rectangular local coordinate system of the transmitting antenna.

[0027] Furthermore, the two sets of polarization orthogonal bases of the receiving antenna and The rotation angle ζ between them is:

[0028]

[0029] Furthermore, the transmitting antenna local rectangular coordinate system o t x t y t z t Two sets of polarization orthogonal basis and The angle ε between them is:

[0030]

[0031] The superscript -1 represents the inversion.

[0032] Furthermore, the θ and θ x relationship and and The relationship is:

[0033]

[0034] Furthermore, the specific process of step 2 is as follows:

[0035]

[0036] Among them, α is the spatial polarization auxiliary angle of the transmitting antenna, β is the spatial polarization phase difference of the transmitting antenna, e is the base of the natural logarithm, j is the imaginary unit, and The electromagnetic wave of the transmitting antenna is orthogonal in polarization The weight on

[0037]

[0038] in, is the spatial polarization auxiliary angle of the receiving antenna, is the spatial polarization phase difference of the receiving antenna, and For receiving antenna electromagnetic waves in polarization orthogonal basis The amount on.

[0039] Furthermore, the specific process of step three is:

[0040] The spatial polarization vector f(α, β) of the transmitting antenna is calculated according to the spatial polarization parameters of the transmitting antenna:

[0041]

[0042] Then the set of spatial polarization vectors at each position is recorded as F;

[0043] Calculate the spatial polarization vector of the receiving antenna based on the spatial polarization parameters of the receiving antenna

[0044]

[0045] Then the set of spatial polarization vectors at each position is recorded as That is, the spatial polarization characteristic matrix of the receiving antenna is obtained and will The spatial polarization characteristics at each position in is recorded as

[0046] Furthermore, the specific process of step 4 is as follows:

[0047] The incident signal angle The corresponding angle in the local rectangular coordinate system of the nth receiving antenna is recorded as

[0048]

[0049] in, is the rotation angle between the local rectangular coordinate system and the global rectangular coordinate system of the nth receiving antenna, is the rotational pitch angle between the local rectangular coordinate system and the global rectangular coordinate system of the nth receiving antenna;

[0050] Then the polarization component of the nth receiving antenna in the global rectangular coordinate system is:

[0051]

[0052] in, is the spatial polarization characteristic matrix of the nth receiving antenna. The spatial polarization vector at For the nth receiving antenna The conversion matrix of the two polarization bases at (n) is the rotation matrix between the local rectangular coordinate system and the global rectangular coordinate system of the nth receiving antenna;

[0053] Polarization loss factor when the nth receiving antenna in a polarization sensitive array receives a signal for:

[0054]

[0055] Among them, f(α,β) is the spatial polarization vector of the transmitting antenna, Q(ε) is The conversion matrix of the two sets of polarization orthogonal bases of the transmitting antenna at , yes The transpose of .

[0056] Furthermore, the specific process of step five is as follows:

[0057] Step 51: The number of narrowband far-field signals incident on the polarization sensitive array is recorded as K, and the spatial domain parameter of the kth incident signal is recorded as Then the spatial response of the kth incident signal is in, is the spatial response of the nth receiving antenna to the kth incident signal;

[0058]

[0059] Where λ is the wavelength of the incident signal, l n is the position coordinate of the nth receiving antenna, and N is the number of receiving antennas;

[0060] Step 52: Calculate the spatial-polarization domain response of the nth receiving antenna to the kth incident signal based on the polarization loss factor when the nth receiving antenna receives the signal and the spatial domain response of the nth receiving antenna to the kth incident signal.

[0061]

[0062] in, is the polarization loss factor of the nth receiving antenna for the kth signal, (α k ,β k ) is the spatial polarization parameter of the transmitting antenna corresponding to the kth incident signal,

[0063] Step 53: According to Calculate the steering vector of the receiving antenna array for the kth incident signal

[0064]

[0065]

[0066] Among them, a (n) for Abbreviation of is the polarization sensitivity matrix of the nth receiving antenna to the kth incident signal, b (n) for Abbreviation of for abbreviation of;

[0067] Step 54: According to the guidance vector Calculate the received signal vector of the receiving antenna array at time t:

[0068]

[0069] Where X(t) is the N×1 dimensional array received data vector, S(t) is the K×1 dimensional spatial signal vector, N(t) is the N×1 dimensional noise data vector, and A is the N×K dimensional steering vector of the array;

[0070]

[0071] S(t)=[s 1 (t),s 2 (t),…,s K (t)] T (twenty four).

[0072] Furthermore, the specific process of step six is ​​as follows:

[0073] Step 6. Calculate the covariance matrix of the received signal X(t) of the receiving antenna array

[0074]

[0075] Among them, X H (t) represents the conjugate transpose of X(t), and E{·} represents the expectation;

[0076] Step 6.2: Covariance matrix Perform eigenvalue decomposition, sort the obtained eigenvalues ​​in order from small to large, and use the eigenvectors corresponding to the first NK eigenvalues ​​to form the noise subspace

[0077] Step 6.3: Using the Noise Subspace Estimate the DOA of the incident signal and the spatial polarization parameters of the transmitting antenna; specifically:

[0078] According to formula (26), the azimuth and elevation angles corresponding to the first K large peaks are calculated:

[0079]

[0080] Substitute the calculated azimuth and elevation angles into equations (26) and (27):

[0081]

[0082] in, represents the generalized eigenvector corresponding to the minimum generalized eigenvalue of the matrix bundle. yes The first element in yes The second element in |·| represents taking the absolute value, det{·} represents calculating the value of the determinant, arg{·} represents finding the argument of the complex number, α k and β k It is the spatial polarization auxiliary angle and spatial polarization phase difference of the transmitting antenna corresponding to the kth incident signal.

[0083] The beneficial effects of the present invention are:

[0084] The present invention proposes a polarization-sensitive array direction-finding method based on the spatial polarization characteristics of antennas. By describing the polarization definitions of the transmitting antenna and the receiving antenna, the rotation of the receiving antenna, and the polarization state of the electromagnetic wave in a unified global rectangular coordinate system during the polarization-sensitive array direction-finding process, the polarization of the antenna can be quantitatively described, making the description of the electromagnetic wave and the antenna polarization more natural. At the same time, the direction-finding method of the present invention also takes into account the influence of the spatial polarization characteristics of the receiving antenna, thereby improving the accuracy of DOA and spatial polarization parameter estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 A flow chart of a polarization sensitive array direction finding method based on antenna spatial polarization characteristics of the present invention;

[0086] FIG. 2( a ) is a polarization characterization relationship diagram of the receiving antenna of the present invention;

[0087] FIG. 2( b ) is a polarization characterization relationship diagram of the transmitting antenna of the present invention;

[0088] Figure 3 It is a schematic diagram of the rotation of the receiving antenna in the present invention;

[0089] Figure 4 A schematic diagram of a polarization sensitive array in the experimental part of the present invention;

[0090] FIG5( a ) is an amplitude diagram of received data obtained by actual testing;

[0091] FIG5( b ) is an amplitude diagram of theoretical received data calculated using the method of the present invention;

[0092] FIG6( a ) is a phase diagram of received data obtained by actual testing;

[0093] FIG6( b ) is a phase diagram of theoretical received data calculated using the method of the present invention;

[0094] Figure 7 It is a schematic diagram showing the estimation results of the method of the present invention and the traditional model as the signal-to-noise ratio changes;

[0095] Figure 8 It is a schematic diagram showing the estimation results of the method of the present invention and the traditional model changing with the pitch angle of the incident signal. DETAILED DESCRIPTION

[0096] Specific implementation method 1: Combination Figure 1 This embodiment describes a polarization-sensitive array direction finding method based on the spatial polarization characteristics of the antenna, assuming that the receiving array receives the main beam of the transmitting antenna, and the measurement result is the main polarization of the transmitting antenna; the method specifically includes the following steps:

[0097] Step 1: define the local rectangular coordinate system of the receiving array as the global rectangular coordinate system, and obtain the representation relationship of two sets of polarization orthogonal bases of the receiving antenna and the representation relationship of two sets of polarization orthogonal bases of the transmitting antenna in the global rectangular coordinate system;

[0098] Step 2: In a global rectangular coordinate system, define the spatial polarization parameters of the transmitting antenna and the spatial polarization parameters of the receiving antenna;

[0099] Step 3: obtaining a spatial polarization vector of the transmitting antenna according to the spatial polarization parameters of the transmitting antenna; obtaining a spatial polarization vector of the receiving antenna according to the spatial polarization parameters of the receiving antenna, and then obtaining a spatial polarization characteristic matrix of the receiving antenna according to the spatial polarization vector of the receiving antenna;

[0100] Step 4: According to the characterization relationship in step 1, the spatial polarization characteristic matrix of the receiving antenna and the spatial polarization vector of the transmitting antenna, a polarization loss factor when the nth receiving antenna in the polarization sensitive array receives a signal is obtained;

[0101] Step 5: Calculate the received signal of the receiving antenna array according to the polarization loss factor;

[0102] Step 6: Estimate the DOA of the incident signal and the spatial polarization parameters of the transmitting antenna based on the received signal of the receiving antenna array.

[0103] The present invention describes the polarization definition of the transmitting antenna and the receiving antenna, the rotation of the receiving antenna, and the polarization state of the electromagnetic wave in a unified global rectangular coordinate system during the polarization-sensitive array direction finding process, and can quantitatively describe the polarization of the antenna, making the description of the electromagnetic wave and the antenna polarization more natural. At the same time, the accuracy of DOA and spatial polarization parameter estimation is improved.

[0104] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the specific process of step 1 is:

[0105] Step 1: As shown in Figure 2(a), in a plane perpendicular to the propagation direction of the electromagnetic wave, a set of polarization orthogonal basis of the receiving antenna is It is expressed as:

[0106]

[0107] in, Parallel to the global rectangular coordinate system o r x r y r z r x r o r y r flat, Perpendicular to and They are called the horizontal direction vector and the vertical direction vector respectively, and the origin o of the global rectangular coordinate system r is the center of the receiving array, z in the global rectangular coordinate system r The x-axis direction is the viewing axis direction of the receiving array, and the x-axis direction is the viewing axis direction of the global rectangular coordinate system. r The axis is parallel to the ground, y r Axis and x r Axis, z r The axes form a right-handed rectangular coordinate system; θ represents the azimuth of the incident direction of the electromagnetic wave in the global rectangular coordinate system, represents the pitch angle of the incident direction of the electromagnetic wave in the global rectangular coordinate system, and T represents the transposition;

[0108] The unit vector of the incident direction of the electromagnetic wave It is expressed as:

[0109]

[0110] Using another pair of polarization orthogonal basis in the plane perpendicular to the propagation direction of the electromagnetic wave represents the electromagnetic wave emitted by the receiving antenna, where is the principal polarization vector, is the cross-polarization vector, In the global rectangular coordinate system x r o r y r Projection of plane and o r y r Axis parallel, In the global rectangular coordinate system x r o r y r Projection of plane and o r x r The axes are parallel, then in the global rectangular coordinate system, the two sets of polarization orthogonal basis of the receiving antenna and The representation relationship is:

[0111]

[0112] Where ζ is the global rectangular coordinate system and The rotation angle between for The Cartesian coordinate matrix in the global rectangular coordinate system, for The Cartesian coordinate matrix in the global rectangular coordinate system, for and The transformation matrix between

[0113] Step 1 and 2, as shown in Figure 2(b), since the x-axis directions of the local rectangular coordinate system of the transmitting antenna and the global rectangular coordinate system are opposite, in the local rectangular coordinate system of the transmitting antenna, the two sets of polarization orthogonal basis of the transmitting antenna are and The representation relationship is:

[0114]

[0115] Among them, Q is and The transformation matrix between them, ε is the local rectangular coordinate system o of the transmitting antenna t x t y t z t middle and The angle between the transmitting antenna and the origin of the local rectangular coordinate system is o t is the center of the transmitting antenna array, and the z coordinate of the local rectangular coordinate system of the transmitting antenna is t Axis and the z of the global rectangular coordinate system r The x axis of the local rectangular coordinate system of the transmitting antenna is opposite to the t Axis and the x of the global rectangular coordinate system r The y axis is in the opposite direction. t Axis and y r The axis direction is the same; θ x is the azimuth of the incident direction of the electromagnetic wave in the local rectangular coordinate system of the transmitting antenna, is the elevation angle of the incident direction of the electromagnetic wave in the rectangular local coordinate system of the transmitting antenna.

[0116] The other steps and parameters are the same as those in the first embodiment.

[0117] Specific implementation method three: This implementation method is different from specific implementation method one or two in that: the two groups of polarization orthogonal bases of the receiving antenna and The rotation angle ζ between them is:

[0118]

[0119] The other steps and parameters are the same as those in the first or second embodiment.

[0120] Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 1 to 3 in that: the transmitting antenna local rectangular coordinate system o t x t y t z t Two sets of polarization orthogonal basis and The angle ε between them is:

[0121]

[0122] The superscript -1 represents the inversion.

[0123] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0124] Specific implementation mode 5: This implementation mode is different from the specific implementation modes 1 to 4 in that: the θ and θ x relationship and and The relationship is:

[0125]

[0126] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0127] According to this embodiment,

[0128] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that the specific process of step 2 is:

[0129] Referring to the polarization representation of electromagnetic waves, the spatial polarization parameters of the antenna are defined as;

[0130]

[0131] Among them, α is the spatial polarization auxiliary angle of the transmitting antenna, β is the spatial polarization phase difference of the transmitting antenna, e is the base of the natural logarithm, j is the imaginary unit, and The electromagnetic wave of the transmitting antenna is orthogonal in polarization The weight on

[0132]

[0133] in, is the spatial polarization auxiliary angle of the receiving antenna, is the spatial polarization phase difference of the receiving antenna, and For receiving antenna electromagnetic waves in polarization orthogonal basis The amount on.

[0134] The other steps and parameters are the same as those in Specific Implementations 1 to 5.

[0135] α and β are based on θ x and Calculated, is based on θ and Calculated.

[0136] 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:

[0137] The spatial polarization vector f(α, β) of the transmitting antenna is calculated according to the spatial polarization parameters of the transmitting antenna:

[0138]

[0139] Then the set of spatial polarization vectors at each position is recorded as F;

[0140] That is, the spatial polarization characteristic matrix F of the transmitting antenna is obtained, and the spatial polarization characteristics at each position in F are recorded as (The spatial polarization characteristics at each position are the spatial polarization vectors at each position);

[0141] Calculate the spatial polarization vector of the receiving antenna based on the spatial polarization parameters of the receiving antenna

[0142]

[0143] Then the set of spatial polarization vectors at each position is recorded as That is, the spatial polarization characteristic matrix of the receiving antenna is obtained and will The spatial polarization characteristics at each position in is recorded as (The spatial polarization characteristics at each position are the spatial polarization vectors at each position).

[0144] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0145] Specific implementation eight: This implementation differs from any one of specific implementations one to seven in that the specific process of step four is as follows:

[0146] The incident signal angle The corresponding angle in the local rectangular coordinate system of the nth receiving antenna is recorded as

[0147]

[0148] Among them, Figure 3 As shown, is the rotation angle between the local rectangular coordinate system and the global rectangular coordinate system of the nth receiving antenna, is the rotational pitch angle between the local rectangular coordinate system of the nth receiving antenna and the global rectangular coordinate system; the origin of the local rectangular coordinate system of the nth receiving antenna is the center of the nth receiving antenna, and the three coordinate axis directions of the local rectangular coordinate system of the nth receiving antenna are: rotate the coordinate axis of the global rectangular coordinate system along the z axis Then, rotate the coordinate axis of the global rectangular coordinate system along the y-axis Then the directions of the three coordinate axes of the local rectangular coordinate system of the nth receiving antenna are the same as the directions of the coordinate axes of the global rectangular coordinate system after rotation;

[0149] Then the polarization component of the nth receiving antenna in the global rectangular coordinate system is:

[0150]

[0151] in, is the spatial polarization characteristic matrix of the nth receiving antenna. The spatial polarization vector at For the nth receiving antenna The conversion matrix of the two polarization bases at (n) is the rotation matrix between the local rectangular coordinate system and the global rectangular coordinate system of the nth receiving antenna;

[0152] Polarization loss factor when the nth receiving antenna in a polarization sensitive array receives a signal for:

[0153]

[0154] Among them, f(α,β) is the spatial polarization vector of the transmitting antenna, Q(ε) is The conversion matrix of the two sets of polarization orthogonal bases of the transmitting antenna at , yes The transpose of .

[0155] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0156] In this embodiment, Recalculate the position Spatial polarization characteristics at

[0157] Specific implementation method 9: This implementation method is different from specific implementation methods 1 to 8 in that the specific process of step 5 is:

[0158] Step 51: The number of narrowband far-field signals incident on the polarization sensitive array is recorded as K, and the spatial domain parameter of the kth incident signal is recorded as Then the spatial response of the kth incident signal is in, is the spatial response of the nth receiving antenna to the kth incident signal;

[0159]

[0160] Where λ is the wavelength of the incident signal, l n is the position coordinate of the nth receiving antenna, and N is the number of receiving antennas;

[0161] Step 52: Calculate the spatial-polarization domain response of the nth receiving antenna to the kth incident signal based on the polarization loss factor when the nth receiving antenna receives the signal and the spatial domain response of the nth receiving antenna to the kth incident signal.

[0162]

[0163] in, is the polarization loss factor of the nth receiving antenna for the kth signal, (α k ,β k ) is the spatial polarization parameter of the transmitting antenna corresponding to the kth incident signal,

[0164] Step 53: According to Calculate the steering vector of the receiving antenna array for the kth incident signal

[0165]

[0166]

[0167] Among them, a (n) for Abbreviation of is the polarization sensitivity matrix of the nth receiving antenna to the kth incident signal, b (n) for Abbreviation of for abbreviation of;

[0168] Step 54: According to the guidance vector Calculate the received signal vector of the receiving antenna array at time t:

[0169]

[0170] Where X(t) is the N×1 dimensional array received data vector, S(t) is the K×1 dimensional spatial signal vector, N(t) is the N×1 dimensional noise data vector, and A is the N×K dimensional steering vector of the array;

[0171]

[0172] S(t)=[s 1 (t),s 2 (t),…,s K (t)] T (twenty four)

[0173] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0174] Specific implementation method 10: This implementation method is different from the specific implementation methods 1 to 9 in that the specific process of step 6 is:

[0175] Step 6. Calculate the covariance matrix of the received signal X(t) of the receiving antenna array

[0176]

[0177] Among them, X H (t) represents the conjugate transpose of X(t), and E{·} represents the expectation;

[0178] Step 6.2: Covariance matrix Perform eigenvalue decomposition, sort the obtained eigenvalues ​​in order from small to large, and use the eigenvectors corresponding to the first NK eigenvalues ​​to form the noise subspace

[0179] Step 6.3: Using the Noise Subspace Estimate the DOA of the incident signal and the spatial polarization parameters of the transmitting antenna; specifically:

[0180] According to formula (26), the azimuth and elevation angles corresponding to the first K large peaks are calculated:

[0181]

[0182] Substitute the calculated azimuth and elevation angles into equations (26) and (27):

[0183]

[0184] in, represents the generalized eigenvector corresponding to the minimum generalized eigenvalue of the matrix bundle. yes The first element in yes The second element in |·| represents taking the absolute value, det{·} represents calculating the value of the determinant, arg{·} represents finding the argument of the complex number, α k and βk It is the spatial polarization auxiliary angle and spatial polarization phase difference of the transmitting antenna corresponding to the kth incident signal.

[0185] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0186] Yes and Calculated by substitution.

[0187] Experimental Section

[0188] A uniform circular array is formed by 7 electric dipole antennas with a radius r of 63 mm. Figure 4 As shown. The frequency of the incident signal is 4 GHz. Assume that the relative angles between the electromagnetic wave of the transmitting antenna and the receiving array are 0° in azimuth and 0° in elevation. In addition, the initial polarization of the transmitting antenna is vertical polarization (relative to the ground). Then, through a mechanical device, the polarization of the transmitting antenna changes from vertical polarization to horizontal polarization, and then to vertical polarization. The polarization change speed of the transmitting antenna is 1° per second. At the same time, the polarization characteristics of different positions of the receiving array are generated using the antenna simulation software CST during simulation. The polarization characteristics of the transmitting antenna are considered to be theoretical linear polarization, and its change speed is consistent with the test situation.

[0189] FIG5(a) shows the relationship between the actual received signal amplitude and time of each array element of the receiving array, and FIG5(b) shows the relationship between the theoretical received signal amplitude and time calculated using the method of the present invention.

[0190] FIG6(a) shows the relationship between the phase of the signal received by each element of the receiving array and the time variation in the actual test, and FIG6(b) shows the relationship between the phase of the signal of the theoretical received data calculated by the method of the present invention and the time variation.

[0191] Within the allowable error range, the array receiving signal amplitude, phase, and polarization change characteristics of the method of the present invention are consistent with the theoretical ones, which proves the reliability and effectiveness of the method proposed by the present invention.

[0192] Assume that the angle between the main lobe of the transmitting antenna and the receiving array is (45.15°, 30.23°), and the spatial polarization parameters (α, β) of the transmitting antenna are (45°, 0°). The signal-to-noise ratio of the incident signal varies from -10dB to 30dB, and the number of snapshots is set to 128. This is compared with the traditional model that does not consider the spatial polarization characteristics of the receiving antenna in the receiving array. The estimated results of the elevation angle of the incident signal and the spatial polarization auxiliary angle of the transmitting antenna are shown in Figure 1. Figure 7 shown.

[0193] Assume that the signal-to-noise ratio is 10 dB, the azimuth angle is 45.15°, and the elevation angle varies from 5° to 30°. All other simulation conditions are the same as Figure 7 Compared with the traditional model that does not consider the spatial polarization characteristics of the receiving antenna in the receiving array, the estimated results of the elevation angle of the incident signal and the spatial polarization auxiliary angle of the transmitting antenna are as follows: Figure 8 shown.

[0194] from Figure 7 and Figure 8 It can be seen that the method of the present invention has higher DOA and polarization parameter estimation accuracy, which is better than the traditional model.

[0195] 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 polarization-sensitive array direction finding method based on antenna spatial polarization characteristics, characterized in that: The method specifically comprises the following steps: Step 1: define the local rectangular coordinate system of the receiving array as the global rectangular coordinate system, and obtain the representation relationship of two sets of polarization orthogonal bases of the receiving antenna and the representation relationship of two sets of polarization orthogonal bases of the transmitting antenna in the global rectangular coordinate system; The specific process of step one is: Step 1: In a plane perpendicular to the propagation direction of the electromagnetic wave, place a set of polarization orthogonal basis It is expressed as: in, Parallel to the global rectangular coordinate system o r x r y r z r x r o r y r flat, Perpendicular to The origin o of the global rectangular coordinate system r is the center of the receiving array, z in the global rectangular coordinate system r The x-axis direction is the viewing axis direction of the receiving array, and the x-axis direction is the viewing axis direction of the global rectangular coordinate system. r The axis is parallel to the ground, y r Axis and x r Axis, z r The axes form a right-handed rectangular coordinate system; θ represents the azimuth of the incident direction of the electromagnetic wave in the global rectangular coordinate system, represents the pitch angle of the incident direction of the electromagnetic wave in the global rectangular coordinate system, and T represents the transposition; The unit vector of the incident direction of the electromagnetic wave It is expressed as: Using another pair of polarization orthogonal basis in the plane perpendicular to the propagation direction of the electromagnetic wave represents the electromagnetic wave emitted by the receiving antenna, where is the principal polarization vector, is the cross-polarization vector, then in the global rectangular coordinate system, the two sets of polarization orthogonal basis of the receiving antenna and The representation relationship is: in, In the global rectangular coordinate system and The rotation angle between for The Cartesian coordinate matrix in the global rectangular coordinate system, for The Cartesian coordinate matrix in the global rectangular coordinate system, for and The transformation matrix between Step 1 and 2: In the local rectangular coordinate system of the transmitting antenna, the two sets of polarization orthogonal basis of the transmitting antenna and The representation relationship is: Among them, Q is and The transformation matrix between them, ε is the local rectangular coordinate system o of the transmitting antenna t x t y t z t middle and The angle between the transmitting antenna and the origin of the local rectangular coordinate system is o t is the center of the transmitting antenna array, and the z coordinate of the local rectangular coordinate system of the transmitting antenna is t Axis and the z of the global rectangular coordinate system r The x axis of the local rectangular coordinate system of the transmitting antenna is opposite to the t Axis and the x of the global rectangular coordinate system r The y axis is in the opposite direction. t Axis and y r The axis direction is the same; θ x is the azimuth of the incident direction of the electromagnetic wave in the local rectangular coordinate system of the transmitting antenna, is the elevation angle of the incident direction of the electromagnetic wave in the rectangular local coordinate system of the transmitting antenna; Step 2: In a global rectangular coordinate system, define the spatial polarization parameters of the transmitting antenna and the spatial polarization parameters of the receiving antenna; Step 3: obtaining a spatial polarization vector of the transmitting antenna according to the spatial polarization parameters of the transmitting antenna; obtaining a spatial polarization vector of the receiving antenna according to the spatial polarization parameters of the receiving antenna, and then obtaining a spatial polarization characteristic matrix of the receiving antenna according to the spatial polarization vector of the receiving antenna; Step 4: According to the characterization relationship in step 1, the spatial polarization characteristic matrix of the receiving antenna and the spatial polarization vector of the transmitting antenna, a polarization loss factor when the nth receiving antenna in the polarization sensitive array receives a signal is obtained; Step 5: Calculate the received signal of the receiving antenna array according to the polarization loss factor; Step 6: Estimate the DOA of the incident signal and the spatial polarization parameters of the transmitting antenna based on the received signal of the receiving antenna array.

2. The polarization sensitive array direction finding method based on the spatial polarization characteristics of the antenna according to claim 1, characterized in that: The two sets of polarization orthogonal bases of the receiving antenna and The rotation angle between for:

3. The polarization sensitive array direction finding method based on the spatial polarization characteristics of the antenna according to claim 2, characterized in that: The transmitting antenna local rectangular coordinate system o t x t y t z t Two sets of polarization orthogonal basis and The angle ε between them is: The superscript -1 represents the inversion.

4. The polarization sensitive array direction finding method based on the spatial polarization characteristics of the antenna according to claim 3, characterized in that: The θ and θ x relationship and and The relationship is:

5. The polarization sensitive array direction finding method based on the spatial polarization characteristics of the antenna according to claim 4, characterized in that: The specific process of step 2 is as follows: Among them, α is the spatial polarization auxiliary angle of the transmitting antenna, β is the spatial polarization phase difference of the transmitting antenna, e is the base of the natural logarithm, j is the imaginary unit, and The electromagnetic wave of the transmitting antenna is orthogonal in polarization The weight on in, is the spatial polarization auxiliary angle of the receiving antenna, is the spatial polarization phase difference of the receiving antenna, and For receiving antenna electromagnetic waves in polarization orthogonal basis The amount on.

6. The polarization sensitive array direction finding method based on antenna spatial polarization characteristics according to claim 5, characterized in that: The specific process of step three is: The spatial polarization vector f(α, β) of the transmitting antenna is calculated according to the spatial polarization parameters of the transmitting antenna: Then the set of spatial polarization vectors at each position is recorded as F; Calculate the spatial polarization vector of the receiving antenna based on the spatial polarization parameters of the receiving antenna Then the set of spatial polarization vectors at each position is recorded as That is, the spatial polarization characteristic matrix of the receiving antenna is obtained and will The spatial polarization characteristics at each position in is recorded as 7. The polarization sensitive array direction finding method based on the spatial polarization characteristics of the antenna according to claim 6, characterized in that: The specific process of step 4 is as follows: The incident signal angle The corresponding angle in the local rectangular coordinate system of the nth receiving antenna is recorded as in, is the rotation angle between the local rectangular coordinate system and the global rectangular coordinate system of the nth receiving antenna, is the rotational pitch angle between the local rectangular coordinate system and the global rectangular coordinate system of the nth receiving antenna; Then the polarization component of the nth receiving antenna in the global rectangular coordinate system is: in, is the spatial polarization characteristic matrix of the nth receiving antenna. The spatial polarization vector at For the nth receiving antenna The conversion matrix of the two polarization bases at (n) is the rotation matrix between the local rectangular coordinate system and the global rectangular coordinate system of the nth receiving antenna; Polarization loss factor when the nth receiving antenna in a polarization sensitive array receives a signal for: Among them, f(α,β) is the spatial polarization vector of the transmitting antenna, Q(ε) is The conversion matrix of the two sets of polarization orthogonal bases of the transmitting antenna at , yes The transpose of .

8. The polarization sensitive array direction finding method based on the spatial polarization characteristics of the antenna according to claim 7, characterized in that: The specific process of step five is as follows: Step 51: The number of narrowband far-field signals incident on the polarization sensitive array is recorded as K, and the spatial domain parameter of the kth incident signal is recorded as 1≤k≤K, then the spatial response of the kth incident signal is in, is the spatial response of the nth receiving antenna to the kth incident signal; Where λ is the wavelength of the incident signal, l n is the position coordinate of the nth receiving antenna, and N is the number of receiving antennas; Step 52: Calculate the spatial-polarization domain response of the nth receiving antenna to the kth incident signal based on the polarization loss factor when the nth receiving antenna receives the signal and the spatial domain response of the nth receiving antenna to the kth incident signal. in, is the polarization loss factor of the nth receiving antenna for the kth signal, (α k ,β k ) is the spatial polarization parameter of the transmitting antenna corresponding to the kth incident signal, Step 53: According to Calculate the steering vector of the receiving antenna array for the kth incident signal Among them, a (n) for Abbreviation of is the polarization sensitivity matrix of the nth receiving antenna to the kth incident signal, b (n) for Abbreviation of for abbreviation of; Step 54: According to the guidance vector Calculate the received signal vector of the receiving antenna array at time t: Where X(t) is the N×1 dimensional array received data vector, S(t) is the K×1 dimensional spatial signal vector, N(t) is the N×1 dimensional noise data vector, and A is the N×K dimensional steering vector of the array; S(t)=[s1(t),s2(t),…,s K (t)] T (24)。 9. The polarization sensitive array direction finding method based on the spatial polarization characteristics of the antenna according to claim 8, characterized in that: The specific process of step six is ​​as follows: Step 6. Calculate the covariance matrix of the received signal X(t) of the receiving antenna array Among them, X H (t) represents the conjugate transpose of X(t), and E{·} represents the expectation; Step 6.2: Covariance matrix Perform eigenvalue decomposition, sort the obtained eigenvalues ​​in order from small to large, and use the eigenvectors corresponding to the first NK eigenvalues ​​to form the noise subspace Step 6.3: Using the Noise Subspace Estimate the DOA of the incident signal and the spatial polarization parameters of the transmitting antenna; specifically: According to formula (26), the azimuth and elevation angles corresponding to the first K large peaks are calculated: Substitute the calculated azimuth and elevation angles into equations (26) and (27): in, represents the generalized eigenvector corresponding to the minimum generalized eigenvalue of the matrix bundle. yes The first element in yes The second element in |·| represents taking the absolute value, det{·} represents calculating the value of the determinant, arg{·} represents finding the argument of the complex number, α k and β k It is the spatial polarization auxiliary angle and spatial polarization phase difference of the transmitting antenna corresponding to the kth incident signal.

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