A search direction finding method based on system orientation-dependent amplitude-phase error parameters

Abstract

The application relates to the technical field of direction of arrival estimation, in particular to a search direction finding method based on system azimuth-dependent amplitude-phase error parameters. The method can better adapt to different direction finding environments, can be applied to air-to-air and air-to-ground at the same time, has small calculation amount and good robustness, can jointly compensate and correct channel error and antenna array error, basically eliminates the influence of antennas and channels on the direction finding result, makes the direction finding result have small error, and improves the accuracy of direction finding.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of direction of arrival estimation, and particularly relates to a search direction finding method based on system azimuth-dependent amplitude-phase error parameters. BACKGROUND

[0002] In the military field, obtaining high-resolution direction of arrival and accurate velocity and distance parameters not only helps the navigation and tracking of our targets, but also enables accurate positioning and attacks on enemy targets; in the field of civilian wireless communication, accurate direction of arrival estimation is beneficial to improving system capacity and reducing multiple access interference; in the field of radio search and rescue, the Beidou system cannot be used due to environmental and human factors, and in this case, the members of the system network can use radio communication to obtain position and azimuth information; in the field of airborne assembly, the commander sends assembly instructions, and the members must quickly know their azimuth and distance from the commander to efficiently complete the assembly. Therefore, how to more effectively perform direction finding is crucial.

[0003] Direction of arrival estimation achieves accurate estimation of parameters such as direction of arrival by performing various processing and calculation on signals in the space of interest. Direction of arrival estimation is also known as angle of arrival estimation or spectral estimation. Among various spatial spectral estimation algorithms, the MUltiple Signal Classification (MUSIC) algorithm is a subspace decomposition-based algorithm, which is characterized by small direction finding error, high precision, high resolution, and high sensitivity, and can make unbiased estimation of the number of incident signals, angle of arrival, and waveform intensity. However, when actually put into use, different errors cannot be avoided. For example, the inconsistency of the directional pattern of each array element due to the error in antenna processing precision; the amplitude-phase error caused by the inconsistency of the gain of the amplifier in the receiving channel; the array flow deviation caused by the installation position error of the array element and the antenna element mutual coupling, etc. will all affect direction finding. At this time, the estimation performance of the commonly used high-resolution spatial spectral estimation MUSIC method will be severely deteriorated, and even fail. Therefore, it is of great significance to study the MUSIC correction algorithm for improving the direction finding accuracy. The directional pattern error of the array element, the amplitude-phase error of the array element, the position error of the array element, and the array mutual coupling parameters can be modeled by the azimuth-dependent amplitude-phase error of the array element. When multiple errors exist simultaneously, blind modeling of the array element can more accurately reflect the actual error model of the array.

[0004] An accurate active correction method is convenient for estimating the amplitude-phase error matrix, has small calculation amount, and is widely used in practice. However, for complex direction finding environments, especially when the amplitude-phase error is related to the azimuth, a single correction that is independent of the azimuth of the signal source cannot achieve ideal direction finding accuracy. SUMMARY

[0005] In view of the problems in the prior art, the present application aims to provide a search direction finding method based on system azimuth-dependent amplitude-phase error parameters.

[0006] In order to achieve the above-mentioned purpose, the present application adopts the following technical solutions.

[0007] A search direction finding method based on system azimuth-dependent amplitude-phase error parameters comprises the following steps:

[0008] Step 1: The radio frequency front end converts the radio frequency analog signal received by the antenna into a digital intermediate frequency signal with a lower frequency.

[0009] Step 2: The I and Q orthogonal down-conversion and filtering are performed on the discrete digital intermediate frequency signals of each array element channel, and after successful acquisition and frame synchronization, the complex covariance matrix is obtained.

[0010] Step 3: The real number transformation is performed on the complex covariance matrix, and the characteristic decomposition and sorting are performed to obtain the signal subspace and the noise subspace.

[0011] Step 4: The amplitude-phase error in different azimuths is calculated according to the signal subspace, and the amplitude-phase error is corrected to obtain N azimuth-dependent amplitude-phase error correction matrices and the phase difference of the array element channel received signals and save them.

[0012] Step 5: The N azimuths are locally searched for spectral peaks by using the correction matrix corresponding to the N azimuths to obtain the first largest peak value, the second largest peak value and the angles corresponding to the two peak values.

[0013] Step 6: The norm of the difference between the phase difference vector received by the channel where the first largest peak value is located and the antenna received signal phase difference corresponding to the channel where the first largest peak value is located is calculated, the norm of the difference between the phase difference vector received by the channel where the second largest peak value is located and the antenna received signal phase difference corresponding to the channel where the second largest peak value is located is calculated, and the final direction finding result is obtained according to the two norms.

[0014] Compared with the prior art, the present application has the beneficial effects that it can better adapt to different direction finding environments and can be applied to air-to-air and air-to-ground at the same time, has small calculation amount and good robustness, has the direction finding ability and high precision and high resolution ability for multiple types of signals (AM, BPSK and QPSK, etc.), can jointly compensate and correct the channel error and the antenna array error, basically eliminates the influence of the antenna and the channel on the direction finding result, makes the direction finding result have small error, and improves the accuracy of direction finding. BRIEF DESCRIPTION OF DRAWINGS

[0015] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0016] Figure 1 The present application is a flowchart of the method.

[0017] Figure 2 A comparison chart of detection success probability at different signal-to-noise ratios using a conventional MUSIC correction algorithm and using the method of the present application;

[0018] Figure 3 A comparison chart of root mean square error at different signal-to-noise ratios using a conventional MUSIC correction algorithm and using the method of the present application. DETAILED DESCRIPTION

[0019] The embodiments of the present application will be described in detail below with reference to the embodiments, but those skilled in the art will understand that the following embodiments are only used to illustrate the present application and should not be regarded as limiting the scope of the present application.

[0020] Without loss of generality, a linear array with M elements is taken as an example for detailed description, and other array types only need to modify the array flow. The implementation mode of FPGA+DSP is adopted. The regular operations such as down-conversion, filtering, capture, synchronization, and covariance matrix calculation are realized by using FPGA chips, and the complex and irregular processes such as matrix eigenvalue decomposition, amplitude and phase error correction, spectrum peak search, and output angle decision are realized in the high-speed and flexible DSP chip.

[0021] REFERENCE Figure 1 A search direction-finding method based on system orientation-dependent amplitude and phase error parameters, comprising the following steps:

[0022] Step 1, after the antenna receives the signal, the radio frequency front end converts the radio frequency analog signal received by the antenna into a digital intermediate frequency signal with a lower frequency;

[0023] The radio frequency front end simultaneously converts the radio frequency analog signals s(t) received by the M-element antenna through filtering and amplification of the preamplifier, and then mixes with the local oscillator signal to down-convert into an intermediate frequency signal, and finally converts the intermediate frequency signal into a discrete-time digital intermediate frequency signal s m (k) through an analog-to-digital converter, m=1, 2, …, M, k=1, 2, …, K.

[0024] Step 2, using an FPGA chip to perform I, Q quadrature down-conversion and filtering on the discrete digital intermediate frequency signals of each element channel, and after successful capture and frame synchronization, a complex covariance matrix is obtained; step 2 includes the following sub-steps:

[0025] Sub-step 2.1, performing quadrature down-conversion on the discrete digital intermediate frequency signals s m (k) of the M-element channel, multiplying the I channel signal by the cosine carrier wave to obtain the I channel signal, and multiplying the Q channel signal by the sine carrier wave;

[0026] Sub-step 2.2 involves low-pass filtering the orthogonal baseband signals I and Q of the M array element channels, respectively. The complex signal received by the m-th array element antenna can then be expressed as x. m (k)=I m (k)+jQ m (k), then the array output vector Y(k) of the M array element channels is = [x1(k) x2(k) … x M (k)] T , where m = 1, 2, ..., M, M is the number of array elements, k = 1, 2, ..., K, K is the time-domain sampling snapshot;

[0027] Sub-step 2.3: After successful capture and frame synchronization, i.e., when Data_Flag = 1, obtain the complex covariance matrix R = Y(k) × Y(k). H R is an M×M complex conjugate symmetric matrix, where Y(k) H Let Y(k) be the conjugate transpose of Y(k).

[0028] Step 3 involves using a DSP chip to perform real-number transformations on the complex covariance matrix and then performing eigenvalue decomposition and sorting to obtain the signal subspace and noise subspace. Step 3 includes the following sub-steps:

[0029] Sub-step 3.1: When the number of array elements is greater than 2, process the complex conjugate symmetric matrix R to restore the rank of the signal covariance matrix to the number of signals. The processed matrix is ​​represented as R. X =B1+jB2, therefore R X =R+I v R * I v Among them, I v It is a 2M×2M reverse identity matrix. Construct a real symmetric matrix

[0030] Sub-step 3.2: Perform eigenvalue decomposition on the real matrix R_real to obtain 2M eigenvalues ​​and corresponding eigenvectors; after removing the repeated roots of each eigenvalue and the corresponding eigenvectors, take the first M elements of the real eigenvectors as the real part of the complex eigenvectors and the last M elements as the imaginary part of the complex eigenvectors to obtain the eigenvalues ​​and eigenvectors of the complex covariance matrix.

[0031] Sort the eigenvalues ​​in descending order, and sort the eigenvectors in descending order of their corresponding eigenvalues; use the eigenvector corresponding to the largest eigenvalue as the signal subspace U. s U s The eigenvectors are M*1 complex vectors (containing only one incoming signal), and the remaining eigenvectors are noise subspaces U. noise U noise It is an M×(M-1) matrix.

[0032] Step 4, using DSP chip to calculate amplitude and phase error in different directions according to signal subspace, and correcting the amplitude and phase error to obtain N amplitude and phase error correction matrices dependent on direction and phase difference of channel received signal and save;

[0033] Step 4 includes the following sub-steps:

[0034] Sub-step 4.1, calculating signal subspace U s Taking modulus and normalizing to obtain amplitude ratio A n dependent on direction n1 a n2 … a nM ] 1×M , wherein a1=1, M is the number of array elements, n=1, 2, …, N, and the specific number of N is related to array type and array element number, for example, for a double antenna, the direction of interest is-70° to 70°, and for a four-antenna circular array, the direction of interest is 0° to 360°;

[0035] Sub-step 4.2, calculating signal subspace U s Taking modulus and normalizing to obtain amplitude ratio A n dependent on direction n1 a n2 … a nM ] 1×M , wherein M is the number of array elements, n=1, 2, …, N;

[0036] Sub-step 4.3, obtaining correction matrix dependent on direction from amplitude ratio A n and antenna received signal phase difference Φ n

[0037] In the formula, is the phase vector generated by the need to be corrected to a certain specific direction (the wave direction is accurately known in the correction stage), and taking a linear array as an example, wherein k=[0 1 …M-1], n=1, 2, …, N, d is the distance between antennas, λ is the wavelength, and θ is the wave direction;

[0038] Sub-step 4.4, repeating sub-step 4.1 to sub-step 4.3 to correct amplitude and phase error in different directions to obtain N amplitude and phase error correction matrices dependent on direction, G=[G1 G2 … G N ]; and N antenna received signal phase differences, Φ=[Φ1 Φ2 … Φ N ].

[0039] ​Step 5, using the DSP chip to perform local spectral peak search on the N directions using the correction matrix corresponding to the N directions to obtain a first peak value, a second peak value, and angles corresponding to the two peak values;

[0040] Step 5 includes the following sub-steps:

[0041] Sub-step 5.1, performing local spectral peak search for the incoming direction θ, and selecting the correction matrix G corresponding to the search direction n during the search n In order to shorten the calculation time, only a range of ±5° for each direction is searched, and the search formula is as follows:

[0042]

[0043] In the formula, the array flow is an M-row 1-column complex vector, where k = [0 1 … M-1] T theta is the search angle, for example, the search range at a 10° direction is 5° to 15°; ii is the number of angles to be searched; U noise is the noise subspace, which is an M×(M-1) complex matrix; G n is an M×M correction matrix, P MUSIC (n,ii) is the ii-th angle search peak value at the n direction;

[0044] Sub-step 5.2, sorting the maximum search peak values in each search direction from large to small, and taking the first sorted value as the first peak value and the second sorted value as the second peak value.

[0045] Step 6, using the DSP chip to calculate the norm of the difference between the received phase difference vector of the channel where the first peak value is located and the antenna received signal phase difference corresponding to the channel where the first peak value is located, and the norm of the difference between the received phase difference vector of the channel where the second peak value is located and the antenna received signal phase difference corresponding to the channel where the second peak value is located, and judging according to the two norms to obtain the final direction finding result.

[0046] Step 6 includes the following sub-steps:

[0047] Sub-step 6.1, defining the channel where the first peak value is located as n1, the measured angle as doa1, the channel where the second peak value is located as n2, and the measured angle as doa2;

[0048] Calculate the received phase difference vector ph_n1 of the channel where the first peak value is located and the received phase difference vector ph_n2 of the channel where the second peak value is located, taking a linear array as an example (if it is a circular array or other array type, only the second term array flow in the formula needs to be modified), and the calculation formula of ph_n1 and ph_n2 is as follows:

[0049]

[0050]

[0051] wherein: n1, n2∈{1 2 … N}, k=[0 1 … M-1];

[0052] Sub-step 6.2, calculating the norm temp1 of the difference between the first large peak value channel receiving phase difference vector ph_n1 and the first large peak value channel corresponding antenna receiving signal phase difference Φ n1 , and the norm temp2 of the difference between the second large peak value channel receiving phase difference vector ph_n2 and the second large peak value channel corresponding antenna receiving signal phase difference Φ n2 ; ideally, temp1 is close to 0;

[0053] Sub-step 6.3, when temp1 < temp2 and temp1 < 0.3 (0.3 radian is an empirical value, which is an environment-related parameter), taking the first large peak value measured angle doa1 as the final direction finding result; when temp1≥temp2 and temp2 < 0.3, taking the second large peak value measured angle doa2 as the final direction finding result; when temp1≥0.3 and temp2≥0.3, selecting the direction closest to the antenna receiving instantaneous phase difference vector from the N antenna receiving signal phase differences Φ=[Φ1 Φ2 … Φ N ] as the final direction finding result.

[0054] Simulation test results

[0055] Simulation conditions: assuming that the BPSK signal incoming direction is 30°, the Gaussian white noise signal-to-noise ratio is -5dB to 10dB, and the direction finding error is within ±3°, the detection success probability using the traditional MUSIC correction algorithm and the detection success probability using the search direction finding method of the present application are compared as shown in Figure 2 , and the root mean square error comparison is as shown in Figure 3 .

[0056] Reference Figure 2 It can be seen that the detection success probability using the method of the present application can reach 100% when the signal-to-noise ratio is 0dB, while the traditional MUSIC correction algorithm needs to reach 100% when the signal-to-noise ratio is 3dB; and when the signal-to-noise ratio is less than 3dB, the detection success probability using the method of the present application is much greater than that using the traditional MUSIC correction algorithm.

[0057] Reference Figure 3It can be seen that the root mean square error of the method of the application can reach 0° when the signal-to-noise ratio is 0dB, while the root mean square error of the traditional MUSIC correction algorithm can reach 0° when the signal-to-noise ratio is 3dB; and when the signal-to-noise ratio is less than 3dB, the root mean square error of the method of the application is much smaller than that of the traditional MUSIC correction algorithm.

[0058] It can be seen from the simulation results that under the same environmental conditions, the detection success probability and the root mean square error of the method of the application are both superior to those of the traditional MUSIC correction algorithm, which illustrates the superiority of the method of the application.

[0059] In actual implementation, the method of the application can reduce the process requirements for the manufacture of antenna array elements to the greatest extent, that is, when the directional diagram of the antenna array elements does not require consistency under the condition of ensuring communication sensitivity, and the antenna installation position is not particularly accurate, the influence of the element mutual coupling can also be reduced.

[0060] Although the application has been described in detail in the specification and specific embodiments, some modifications or improvements can be made on the basis of the application, which is obvious to those skilled in the art. Therefore, these modifications or improvements made on the basis of not deviating from the spirit of the application shall fall within the scope of protection of the application.

Claims

1. A search direction finding method based on system orientation dependent amplitude and phase error parameters, characterized by, The method comprises the following steps: Step 1, the radio frequency front end converts the radio frequency analog signal received by the antenna into a digital intermediate frequency signal with a lower frequency; Step 2, the I and Q orthogonal down-conversion and filtering are performed on the discrete digital intermediate frequency signals of each array element channel, and the complex covariance matrix is obtained after successful acquisition and frame synchronization; Step 3, the real number transformation is performed on the complex covariance matrix, and the eigenvalue decomposition and sorting are performed, so as to obtain the signal subspace and the noise subspace; Step 4, the amplitude and phase errors in different directions are calculated according to the signal subspace, the amplitude and phase errors are corrected, N direction-dependent amplitude and phase error correction matrices and array element channel received signal phase differences are obtained and saved; step 4 comprises the following sub-steps: Sub-step 4.1, obtaining signal subspace U s Taking modulo and normalizing to obtain the azimuth-dependent amplitude ratio A n = [a n1 a n2 …a nM ] 1×M , where a1=1, M is the number of array elements, n=1, 2, …, N, and the specific number of N is related to the array type and the number of array elements. Sub-step 4.2, obtaining the signal subspace U s solving the complex phase angle, extracting the phase, obtaining the received phase of each array element channel; then solving the phase difference of each array element channel relative to the first array element channel, obtaining the azimuth-dependent antenna received signal phase difference Φ n = [φ n1 φ n2 …φ nM ] 1×M , where M is the number of array elements, n = 1, 2, …, N; Sub-step 4.3, from the amplitude ratio A n and the phase difference Φ of the antenna reception signals n results in a position-dependent correction matrix In the formula, The phase vector generated by the need to correct to a certain direction, the correction stage to come wave direction is known accurately, taking a straight line array as an example, Wherein k=[0 1…M-1], n=1, 2, …, N, d is the antenna spacing, λ is the wavelength, and θ is the direction of arrival. Sub-step 4.4 repeats sub-steps 4.1 to 4.3 to correct the amplitude and phase errors in different azimuths, resulting in N azimuth-dependent amplitude and phase error correction matrices, where G = [G1 G2…G N ]; and the phase difference of the signals received by N antennas, Φ=[Φ1Φ2…Φ N ]; Step 5, the local spectral peak search is performed on N directions by using the correction matrix corresponding to N directions, so as to obtain the first maximum peak value, the second maximum peak value and the angles corresponding to the two peak values; Step 6, the norm of the difference between the received phase difference vector of the channel where the first maximum peak is located and the antenna received signal phase difference corresponding to the channel where the first maximum peak is located is calculated, the norm of the difference between the received phase difference vector of the channel where the second maximum peak is located and the antenna received signal phase difference corresponding to the channel where the second maximum peak is located is calculated, and the final direction finding result is obtained according to the two norms.

2. The search direction finding method based on system position dependent amplitude and phase error parameters according to claim 1, characterized in that, Step 5 comprises the following sub-steps: Sub-step 5.1, do local spectrum peak search for the direction of arrival θ, and select the correction matrix G corresponding to the search direction n during the search n Only search in the range of ±5° for each direction, and the search formula is as follows: wherein the array is popular is an M-row 1-column complex vector, where k = [0 1 … M-1] T theta is the search angle; ii is the number of angles to be searched; U noise is the noise subspace, an M x (M-1) complex matrix; G n is the M x M correction matrix, P MUSIC (n,ii) is the ii-th angle search peak in the n orientation; Sub-step 5.2, the maximum search peak values in each search direction are sorted from large to small, and the first sorted value is taken as the first maximum peak value and the second sorted value is taken as the second maximum peak value.

3. The search direction finding method based on system position dependent amplitude and phase error parameters according to claim 1, characterized in that, Step 6 comprises the following sub-steps: Sub-step 6.1, the channel where the first maximum peak value is located is defined as n1, and the measured angle is doa1; the channel where the second maximum peak value is located is defined as n2, and the measured angle is doa2; the received phase difference vector ph_n1 of the channel where the first maximum peak value is located and the received phase difference vector ph_n2 of the channel where the second maximum peak value is located are calculated; Sub-step 6.2, calculating the norm temp1 of the difference between the receiving phase difference vector ph_n1 of the channel where the first large peak is located and the antenna receiving signal phase difference Φ corresponding to the channel where the first large peak is located, and the norm temp2 of the difference between the receiving phase difference vector ph_n2 of the channel where the second large peak is located and the antenna receiving signal phase difference Φ corresponding to the channel where the second large peak is located. n1 n2 Sub-step 6.2, calculating the norm temp1 of the difference between the receiving phase difference vector ph_n1 of the channel where the first large peak is located and the antenna receiving signal phase difference Φ corresponding to the channel where the first large peak is located, and the norm temp2 of the difference between the receiving phase difference vector ph_n2 of the channel where the second large peak is located and the antenna receiving signal phase difference Φ corresponding to the channel where the second large peak is located.​ Sub-step 6.3, when temp1 < temp2 and temp1 < 0.3, the measured angle doa1 of the first maximum peak value is taken as the final direction finding result; when temp1 >= temp2 and temp2 < 0.3, the measured angle doa2 of the second maximum peak value is taken as the final direction finding result; when temp1 >= 0.3 and temp2 >= 0.3, the direction closest to the antenna received instantaneous phase difference vector is selected from the N antenna received signal phase differences as the final direction finding result.

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