CN101309101A - Array Synthetic Direction Finding Method for Wireless Signal Receiving System - Google Patents

Abstract

The array comprehensive direction finding method of the wireless signal receiving system belongs to the category of signal receiving. Steps: Determine the modulus vector and its autocorrelation matrix of the signal received by the phase incompletely synchronous array, and determine the noise subspace through the eigendecomposition of the modulus autocorrelation matrix; use the orthogonality between the noise subspace and the phase incompletely synchronous array search vector to determine the direction Difference space spectrum, determine the direction difference between other signals and the reference signal by its peak position; determine the autocorrelation matrix of the received signal of the phase complete synchronization subarray, and determine the noise subspace through the eigendecomposition of the autocorrelation matrix; use the noise subspace and the phase complete synchronization subarray The complete orthogonality between the array search vectors determines the direction space spectrum of the reference signal, and the direction of the reference signal is determined by its peak position; the direction of other signals is estimated by using the direction difference between the direction of the reference signal and the direction of other signals and the reference signal. The method can reduce the phase synchronization requirements among signal receivers, maintain high resolution, and effectively reduce system cost.

Description

Array Synthetic Direction Finding Method for Wireless Signal Receiving System

Technical field

The invention belongs to the category of wireless reception, and relates to an array comprehensive direction finding method for a wireless signal receiving system, in particular to a high-resolution direction finding method for an array composed of a part of phase-synchronized sub-arrays and another part of phase-asynchronous sub-arrays.

Background technique

In a wireless signal receiving system, when an array composed of multiple array elements receives wireless signals such as electromagnetic waves and sound waves, there is a certain phase difference between the incoming wave signal received by each array element and a designated reference array element. Since there is a one-to-one relationship between the direction of arrival of the signal and the phase difference, the array direction finding technology can be designed by using this relationship, and the array direction finding can be realized by processing the signal received by the array. Among the existing array direction finding methods based on this principle, the typical one is the multiple signal classification (MUSIC, MUltiple SIgnals Classification) method with high resolution.

The disadvantage of this method is that when the phases of the signal receivers of each array element are not synchronized, an additional, unknown and random phase difference will be added to the phase difference determined by the signal direction of arrival. If the relationship between the phase difference and the direction of arrival is still used to design the array direction finding method, the direction finding performance will be significantly deteriorated. At the same time, when performing high-resolution direction finding on multiple targets at the same time, it is necessary to use an array with a larger aperture and a larger number of elements. Since the phase synchronization of the signal receivers of each array element requires the same local oscillator, when the array is large and the number of array elements is large, the cost of the array direction finding system will increase significantly.

Contents of the invention

The purpose of the present invention is to provide a low-cost high-resolution direction finding method for an array system (array composed of a part of phase-synchronized sub-arrays and another part of phase-asynchronous sub-arrays) in a wireless receiving system with incomplete phase synchronization method. The method comprehensively utilizes the direction of the reference signal and the direction difference between other signals and the reference signal to estimate the direction of arrival of other signals. Using this method can reduce the requirements for phase synchronization between the signal receivers of each array element as much as possible in the case of a large array and a large number of array elements, and will effectively maintain high-resolution direction finding performance Reduce the cost of the array direction finding system.

The purpose of the present invention is achieved like this:

Firstly, using the modulus vector of the received signal of the array that is not affected by incomplete phase synchronization, the direction difference estimation between other signals and the reference signal is obtained, and then using the complex vector of the received signal of the fully phase-synchronized sub-array and the complete subspace orthogonality characteristic, to obtain The direction of the reference signal is used to complete the direction of arrival estimation for all signals.

The specific steps are:

The first step is to determine the modulus vector and its autocorrelation matrix of the signal received by the phase incompletely synchronous array, and perform eigendecomposition on the modulus autocorrelation matrix to determine the noise subspace of the phase incompletely synchronous array;

The second step is to determine the search vector of the phase incompletely synchronized array, and use the orthogonality between the noise subspace and the search vector of the phase incompletely synchronized array to determine the direction difference space spectrum and its peak position of the phase incompletely synchronized array, The peak position determines the direction difference of other signals from the reference signal;

The third step is to determine the autocorrelation matrix of the signal received by the fully phase-synchronized subarray, perform eigendecomposition on the autocorrelation matrix, and determine the noise subspace of the fully phase-synchronized subarray;

The fourth step is to determine the search vector of the fully phase-synchronized subarray, and use the complete orthogonality between the noise subspace and the search vector of the fully phase-synchronized subarray to determine the spatial spectrum of the reference signal and its peak position, and determine the peak position of the reference signal direction;

Finally, the direction of arrival of other signals is estimated by using the direction of the reference signal and the direction difference between other signals and the reference signal.

The reference signal refers to the signal with the smallest direction.

The modulus vector of the received signal of the phase incompletely synchronous array is:

$\mathrm{the\; y}\left(t\right)=\left[\begin{array}{c}{\left|x_1\left(t\right)\right|}^2\\ {\left|x_2\left(t\right)\right|}^2\\ \&Center\; Dot;\\ \·\\ \&Center\; Dot;\\ {\left|x_m\left(t\right)\right|}^2\end{array}\right]$ in, $\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ \&Center\; Dot;\\ \&Center\; Dot;\\ \·\\ x_m\left(t\right)\end{array}\right]$ is the received signal vector of the phase incompletely synchronized array at time t,

M is the number of elements of the phase incompletely synchronous array, and || ² means taking the modulus of a complex number;

The modulus autocorrelation matrix of the array receiving samples with incomplete phase synchronization is: $R_{\mathrm{the\; y}}=\frac{1}{N}\underset{t=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{the\; y}\left(t\right){\mathrm{the\; y}}^T\left(t\right)$

可以为任何非零值。Among them, [] ^T represents vector transposition, and N is the snapshot number of data received by the array. In the formula

Can be any non-zero value.

The eigendecomposition to calculate the autocorrelation matrix of the array modulus with incomplete phase synchronization is:

R _y =QΛQ ^T Wherein, matrix Λ is a diagonal matrix with eigenvalues as diagonal elements,

λ ₁ ≥λ ₂ ≥…≥λ _M matrix Q is a matrix in which the corresponding eigenvectors are column vectors;

The array noise subspace of the phase incomplete synchronization is

Q _{n =} [q _{L +1} q _{L+2 .}

The array search vector for which the phase is not fully synchronized is

$b\left(\mathrm{\φ}\right)=\left[\begin{array}{c}1\\ \cos \left(\frac{2\mathrm{\π}}{\mathrm{\λ}}\mathrm{d\φ}\right)\\ \cos \left(\frac{2\mathrm{\π}}{\mathrm{\λ}}2\mathrm{d\φ}\right)\\ \·\\ \·\\ \·\\ \cos \left(\frac{2\mathrm{\π}}{\mathrm{\λ}}(m-1)\mathrm{d\φ}\right)\end{array}\right]$ and $c\left(\mathrm{\φ}\right)=\left[\begin{array}{c}1\\ \sin \left(\frac{2\mathrm{\π}}{\mathrm{\λ}}\mathrm{d\φ}\right)\\ \sin \left(\frac{2\mathrm{\π}}{\mathrm{\λ}}2\mathrm{d\φ}\right)\\ \&Center\; Dot;\\ \&Center\; Dot;\\ \·\\ \sin \left(\frac{2\mathrm{\π}}{\mathrm{\λ}}(m-1)\mathrm{d\φ}\right)\end{array}\right]$

Among them, d is the spacing between adjacent array elements, λ is the wavelength of the received signal, 0≤φ≤1, and the right sides of the above two formulas can be multiplied by any non-zero constant;

The direction difference spatial spectrum of the array with incomplete phase synchronization is:

$g_{\mathrm{ISP}}\left(\mathrm{\φ}\right)=\frac{1}{b^T\left(\mathrm{\φ}\right)Q_{\mathrm{no}}{Q}_{\mathrm{no}}^{T}b\left(\mathrm{\φ}\right)+c^T\left(\mathrm{\φ}\right)Q_{\mathrm{no}}{Q}_{\mathrm{no}}^{T}c\left(\mathrm{\φ}\right)}$ The right side of the formula can be multiplied by any non-negative value.

The autocorrelation matrix of the samples received by the phase synchronization subarray is: $R_z=\frac{1}{N}\underset{t=1}{\overset{N}{\mathrm{\Σ}}}z\left(t\right)z^h\left(t\right)$

in, $z\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ \&Center\; Dot;\\ \&Center\; Dot;\\ \&Center\; Dot;\\ x_m\left(t\right)\end{array}\right]$ is the received signal vector of the phase synchronization subarray, [] ^H represents the conjugate transpose of the vector;

The eigendecomposition of the autocorrelation matrix of the phase-synchronized subarray is:

η₁≥η₂≥…≥η_m，矩阵Ω是以对应的特征向量为列向量的矩阵；R _z ＝PΩP ^H Among them, matrix Ω is a diagonal matrix whose eigenvalues are diagonal elements,

η ₁ ≥η ₂ ≥…≥η _m , the matrix Ω is a matrix in which the corresponding eigenvectors are column vectors;

The noise subspace of the phase synchronization subarray is: P _n =[p _h+1 p _h+2 …p _m ]

Wherein, the matrix p _n is a matrix composed of eigenvectors corresponding to the mh smallest eigenvalues of the autocorrelation matrix R _z of the phase synchronization subarray;

The search vector of the phase synchronization subarray is:

$a_m(\mathrm{\θ},{\mathrm{\φ}}_i)=\left[\begin{array}{c}1\\ e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}d(\sin \left(\mathrm{\θ}\right)+{\mathrm{\φ}}_i)}\\ e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}2d(\sin \left(\mathrm{\θ}\right)+{\mathrm{\φ}}_i)}\\ \&Center\; Dot;\\ \&Center\; Dot;\\ \&Center\; Dot;\\ e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}(m-1)d(\sin \left(\mathrm{\θ}\right)+{\mathrm{\φ}}_i)}\end{array}\right]$ in, $-\frac{\mathrm{\π}}{2}\≤\mathrm{\θ}\≤\frac{\mathrm{\π}}{2},$ i=1, 2, . . . , D-1,

The right side of the formula can be multiplied by any non-zero constant.

The reference signal direction space spectrum is $g_{\mathrm{SP}}\left(\mathrm{\φ}\right)=\frac{1}{\underset{i=1}{\overset{\mathrm{D.}-1}{\mathrm{\Σ}}}{a}_m^h(\mathrm{\θ},{\mathrm{\φ}}_i)P_{\mathrm{no}}{P}_{\mathrm{no}}^h{a}_m(\mathrm{\θ},{\mathrm{\φ}}_i)}$ The right side of the formula can be multiplied by any non-zero value.

Space Spectrum Search Equation of Direction Difference for Arrays with Different Phases $g_{\mathrm{ISP}}\left(\mathrm{\φ}\right)=\frac{1}{b^T\left(\mathrm{\φ}\right)Q_{\mathrm{no}}{Q}_{\mathrm{no}}^{T}b\left(\mathrm{\φ}\right)+c^T\left(\mathrm{\φ}\right)Q_{\mathrm{no}}{Q}_{\mathrm{no}}^{T}c\left(\mathrm{\φ}\right)}$ When the right side of is multiplied by any non-negative number, the peak position of the direction difference spatial spectrum of the array with not exactly the same phase is obtained, and the peak position determines the direction difference φ _i (i=1, 2, ..., D-1) between other signals and the reference signal, When the right side of the search expression is multiplied by any negative number, it is the corresponding direction obtained from the valley position of the search space spectrum. In the formula, the subscript ISP represents the array whose phase is not completely synchronized,

Reference Signal Direction Spatial Spectrum Search Formula $g_{\mathrm{SP}}\left(\mathrm{\φ}\right)=\frac{1}{\underset{i=1}{\overset{\mathrm{D.}-1}{\mathrm{\Σ}}}{a}_m^h(\mathrm{\θ},{\mathrm{\φ}}_i)P_{\mathrm{no}}{P}_{\mathrm{no}}^h{a}_m(\mathrm{\θ},{\mathrm{\φ}}_i)}$ The right side of is multiplied by the peak position of any non-negative reference signal direction difference spatial spectrum. The peak position determines the direction of the reference signal. When the right side of the search formula is multiplied by any negative number, it is the corresponding direction obtained by searching the valley position of the spatial spectrum. In the formula, the subscript SP represents the synchronous subarray of the phase incompletely synchronous array.

The phase incomplete synchronous array is a uniform line array or a non-uniform line array or a circular array or a randomly distributed array, which is not limited by its shape.

Outstanding advantage of the present invention is:

1. Comprehensively determine the spatial spectrum of the direction difference and its peak position of the phase incomplete array and the reference signal space spectrum and its peak position of the minimum direction of the phase synchronization subarray, and use the peak position of the direction difference space spectrum of the phase incompletely synchronous array The direction difference between other signals and the reference signal is determined; the direction of the reference signal is determined by using the peak position of the reference direction space spectrum of the phase synchronous subarray. Furthermore, the direction of the reference signal and the direction difference between other signals and the reference signal are used to estimate the direction of arrival of other signals, so as to ensure the effect of high resolution.

2. In the case of a large array and a large number of array elements, the requirements for phase synchronization between the signal receivers of each array element can be reduced as much as possible, and the cost can be lowered.

3. This method has a wide application range and is not limited by the shape of the array of the receiving system. It can be widely used to enhance the resolution of existing array direction finding systems, so as to meet the requirements of array systems such as smart antenna arrays, sonar arrays, and radio imaging arrays for high-resolution direction finding performance.

4. Carrying out experiments according to the comprehensive method of the present invention shows that the number of sub-array array elements applied to phase synchronization by this method is 6, the number of sub-array array elements whose phases are not synchronized is 26, and the interval between adjacent array elements is half The uniform linear array whose wavelength phase is not fully synchronized can clearly distinguish three signals with a signal-to-noise ratio of 6.0dB and directions equal to 7.0, 18.0, and 22.0 degrees respectively when the number of snapshots is equal to 256, which meets the direction finding requirements. System requirements for high-resolution performance. However, the commonly used MUSIC method under the same conditions has been unable to distinguish these three signals.

Description of drawings

Figure 1 shows a block flow diagram of the present invention.

Fig. 2 shows the structural diagram of the phase incompletely synchronous array of the present invention.

Fig. 3 shows the normalized spatial spectrum estimation results obtained by using the existing array direction finding method for the phase incompletely synchronized array system in the case of three signals.

Fig. 4 shows the results of normalized direction difference spatial spectrum estimation obtained by using the comprehensive direction finding method of the present invention for the phase incompletely synchronized array system in the case of three signals.

Fig. 5 shows the normalized reference signal spatial spectrum estimation results obtained by using the comprehensive direction finding method of the present invention in the phase incompletely synchronized array system in the case of three signals.

Detailed ways

Accompanying drawing is also embodiment. The present invention will be described in detail below in conjunction with the accompanying drawings. Taking the uniform line array with incomplete phase synchronization shown in Figure 2 as an example, the array elements of the array are M, and the distance between adjacent array elements is d, wherein m adjacent array elements form a phase-synchronized sub-array, and in addition Mm adjacent array elements form a sub-array with asynchronous phases. Assume that there are D non-coherent narrowband signals s _{k (} t) in space, k=1, 2, . Taking the first element of the array whose phase is not fully synchronized as the reference element, the received signal vector of the array at time t is

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; As</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

in,

s(t)=[s ₁ (t)s ₂ (t)...s _D (t)] ^T (2)

A＝[a _M (θ ₁ )a _M (θ ₂ )…a _M (θ _D )] (3)

表示相位不同步子阵列各阵元接收机的随机相位，[]^T表示向量转置，λ为信号的波长，v(t)为加性白噪声向量，与信号s(t)相互独立。

Indicates the random phase of each element receiver of the phase asynchronous subarray, [] ^T indicates vector transposition, λ is the wavelength of the signal, and v(t) is the additive white noise vector, which is independent of the signal s(t).

Corresponding to the phase synchronous sub-array and the phase non-synchronous sub-array of the phase incompletely synchronous array, the received signal vector of the phase incompletely synchronous array at time t can be expressed as

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right]$

in, $z\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&Center\; Dot;\\ x_m\left(t\right)\end{array}\right]$ is the received signal vector of the phase synchronous subarray, $w\left(t\right)=\left[\begin{array}{c}{x}_{m+1}\left(t\right)\\ x_{m+2}\left(t\right)\\ \&Center\; Dot;\\ \&Center\; Dot;\\ \&Center\; Dot;\\ x_m\left(t\right)\end{array}\right]$ is the received signal vector of the out-of-phase subarray.

See attached drawing 1. The flow starts from step 201. In step 2021, it is first determined that the modulus vector of the array receiving samples whose phases are not fully synchronized is:

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{c}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ {<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Among them, || ² means taking the modulus of a complex number, and N is the snapshot number of data received by the array.

In step 2022, it is determined that the modulus autocorrelation matrix of the array received samples whose phases are not fully synchronized is:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

In step 2023, calculate the eigendecomposition of the array modulus autocorrelation matrix with incomplete phase synchronization as

R _y ＝QΛQ ^T (7)

Among them, matrix Λ is a diagonal matrix whose eigenvalues are diagonal elements,

λ ₁ ≥ λ ₂ ≥... ≥ λ _M ,

Matrix Q is a matrix in which the corresponding eigenvectors are column vectors.

In step 2024, it is determined that the array noise subspace with incomplete phase synchronization is

Q _n ＝[q _L+1 q _L+2 ...q _M ] (8)

Among them, the matrix Q _n is a matrix composed of eigenvectors corresponding to the ML minimum eigenvalues of the array modulus autocorrelation matrix R _y whose phases are not completely synchronized.

In step 2031, it is determined that the phase incompletely synchronized array search vector is

$\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\mathrm{<span\; class="notranslate">\; d\&phi;</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; d\&phi;</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&phi;</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

and

$\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\mathrm{<span\; class="notranslate">\; d\&phi;</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; d\&phi;</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ \mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&phi;</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

Among them, 0≤φ≤1.

In step 2032, first determine the direction difference spatial spectrum of the comprehensive direction finding technology designed by the present invention:

${\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; ISP</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

The subscript 'ISP' indicates that the array direction finding method of the present invention is aimed at arrays with incompletely synchronized phases (Incompletely Synchronized Phase). Then determine the direction difference between other signals and the reference signal (the signal with the smallest direction) by searching the peak position of the direction difference spatial spectrum represented by formula (11): φ _i (i=1, 2, . . . , D-1).

In step 2041, determine the autocorrelation matrix of the samples received by the phase synchronization subarray as:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

where [] ^H represents the vector conjugate transpose.

In step 2042, the eigendecomposition of the autocorrelation matrix of the phase-synchronized subarray is calculated as

R _z = PΩP ^H (13)

Among them, the matrix Ω is a diagonal matrix whose eigenvalues are diagonal elements,

η ₁ ≥ η ₂ ≥... ≥ η _m ,

The matrix Ω is a matrix in which the corresponding eigenvectors are column vectors.

In step 2043, determine the noise subspace of the phase synchronous subarray as

P _n ＝[p _h+1 p _h+2 ... p _m ] (14)

Wherein, the matrix P _n is a matrix composed of eigenvectors corresponding to the mh minimum eigenvalues of the autocorrelation matrix R _z of the phase synchronization subarray.

In step 2051, determine the search vector of the phase synchronization subarray as

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ {\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

in, $-\frac{\mathrm{\&pi;}}{2}\&le;\mathrm{\&theta;}\&le;\frac{\mathrm{\&pi;}}{2},$ i=1, 2, . . . , D-1.

In step 2052, first determine the reference signal direction spatial spectrum of the comprehensive direction finding technology designed by the present invention:

${\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; SP</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

The subscript 'SP' represents the synchronous subarray (Synchronous Phase) of the phase incompletely synchronous array. Then determine the direction of the reference signal by searching the peak position of the reference signal direction spatial spectrum represented by formula (16).

In step 206, the direction of arrival of other signals is estimated by using the direction of the reference signal and the direction difference between the other signals and the reference signal.

The flow according to the method ends at step 207 .

The above-mentioned embodiments of the method are compared and illustrated in more detail below.

The spatial spectrum output by existing methods is equal to

${\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; MUSIC</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

The subscripts 'MUSIC' represent the multi-signal classification method (MUSIC), and U _n is a matrix composed of eigenvectors corresponding to the MD minimum eigenvalues of the sample autocorrelation matrix R.

See Figure 3 and Figure 4. In the same situation where the number of phase synchronous array elements is 6, the number of phase asynchronous array elements is 26, the number of signals is 3, and the direction of arrival (degrees) [7.0, 18.0, 22.0] signal-to-noise ratio (db) [6.0, 6.0, 6.0], Compared with the existing MUSIC, the comprehensive direction finding technology designed by the present invention has higher direction resolution than MUSIC. It can be seen from FIG. 3 that the existing MUSIC has indistinguishable signals, but the present invention can clearly distinguish all signals.

Although the comprehensive direction finding method of the present invention has been described by way of example with reference to the accompanying drawings, the present invention is not limited to the above details, and the present application covers various modifications or changes within the scope of the claims.

Claims (9)

1. An array comprehensive direction-finding method for a wireless signal receiving system, characterized in that: firstly, using the modulus vector of the array receiving signal not affected by the incomplete synchronization of the phase, to obtain the direction difference estimation of other signals and the reference signal, and then using the phase Completely synchronous subarrays receive complex vectors of signals and complete subspace orthogonality characteristics, obtain the direction of reference signals, and complete the direction of arrival estimation of all signals. The specific steps are: The first step is to determine the modulus vector and its autocorrelation matrix of the signal received by the phase incompletely synchronous array, and perform eigendecomposition on the modulus autocorrelation matrix to determine the noise subspace of the phase incompletely synchronous array; The second step is to determine the search vector of the phase incompletely synchronized array, and use the orthogonality between the noise subspace and the search vector of the phase incompletely synchronized array to determine the direction difference space spectrum and its peak position of the phase incompletely synchronized array, The peak position determines the direction difference of other signals from the reference signal; The third step is to determine the autocorrelation matrix of the signal received by the fully phase-synchronized subarray, perform eigendecomposition on the autocorrelation matrix, and determine the noise subspace of the fully phase-synchronized subarray; The fourth step is to determine the search vector of the fully phase-synchronized subarray, and use the complete orthogonality between the noise subspace and the search vector of the fully phase-synchronized subarray to determine the reference signal space spectrum and its peak position, and the peak position determines the reference signal the direction of Finally, the direction of arrival of other signals is estimated by using the direction of the reference signal and the direction difference between other signals and the reference signal. 2. The method for array comprehensive direction finding according to claim 1, characterized in that: the reference signal refers to the signal with the smallest direction. 3. according to claim 1 or 2 or 3 described array comprehensive direction-finding methods, it is characterized in that: the mode vector of described phase incompletely synchronous array receiving signal is: $\mathrm{the\; y}\left(t\right)=\left[\begin{array}{c}{\left|x_1\left(t\right)\right|}^2\\ {\left|x_2\left(t\right)\right|}^2\\ .\\ .\\ .\\ {\left|x_m\left(t\right)\right|}^2\end{array}\right]$ in, $\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ .\\ .\\ .\\ x_m\left(t\right)\end{array}\right]$ is the received signal vector of the phase incompletely synchronized array at time t, M is the number of array elements of the phase incompletely synchronous array, | | ² means taking the modulus of a complex number; The modulus autocorrelation matrix of the array receiving samples with incomplete phase synchronization is: $R_{\mathrm{the\; y}}=\frac{1}{N}\underset{t=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{the\; y}\left(t\right){\mathrm{the\; y}}^T\left(t\right)$ Among them, [] ^T represents the vector transpose, N is the snapshot number of the data received by the array, where

Can be any non-zero value; The eigendecomposition to calculate the autocorrelation matrix of the array modulus with incomplete phase synchronization is: R _y =QΛQ ^T Wherein, matrix Λ is a diagonal matrix with eigenvalues as diagonal elements,

λ ₁ ≥λ ₂ ≥…≥λ _M matrix Q is a matrix in which the corresponding eigenvectors are column vectors; The array noise subspace of the phase incomplete synchronization is Q _{n =} [q _{L +1} q _{L+2 .} 4. according to claim 1 and 2 described array comprehensive direction finding methods, it is characterized in that: the array search vector of described phase incomplete synchronization is $b\left(\mathrm{\&phi;}\right)=\left[\begin{array}{c}1\\ \cos \left(\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\mathrm{d\&phi;}\right)\\ \cos \left(\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}2\mathrm{d\&phi;}\right)\\ .\\ .\\ .\\ \cos \left(\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(m-1)\mathrm{d\&phi;}\right)\end{array}\right]$ and $c\left(\mathrm{\&phi;}\right)=\left[\begin{array}{c}1\\ \sin \left(\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\mathrm{d\&phi;}\right)\\ \sin \left(\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}2\mathrm{d\&phi;}\right)\\ .\\ .\\ .\\ \sin \left(\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(m-1)\mathrm{d\&phi;}\right)\end{array}\right]$ Among them, d is the distance between adjacent array elements, λ is the wavelength of the received signal, 0≤φ≤1, and the right sides of the above two formulas can be multiplied by any non-zero constant; The direction difference spatial spectrum of the array with incomplete phase synchronization is: $g_{\mathrm{ISP}}\left(\mathrm{\&phi;}\right)=\frac{1}{b^T\left(\mathrm{\&phi;}\right)Q_{\mathrm{no}}{Q}_{\mathrm{no}}^{T}b\left(\mathrm{\&phi;}\right)+c^T\left(\mathrm{\&phi;}\right)Q_{\mathrm{no}}{Q}_{\mathrm{no}}^{T}c\left(\mathrm{\&phi;}\right)}$ The right side of the formula can be multiplied by any non-negative value. 5. The array comprehensive direction finding method according to claim 1 or 2, characterized in that: the autocorrelation matrix of the phase synchronization subarray receiving samples is: $R_z=\frac{1}{N}\underset{t=1}{\overset{N}{\mathrm{\&Sigma;}}}z\left(t\right)z^h\left(t\right)$ in, $z\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ .\\ .\\ .\\ x_m\left(t\right)\end{array}\right]$ is the received signal vector of the phase synchronization subarray, [] ^H represents the conjugate transpose of the vector; The eigendecomposition of the autocorrelation matrix of the phase-synchronized subarray is: R _z ＝PΩP ^H Among them, matrix Ω is a diagonal matrix whose eigenvalues are diagonal elements, η ₁ ≥η ₂ ≥…≥η _m , the matrix Ω is a matrix in which the corresponding eigenvectors are column vectors; The noise subspace of the phase synchronization subarray is: P _n =[p _h+1 p _h+2 ... p _m ] Wherein, the matrix P _n is a matrix composed of eigenvectors corresponding to the mh minimum eigenvalues of the autocorrelation matrix R _z of the phase synchronization subarray. 6. The array comprehensive direction finding method according to claim 5, characterized in that: the search vector of the phase synchronization sub-array is: $a_m(\mathrm{\&theta;},{\mathrm{\&phi;}}_i)=\left[\begin{array}{c}1\\ e^{j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}d(\sin \left(\mathrm{\&theta;}\right)+{\mathrm{\&phi;}}_i)}\\ e^{j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}2d(\sin \left(\mathrm{\&theta;}\right)+{\mathrm{\&phi;}}_i)}\\ .\\ .\\ .\\ e^{j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(m-1)d(\sin \left(\mathrm{\&theta;}\right)+{\mathrm{\&phi;}}_i)}\end{array}\right]$ in, $-\frac{\mathrm{\&pi;}}{2}\&le;\mathrm{\&theta;}\&le;\frac{\mathrm{\&pi;}}{2},$ i=1, 2, . . . , D-1, The right side of the formula can be multiplied by any non-zero constant. 7. The array comprehensive direction finding method according to claim 1 or 2, characterized in that: the direction difference space spectrum search formula of the arrays with not exactly the same phase $g_{\mathrm{ISP}}\left(\mathrm{\&phi;}\right)=\frac{1}{b^T\left(\mathrm{\&phi;}\right)Q_{\mathrm{no}}{Q}_{\mathrm{no}}^{T}b\left(\mathrm{\&phi;}\right)+c^T\left(\mathrm{\&phi;}\right)Q_{\mathrm{no}}{Q}_{\mathrm{no}}^{T}c\left(\mathrm{\&phi;}\right)}$ When the right side of is multiplied by any non-negative number, the peak position of the signal with not exactly the same phase is obtained, and the peak position determines that the direction difference between the corresponding signal and the reference signal is φ _i (i=1, 2, ..., D-1); the right side of the search formula When multiplied by any negative number, is the corresponding direction obtained from the valley position of the search space spectrum. 8. The array comprehensive direction finding method according to claim 1 or 2, characterized in that: the reference signal direction space spectrum search formula $g_{\mathrm{SP}}\left(\mathrm{\&phi;}\right)=\frac{1}{\underset{i=1}{\overset{\mathrm{D.}-1}{\mathrm{\&Sigma;}}}{a}_m^h(\mathrm{\&theta;},{\mathrm{\&phi;}}_i)P_{\mathrm{no}}{P}_{\mathrm{no}}^h{a}_m(\mathrm{\&theta;},{\mathrm{\&phi;}}_i)}$ When the right side of is multiplied by any non-negative number, the peak position of the reference signal direction spatial spectrum is obtained, and the peak position determines the direction of the reference signal; when the right side of the search expression is multiplied by any negative number, it is the corresponding direction obtained by searching the valley position of the spatial spectrum. 9. The method for array comprehensive direction finding according to claim 4, characterized in that: the phase incompletely synchronous array is a uniform line array or a non-uniform line array or a circular array or a randomly distributed array.

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