CN101309101A

CN101309101A - Array synthetic direction-finding method of wireless signal receiving system

Info

Publication number: CN101309101A
Application number: CNA2007100490797A
Authority: CN
Inventors: 万群; 杨万麟; 窦衡; 沈晓峰; 杨瑞明
Original assignee: University of Electronic Science and Technology of China
Current assignee: University of Electronic Science and Technology of China
Priority date: 2007-05-14
Filing date: 2007-05-14
Publication date: 2008-11-19
Anticipated expiration: 2027-05-14
Also published as: CN101309101B

Abstract

Disclosed is a comprehensive direction finding method for an array of a wireless signal receiving system, which belongs to the signal receiving category. The steps are as follows: identify the mode vector and the autocorrelation matrix of the received signal of a phase incompletely synchronized array, decompose and identify the noise subspace through the character of the mode autocorrelation matrix; then search the orthogonal properties between the vectors to identify the direction error space spectrum by using the noise subspace and the phase incompletely synchronized array, and then identify the direction error between other signals and reference signal through the peak position. Identify the autocorrelation matrix of the received signal of a phase completely synchronized subarray, decompose and identify the noise subspace through the character of the autocorrelation matrix; then search the complete orthogonal properties between the vectors to identify the direction space spectrum of the reference signal by using the noise subspace and the phase completely synchronized subarray, and then identify the reference signal direction through the peak position. Finally, use the reference signal direction and the direction error between other signals and the reference signal to estimate the direction of other signals. The comprehensive direction finding method for an array of a wireless signal receiving system of the invention can reduce the requirement of phase synchronization between each signal receiver, maintain a high resolution and effectively reduce the system cost.

Description

Array comprehensive direction finding method of wireless signal receiving system

Technical Field

The invention belongs to the field of wireless receiving, and relates to an array comprehensive direction finding method of a wireless signal receiving system, in particular to a high-resolution direction finding method of an array consisting of a part of sub-arrays with synchronous phases and another part of sub-arrays with asynchronous phases.

Background

In a radio signal receiving system, when an array including a plurality of array elements receives radio signals such as electromagnetic waves and acoustic waves, a certain phase difference exists between an incoming wave signal received by each array element and a certain specified reference array element. Because the direction of arrival of the signal and the phase difference have a one-to-one correspondence relationship, an array direction-finding technology can be designed by utilizing the relationship, and the array direction-finding is realized by processing the signals received by the array. Among existing array direction finding methods based on this principle, a multi-signal classification (MUSIC) method with high resolution is typical.

The disadvantage of this method is that when the phase of the signal receiver itself of each array element is not synchronized, an additional, unknown, random phase difference will be added to the phase difference determined by the signal direction of arrival, which will result in a significant deterioration of the direction-finding performance if the array direction-finding method is still designed using the relationship between the phase difference and the direction of arrival. Meanwhile, when high-resolution direction finding is carried out on a plurality of targets at the same time, an array with larger aperture and more array elements is needed. Because the same local oscillator is needed for keeping the phase of the signal receiver of each array element synchronous, when the array is large and the number of the array elements is large, the cost of the array direction-finding system is obviously increased.

Disclosure of Invention

The invention aims to provide a low-cost high-resolution direction finding method for an array system (an array consisting of a part of sub-arrays with synchronous phases and another part of sub-arrays with asynchronous phases) with incomplete synchronous phases in a wireless receiving system. 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. The method can reduce the requirement on the phase synchronization among the array element signal receivers as much as possible under the conditions of larger array and more array element numbers, and effectively reduce the cost of the array direction-finding system while maintaining the high-resolution direction-finding performance.

The purpose of the invention is achieved by the following steps:

firstly, the mode vector of the array receiving signal which is not affected by the incomplete synchronization of the phase is utilized to obtain the direction difference estimation of other signals and the reference signal, and then the complex vector and the complete subspace orthogonal characteristic of the sub-array receiving signal of the complete synchronization of the phase are utilized to obtain the direction of the reference signal, thereby completing the direction of arrival estimation of all signals.

The method comprises the following specific steps:

determining a modulus vector and an autocorrelation matrix of a received signal of an incomplete phase synchronization array, performing characteristic decomposition on the modulus autocorrelation matrix, and determining a noise subspace of the incomplete phase synchronization array;

determining a search vector of the incomplete phase synchronization array, determining a direction difference space spectrum and a peak position of the incomplete phase synchronization array by utilizing the orthogonal characteristic between a noise subspace and the search vector of the incomplete phase synchronization array, and determining the direction difference between other signals and a reference signal at the peak position;

thirdly, determining an autocorrelation matrix of a receiving signal of the phase complete synchronization subarray, performing characteristic decomposition on the autocorrelation matrix, and determining a noise subspace of the phase complete synchronization subarray;

fourthly, determining a search vector of the phase complete synchronization subarray, determining a reference signal space spectrum and a peak position thereof by using complete orthogonal characteristics between the noise subspace and the search vector of the phase complete synchronization subarray, and determining the direction of the reference signal by the peak position;

and finally, estimating the direction of arrival of other signals by using the direction of the reference signal and the direction difference between the other signals and the reference signal.

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

The modulus vector of the phase incomplete synchronization array receiving signal is as follows:

wherein,

for the received signal vector of the partially phased array at time t,

m is the array element number of the incomplete synchronous array of phase (| non-woven phosphor)²Representing a modulus of the complex number;

the modulo autocorrelation matrix of the array receiving samples whose phases are not fully synchronized is:

wherein, the [ alpha ], [ beta ]]^TIndicating vector transposition and N being the number of snapshots of the array received data. In the formula

And may be any non-zero value.

The characteristic decomposition of the array mode autocorrelation matrix of which the phase is not completely synchronous is calculated as follows:

R_y＝QΛQ^Twherein the matrix Λ is a diagonal matrix with eigenvalues as diagonal elements,

λ₁≥λ₂≥…≥λ_Mthe matrix Q is a matrix taking the corresponding characteristic vector as a column vector;

the array noise subspace with incompletely synchronized phases is

Q_n＝[q_L+1 q_L+2…q_M]Wherein, the matrix Q_nIs an array mode autocorrelation matrix R with incompletely synchronized phases_yAnd (4) forming a matrix by eigenvectors corresponding to the M-L minimum eigenvalues.

The array search vector with incompletely synchronized phases is

And

wherein d is the distance between adjacent array elements, lambda is the wavelength of the received signal, phi is more than or equal to 0 and less than or equal to 1, and the right sides of the two formulas can be multiplied by any nonzero constant;

the direction difference spatial spectrum of the array with incompletely synchronized phases is:

the right side in the equation may be multiplied by any non-negative value.

The autocorrelation matrix of the phase synchronization subarray received samples is:

wherein,

is a received signal vector of a phase synchronization sub-array]^HRepresenting a vector conjugate transpose;

the characteristic decomposition of the autocorrelation matrix of the phase synchronization sub-array is:

R_z＝PΩP^Hwherein the matrix omega is a diagonal matrix with eigenvalues as diagonal elements,

η₁≥η₂≥…≥η_mthe matrix Ω is a matrix in which the corresponding eigenvector is a column vector;

the noise subspace of the phase synchronization subarray is: p_n＝[p_h+1 p_h+2…p_m]

Wherein, the matrix p_nAutocorrelation matrix R being a phase-synchronized sub-array_zA matrix formed by eigenvectors corresponding to the m-h minimum eigenvalues;

the search vector of the phase synchronization subarray is as follows:

wherein,

i＝1，2，…，D-1，

the right side in the equation may be multiplied by any non-zero constant.

The reference signal direction space spectrum is

The right side in the equation may be multiplied by any non-zero value.

Direction difference space spectrum searching formula of array with incompletely identical phase

The right side of the array is multiplied by any non-negative number to obtain the peak position of the direction difference space spectrum of the array with the incompletely same phase, and the peak position determines the direction difference phi between other signals and the reference signal_i(i＝1，2，…，D-1)，The right side of the search expression multiplied by any negative number is the corresponding direction found by the valley position of the search space spectrum. Where the subscript ISP denotes an array that is not fully synchronized in phase,

reference signal direction space spectrum searching type

The right side of the search expression is multiplied by the peak position of any non-negative reference signal direction difference space spectrum, the peak position determines the direction of the reference signal, and the right side of the search expression is multiplied by any negative number to be the corresponding direction obtained by searching the valley position of the space spectrum. In the formula, the subscript SP denotes a synchronization sub-array of the incomplete phase synchronization array.

The phase incomplete synchronization array is a uniform line array or a non-uniform line array or a circular array or an array distributed randomly, and is not limited by form.

The invention has the outstanding advantages that:

1. comprehensively determining a direction difference space spectrum and a peak position thereof of an array with incompletely identical phases and a reference signal space spectrum and a peak position thereof with the smallest direction of a phase synchronization sub-array, and determining the direction difference between other signals and the reference signal by using the peak position of the direction difference space spectrum of the incompletely synchronized phase array; and determining the direction of the reference signal by using the peak position of the reference direction space spectrum of the phase synchronization sub-array. And then the direction of arrival of other signals is estimated by utilizing the direction of the reference signal and the direction difference between the other signals and the reference signal, so that the effect of high resolution is ensured.

2. The requirement on phase synchronization among array element signal receivers can be reduced as much as possible under the conditions of larger array and more array element numbers, and lower cost is achieved.

3. The method has wide application range and is not limited by the array shape of the receiving system. The method can be widely applied to enhancing the resolution of the existing array direction-finding system, thereby meeting the requirements of array systems such as intelligent antenna arrays, sonar arrays, radio imaging arrays and the like on high-resolution direction-finding performance.

4. Experiments carried out according to the comprehensive method show that the method is applied to the uniform linear array with incomplete synchronous phases, the number of the sub-array elements with synchronous phases is 6, the number of the sub-array elements with asynchronous phases is 26, and the interval between the adjacent array elements is half wavelength, so that under the condition that the fast shooting number is equal to 256, three signals with the signal-to-noise ratio of 6.0dB and the directions of 7.0, 18.0 and 22.0 degrees are clearly distinguished, and the requirement of a direction-finding system on high resolution performance is met. The commonly used MUSIC method under the same conditions cannot distinguish the three signals.

Drawings

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

Fig. 2 shows a block diagram of a phased partially synchronized array of the present invention.

Fig. 3 shows a normalized spatial spectrum estimation result obtained by the existing array direction finding method in the incomplete phase synchronization array system under the condition of 3 signals.

Fig. 4 shows a normalized direction difference spatial spectrum estimation result diagram obtained by the comprehensive direction finding method of the present invention in the incomplete phase synchronization array system under the condition of 3 signals.

Fig. 5 is a diagram showing a normalized reference signal spatial spectrum estimation result obtained by the comprehensive direction finding method of the present invention in the phase incomplete synchronization array system under the condition of 3 signals.

Detailed Description

The attached drawings are embodiments. The present invention will be described in detail with reference to the accompanying drawings. Taking the uniform linear array with incompletely synchronized phases as an example shown in fig. 2, the array elements of the array are M, the spacing between adjacent array elements is d, wherein M adjacent array elements form a sub-array with synchronized phases, and M-M adjacent array elements form a sub-array with unsynchronized phases. Suppose that there are D incoherent narrow-band signals s in space_k(t), k is 1, 2, D, reaches the linear array, and forms an angle theta with the normal direction of the linear array_k. The first array element of the array with incomplete synchronous phase is taken as a reference array element, and the received signal vector of the array at the time t is taken as

Wherein,

s(t)＝[s₁(t)s₂(t)…s_D(t)]^T (2)

A＝[a_M(θ₁)a_M(θ₂)…a_M(θ_D)] (3)

a random phase value representing the receiver of each array element of the phase asynchronous subarray]^TDenotes vector transposition, λ is the wavelength of the signal, v (t) is an additive white noise vector, independent of s (t) the signal.

Corresponding to the phase synchronization subarray and the phase non-synchronization subarray of the incomplete phase synchronization array, the received signal vector of the incomplete phase synchronization array at the time t can be expressed as

x (t) = [\begin{matrix} z (t) \\ w (t) \end{matrix}]

Wherein,

is the received signal vector of the phase synchronized sub-array,

is the received signal vector of the out-of-phase subarray.

See figure 1. The flow starts at step 201. In step 2021, it is first determined that the modulus vectors of the received samples of the array whose phases are not completely synchronized are:

wherein | andi²The expression takes the modulus of a complex number, and N is the snapshot number of the array receiving data.

At step 2022, the modulo autocorrelation matrix for the array received samples whose phases are not fully synchronized is determined to be:

at step 2023, the eigen decomposition of the array modulo autocorrelation matrix, for which the phase is not fully synchronized, is computed as

R_y＝QΛQ^T (7)

Wherein the matrix Λ is a diagonal matrix with eigenvalues as diagonal elements,

λ₁≥λ₂≥…≥λ_M，

the matrix Q is a matrix in which the corresponding feature vector is a column vector.

In step 2024, the array noise subspace where the phases are not fully synchronized is determined to be

Q_n＝[q_L+1 q_L+2…q_M] (8)

Wherein, the matrix Q_nIs an array mode autocorrelation matrix R with incompletely synchronized phases_yAnd (4) forming a matrix by eigenvectors corresponding to the M-L minimum eigenvalues.

At step 2031, an array search vector is determined with incomplete synchronization of phase as

And

wherein phi is more than or equal to 0 and less than or equal to 1.

In step 2032, the direction difference spatial spectrum of the integrated direction finding technology designed by the present invention is determined:

wherein the subscript 'ISP' indicates that the array direction finding method of the present invention is directed toAn array of incompletely synchronized phases (IncomplelySynchronized Phase). Then, the direction difference between the other signal and the reference signal (the signal with the smallest direction) is determined by searching for the peak position of the direction difference spatial spectrum represented by equation (11): phi is a_i(i＝1，2，…，D-1)。

In step 2041, the autocorrelation matrix of the received samples of the phased locked sub-array is determined as:

wherein, the [ alpha ], [ beta ]]^HRepresenting the vector conjugate transpose.

At step 2042, the autocorrelation matrix of the phased synchronized subarray is calculated for eigendecomposition into

R_z＝PΩP^H (13)

Wherein the matrix omega is a diagonal matrix with eigenvalues as diagonal elements,

η₁≥η₂≥…≥η_m，

the matrix Ω is a matrix in which the corresponding eigenvector is a column vector.

In step 2043, the noise subspace of the phasic synchrony subarray is determined to be

P_n＝[p_h+1 p_h+2…p_m] (14)

Wherein, the matrix P_nAutocorrelation matrix R being a phase-synchronized sub-array_zAnd (4) forming a matrix by eigenvectors corresponding to the m-h minimum eigenvalues.

At step 2051, a search vector for the phased synchronized sub-array is determined as

Wherein,

i＝1，2，…，D-1。

in step 2052, the reference signal direction spatial spectrum of the integrated direction finding technique designed by the present invention is determined:

where the subscript 'SP' denotes a Synchronous sub-array (Synchronous Phase) of the incompletely phased array. The direction of the reference signal is then determined by searching for the peak position of the reference signal direction spatial spectrum represented by equation (16).

In step 206, the direction of arrival of the other signal is estimated using the direction of the reference signal and the difference in the direction of the other signal from the reference signal.

The flow according to the method ends in step 207.

The above-described embodiments of the present method are compared and exemplified in more detail below.

The spatial spectrum output by the existing method is equal to

<math> <mrow> <msub> <mi>g</mi> <mi>MUSIC</mi> </msub> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msup> <mi>a</mi> <mi>H</mi> </msup> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> <msub> <mi>U</mi> <mi>n</mi> </msub> <msubsup> <mi>U</mi> <mi>n</mi> <mi>H</mi> </msubsup> <mi>a</mi> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein the subscript 'MUSIC' denotes a multiple signal classification Method (MUSIC), U, respectively_nAnd forming a matrix by eigenvectors corresponding to the M-D minimum eigenvalues of the sample autocorrelation matrix R.

See fig. 3, 4. Compared with the existing MUSIC, the comprehensive direction finding technology designed by the invention has higher direction resolution than the MUSIC under the same conditions of 6 elements of a phase synchronization array, 26 elements of a phase asynchronization array, 3 elements of signals, 7.0 (degree) of arrival direction (db) (6.0, 6.0, 6.0) and 6.0 (degree) of signal to noise ratio (db) (6.0, 6.0 and 6.0). As can be seen from fig. 3, the existing MUSIC has signals which cannot be resolved, and all signals can be clearly resolved by using the present invention.

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

Claims

1. An array integrated direction finding method of a wireless signal receiving system is characterized in that: firstly, obtaining direction difference estimation of other signals and a reference signal by using a mode vector of an array receiving signal which is not influenced by incomplete phase synchronization, and then obtaining the direction of the reference signal by using a complex vector and complete subspace orthogonality of a phase complete synchronization sub-array receiving signal to finish the direction of arrival estimation of all signals, wherein the specific steps are as follows:

fourthly, determining a search vector of the phase complete synchronization subarray, determining a reference signal space spectrum and a peak position thereof by utilizing the complete orthogonal characteristic between the noise subspace and the search vector of the phase complete synchronization subarray, wherein the peak position determines the direction of the reference signal;

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

2. The array integrated direction finding method of claim 1, wherein: the reference signal refers to a signal with the smallest direction.

3. The array integrated direction finding method according to claim 1, 2 or 3, characterized in that: the modulus vector of the phase incomplete synchronization array receiving signal is as follows:

y (t) = [\begin{matrix} {| x_{1} (t) |}^{2} \\ {| x_{2} (t) |}^{2} \\ . \\ . \\ . \\ {| x_{M} (t) |}^{2} \end{matrix}]

wherein,

[\begin{matrix} x_{1} (t) \\ x_{2} (t) \\ . \\ . \\ . \\ x_{M} (t) \end{matrix}]

for the received signal vector of the partially phased array at time t,

wherein, the [ alpha ], [ beta ]]^TRepresenting the vector transposition, N being the number of snapshots of the array received data, where

May be any non-zero value;

the array noise subspace with incompletely synchronized phases is

Q_n＝[q_L+1 q_L+2 …q_M]Wherein, the matrix Q_nIs an array mode autocorrelation matrix R with incompletely synchronized phases_yAnd (4) forming a matrix by eigenvectors corresponding to the M-L minimum eigenvalues.

4. The array integrated direction finding method according to claim 1 or 2, characterized in that: the array search vector with incompletely synchronized phases is

And

the right side in the equation may be multiplied by any non-negative value.

5. The array integrated direction finding method according to claim 1 or 2, characterized in that: the autocorrelation matrix of the phase synchronization subarray received samples is:

wherein,

z (t) = [\begin{matrix} x_{1} (t) \\ x_{2} (t) \\ . \\ . \\ . \\ x_{m} (t) \end{matrix}]

R_z＝PΩP^Hwherein the matrix omega is a diagonal matrix with eigenvalues as diagonal elements,η₁≥η₂≥…≥η_mthe matrix Ω is a matrix in which the corresponding eigenvector is a column vector;

the noise subspace of the phase synchronization subarray is: p_n＝[p_h+1 p_h+2 … p_m]

6. The array integrated direction finding method of claim 5, wherein: the search vector of the phase synchronization subarray is as follows:

wherein,

i＝1，2，…，D-1，

the right side in the equation may be multiplied by any non-zero constant.

7. The array integrated direction finding method according to claim 1 or 2, characterized in that: direction difference space spectrum search formula of array with incompletely identical phase

The right side of (A) is multiplied by any non-negative number to obtain the peak position of the signal with the same phase, and the peak position determines the direction difference between the corresponding signal and the reference signal to be phi_i(i-1, 2, …, D-1); the right side of the search expression, when multiplied by any negative number, is the corresponding direction obtained by searching the valley position of the spatial spectrum.

8. The array integrated direction finding method according to claim 1 or 2, characterized in that: the reference signal direction space spectrum searching type

The right side of the reference signal is multiplied by any non-negative number to obtain the peak position of the reference signal direction space spectrum, and the peak position determines the direction of the reference signal; the right side of the search expression, when multiplied by any negative number, is the corresponding direction obtained by searching the valley position of the spatial spectrum.

9. The array integrated direction finding method of claim 4, wherein: the phase non-perfectly synchronous array is a uniform linear array or a non-uniform linear array or a circular array or a randomly distributed array.