CN102608565A - Direction-of-arrival estimation method on basis of uniform circular array - Google Patents

Abstract

The invention relates to a direction-of-arrival estimation method on the basis of a uniform circular array, in particular to a direction-of-arrival estimation method for independent signals and coherent signals on the basis of the uniform circular array. The direction-of-arrival estimation method on the basis of the uniform circular array includes: preprocessing estimation parameters of direction-of-arrival; removing noise of pattern space; increasing aperture of the array and performing direction-of-arrival estimation to independent signals; and eliminating independent signals and performing direction-of-arrival estimation to coherent signals. The direction-of-arrival estimation method has higher estimation precision, the aperture of the array can be utilized more sufficiently, the loss of the aperture of the array due to array transformation of a virtual array is recovered, estimation performance can be improved further, calculation is simple and calculation quantity is low.

Description

Direction-of-arrival estimation method based on uniform circular array

Technical Field

The invention relates to a Direction of Arrival (DOA) estimation method, in particular to a Uniform Circular Array (UCA) based Direction of Arrival estimation method for independent signals and coherent signals.

Background

In an actual signal environment, independent signals and coherent signals often coexist, most of DOA estimation algorithms are mainly designed for the independent signals or the coherent signals separately, the coexistence of the independent signals and the coherent signals is not considered, and the characteristics of the independent signals and the coherent signals are not fully utilized to estimate DOA. In the literature: ye Z F, Zhang Y F, LiuC, direction-of-arrival for undercorrelated and coherent signals with powers sensors [ J ]. IEEE Trans. 473-.

The UCA array is distributed in a plane that provides both azimuth and elevation information, and provides 360 ° unambiguous azimuth information. However, since UCA array steering vectors do not have van der mond structures, many ULA array-based direction finding algorithms cannot be used with UCA arrays, especially in the presence of coherent signals. In order to adapt the direction-finding algorithm based on the ULA array to the UCA array or even any array, a great number of methods are proposed by most scholars to virtually transform a non-ULA array into a ULA array. Among the more classical methods are: mode space transformation for UCA arrays, interpolation transformation techniques for arbitrary arrays, and popular separation techniques. Any array can be virtualized into a ULA array by using the array virtual transformation technology, and then the corresponding direction of arrival is obtained by using a DOA estimation algorithm based on the ULA array. However, the virtually transformed array often has array aperture losses of different degrees, so that the estimation performance is reduced; moreover, the noise may be amplified nonlinearly after the virtual transformation, which may further deteriorate the estimation performance, especially when the signal-to-noise ratio is small.

Disclosure of Invention

The invention aims to provide a direction of arrival estimation method based on a uniform circular array, which is simple in estimation process and small in calculation amount.

The purpose of the invention is realized as follows:

the invention discloses a direction of arrival estimation method based on a uniform circular array, which comprises the following steps:

(1) preprocessing the estimation parameters of the direction of arrival:

a. output data matrix X from array: and (3) solving a covariance matrix R of the received data of the uniform circular array when X is AS + Z: r ═ E [ XX ]^H]＝AR_SA^H+σ²I；

Wherein, A represents an M multiplied by N dimensional array flow pattern matrix of a uniform circular array, M represents the number of array elements, N represents the number of signals, and the number of independent signals and coherent signals in N are respectively N_iAnd N_c，

D is the number of coherent source groups, n_kThe number of the signals of the kth group of coherent information sources is S represents an NxL dimensional signal data matrix, L represents a fast beat number, Z represents an MxL dimensional Gaussian white noise data matrix, and X represents^HDenotes the conjugate transpose of X, R_SAs a covariance matrix, σ, of the signal data²Is the power of Gaussian white noise, and I is a unit array with the same dimension as R;

b. using the pattern space transformation matrix T:

transforming the received data R of the uniform circular array to obtain a received data covariance of the uniform linear array in the mode spaceDifference matrix R₁：

Wherein, J₀Is a 2K +1 dimensional diagonal matrix, J₀The element in the diagonal position is J₀(k，k)＝j^(k-1-K)B_(k-1-K)(-β)，B_(k-1-K)(. cndot.) is a first class of Bessel function of order K-1-K, K being 1, …, 2K + 1; f is a discrete Fourier transform matrix, and [ w ]_-K w_-K+1…w_K]，w_q＝[1e^-jp…e^-jp(M-1)]^H，

q＝-K，…，K；A₁(2K +1) xN dimensional flow pattern matrix as virtual uniform linear array, A₁＝[a₁ a₂…a_N]，

i＝1，…，N；

(2) Removing mode spatial noise:

solving a data covariance matrix R without noise components₂：

Noise power σ²Decomposing the characteristic value of R and carrying out M- (N) on R_i+ D) averaging small characteristic values to obtain;

(3) increasing the aperture of the array, and estimating the direction of arrival of the independent signals:

estimating direction of arrival by using multi-signal spectral peak searching method, and searching out N_iThe corresponding estimated angles of the spectrum peaks corresponding to the + D large eigenvalues comprise N_iThe direction of arrival angle corresponding to the independent signals and the direction of arrival angle corresponding to the D groups of coherent signals are selected, and N with the maximum amplitude is selected_iThe direction of arrival angle corresponding to the amplitude of each spectral peak is taken as the direction of arrival of the independent signalEstimating a result;

(4) eliminating independent signals, and carrying out direction-of-arrival estimation on coherent signals:

data covariance matrix R of coherent signal₃：

Wherein J is and R₂Co-dimensional inverse diagonal identity matrix, A_1cRepresenting a flow pattern matrix consisting of steering vectors of coherent signals, R_ScA signal covariance matrix representing the coherent signal,

represents R_ScAnd performing decorrelation by using a forward and backward vector reconstruction algorithm to obtain a coherent signal data matrix without rank loss, and solving the direction of arrival of a coherent signal by using a total least square-rotation invariant subspace algorithm.

The invention has the beneficial effects that:

compared with the existing direction finding algorithm based on the uniform circular array, the direction finding method based on the uniform circular array has the advantages that the direction finding algorithm is not influenced by noise in the DOA estimation process, the estimation precision is higher, and especially the estimation performance is greatly improved when the signal-to-noise ratio is small; by separately estimating the independent signal and the coherent signal, the array aperture is more fully utilized, the loss of the array aperture caused by virtual array transformation is made up, and the estimation performance is further improved; because the mode space transformation is adopted, the algorithm suitable for the uniform linear array is adopted in the DOA estimation, the calculation is simple and convenient, and the operand is small.

Drawings

FIG. 1 is a flow chart of a direction of arrival estimation method based on a uniform circular array according to the present invention;

FIG. 2 is a schematic diagram showing the comparison of the root mean square error estimation of the method of the present invention and the un-denoised model space MUSIC algorithm when the incident signal is an independent signal under the same conditions;

FIG. 3 is a schematic diagram of the comparison of the estimated root mean square error of the TLS-ESPRIT algorithm based on the Toeplitz decorrelation method when the incident signal is a mixture of independent and coherent signals under the same conditions.

Detailed Description

The core idea of the invention is to eliminate the influence of uniform white Gaussian noise on DOA estimation by using the data structure characteristics in the mode space transformation process and improve the estimation performance; and the noise influence of the UCA array after mode space transformation is eliminated by adopting a method of separately estimating independent signals and coherent signals, and the effective array aperture of the UCA array after mode space transformation is increased.

UCA arrays are advantageous because they provide unambiguous azimuth information as well as two-dimensional angular information. However, due to the particularity of the array element positions, many traditional direction-finding algorithms based on the ULA array are not suitable for the UCA array, especially in the case of coherent signals. With the introduction of the mode space transformation method, the UCA array can be virtually converted into the ULA array, but there is an array aperture loss after conversion, and noise power is amplified in the mode space, thereby affecting the accuracy of DOA estimation.

When independent signals and coherent signals exist simultaneously, if the characteristics of the two signals are utilized and the DOA estimation is separately carried out, the array aperture is effectively improved. In the estimation process, a reasonable noise elimination method is designed according to a data structure, so that the DOA estimation precision is greatly improved.

The direction of arrival estimation method of the present invention is described in detail below with reference to the drawings.

Fig. 1 is a flowchart of a direction of arrival estimation method based on UCA array according to the present invention. As shown in fig. 1, the method comprises the steps of:

(1) preprocessing the estimation parameters of the direction of arrival:

firstly, acquiring array output data matrix X by snapshot data received by each array element, wherein X is AS + Z, A represents M multiplied by N dimension array flow type matrix of UCA array, M represents array element number, N represents signal number, and the number of independent signals and coherent signals is N respectively_iAnd

d is the number of coherent source groups, n_kThe number of signals of the kth group of coherent sources); z represents an NxL dimensional signal data matrix, and L represents a fast beat number; n denotes an mxl-dimensional gaussian white noise data matrix. Solving a covariance matrix R of the receiving data of the UCA array by X:

R＝E[XX^H]＝AR_SA^H+σ²I

wherein, X^HDenotes the conjugate transpose of X, R_SAs a covariance matrix, σ, of the signal data²I is the unit matrix of the same dimension as R, which is the power of gaussian white noise.

Secondly, constructing a mode space transformation matrix T as follows:

$T=\frac{1}{M}{J_0}^{-1}{F}^H$

wherein, J₀Is a 2K +1 dimensional diagonal matrix, then J₀The element in the diagonal position is J₀(k，k)＝j^(k-1-K)B_(k-1-K)(-β)，B_(k-1-K)(. cndot.) is a first class of Bessel function of order K-1-K, K being 1, …, 2K + 1; f is a discrete Fourier transform matrix, and [ w ]_-K w_-K+1…w_K]，w_q＝[1e^-jp…e^-jp(M-1)]^H，

q＝-K，…，K。

Carrying out mode space transformation on the R to obtain a data covariance matrix R in a mode space₁：

<math> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>=</mo> <msup> <mi>TRT</mi> <mi>H</mi> </msup> <mo>=</mo> <msub> <mi>A</mi> <mn>1</mn> </msub> <msub> <mi>R</mi> <mi>S</mi> </msub> <msubsup> <mi>A</mi> <mn>1</mn> <mi>H</mi> </msubsup> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msup> <mi>TT</mi> <mi>H</mi> </msup> </mrow> </math> (formula 5)

Wherein A is₁(2K +1) xN dimensional flow pattern matrix as virtual uniform linear array, A₁＝[a₁ a₂…a_N]，

i＝1，…，N。

(2) Removing mode spatial noise:

from the formula 5 in the third step, the original spatial white noise is still white noise in the mode space, but the noise power becomes large and uneven, which seriously affects the estimation performance. From R₁Solving a data covariance matrix R containing no noise component₂：

<math> <mrow> <msub> <mi>R</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>-</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msup> <mi>TT</mi> <mi>H</mi> </msup> <mo>=</mo> <msub> <mi>A</mi> <mn>1</mn> </msub> <msub> <mi>R</mi> <mi>S</mi> </msub> <msubsup> <mi>A</mi> <mn>1</mn> <mi>H</mi> </msubsup> </mrow> </math> (formula 6)

From equation 6, it can be seen that the noise power σ is known²And the sum T can obtain a data covariance matrix R without noise₂. Noise power σ²Can be obtained by decomposing the characteristic value of R and carrying out M- (N) on the R_i+ D) averaging small characteristic values to obtain; and T has been found in step two.

(3) Increasing the aperture of the array, and estimating the direction of arrival of the independent signals:

to R₂Performing singular value decomposition to obtain M- (N)_i+ D) noise subspace U corresponding to small eigenvalues_N. And (3) performing DOA estimation by adopting an MUSIC spectral peak search method:

<math> <mrow> <msub> <mi>P</mi> <mi>MUSIC</mi> </msub> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msup> <mi>a</mi> <mi>H</mi> </msup> <mrow> <mo>(</mo> <mi>&theta;</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>&theta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>.</mo> </mrow> </math>

can search out N_iThe corresponding estimated angles of the spectrum peaks corresponding to the + D large eigenvalues comprise N_iDOA angles corresponding to the independent signals and DOA angles corresponding to the D groups of coherent signals. Since the steering vector corresponding to a set of coherent signals is not in a standard form, its orthogonality to the noise subspace is not as good as that of the independent signals, and the corresponding spectral peak amplitudes are smaller. The DOA angles corresponding to the Ni spectral peak amplitudes with the largest amplitude may be selected as the estimation result of the direction of arrival of the independent signal.

(4) Eliminating independent signals, and carrying out direction-of-arrival estimation on coherent signals:

in step five, DOA estimation has been performed on the independent signals, and in order to avoid repeated estimation to improve the array utilization, it is necessary to remove information of all the independent signals. Obtaining a data covariance matrix R of the coherent signal according to formula 6 by using Toeplitz characteristics of the covariance matrices of the independent signal and the noise data₃：

${\mathrm{<figure-callout\; id="3"\; label="R"\; filenames="HDA0000146190930000021.png"\; state="\{\{state\}\}">R</figure-callout>}}_3=R_2-{\mathrm{JR}}_2^{T}J=A_{1c}(R_{\mathrm{Sc}}-R_{\mathrm{Sc}}^T)A_{1c}^H$ (formula 7)

Wherein J is and R₂Co-dimensional inverse diagonal identity matrix, A_1cRepresenting a flow pattern matrix consisting of steering vectors of coherent signals, R_ScSignal covariance representing coherent signalsThe matrix is a matrix of a plurality of matrices,

represents R_ScThe transposing of (1). Obviously, R₃Does not contain any information of independent signals and noise.

Performing decorrelation by using a forward and backward vector reconstruction algorithm to R₃Singular value decomposition is carried out to obtain signal subspaces U corresponding to 2D large eigenvalues_S。

To R₄Singular value decomposition is carried out, and the signal subspace U corresponding to the D large eigenvalues is taken_S1＝[u₁，u₂，…，u_D]Constructing a coherent signal data matrix with full column rank:

<math> <mrow> <msub> <mi>R</mi> <mn>5</mn> </msub> <mo>=</mo> <mo>[</mo> <msubsup> <mi>R</mi> <mn>1</mn> <mi>fb</mi> </msubsup> <mo>,</mo> <msubsup> <mi>R</mi> <mn>2</mn> <mi>fb</mi> </msubsup> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msubsup> <mi>R</mi> <mi>D</mi> <mi>fb</mi> </msubsup> <mo>]</mo> </mrow> </math>

wherein,

k＝1，…，D。

is composed of u_kM of (a)₀×L_fkDimensional data matrix, M₀＝M+1-max{L_fk}，

Is composed of

M of (a)₀×L_fkDimensional data matrix, L_fb＝n_k-L_fk。

Solving the direction of arrival of the coherent signal using a total least squares-rotation invariant subspace algorithm (TLS-ESPRIT): r₅₁And R₅₂Respectively correspond to R₅Front M of₀-1 line and back M₀-a matrix of 1 row, R₆＝[R₅₁，R₅₂]. To R₆Performing singular value decomposition, Q being N in right singular matrix_cA feature vector matrix corresponding to the small eigenvalue with dimension 2 NXN, and Q ═ Q₁；Q₂]，Q₁And Q₂Are all NxN matrices, according to TLS-ESPRIT principle

<math> <mrow> <mi>&Psi;</mi> <mo>=</mo> <mo>-</mo> <msub> <mi>Q</mi> <mn>1</mn> </msub> <msubsup> <mi>Q</mi> <mn>2</mn> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </math>

Carrying out characteristic decomposition on psi, and obtaining the direction of arrival of the coherent signal according to the characteristic value

Wherein i is 1, …, N_c，γ_i(Ψ) represents the ith eigenvalue of the matrix Ψ.

The DOA estimation method provided by the invention is not influenced by mode space noise, and the estimation performance of the direction finding algorithm is greatly improved. The independent signal and the coherent signal are estimated separately, so that the array aperture is effectively utilized, and the defect of array aperture loss caused by mode space transformation is overcome. The implementation of the two points effectively solves two defects of the UCA array in DOA estimation, and greatly expands the application field of the UCA array.

Claims (1)

1. A direction of arrival estimation method based on a uniform circular array is characterized by comprising the following steps:

(1) preprocessing the estimation parameters of the direction of arrival:

a. output data matrix X from array: and (3) solving a covariance matrix R of the received data of the uniform circular array when X is AS + Z: r ═ E [ XX ]^H]＝AR_SA^H+σ²I；

Wherein, A represents the M multiplied by N dimension array flow pattern matrix of the uniform circular array, M represents the number of array elements, N represents the number of signals, and N is an independent signal and a coherent signalThe number of each is N_iAnd N_c，

D is the number of coherent source groups, n_kThe number of the signals of the kth group of coherent information sources is S represents an NxL dimensional signal data matrix, L represents a fast beat number, Z represents an MxL dimensional Gaussian white noise data matrix, and X represents^HDenotes the conjugate transpose of X, R_SAs a covariance matrix, σ, of the signal data²Is the power of Gaussian white noise, and I is a unit array with the same dimension as R;

b. using the pattern space transformation matrix T:

transforming the received data R of the uniform circular array to obtain a covariance matrix R of the received data of the uniform linear array in the mode space₁：

Wherein, J₀Is a 2K +1 dimensional diagonal matrix, J₀The element in the diagonal position is J₀(k，k)＝j^(k-1-K)B_(k-1-K)(-β)，B_(k-1-K)(. cndot.) is a first class of Bessel function of order K-1-K, K being 1, …, 2K + 1; f is a discrete Fourier transform matrix, and [ w ]_-K w_-K+1…w_K]，w_q＝[1 e^-jp … e^-jp(M-1)]^H，q＝-K，…，K；A₁(2K +1) xN dimensional flow pattern matrix as virtual uniform linear array, A₁＝[a₁ a₂ … a_N]，i＝1，…，N；

(2) Removing mode spatial noise:

method for obtaining data association without noise componentVariance matrix R₂：

Noise power σ²Decomposing the characteristic value of R and carrying out M- (N) on R_i+ D) averaging small characteristic values to obtain;

(3) increasing the aperture of the array, and estimating the direction of arrival of the independent signals:

estimating direction of arrival by using multi-signal spectral peak searching method, and searching out N_iThe corresponding estimated angles of the spectrum peaks corresponding to the + D large eigenvalues comprise N_iThe direction of arrival angle corresponding to the independent signals and the direction of arrival angle corresponding to the D groups of coherent signals are selected, and N with the maximum amplitude is selected_iThe direction of arrival angle corresponding to the amplitude of each spectral peak is used as the estimation result of the direction of arrival of the independent signal;

(4) eliminating independent signals, and carrying out direction-of-arrival estimation on coherent signals:

data covariance matrix R of coherent signal₃：

Wherein J is and R₂Co-dimensional inverse diagonal identity matrix, A_1cRepresenting a flow pattern matrix consisting of steering vectors of coherent signals, R_ScA signal covariance matrix representing the coherent signal,

represents R_ScAnd performing decorrelation by using a forward and backward vector reconstruction algorithm to obtain a coherent signal data matrix without rank loss, and solving the direction of arrival of a coherent signal by using a total least square-rotation invariant subspace algorithm.

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