CN103051368B - Airspace self-adaptive filtering method - Google Patents

Abstract

The invention provides an airspace self-adaptive filtering method, which comprises the following realization steps that 1) received data is subjected to K times of sampling, and signals received by an array antenna are X=[x(1) to x(K)]; 2) received data is subjected to orthogonal transformation to obtain analysis signals shown in the description; 3) the initial value of the weight vector is set into the direction vector v0 of expected signals, M times of iteration is carried out according to the formula shown in the description for updating and calculating the weight vector, and the optimized weight vector w(M) is calculated; 4) the airspace filtering is carried out according to the obtained weight vector w(M), and the filtering output signals are shown in the description. The selection of step length factors is not needed by the weight vector iteration calculation method provided by the invention, the convergence speed is high, and the realization of FPGA (field programmable gate array) or DSP (digital signal processing) is easy.

Description

A kind of Spatially adaptive filtering method

Technical field

The present invention relates to signal transacting field, be specifically related to a kind of Spatially adaptive filtering method.

Technical background

Airspace filter is the pith of Array Signal Processing, is widely used in the systems such as communication, radar, sonar.At present, strive various airspace filter method, LMS(Least Mean Square) adaptive algorithm calculates simple, is widely used in airspace filter and development.When realizing LMS algorithm with FPGA or DSP and asking weight vector, need to calculate according to data covariance matrix characteristic value the iteration that suitable step factor realizes weight vector.But owing to receiving data covariance matrix characteristic value and being not easy to obtain, step factor is also not easy to choose.If the twice of the inverse of the data matrix eigenvalue of maximum that the array antenna received that is greater than step factor arrives, then weight vector is dispersed; If step factor is less than and the twice of the inverse of the data matrix eigenvalue of maximum arrived close to array antenna received, though weight vector convergence is fast, imbalance is large; If the twice of the inverse of the data matrix eigenvalue of maximum that step factor arrives much smaller than array antenna received, though imbalance is little, weight vector convergence is slow.

Summary of the invention

Technical problem to be solved by this invention is: when LMS iterative computation weight vector, and step factor is not easy to obtain.

Content of the present invention is a kind of Spatially adaptive filtering method, and implementation step is:

The first step: the even linear array formed N number of array element, array element distance d is half wavelength λ/2, and with first array element for reference array element, carry out K sampling to received signal, sample frequency is f _s, array antenna received to signal be that N × K ties up matrix X=[x (1) ... x (K)], this matrix kth column vector x (k) is made up of the kth time sampling snap of each array element Received signal strength, namely $x\left(k\right)=\left[\begin{array}{c}{x}_1\left(k\right)\\ ...\\ x_N\left(k\right)\end{array}\right],$ K, N are natural number, k=1 ..., K;

Second step: orthogonal transform is carried out to the real data matrix X received, real signal is become corresponding analytic signal $\hat{X}=\left[\begin{array}{ccc}\hat{x}\left(1\right)& ...& \hat{x}\left(K\right)\end{array}\right];$

3rd step: according to analytic signal with known desired signal direction of arrival θ ₀, calculate weight vector as follows:

(1) calculation expectation sense vector $v_0=\left[\begin{array}{c}1\\ e^{\mathrm{j\π}\sin {\mathrm{\θ}}_0}\\ ...\\ e^{\mathrm{j\π}(N-1)\sin {\mathrm{\θ}}_0}\end{array}\right];$

(2) variable m=1 is got, weight vector initial value w (1)=v ₀;

(3) calculating K dimension row vector $y=\left[\begin{array}{ccc}{y}_1& ...& y_K\end{array}\right]=w^H\left(m\right)\hat{X},$ Symbol H represents conjugate transpose;

(4) hard-limiting computing is carried out to row vector y, obtain K and tie up row vector $r=\left[\begin{array}{ccc}\frac{y_1}{\left|y_1\right|}& ...& \frac{y_K}{\left|y_K\right|}\end{array}\right];$

(5) make m=m+1, upgrade weight vector $w\left(m\right)={\left(\hat{X}{\hat{X}}^H\right)}^{-1}\hat{X}{r}^H;$

(6) repeat above-mentioned (3)-(5) step, until m=M, obtain final weight vector w (M) as airspace filter weight vector, wherein M is the natural number being less than K;

4th step, Spatially adaptive filtering output signal is

The invention has the beneficial effects as follows: new method does not need to choose suitable step factor and upgrades to the iteration realizing weight vector, and the method fast convergence rate, calculates simple, is easy to FPGA or DSP and realizes.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of array received signal under even linear array;

Fig. 2 is Spatially adaptive filtering structured flowchart;

Fig. 3 is the schematic flow sheet of the inventive method.

Specific implementation method

A kind of Spatially adaptive filtering method, does not need to choose suitable step factor and upgrades to the iteration realizing weight vector, and the method fast convergence rate, calculates simple, is easy to FPGA or DSP and realizes.

The inventive method is for the incoherent narrow band signal in far field, and Fig. 1 is the schematic diagram of array received signal under even linear array.Array is made up of N number of identical array element, and array element distance d is half wavelength λ/2, and fast umber of beats of sampling is K.There is a desired signal in space, and direction of arrival (Direction of Arrival, DOA) is θ ₀, have J interference signal, direction of arrival DOA is respectively θ simultaneously _j, j=1,2 ..., J, each DOA is positioned at interval j<N-1.Be that in the even linear array of N array element formation, arranging first array element is reference array element, is positioned at the origin of coordinates, be then s when a jth signal arrives this at systems array _j(t).Array received signal can be expressed as N × K and tie up matrix X=[x (1) ... x (K)], and $x\left(k\right)=\left[\begin{array}{c}{x}_1\left(k\right)\\ ...\\ x_N\left(k\right)\end{array}\right],$ Wherein first array element receives signal can be expressed as n ₁k () is the noise signal that first array element receives, then l array element Received signal strength is τ _lbe the time delay of the signal that signal that l array element receives receives relative to first array element, n _lk () is the noise signal that l array element receives.

Fig. 2 is the structured flowchart of Spatially adaptive filtering, according to nyquist sampling theorem, real signal x (t) of antenna array receiver obtains digital real signal x (k) through sampling, and real signal x (k) becomes analytic signal through orthogonal transform analytic signal with weight vector w (k) weighted sum, obtain array and export y (k).

Fig. 3 is the schematic flow sheet of the inventive method, and concrete grammar is divided into four steps:

The first step, has the even linear array of N number of array element, and array element distance d is half wavelength λ/2, and carry out K sampling to the narrow band signal that array element receives, sample frequency is f _s, array received signal can be expressed as N × K and tie up matrix X=[x (1) ... x (K)], and $x\left(k\right)=\left[\begin{array}{c}{x}_1\left(k\right)\\ ...\\ x_N\left(k\right)\end{array}\right],$ Wherein k is kth time snap, N and K is natural number, k=1 ..., K;

Second step, carries out orthogonal transform to all reception real data matrixes, obtains corresponding analytic signal $\hat{X}=\left[\begin{array}{ccc}\hat{x}& ...& \hat{x}\left(K\right)\end{array}\right],$ And $\hat{x}\left(k\right)=\left[\begin{array}{c}{\hat{x}}_1\\ ...\\ {\hat{x}}_N\left(k\right)\end{array}\right];$

3rd step: according to analytic signal with known desired signal direction of arrival θ ₀, calculate weight vector as follows:

(1) calculation expectation sense vector $v_0=\left[\begin{array}{c}1\\ e^{\mathrm{j\&pi;}\sin {\mathrm{\&theta;}}_0}\\ ...\\ e^{\mathrm{j\&pi;}(N-1)\sin {\mathrm{\&theta;}}_0}\end{array}\right];$

(2) variable m=1 is got, weight vector initial value w (1)=v ₀;

(3) calculating K dimension row vector $y=\left[\begin{array}{ccc}{y}_1& ...& y_K\end{array}\right]=w^H\left(m\right)\hat{X},$ Symbol H represents conjugate transpose;

(4) hard-limiting computing is carried out to row vector y, obtain K and tie up row vector $r=\left[\begin{array}{ccc}\frac{y_1}{\left|y_1\right|}& ...& \frac{y_K}{\left|y_K\right|}\end{array}\right];$

(5) make m=m+1, upgrade weight vector $w\left(m\right)={\left(\hat{X}{\hat{X}}^H\right)}^{-1}\hat{X}{r}^H;$

(6) repeat above-mentioned (3)-(5) step, until m=M, obtain final weight vector w (M) as airspace filter weight vector, wherein M is the natural number being less than K;

4th step, Spatially adaptive filtering output signal is

A kind of Spatially adaptive filtering method of the present invention is compared to the LMS algorithm of extensive use, and need not choose suitable step factor and upgrade to the iteration realizing weight vector, weight vector convergence is fast, is easy to FPGA or DSP and realizes.

Claims (1)

1. a Spatially adaptive filtering method, implementation step is:

The first step: the even linear array formed N number of array element, array element distance d is half wavelength λ/2, and with first array element for reference array element, carry out K sampling to received signal, sample frequency is f _s, array antenna received to signal be that N × K ties up matrix X=[x (1) ... x (K)], this matrix kth column vector x (k) is made up of the kth time sampling snap of each array element Received signal strength, namely $x\left(k\right)=\left[\begin{array}{c}{x}_1\left(k\right)\\ ...\\ x_N\left(k\right)\end{array}\right],$ K, N are natural number, k=1 ..., K;

Second step: orthogonal transform is carried out to the real data matrix X received, real signal is become corresponding analytic signal $\hat{X}=\left[\begin{array}{ccc}\hat{x}\left(1\right)& ...& \hat{x}\left(K\right)\end{array}\right];$

3rd step: according to analytic signal with known desired signal direction of arrival θ ₀, calculate weight vector as follows:

(1) calculation expectation sense vector $v_0=\left[\begin{array}{c}1\\ e^{\mathrm{j\&pi;}\sin {\mathrm{\&theta;}}_0}\\ ...\\ e^{\mathrm{j\&pi;}(N-1)\sin {\mathrm{\&theta;}}_0}\end{array}\right];$

(2) variable m=1 is got, weight vector initial value w (1)=v ₀;

(3) calculating K dimension row vector $y=\left[\begin{array}{ccc}{y}_1& ...& y_K\end{array}\right]=w^H\left(m\right)\hat{X},$ Symbol H represents conjugate transpose;

(4) hard-limiting computing is carried out to row vector y, obtain K and tie up row vector $r=\left[\begin{array}{ccc}\frac{y_1}{\left|y_1\right|}& ...& \frac{y_K}{\left|y_K\right|}\end{array}\right];$

(5) make m=m+1, upgrade weight vector $w\left(m\right)={\left(\hat{X}{\hat{X}}^H\right)}^{-1}\hat{X}{r}^H;$

(6) repeat above-mentioned (3)-(5) step, until m=M, obtain final weight vector w (M) as airspace filter weight vector, wherein M is the natural number being less than K;

4th step, Spatially adaptive filtering output signal is