CN114035151A - Direction of arrival estimation method, direction of arrival estimation device and system - Google Patents

Abstract

The invention discloses a direction of arrival estimation method, a direction of arrival estimation device and a system. The method comprises: using an antenna to form a uniform linear array, establishing a received signal model according to an array signal input signal, and determining a received signal matrix; Perform low-rank matrix approximation on the received signal matrix to obtain a low-noise and low-dimensional matrix; update the variable step size of the least mean square algorithm LMS through the statistical parameters of the low-noise and low-dimensional matrix, update and iteratively calculate the weight vector coefficients; according to the obtained weight vector The coefficients calculate the antenna array pattern and spatial spectrum, and estimate the direction of arrival of the signal. The present invention obtains a low-noise and low-dimensional matrix by using a low-rank matrix approximation method to obtain a low-noise and low-dimensional matrix, and utilizes the instantaneous prediction error of the low-noise and low-dimensional matrix and the variable step size of the noise reduction signal power update algorithm. , under unfavorable conditions such as low signal-to-noise ratio, small number of antenna array elements, and small amount of signal sampling data, accurate DOA estimation can still be guaranteed.

Description

Direction of arrival estimation method, direction of arrival estimation device and system

technical field

The present invention relates to the technical field of wireless communication and signal processing, and in particular, to a direction of arrival estimation method, a direction of arrival estimation device and a system.

Background technique

Direction of arrival (DOA) estimation is to use antenna arrays distributed in different physical locations in space to receive signals from multiple signal sources in different directions, and use signal processing methods to calculate the direction of signal sources. Wireless communication and other fields have a wide range of applications.

In order to obtain good estimation performance in harsh environments, traditional DOA estimation techniques mainly employ the Multiple Signal Classification (MUSIC) method and algorithms of related MUSIC variants, which usually use subspace decomposition based on signal statistical properties, and therefore require computational Signal space covariance (SCM) and corresponding eigenvalue decomposition (EVD), resulting in high computational complexity. On the other hand, the DOA estimation method based on a fixed-step minimum mean square (FSS-LMS) filter based on subspace decomposition can iteratively update the weight vector coefficients of the array antenna elements without calculating the SCM and its EVD, and adaptively The zeros in the signal direction are formed, and the direction of arrival is estimated from the spatial spectrum peak formed by the reciprocal of the antenna array pattern. Currently disclosed DOA estimation methods, such as VSS-LMS, VSS-BC-LMS, and NA-MMUSIC, etc., have significant performance degradation in harsh environments, such as low signal-to-noise ratio (SNR), small number of antenna array elements, signal sampling The amount of data is small, and the signal sources are relatively close. In addition, these estimation methods need to adjust multiple parameters to effectively control algorithm convergence to obtain accurate estimation, which is difficult to achieve in practical scenarios.

Therefore, a direction of arrival estimation method is needed to solve the above-mentioned problems of high computational complexity and significant performance degradation in harsh environments.

SUMMARY OF THE INVENTION

According to a first aspect of the present invention, a method for estimating a direction of arrival is provided, comprising:

The antenna is used to form a uniform linear array, the received signal model is established according to the input signal of the array signal, and the received signal matrix X is determined;

A low-rank matrix approximation is performed on the received signal matrix X by a low-rank matrix estimation algorithm, and a low-noise and low-dimensional matrix is obtained.

的统计参数更新最小均方算法LMS的可变步长μ(k)，更新迭代计算权向量系数w(k)；through low-noise low-dimensional matrices

The statistical parameters of update the variable step size μ(k) of the least mean square algorithm LMS, and update the iterative calculation weight vector coefficient w(k);

Calculate the antenna array pattern J(θ) and spatial spectrum S(θ) according to the obtained weight vector coefficient w(k), and estimate the direction of arrival of the signal.

In some embodiments, the uniform linear array is formed by using an antenna, a received signal model is established according to the array signal input signal, and the received signal matrix X is determined, including:

Taking the signal received by the first antenna as the reference signal and the signals received by the other antennas as auxiliary signals, the expression for the reference signal of the received signal at any sampling time k is:

x ₀ (k)=b ₀ (k)+b ₁ (k)+...+b _M-1 (k)+v ₀ (k); (1)

Among them, b _i (k) represents the mth signal source at time k; v ₀ (k) represents the noise signal in the signal received by the first antenna at time k;

The expression for the auxiliary signal of the received signal at any sampling time k is:

表示在第n根天线接收信号上对应第m个信号源的转向因子；v_i(k)表示时刻k第n根天线接收信号中的噪声信号；in,

represents the steering factor corresponding to the mth signal source on the received signal of the nth antenna; v _i (k) represents the noise signal in the received signal of the nth antenna at time k;

The expression for the total received signal vector for any received signal at time k is:

Where, x(k)=[x ₀ (k), x ₁ (k),...,x _N-1 (k)] ^H ∈ C ^N×1 represents the actual signal received by each antenna at time k of the array;

表示阵列在第m个信号源b_m(k)的导向向量；

represents the steering vector of the array at the mth signal source b _m (k);

v(k)=[v ₀ (k), v ₁ (k),...v _N-1 (k)]∈C ^N×1 represents the noise signal received by each antenna at the time of array k;

The received signal matrix X corresponding to K samples is:

包括：In some embodiments, the low-rank matrix approximation is performed on the received signal matrix X through a low-rank matrix estimation algorithm to obtain a low-noise and low-dimensional matrix

include:

The variables G and H are introduced to construct the following optimization problem:

G∈C^N×l,H∈C^l×K；in,

G∈C ^N×l , H∈C ^l×K ;

Solve the optimization problem, fix the value of H _i , iteratively update the value of G _i+1 , and update H _i+1 to get:

Among them, H represents the conjugate transpose, + represents the matrix pseudo-inverse operation;

When the low-rank matrix estimation algorithm reaches the termination condition, it exits the iteration early, namely:

Among them, τ is a constant number, and the value range of τ can be 10 ^-4 to 10 ^-6 .

的统计参数更新最小均方算法LMS的可变步长μ(k)，更新迭代计算权向量系数w(k)，包括：In some embodiments, the low-noise low-dimensional matrix

The statistical parameters of update the variable step size μ(k) of the least mean square algorithm LMS, update the iterative calculation of the weight vector coefficient w(k), including:

表示第k列低噪低维矩阵

去掉首元素x₀(k)后降噪信号；in,

Represents the kth column of a low-noise low-dimensional matrix

Denoise the signal after removing the first element x ₀ (k);

Update the expression for iterative calculation of the weight vector coefficients w(k):

的统计参数包括瞬时预测误差

和降噪信号功率

low-noise low-dimensional matrix

Statistical parameters include instantaneous prediction error

and noise reduction signal power

Update the expression for variable step size μ(k):

λ是一个(0,1)的常数，瞬时预测误差的累加δ_e(k)＝δ_e(k-1)+|e²(k)|，降噪信号功率

in,

λ is a constant of (0,1), the accumulation of instantaneous prediction error δ _e (k)=δ _e (k-1)+|e ² (k)|, the noise reduction signal power

In some embodiments, the iteration is stopped when the weight vector coefficient w(k) is updated to the optimal solution; or, the maximum number of iterations K is preset, and when the iteration number k>K of the weight vector coefficient w(k), Stop iterating.

In some embodiments, calculating the antenna array pattern J(θ) and the spatial spectrum S(θ) according to the obtained weight vector coefficients w(k), and estimating the direction of arrival of the signal, including:

表示包含参考信号和辅助信号的权向量系数；a(θ)∈C^{N ×Ω}表示阵列导向向量，Ω＝[-90:0.1:90]是角度网格参数。in,

represents the weight vector coefficients including the reference signal and auxiliary signal; a(θ)∈C ^{N ×Ω} represents the array steering vector, and Ω=[-90:0.1:90] is the angle grid parameter.

According to a second aspect of the present invention, there is provided a direction of arrival estimation device, comprising:

a matrix determination unit, configured to establish a received signal model according to the array signal input signal, and to determine the received signal matrix X;

The preprocessing unit is used to perform low-rank matrix approximation on the received signal matrix X through a low-rank matrix estimation algorithm to obtain a low-noise and low-dimensional matrix

的统计参数更新最小均方算法LMS的可变步长μ(k)，更新迭代计算权向量系数w(k)；update unit for passing low-noise low-dimensional matrices

The statistical parameters of update the variable step size μ(k) of the least mean square algorithm LMS, and update the iterative calculation weight vector coefficient w(k);

The calculation unit is used for calculating the antenna array pattern J(θ) and the spatial spectrum S(θ) according to the obtained weight vector coefficient w(k), and estimating the direction of arrival of the signal.

According to a third aspect of the present invention, there is provided a direction of arrival estimation system, including an antenna array, which uses the direction of arrival method for estimating a direction of any one of the above.

According to a fourth aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium stores a computer program, and the computer program uses the DOA estimation according to any one of the above when executed. method.

The beneficial effects of the present invention are as follows: the method of the present invention establishes a received signal matrix from the received input signal according to the proposed model, obtains a low-noise and low-dimensional matrix by applying the low-rank matrix approximation method to the received signal matrix, and then uses the low-noise and low-dimensional matrix The instantaneous prediction error and the variable step size of the noise reduction signal power update algorithm, due to the noise reduction preprocessing, are still under unfavorable conditions such as low signal-to-noise ratio, small number of antenna array elements, and small amount of signal sampling data. Accurate DOA estimation can be guaranteed. Secondly, the method of the present invention does not need to use the covariance matrix and its eigenvalue decomposition (EVD) in the traditional method, which reduces the computational complexity.

Description of drawings

1 is a flowchart of a method for estimating a direction of arrival according to Embodiment 1 of the present invention;

Fig. 2 is the structural block diagram of the low-rank matrix approximation based on the received signal matrix according to the present invention;

Fig. 3 is the structural block diagram of the least mean square filter adaptive algorithm based on low-noise and low-dimensional matrix of the present invention;

Fig. 4 is the structural block diagram of the present invention;

Fig. 5 is the experimental comparison diagram of the present invention and the existing direction of arrival estimation method with respect to the spatial spectrum;

6 is an experimental comparison diagram of the present invention and an existing DOA estimation method with respect to root mean square error (RMSE);

7 is an experimental comparison diagram of the present invention and an existing DOA estimation method with respect to the probability of successful resolution;

8 is an experimental comparison diagram of the present invention and an existing DOA estimation method with respect to computational complexity;

9 is a flowchart of a method for estimating a direction of arrival according to Embodiment 2 of the present invention;

FIG. 10 is a structural block diagram of a direction of arrival estimation apparatus according to Embodiment 3 of the present invention.

Detailed ways

For better understanding and implementation, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention. not all examples. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

The terms "comprising" and "having" and any variations thereof in the embodiments of the present invention are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device comprising a series of steps or modules is not necessarily limited to the explicit Those steps or modules listed may instead include other steps or modules not expressly listed or inherent to the process, method, product or apparatus.

Example 1

As shown in FIG. 1 to FIG. 4 , an embodiment of the present invention discloses a method for estimating a direction of arrival. The method can be applied to systems such as radar, sonar, satellite, and wireless communication. However, for this application system, the embodiment of the present invention Without limitation, a method for estimating a direction of arrival in this embodiment may include the following operations:

S10: A uniform linear array is formed by using an antenna, a received signal model is established according to an input signal of the array signal, and a received signal matrix X is determined.

Specifically, N omnidirectional station antennas can be used to form a uniform linear array, and the direction of arrival can be estimated for M narrowband signal sources in space;

Taking the signal received by the first antenna as the reference signal, the first antenna is the reference antenna unit, and the signals received by the other antennas are used as auxiliary signals, the expression of the reference signal for the received signal at any sampling time k is:

x ₀ (k)=b ₀ (k)+b ₁ (k)+...+b _M-1 (k)+v ₀ (k); (1)

Among them, x ₀ (k) represents the reference signal, b _i (k) represents the mth signal source at time k, and b ₀ (k)+b ₁ (k)+...+b _M-1 (k) represents the reference antenna unit The noise-free signal received by the (first antenna), v ₀ (k) represents the noise signal in the received signal of the reference antenna unit (first antenna) at time k.

The expression for the auxiliary signal of the received signal at any sampling time k is:

表示在第n根天线接收信号上对应第m个信号源的转向因子，

表示无噪声辅助阵列信号向量，v_i(k)表示辅助阵列的噪声信号，即时刻k第n根天线接收信号中的噪声信号。where x _i (k) represents the auxiliary signal,

represents the steering factor corresponding to the mth signal source on the received signal of the nth antenna,

represents the signal vector of the non-noise auxiliary array, and v _i (k) represents the noise signal of the auxiliary array, that is, the noise signal in the signal received by the nth antenna at time k.

The expression for the total received signal vector for any received signal at time k is:

Where, x(k)=[x ₀ (k), x ₁ (k),...,x _N-1 (k)] ^H ∈ C ^N×1 represents the actual signal received by each antenna at time k of the array;

表示阵列k时刻各天线接收到的无噪声信号；

represents the noise-free signal received by each antenna at time k of the array;

表示阵列在第m个信号源b_m(k)的导向向量；b_m(k)表示第m个源信号，(m＝0,1…M-1)；

Represents the steering vector of the array at the mth signal source b _m (k); b _m (k) represents the mth source signal, (m=0,1...M-1);

v(k)=[v ₀ (k), v ₁ (k),...v _N-1 (k)]∈C ^N×1 represents the noise signal received by each antenna at the time of array k;

The received signal matrix X corresponding to K samples is:

X=U+V

X is a received signal matrix, which includes a noise-free signal and a noise signal, U represents a noise-free signal matrix, and V represents a noise-signal matrix.

Representing the received signal by the above array, it is natural to superimpose the original signal and the noise signal in the same received signal matrix for processing, but in fact, it is impossible to completely separate the original signal and the noise signal. Therefore, if the received signal is preprocessed to obtain a matrix that approximates the original signal, the relevant information such as the direction of arrival of the original signal can be easily analyzed according to the approximate matrix. This process is called low-rank matrix approximation. . In addition, the received signal is expanded according to the sampling time, and the estimation algorithm of DOA can be improved by analyzing the instantaneous error corresponding to different sampling time, which avoids the complexity of the traditional method for calculating the covariance matrix.

S20: Perform low-rank matrix approximation on the received signal matrix X through a low-rank matrix estimation algorithm to obtain a low-noise and low-dimensional matrix

低秩矩阵逼近的方法有很多种，本实施例给出一种低秩矩阵逼近算法(LRMA)的实施方法：This step is the process of preprocessing the received signal: as shown in Figure 2, after down-converting, demodulating, and analog-to-digital conversion of the received signal, a low-rank matrix approximation method is used to obtain a Low-Noise Low-Dimensional Matrix for Matrix X Approximation

There are many methods for low-rank matrix approximation. This embodiment provides an implementation method of a low-rank matrix approximation algorithm (LRMA):

The variables G and H are introduced to construct the following optimization problem:

G∈C^N×l,H∈C^l×K；in,

G∈C ^N×l , H∈C ^l×K ;

Solve the optimization problem, fix the value of H _i , iteratively update the value of G _i+1 , and update H _i+1 to get:

Among them, H represents the conjugate transpose, + represents the matrix pseudo-inverse operation;

When the low-rank matrix estimation algorithm reaches the termination condition, it exits the iteration early, namely:

Among them, τ is a small positive constant, and the value of τ ranges from 10 ^-4 to 10 ^-6 .

Using the above-mentioned low-rank matrix estimation algorithm (LRMA) to denoise the observed values of the entire antenna array to obtain a low-noise and low-dimensional matrix

的统计参数更新最小均方算法LMS的可变步长μ(k)，更新迭代计算权向量系数w(k)。如图3所示，本步骤具体包括：S30: Pass low-noise low-dimensional matrices

The statistical parameters of update the variable step size μ(k) of the least mean square algorithm LMS, and update iteratively calculate the weight vector coefficient w(k). As shown in Figure 3, this step specifically includes:

改进可变步长的最小均方算法(VSS-LMS)。S31: Utilize low-noise low-dimensional matrices

Improved Variable Step Size Least Mean Squares (VSS-LMS).

表示第k列低噪低维矩阵

去掉首元素x₀(k)后降噪信号，权向量系数w(k)要更新迭代以接近最优解w₀。图3和图4中的

即也可以表示为e(k)＝x₀k-y(k)。where e(k) represents the signal estimation error,

Represents the kth column of a low-noise low-dimensional matrix

After removing the first element x ₀ (k) to de-noise the signal, the weight vector coefficient w(k) needs to be updated iteratively to approach the optimal solution w ₀ . Figures 3 and 4 in

That is, it can also be expressed as e(k)=x ₀ ky(k).

S32: The weight vector coefficient w(k) is updated and iteratively calculated by the following expression.

The weight vector coefficient w(k) will reduce the error from the optimal solution w ₀ after each iteration of the algorithm compared with the previous one, so the iteration is updated to the optimal solution w ₀ or a value near w ₀ within the acceptable error range, and then the iteration is stopped. .

S33: Update the value of the variable step size μ(k).

的统计参数瞬时预测误差

和降噪信号功率

计算出可变步长μ(k)的值；According to the low-noise low-dimensional matrix

The statistical parameter instantaneous prediction error of

and noise reduction signal power

Calculate the value of the variable step size μ(k);

Update the expression for variable step size μ(k):

λ是一个(0,1)的常数，瞬时预测误差的累加δ_e(k)＝δ_e(k-1)+|e²(k)|，降噪信号功率

in,

λ is a constant of (0,1), the accumulation of instantaneous prediction error δ _e (k)=δ _e (k-1)+|e ² (k)|, the noise reduction signal power

瞬态的统计参数更新LMS算法的可变步长，这是在原始LMS算法性能上非常大的改进，保证步长在最合适的范围内能使算法以最快的速度达到收敛从而得到权向量系数w(k)的最优解。According to the low-noise low-dimensional matrix

The transient statistical parameters update the variable step size of the LMS algorithm, which is a very large improvement in the performance of the original LMS algorithm, ensuring that the step size is within the most suitable range, so that the algorithm can converge at the fastest speed to obtain the weight vector The optimal solution for the coefficients w(k).

S40: Calculate the antenna array pattern J(θ) and the spatial spectrum S(θ) according to the obtained weight vector coefficient w(k), and estimate the direction of arrival of the signal.

表示包含参考信号和辅助信号的权向量系数；a(θ)∈C^N×Ω表示阵列导向向量，Ω＝[-90:0.1:90]是角度网格参数。in,

represents the weight vector coefficients including the reference signal and the auxiliary signal; a(θ)∈C ^N×Ω represents the array steering vector, and Ω=[-90:0.1:90] is the angle grid parameter.

Simulation experiment and analysis of this embodiment

The performance of the method in terms of spatial spectrum, root mean square error (RMSE), resolution probability and computational complexity is analyzed by numerical simulation, and compared with MUSIC, FSS-LMS, VSS-LMS, VSS-BC-LMS and NA-MMUSIC methods were compared. Consider a uniform linear array (ULA) consisting of 12 omnidirectional antenna elements with half-wavelength element spacing.

(1) Regarding the experimental analysis of the spatial spectrum, the spatial spectrum is calculated based on 12 antennas and 300 iterations using signals in three different directions of 0°, 5° and 30°. The simulation results are shown in Figure 5. Figures 5(a), 5(b), 5(c), and 5(d) represent the results at different signal-to-noise ratios of -10dB, -5dB, 0dB and 5dB. The simulation results show that because the received signal is preprocessed by noise reduction, the method of this embodiment can estimate the signal source direction more accurately, while the MUSIC, FSS-LMS, VSS-LMS, VSS-BC-LMS and NA-MMUSIC methods are at low At the signal-to-noise ratio, they cannot resolve the signal direction of closely spaced sources at 0° and 5°.

(2) The experimental analysis of the root mean square error (RMSE), calculated the root mean square error (RMSE) of MUSIC, FSS-LMS, VSS-LMS, VSS-BC-LMS and NA-MMUSIC and the method proposed in this example ), and the results are shown in Figure 6. Figures 6(a), 6(b), 6(c), and 6(d) show the analysis results corresponding to different signal-to-noise ratios, different numbers of antennas, different iteration times, and different separation source angles between two signal sources, respectively . It can be seen from Fig. 6 that in the case of low signal-to-noise ratio, the RMSE of the method proposed in this embodiment is the smallest, and the RMSE of the method proposed in this embodiment is the smallest at different numbers of antennas, different iteration times and different spacing source angles between the two signal sources. In this case, the RMSE of the method proposed in this embodiment is the smallest compared to other algorithms, which shows that the method in this embodiment has good robustness under various conditions and has a large performance advantage.

(3) Regarding the experimental analysis of the probability of successfully distinguishing the signal source, the probability of MUSIC, FSS-LMS, VSS-LMS, VSS-BC-LMS and NA-MMUSIC and the method proposed in this embodiment are calculated, and the results are shown in Figure 7 . Figures 7(a), 7(b), and 7(c) respectively represent the probability of successfully distinguishing the signal source directions as 0° and 5° for different signal-to-noise ratios, different antenna numbers, and different iteration times; it can be seen from the figures that this implementation The proposed method has the highest probability of successfully distinguishing the signal source among all algorithms under harsh conditions such as low signal-to-noise ratio, small number of antenna array elements, and small number of iterations (small amount of signal sampling data). Under the conditions of a large number of antenna array elements and a large number of iterations, the probability of successfully distinguishing the signal source is comparable to other algorithms. Figure 7(d) shows the analysis results corresponding to different separation source angles between the two signal sources (the separation angle is 3°-6°). It can be seen from the figure that when the separation angle between the two signal sources is less than 5° , the probability of successfully distinguishing the signal source by the method proposed in this embodiment is the highest, and when it is greater than 5°, the probability of successfully distinguishing the signal source is equivalent to that of the MUSIC algorithm.

(4) Regarding the experimental analysis of computational complexity, the computational complexity of MUSIC, FSS-LMS, VSS-LMS, VSS-BC-LMS, and NA-MMUSIC and the proposed method are calculated, and the results are shown in Figure 8. Figures 8(a) and 8(b) respectively show the analysis results corresponding to different numbers of antennas and different iteration times. Since the method proposed in this embodiment does not need to use the covariance matrix and the eigenvalue decomposition (EVD) method of the traditional method, it has lower computational complexity.

The direction of arrival estimation method of the present invention is based on the received signal modeling, combined with the low-rank matrix approximation and the variable-step minimum mean square adaptive filter method, and gradually analyzes and improves to obtain a new DOA estimation algorithm, which realizes the following three Great technical effect. First, under severe conditions such as low signal-to-noise ratio, small number of antenna array elements, and small amount of signal sampling data, high-precision estimation can still be guaranteed. Second, the proposed method has low computational complexity since it does not require the covariance matrix and its eigenvalue decomposition (EVD) method on the traditional method. Moreover, in terms of parameter adjustment, there are few adjustment parameters and only one w(k), which has better operability than other DOA estimation algorithms.

Embodiment 2

As shown in FIG. 9 , an embodiment of the present invention discloses a method for estimating a direction of arrival. The method can be applied to systems such as radar, sonar, satellite, and wireless communication. However, the application system is not limited in the embodiment of the present invention. , a method for estimating a direction of arrival in this embodiment may include the following operations:

The implementation of steps S10 to S40 is basically the same as that of the first embodiment, and only the differences are described. In this embodiment, the weight vector coefficient w(k) is updated and iteratively calculated by the following expression.

In this step, the conditions for stopping the iteration of the weight vector coefficient w(k) are different. Initially, k=1, the maximum number of iterations K is preset, and then the iteration weight vector coefficient w(k) starts to be updated. When k>K, Stop the iteration, and output the value of the weight vector coefficient w(k) after the iteration.

Embodiment 3

As shown in FIG. 10, an embodiment of the present invention discloses a direction of arrival estimation device 5, the device 5 receives a signal source signal through an antenna array, and the device 5 includes: a matrix determination unit 51, a preprocessing unit 52, an update unit 53 and a calculation unit 54.

The matrix determining unit 51 is configured to establish a received signal model according to the array signal input signal, and determine the received signal matrix X. Specifically, the matrix determination unit 51 performs the following steps to establish a received signal model and determine the received signal matrix X:

Taking the signal received by the first antenna as the reference signal, the first antenna is the reference antenna unit, and the signals received by the other antennas are used as auxiliary signals, the expression of the reference signal for the received signal at any sampling time k is:

x ₀ (k)=b ₀ (k)+b ₁ (k)+...+b _M-1 (k)+v ₀ (k); (1)

Among them, x ₀ (k) represents the reference signal, b _i (k) represents the mth signal source at time k, and b ₀ (k)+b ₁ (k)+...+b _M-1 (k) represents the reference antenna unit The noise-free signal received by the (first antenna), v ₀ (k) represents the noise signal in the received signal of the reference antenna unit (first antenna) at time k.

The expression for the auxiliary signal of the received signal at any sampling time k is:

表示在第n根天线接收信号上对应第m个信号源的转向因子，

表示无噪声辅助阵列信号向量，v_i(k)表示辅助阵列的噪声信号，即时刻k第n根天线接收信号中的噪声信号。where x _i (k) represents the auxiliary signal,

represents the steering factor corresponding to the mth signal source on the received signal of the nth antenna,

represents the signal vector of the non-noise auxiliary array, and v _i (k) represents the noise signal of the auxiliary array, that is, the noise signal in the signal received by the nth antenna at time k.

The expression for the total received signal vector for any received signal at time k is:

Where, x(k)=[x ₀ (k), x ₁ (k),...,x _N-1 (k)] ^H ∈ C ^N×1 represents the actual signal received by each antenna at time k of the array;

表示阵列k时刻各天线接收到的无噪声信号；

represents the noise-free signal received by each antenna at time k of the array;

表示阵列在第m个信号源b_m(k)的导向向量；b_m(k)表示第m个源信号，(m＝0,1…M-1)；

Represents the steering vector of the array at the mth signal source b _m (k); b _m (k) represents the mth source signal, (m=0,1...M-1);

v(k)=[v ₀ (k), v ₁ (k),...v _N-1 (k)]∈C ^N×1 represents the noise signal received by each antenna at the time of array k;

The received signal matrix X corresponding to K samples is:

X=U+V

X is a received signal matrix, which includes a noise-free signal and a noise signal, U represents a noise-free signal matrix, and V represents a noise-signal matrix.

Representing the received signal by the above array, it is natural to superimpose the original signal and the noise signal in the same received signal matrix for processing, but in fact, it is impossible to completely separate the original signal and the noise signal. Therefore, if the received signal is preprocessed to obtain a matrix that approximates the original signal, the relevant information such as the direction of arrival of the original signal can be easily analyzed according to the approximate matrix. This process is called low-rank matrix approximation. . In addition, the received signal is expanded according to the sampling time, and the estimation algorithm of DOA can be improved by analyzing the instantaneous error corresponding to different sampling time, which avoids the complexity of the traditional method for calculating the covariance matrix.

具体的，预处理单元52执行如下的LRMA算法对接收信号矩阵X进行低秩矩阵逼近，得到低噪低维矩阵

The preprocessing unit 52 is configured to perform low-rank matrix approximation on the received signal matrix X through a low-rank matrix estimation algorithm to obtain a low-noise and low-dimensional matrix

Specifically, the preprocessing unit 52 performs the following LRMA algorithm to perform low-rank matrix approximation on the received signal matrix X to obtain a low-noise and low-dimensional matrix

The variables G and H are introduced to construct the following optimization problem:

G∈C^N×l,H∈C^l×K；in,

G∈C ^N×l , H∈C ^l×K ;

Solve the optimization problem, fix the value of H _i , iteratively update the value of G _i+1 , and update H _i+1 to get:

Among them, H represents the conjugate transpose, + represents the matrix pseudo-inverse operation;

When the low-rank matrix estimation algorithm reaches the termination condition, it exits the iteration early, namely:

Among them, τ is a small positive constant, and the value of τ ranges from 10 ^-4 to 10 ^-6 .

的统计参数更新最小均方算法LMS的可变步长μ(k)，更新迭代计算权向量系数w(k)。具体的，更新单元53利用低噪低维矩阵

改进可变步长的最小均方算法(VSS-LMS)；The update unit 53 is used to pass the low-noise and low-dimensional matrix

The statistical parameters of update the variable step size μ(k) of the least mean square algorithm LMS, and update iteratively calculate the weight vector coefficient w(k). Specifically, the updating unit 53 uses a low-noise and low-dimensional matrix

Improved variable step size least mean square algorithm (VSS-LMS);

表示第k列低噪低维矩阵

去掉首元素x₀(k)后降噪信号，权向量系数w(k)要更新迭代以接近最优解w₀。图3和图4中的

即也可以表示为e(k)＝x₀k-y(k)。where e(k) represents the signal estimation error,

Represents the kth column of a low-noise low-dimensional matrix

After removing the first element x ₀ (k) to de-noise the signal, the weight vector coefficient w(k) needs to be updated iteratively to approach the optimal solution w ₀ . Figures 3 and 4 in

That is, it can also be expressed as e(k)=x ₀ ky(k).

The updating unit 53 updates the iterative calculation weight vector coefficient w(k) by the following expression.

The weight vector coefficient w(k) is updated and iterated to the optimal solution w ₀ and then the iteration is stopped.

The updating unit 53 updates the value of the variable step size μ(k).

的统计参数瞬时预测误差

和降噪信号功率

计算出可变步长μ(k)的值；According to the low-noise low-dimensional matrix

The statistical parameter instantaneous prediction error of

and noise reduction signal power

Calculate the value of the variable step size μ(k);

The update unit 53 updates the expression of the variable step size μ(k):

λ是一个(0,1)的常数，瞬时预测误差的累加δ_e(k)＝δ_e(k-1)+|e²(k)|，降噪信号功率

in,

λ is a constant of (0,1), the accumulation of instantaneous prediction error δ _e (k)=δ _e (k-1)+|e ² (k)|, the noise reduction signal power

瞬态的统计参数更新LMS算法的可变步长，这是在原始LMS算法性能上非常大的改进，保证步长在最合适的范围内能使算法以最快的速度达到收敛从而得到权向量系数w(k)的最优解。According to the low-noise low-dimensional matrix

The transient statistical parameters update the variable step size of the LMS algorithm, which is a very large improvement in the performance of the original LMS algorithm, ensuring that the step size is within the most suitable range, so that the algorithm can converge at the fastest speed to obtain the weight vector The optimal solution for the coefficients w(k).

The calculation unit 54 is configured to calculate the antenna array pattern J(θ) and the spatial spectrum S(θ) according to the obtained weight vector coefficients w(k), and estimate the direction of arrival of the signal. Specifically, the calculation unit 54 executes the following expression to realize the direction of arrival estimation of the signal.

表示包含参考信号和辅助信号的权向量系数；a(θ)∈C^N×Ω表示阵列导向向量，Ω＝[-90:0.1:90]是角度网格参数。in,

represents the weight vector coefficients including the reference signal and the auxiliary signal; a(θ)∈C ^N×Ω represents the array steering vector, and Ω=[-90:0.1:90] is the angle grid parameter.

Embodiment 4

The embodiments of the present invention provide a direction of arrival estimation system, including an antenna array, the antenna array is constructed as a uniform linear array, and may also include a processor, a memory, and a computer program stored in the memory and executable on the processor, processing When the computer executes the computer program, the steps of the method for estimating the direction of arrival in the first embodiment or the second embodiment are realized.

Embodiment 5

An embodiment of the present invention discloses a computer-readable storage medium, which stores a computer program for electronic data exchange, wherein the computer program enables a computer to execute the direction of arrival estimation method described in Embodiment 1 or Embodiment 2.

Embodiment 6

An embodiment of the present invention discloses a computer program product. The computer program product includes a non-transitory computer-readable storage medium storing a computer program, and the computer program is operable to cause a computer to execute the first or second embodiment. Describes the DOA estimation algorithm.

The embodiments described above are only illustrative, wherein the modules described as separate components may or may not be physically separated, and the components shown as modules may or may not be physical modules, that is, they may be located in a local, or it can be distributed over multiple network modules. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution in this embodiment. Those of ordinary skill in the art can understand and implement it without creative effort.

From the specific description of the above embodiments, those skilled in the art can clearly understand that each implementation manner can be implemented by means of software plus a necessary general hardware platform, and certainly can also be implemented by means of hardware. Based on such understanding, the above-mentioned technical solutions can be embodied in the form of software products in essence or that make contributions to the prior art. The computer software products can be stored in a computer-readable storage medium, and the storage medium includes a read-only memory. (Read-Only Memory, ROM), Random Access Memory (Random Access Memory, RAM), Programmable Read-only Memory (Programmable Read-only Memory, PROM), Erasable Programmable Read Only Memory (Erasable Programmable Read Only Memory, EPROM) , One-time Programmable Read-Only Memory (One-time Programmable Read-Only Memory, OTPROM), Electronically-Erasable Programmable Read-Only Memory (EEPROM), CompactDisc Read-Only Memory , CD-ROM) or other optical disk storage, magnetic disk storage, magnetic tape storage, or any other computer-readable medium that can be used to carry or store data.

Finally, it should be noted that: the method for estimating a direction of arrival disclosed in the embodiment of the present invention is only a preferred embodiment of the present invention, and is only used to illustrate the technical solution of the present invention, but not to limit it; although refer to The foregoing embodiments have described the present invention in detail, and those of ordinary skill in the art should understand that; it is still possible to modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements to some of the technical features; and these modifications Or replacement, does not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (9)

1. A method of direction of arrival estimation, comprising:

forming a uniform linear array by adopting an antenna, establishing a received signal model according to an array signal input signal, and determining a received signal matrix X;

performing low-rank matrix approximation on the received signal matrix X through a low-rank matrix estimation algorithm to obtain a low-noise and low-dimensional matrix

By means of low-noise low-dimensional matrices

Updating the variable step length mu (k) of the least mean square algorithm LMS by the statistical parameters, and updating the iterative computation weight vector coefficient w (k);

and calculating an antenna array directional diagram J (theta) and a space spectrum S (theta) according to the obtained weight vector coefficient w (k), and estimating the arrival direction of the signal.

2. The method of claim 1, wherein the forming a uniform linear array using the antennas, modeling the received signals according to the array signal input signals, and determining the received signal matrix X comprises:

taking the first antenna receiving signal as a reference signal, and the other antenna receiving signals as auxiliary signals, the expression of the reference signal for the receiving signal at any sampling time k is as follows:

x₀(k)＝b₀(k)+b₁(k)+…+b_M-1(k)+v₀(k)； (1)

wherein, b_i(k) Representing the mth signal source at time k; v. of₀(k) Representing a noise signal in a signal received by the first antenna at the time k;

the expression for the auxiliary signal of the received signal at any sampling instant k is:

wherein,

representing a steering factor corresponding to the mth signal source on the nth antenna received signal; v. of_i(k) Representing a noise signal in the nth antenna receiving signal at the time k;

the expression for the total received signal vector for any received signal at time k is:

wherein x (k) ═ x₀(k),x₁(k),…,x_N-1(k)]^H∈C^N×1Representing the actual signals received by each antenna at the moment of array k;

representing the array at the m-th signal source b_m(k) A guide vector of (a);

v(k)＝[v₀(k),v₁(k),…v_N-1(k)]∈C^N×1representing the noise signals received by each antenna at the moment of array k;

the received signal matrix X corresponding to K samples is:

3. the method of claim 2, wherein the low rank matrix approximation is performed on the received signal matrix X by a low rank matrix estimation algorithm to obtain a low noise and low dimensional matrix

The method comprises the following steps:

introducing variables G and H, and constructing the following optimization problem:

wherein,

solving the optimization problem, fixing H_iValue of (a), iteratively updating G_i+1Is thus updated to H_i+1The following can be obtained:

wherein H represents conjugate transpose, + represents matrix pseudo-inverse operation;

when the low-rank matrix estimation algorithm reaches a termination condition, exiting iteration in advance, namely:

wherein tau is a normal number, and the value range of tau is 10^-4To 10^-6。

4. A direction of arrival estimation method according to claim 3 wherein said low noise low dimensional matrix is passed

The updating of the variable step length mu (k) of the least mean square algorithm LMS and the updating of the iterative computation weight vector coefficient w (k) comprise:

wherein,

low noise and low dimensional matrix for representing k column

Removing the first element x₀(k) A post-noise reduction signal;

updating the expression of the iteratively calculated weight vector coefficients w (k):

low-noise low-dimensional matrix

Including instantaneous prediction error

And noise reduction signal power

Updating the expression for the variable step size μ (k):

wherein,

λ is a constant of (0,1), and the instantaneous prediction error is accumulated by δ_e(k)＝δ_e(k-1)+|e²(k) Power of noise-reduced signal

5. The method according to claim 4, wherein the iteration is stopped when the weight vector coefficient w (k) is updated and iterated to the optimal solution; or,

presetting maximum iteration number K, and stopping iteration when the iteration number K of the weight vector coefficient w (K) is larger than K.

6. The method according to claim 5, wherein said calculating an antenna array pattern J (θ) and a spatial spectrum S (θ) according to the obtained weight vector coefficients w (k) to estimate the direction of arrival of the signal comprises:

wherein,

representing weight vector coefficients comprising a reference signal and an auxiliary signal; a (theta) is belonged to C^N×ΩDenotes the array steering vector, Ω [ -90:0.1:90]Is an angle grid parameter.

7. A direction-of-arrival estimation apparatus of the direction-of-arrival estimation method according to any one of claims 1 to 6, comprising:

the matrix determining unit is used for establishing a received signal model according to the array signal input signal and determining a received signal matrix X;

a preprocessing unit for performing low-rank matrix approximation on the received signal matrix X by a low-rank matrix estimation algorithm to obtain a low-noise and low-dimensional matrix

An update unit for passing through the low-noise low-dimensional matrix

Updating the variable step length mu (k) of the least mean square algorithm LMS by the statistical parameters, and updating the iterative computation weight vector coefficient w (k);

and the calculating unit is used for calculating an antenna array directional diagram J (theta) and a space spectrum S (theta) according to the obtained weight vector coefficient w (k) and estimating the arrival direction of the signal.

8. A direction-of-arrival estimation system comprising an antenna array, further comprising the direction-of-arrival estimation apparatus of claim 7.

9. A computer-readable storage medium storing a computer program, wherein the computer program is executed using the direction of arrival estimation method according to any one of claims 1-6.

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