阅读说明：本技术 一种脉冲噪声环境下的窄带多径信号超分辨率时延估计的方法 (Method for estimating time delay of super-resolution narrow-band multi-path signal in impulse noise environment ) 是由 邱天爽 刘浩 李景春 李蓉 唱亮 于 2020-12-18 设计创作，主要内容包括：本发明公开一种脉冲噪声环境下的窄带多径信号超分辨率时延估计的方法,属于信号处理技术领域。其特征是利用指数高斯核函数抑制脉冲噪声,以得到较高的时延估计正确率；利用傅里叶变换和傅里叶反变换将多径信号模型进行转换,得到适用于MUSIC算法的伪信号模型,从而实现超分辨率时延估计。实验证明,本发明能够在噪声具有较强脉冲性的情况下得到较高的时延估计正确率。(The invention discloses a method for estimating time delay of super-resolution narrow-band multipath signals in an impulse noise environment, and belongs to the technical field of signal processing. The method is characterized in that an exponential Gaussian kernel function is used for inhibiting pulse noise so as to obtain higher time delay estimation accuracy; and transforming the multipath signal model by utilizing Fourier transform and inverse Fourier transform to obtain a pseudo signal model suitable for the MUSIC algorithm, thereby realizing super-resolution time delay estimation. Experiments prove that the method can obtain higher time delay estimation accuracy under the condition that noise has stronger impulse.)

1. A method for estimating time delay of super-resolution narrow-band multi-path signals in an impulse noise environment is characterized by comprising the following steps:

firstly, establishing a signal model for super-resolution time delay estimation of multipath signals

The ideal wireless signal propagation model assumes that signals received by Q antennas in space are a combination of source signal delay, attenuated signals and additive noise; signal r received by the q-th antenna_qExpressed as:

r_q＝λ_qs(n-t-f_q(τ))+w_q(n),q＝0,1,2…,Q-1 (1)

in the formula, λ_qIs the attenuation coefficient due to propagation, s (n) is the source signal, t is the absolute time delay of the source signal to some reference receiver, f_q(τ) — k τ is the relative delay between the linearly aligned reference receiver and the other receivers, w_q(n) impulse noise that is uncorrelated with both the source signal and noise at other receivers;

in an actual environment, due to a multipath phenomenon, signals received by each receiver are superposed by delay signals of different paths; in this case, the signal received by the q-th antenna is represented as:

where d is the number of multipath signals, λ_qiIs the attenuation coefficient, τ, of the ith path signal to the qth receiver_qiRelative time delay of an ith path signal arriving at a qth receiver relative to a reference receiver;

for a single antenna signal model, the signal model is simplified as follows:

where r (N) is the received signal, N is the number of beats, N_rFor the length of the received signal, λ_iIs the attenuation coefficient, τ, caused by the propagation of the ith path signal_iThe relative time delay of the ith path signal received by the antenna relative to the reference signal, w (n) is impulse noise which is not related to noise at the source signal and other receivers;

second, the exponential kernel function-based correlation R (τ) of R (n) and s (n) is calculated:

in the formula, E (-) is the average value^*For the operation of conjugate calculation, k is a variable introduced during Fourier transform, tau is a time shift variable introduced during correlation function calculation, j is an imaginary unit, pi is a circumferential rate,β (k) is the Fourier transform of β (n),σ is the kernel length of the kernel function, K_A＝N_r+N_s-1，N_sThe Fourier transform of m (n) and s (n) is the length of the source signal, M (k), S (k) and s (n), wherein zeta is a variable introduced in the convolution,w (k) is the Fourier transform of w (n);

thirdly, a pseudo signal model is derived by using correlation based on an exponential kernel function:

from equation (4), a pseudo signal model can be extracted, which is expressed as:

comparing equation (4) with equation (5) yields the power spectrum of y (k) as the square of the envelope of R (τ):

|R(τ)|²＝|DFT[y(k)]|² (6)

fourthly, estimating time delay by using MUSIC algorithm

4.1) calculating the covariance matrix of the pseudo-signal model

4.2) pairsCarrying out eigenvalue decomposition;

4.3) respectively opening the signal characteristic value and the noise characteristic value into a signal subspace and a noise subspace;

4.4) searching a spectrum peak to obtain a time delay estimation value.

Technical Field

The invention belongs to the technical field of signal processing, and relates to a method for estimating time delay of super-resolution narrow-band multipath signals in an impulse noise environment.

Background

Time delay estimation is an important component of radio signal positioning and parameter estimation in modern signal processing, and the key to the research is to accurately estimate the time delay between a received signal and a reference signal. The resolution problem of the traditional time delay estimation method is mainly embodied in time delay estimation of a narrow-band signal, when the time delay of the narrow-band signal is estimated by a cross-correlation algorithm, the correlation peaks of multi-path time delay are fused with each other due to the fact that the envelope of the correlation peaks is very wide, and the multi-path time delay cannot be resolved. In order to further realize high-resolution time delay estimation, various algorithms are proposed in sequence, for example, a high-resolution time delay estimation technology based on the sliding discrete fourier transform is obviously superior to a standard correlator. In addition, the time delay estimation under the multipath environment can be converted into a frequency domain, and the time delay estimation is equivalent to a sine frequency estimation problem in the frequency domain, so that the super-resolution multipath time delay estimation is realized by using a multiple signal classification (MUSIC) method. The above algorithms are based on second or higher order statistics, and although these methods may exhibit good performance in the presence of gaussian noise, their performance may be significantly degraded in the presence of impulse noise. Aiming at the time delay estimation problem of a narrow-band signal under impulse noise, a narrow-band radio frequency signal time delay estimation method based on a correlation entropy Hilbert difference value is provided, and the method has the characteristics of small influence of the relative bandwidth of the signal, strong capacity of inhibiting impulse noise and the like. However, the method still uses the correlation of the signal to estimate the parameters, and does not fundamentally solve the aliasing problem which easily occurs in the frequency domain of the narrow-band signal. Aiming at the limitations of the algorithms, the invention utilizes the exponential kernel function to inhibit the pulse noise and applies the MUSIC time delay to the narrow-band multi-path time delay estimation so as to realize the super-resolution time delay estimation of the multi-path signals under the pulse noise.

Disclosure of Invention

The invention provides a super-resolution time delay estimation method for a narrow-band multi-path signal in an impulse noise environment, aiming at solving the problem that the time delay estimation accuracy rate rapidly decreases along with the reduction of a characteristic index and a generalized signal-to-noise ratio in a narrow-band multi-path signal model in the impulse noise existing in the existing method.

The technical scheme adopted by the invention is as follows:

a narrow-band multi-path signal super-resolution time delay estimation method under an impulse noise environment converts a narrow-band multi-path signal model into a signal model of a MUSIC algorithm through Fourier transform and inverse transform, so that the time delay of the multi-path signal is accurately estimated by utilizing the super-resolution parameter estimation characteristic of the MUSIC algorithm. The method comprises the following steps:

1.1) establishing a signal model of super-resolution time delay estimation of multipath signals and obtaining a signal model in single antenna;

1.2) restraining impulse noise by using an exponential kernel function, and providing a correlation expression based on the exponential kernel function;

1.3) converting the expression provided by 1.2) by utilizing Fourier transform and inverse transform to obtain a pseudo signal model in the form of an MUSIC algorithm;

1.4) calculating the covariance matrix of the pseudo-signal model

1.5) pairsCarrying out eigenvalue decomposition;

1.6) respectively opening the signal characteristic value and the noise characteristic value into a signal subspace and a noise subspace;

1.7) searching a spectrum peak to obtain a time delay estimation value.

Meanwhile, in order to verify the advantages of the invention, the PFLOM-MUSIC algorithm and the MUSIC-Type are compared and analyzed in a simulation experiment.

The invention has the beneficial effects that: when impulse noise exists, the super-resolution time delay estimation method can carry out super-resolution time delay estimation on the narrow-band multi-path signal; the method can effectively inhibit impulse noise and can obtain higher time delay estimation accuracy rate in the environment with lower characteristic index and generalized signal-to-noise ratio.

Drawings

FIG. 1 is a comparison of the present invention (GCCE) with PFLOM and MUSIC-Type algorithms at different generalized signal-to-noise ratios.

FIG. 2 is a comparison of the present invention (GCCE) with PFLOM and MUSIC-Type algorithms at different feature indices.

Fig. 3 is an overall flow chart of the algorithm of the present invention.

Detailed Description

The following further describes a specific implementation mode of the invention by combining the drawings and the technical scheme, and the steps are as follows:

firstly, establishing a signal model for super-resolution time delay estimation of multipath signals

The ideal wireless signal propagation model assumes that the signals received by the Q antennas in space are a combination of the source signal delay, the attenuated signal, and the additive noise. Signal r received by the q-th antenna_qMathematically, it can be expressed as:

r_q＝λ_qs(n-t-f_q(τ))+w_q(n),q＝0,1,2…,Q-1 (1)

in the formula, λ_qIs the attenuation coefficient due to propagation, s (n) is the source signal, t is the absolute time delay of the source signal to some reference receiver, f_q(τ) — k τ is the relative delay between the linearly aligned reference receiver and the other receivers, w_q(n) is impulse noise that is uncorrelated with both the source signal and noise at other receivers.

In practical environments, due to the multipath phenomenon, the signal received by each receiver is a superposition of different path delay signals. In this case, the signal received by the q-th antenna can be mathematically expressed as:

where d is the number of multipath signals, λ_qiIs the attenuation coefficient, τ, of the ith path signal to the qth receiver_qiFor the i-th path signal arriving at the q-th receiver relative to the reference receiverAnd (4) time delay.

For a single antenna signal model, the signal model can be further simplified as:

where r (N) is the received signal, N is the number of beats, N_rFor the length of the received signal, λ_iIs the attenuation coefficient, τ, caused by the propagation of the ith path signal_iW (n) is the relative time delay of the i-th path signal received by the antenna with respect to the reference signal, and is impulse noise that is uncorrelated with noise at both the source signal and other receivers.

Second, the exponential kernel function-based correlation R (τ) of R (n) and s (n) is calculated:

in the formula, E (-) is the average value^*For the operation of conjugate calculation, k is a variable introduced during Fourier transform, tau is a time shift variable introduced during correlation function calculation, j is an imaginary unit, pi is a circumferential rate,β (k) is the Fourier transform of β (n),σ is the kernel length of the kernel function, K_A＝N_r+N_s-1，N_sIs the source signal length.

For the convenience of derivation, take d as 2:

wherein M (k), S (k) are m (n), s (n) are Fourier transforms, and ζ is a variable introduced in the convolution,therefore, the method can obtain:

wherein W (k) is the Fourier transform of w (n).

Thirdly, a pseudo signal model is derived by using correlation based on an exponential kernel function:

from equation (7), a pseudo signal model can be extracted, which is expressed as:

comparing equation (7) with equation (8) yields the power spectrum of y (k) as the square of the envelope of R (τ):

|R(τ)|²＝|DFT[y(k)]|² (8)

fourthly, estimating time delay by using MUSIC algorithm

4.1) calculating the covariance matrix of the pseudo-signal model

4.2) pairsCarrying out eigenvalue decomposition;

4.3) respectively opening the signal characteristic value and the noise characteristic value into a signal subspace and a noise subspace;

4.4) searching a spectrum peak to obtain a time delay estimation value.

In fig. 1, the two-path signal has a delay value of 45 and is mixed with impulse noise having a characteristic index of 1.5. Although each algorithm is improved to a certain extent along with the increase of the generalized signal-to-noise ratio GSNR, the algorithm performance of the GCCE is always superior to that of the other two algorithms.

In fig. 2, the two-path signal has a delay value of 45 and is mixed with impulse noise having a generalized signal-to-noise ratio of 6 dB. With the increase of the eigenvalue index, each algorithm is improved to a certain extent. However, the algorithm performance of the GCCE has higher time delay estimation accuracy even when the characteristic index is 0.6, and is obviously superior to the other two algorithms.