CN104038181A - Self-adapting filter construction method based on NLMS algorithm - Google Patents

Abstract

The invention discloses a self-adapting filter construction method based on an NLMS algorithm. The self-adapting filter construction method based on the NLMS algorithm includes a first step of determining parameters, a second step of initializing and a third step of determining data. By means of the self-adapting filter construction method based on the NLMS algorithm, the filter performance of the self-adapting filter is reinforced through the step length change, and especially, the anti-noise property of a filter system is improved under the low-signal to noise ratio environment. The self-adapting filter construction method based on the NLMS algorithm has good practical value and broad application prospect in the self-adapting filter technology field.

Description

A kind of construction method of the sef-adapting filter based on NLMS algorithm

Technical field

The present invention relates to a kind of construction method of the sef-adapting filter based on NLMS algorithm, belong to auto-adaptive filtering technique field, it utilizes the variation of step-length in sef-adapting filter, strengthens its filtering performance.The present invention especially, under low signal-to-noise ratio environment, improves the anti-noise ability of filtering system.

Background technology

Information is a relatively abstract concept, and it is included in message, is the object transmitting in communication system.Message is concrete but is not physics, such as language, word, symbol etc.Signal is the carrier of information, means the physical quantity of message, and for example amplitude, frequency and phase place all can represent message.When receiving signal, intersymbol interference and noise (internal thermal noise and external disturbance) all make signal sustain damage.The key problem that signal is processed is expression, conversion and the computing of signal, and extracts feature and information wherein.Filter is commonly used to from interested containing noisy extracting data people, to approach definite quality information.Under this meaning, filtering method and various fields such as communication, radar, sonar of theoretical application thereof.

The classification of signal has a lot, but on the whole, according to temporal characteristics, can be divided into continuous time signal and discrete-time signal; According to amplitude Characteristics, can be divided into amplitude continuous signal and amplitude discrete signal.Time, amplitude continuous signal are called analog signal, and the system of processing it is called analogue system; Time, amplitude discrete signal are called digital signal, and the system of processing it is called digital system.Digital filter have high accuracy, high reliability, program-controlled change characteristic or multiplexing, be convenient to the advantages such as integrated.Digital filter is processed in Speech signal processing, picture signal, medical biotechnology signal is processed and other applications are all widely applied.Due to the development of electronic computer technology and large scale integrated circuit, digital filter available computers software is realized, also available large-scale integrated digital hardware real-time implementation.Digital filter is a discrete-time system (by predetermined algorithm, input discrete-time signal being converted to the specific function device of desired output discrete-time signal).During NEURAL DISCHARGE BY DIGITAL FILTER Analog signals, first must limit band, sampling and analog-to-digital conversion to input analog signal.The sampling rate of digital filter input signal should be greater than the twice of processed signal bandwidth, and its frequency response has take the characteristic of cycle repetition that sampling frequency is interval, and with folding frequency 1/2 sampling frequency point be mirror image symmetry.For obtaining analog signal, the output digit signals that digital filter is processed must be through digital-to-analogue conversion, level and smooth.Digital filter have high accuracy, high reliability, program-controlled change characteristic or multiplexing, be convenient to the advantages such as integrated.Digital filter is processed in Speech signal processing, picture signal, medical biotechnology signal is processed and other applications are all widely applied.

The sorting technique of digital filter is a lot.From filtering characteristic, can be divided into high pass filter, low pass filter, band pass filter, band stop filter, all-pass filter etc.; Method for designing, can be divided into Chebyshev and Butterworth; From network configuration or the unit sample respo realized, be divided into finite impulse response filter (FIR filter) and infinite impulse response filter (iir filter); Structure way of realization, can be divided into transversal filter and lattice filter; By the physical quantity of selecting, can be divided into the four class filters such as frequency selection, amplitude selection, selection of time and Information Selection; And on the whole from how processing signals aspect can be divided into classical filter device and Modern Filter.Classical filter device is according to a concept of engineering of Fourier analysis and conversion proposition, according to Fourier analysis and shift design out, only allow the signal component within the scope of certain frequency normally to pass through, and the electronic installation that stops another part frequency content to be passed through.Such as low pass, the filters such as high pass contain interference in input signal, and during the frequency band non-overlapping copies of signal and interference, can obtain pure signal by frequency-selecting filtering interfering.And Modern Filter is to be based upon on the basis of random signal treatment theory, utilize the statistical property of random signal inside signal to be carried out to filtering, detection or valuation etc., such as Weiner filter, Kalman filter, matched filter and sef-adapting filter etc.Weiner filter (Wiener filter) is that proposed by mathematician Wei Na (Rorbert Wiener) a kind of be take the linear filter that least square is optiaml ciriterion.Weiner filter be otherwise known as least square filter or least square filter, it is a kind of primary filter in Modern Filter, it is only applicable under Stationary Random Environments, utilize the auto-correlation function of input signal and the best impulse response that cross-correlation function removes to calculate linear filter, make output waveform as the estimation of input waveform, it is minimum that its mean square error reaches.Kalman filter is under steady and non-stationary environment, to utilize the optimum linear recurrence method based on state space to realize filtering.The state equation that it is known by oneself and measurement equation profit obtains when previous estimated value and a nearest measured value and then carrys out the currency of estimated signal.Matched filter refers under white noise background, when the performance of filter and the characteristic of signal obtain certain when consistent (transmission characteristic of filter and the complex conjugate of input signal spectrum are consistent), make ratio (output signal-to-noise ratio) maximum of signal transient power and the noise average power of filter output.When signal and noise enter filter simultaneously, it makes signal component occur in a flash kurtosis at certain, and noise contribution is suppressed.A kind of matched filter can only carry out filtering to specific input signal.Matched filter has time delay adaptability, does not have frequency displacement adaptability, the occasion that it can not be estimated for waveform.Matched filter is one of the study hotspot in input field at present, and it is mainly used to finding target echo containing in noisy signal.

Above-mentioned several Modern Filter has certain weak point in actual applications, their filter construction and coefficient are just selected in the design phase, and normal in service the remaining unchanged of filter, can not be by the signal handling capacity that contacts to change self with external environment.And sef-adapting filter arises at the historic moment just in this case, its automatic adaptation signal transmits environment and the requirement changing, and need not know structure and the priori of signal, also the accurate structure and parameter of modelled signal treatment system.Sef-adapting filter is widely used in the aspects such as automatic equalization, the echo of the communications field are eliminated, antenna array wave beam forms, parameter identification, noise elimination, spectrum estimation.The basic ideas of adaptive-filtering are, input signal enters system and obtains output signal by filter structure, output signal and Expected Response are subtracted each other and obtain error amount, and adaptive algorithm changes the filter factor of filter structure according to this error amount, thereby reaches the effect of adaptive-filtering.In order to have improved self adaptation, propagate its performance, scholars proposed many adaptive algorithms as change step length least mean square LMS adaptive algorithm, Normalized LMS Algorithm be NLMS algorithm, area block LMS algorithm etc.Although NLMS algorithm has reduced the degree that the gradient noise in LMS algorithm iteration process amplifies, the difference of the size that convergence rate and stable state imbalance are got step factor requires to remain the principal contradiction that affects algorithm performance.Therefore, researcher has also carried out the performance that the suitable step factor of large quantity research How to choose improves algorithm, has proposed multiple variable step NLMS algorithm.

Summary of the invention

By the analysis of existing variable step NLMS algorithm is found, variable step NLMS algorithm needs: step-length is in the primary iteration stage, and step factor remains in larger level, makes filter Fast Convergent; In the filter iteration convergence stage, use step factor to adjust mechanism, make its impact increasing, cause step factor more and more less, thereby make stable state imbalance less, this step factor adjustment mechanism is the core of algorithm.Many algorithms are all the adjustment mechanism of step factor that designs by mean square error, adjust machine-processed step-length regulating effect, and anti-noise ability and computation complexity are the principal elements of evaluation algorithms performance.Fig. 1 is the system construction drawing of this algorithm.

In sum, the present invention is a kind of construction method of the sef-adapting filter based on NLMS algorithm, and the method concrete steps are as follows:

Step 1: determine parameter:

M=tap number (filter length), μ (n)=self adaptation constant (step factor);

Wherein the algorithm of μ (n) is

$\mathrm{\β}\left(n\right)=2-\frac{2\mathrm{\ϵ}}{\mathrm{\ϵ}+{\mathrm{\σ}}^3\left(n\right)}$

$\mathrm{\μ}\left(n\right)=\left\{\begin{array}{cc}\frac{{\mathrm{\μ}}_{\max }}{\mathrm{\δ}+X^{T}X}& (\mathrm{\β}\left(n\right)\≥{\mathrm{\μ}}_{\max })\\ \frac{\mathrm{\β}\left(n\right)}{\mathrm{\δ}+X^{T}X}& ({\mathrm{\μ}}_{\max }>\mathrm{\β}\left(n\right))\end{array}\right.$

In formula, δ is steadiness parameter, and ε adjusts parameter, and X is input signal.σ(n)＝λσ(n-1)+(1-λ)|e(n)e(n-1)|

In iteration initial stage, | e (n) e (n-1) | be a larger value, thereby ε < σ (n) cause close to zero, can be cast out β (n)=2.Step factor is approximately

$\mathrm{\&mu;}\left(n\right)=\frac{2}{X^T\left(n\right)X\left(n\right)}$ Or $\mathrm{\&mu;}\left(n\right)=\frac{{\mathrm{\&mu;}}_{\max }}{X^T\left(n\right)X\left(n\right)}$

Therefore, in iteration initial stage step-length, remain in a higher level.

On the other hand, when evaluated error e (n) is smaller, ε > σ (n), can obtain $\mathrm{\&mu;}\left(n\right)\&ap;\frac{2-2}{\mathrm{\&delta;}+X^{T}X}=0$

Therefore, in converged state step-length, remain in a smaller level.Can find out that will make to improve algorithm reaches good effect, we must find a suitable adjustment parameter ε, make it at iteration starting stage ε < σ (n), and at converged state ε > σ (n), Fig. 2 is core signal flow chart of the present invention.

Step 2: initialization:

If know tap weights vector priori, with it come for select suitable value; Otherwise order $\widehat{\mathrm{\&omega;}}\left(0\right)=0.$

Step 3: specified data:

A) given: x (n)=n time M * 1 tap input vector,

The Expected Response of d (n)=n time step;

B) to calculate:

According to overlapping storage method, carrying out the filter frequency domain output vector that linear convolution obtains M * 1 dimension is:

$\begin{array}{c}{y}^T\left(k\right)=[y\left(\mathrm{kM}\right),y(\mathrm{kM}+1),...,y(\mathrm{kM}+M-1)]\\ =\mathrm{last\; M\; elements\; of\; IFFT}\left[U\left(k\right)\hat{W}\left(k\right)\right]\end{array}$

Error signal vector is:

e(k)＝[e(kM),e(kM+1),…,e(kM+M-1)] ^T＝d(k)-y(k)

Filter tap weight coefficient upgrades:

$\hat{W}(k+1)=\hat{W}\left(k\right)+\mathrm{\&mu;FFT}\left[\begin{array}{c}\hat{F}\left(k\right)\\ 0\end{array}\right]$

Wherein:

$\hat{F}\left(k\right)=\mathrm{first\; M\; elements\; of\; IFFT}\left[U^H\left(k\right)E\left(k\right)\right]$

In formula, μ represents the step factor of area block algorithm.X (n) represents n input signal vector constantly, x (n)=[x (n), x (n-1),, x (n-M+1)], M represents the length of filter, Expected Response vector when d (k) represents k piece, w (k) represents the time domain tap vector of k piece.

The present invention can improve the antijamming capability of filter to noise.Mainly possess following advantage:

(1) step size computation of the present invention has been introduced the auto-correlation item of error, and the convergence rate of filter is accelerated greatly.

(2) step size computation structure of the present invention can make system when stable state, have less steady-state error.

(3) algorithm structure of the present invention is simple, is easy to hardware and realizes.

Accompanying drawing explanation

Fig. 1 is the system construction drawing that the technology of the present invention relates to

Fig. 2 is core signal flow chart of the present invention

Fig. 3 is real-time conceptual scheme of the present invention

Fig. 4 is method invention FB(flow block)

In figure, symbol description is as follows:

In Fig. 1, y is filter output signal, and d is baseband signal, and e is error signal

In Fig. 2, μ is step factor, X (n) is n input signal constantly, and d (n) is n baseband signal constantly, and e (n) is n error signal constantly, w (n) is n filter tap weight coefficient constantly, and w (n+1) is the renewal of filter tap weight coefficient.

In Fig. 3, μ is step factor, after two continuous input block FFT of the matrix that U (k) is N * N by time domain, obtain, u (n) is n input signal constantly, the output signal that y (k) is k piece, d (n) is n baseband signal constantly, e (n) is n error signal constantly, E (k) is signal after e (n) FFT, w (n) is n filter tap weight coefficient constantly, and w (k) is that k blocking filter tap weights coefficient w (k+1) is k blocking filter tap weights coefficient update.U in Fig. 4 (n) is n input signal constantly, the output signal that y (k) is k piece, d (k) is k piece baseband signal, e (k) is that k piece error signal w (n) is n moment filter tap weight coefficient, and w (k) is that k blocking filter tap weights coefficient w (k+1) is k blocking filter tap weights coefficient update.

Embodiment

See Fig. 1-Fig. 4, the construction method of a kind of sef-adapting filter based on NLMS algorithm of the present invention.Utilize FPGA technology to realize area block LMS adaptive filter algorithm, the method concrete steps are as follows:

Step 1: determine parameter:

M=tap number (filter length); μ (n)=self adaptation constant (step factor)

Wherein the algorithm of μ (n) is

$\mathrm{\&beta;}\left(n\right)=2-\frac{2\mathrm{\&epsiv;}}{\mathrm{\&epsiv;}+{\mathrm{\&sigma;}}^3\left(n\right)}$

$\mathrm{\&mu;}\left(n\right)=\left\{\begin{array}{cc}\frac{{\mathrm{\&mu;}}_{\max }}{\mathrm{\&delta;}+X^{T}X}& (\mathrm{\&beta;}\left(n\right)\&GreaterEqual;{\mathrm{\&mu;}}_{\max })\\ \frac{\mathrm{\&beta;}\left(n\right)}{\mathrm{\&delta;}+X^{T}X}& ({\mathrm{\&mu;}}_{\max }>\mathrm{\&beta;}\left(n\right))\end{array}\right.$

In formula, δ is steadiness parameter, and ε adjusts parameter, and X is input signal.σ(n)＝λσ(n-1)+(1-λ)|e(n)e(n-1)|

Step 2: initialization:

If know tap weights vector priori, with it come for select suitable value; Otherwise order $\widehat{\mathrm{\&omega;}}\left(0\right)=0.$

Step 3: specified data:

Given: x (n)=n time M * 1 tap input vector,

The Expected Response of d (n)=n time step;

Calculate: output vector, error vector, filter tap weight coefficient upgrade, specific as follows.

Its algorithm principle is, in the present invention, as shown in Figure 3, this part need to complete the design of area block NLMS sef-adapting filter in core.Principle be by input data sequence x (n) by string-and conversion be divided into long piece of ordering for L, and such input block is delivered to the sef-adapting filter that exponent number is M block by block.After collecting each data block, carry out the renewal of sef-adapting filter tap weight value, the adaptive process of filter is carried out block by block.

The core of NLMS algorithm is the linear convolution of calculating filter tap coefficient and input signal, and the linear correlation of input signal and error signal.Known according to digital signal processing theory: fft algorithm provides strong instrument for fast convolution and fast correlation computing, and can adopt overlap-save method and these two kinds of methods of overlap-add method, and wherein overlap-save method is more common method.Although overlap-save method is not stipulated the length of its lap, when carrying out 1/2 when overlapping, the size of piece equals the number of coefficient, and now operation efficiency is the highest.

Area block NLMS algorithm forms respectively N point data block by input signal and desired signal, then does leaf transformation in N point discrete Fourier, and the every N of weight coefficient sampling point upgrades once, and each more new capital is controlled by N error signal sampling point accumulation result.

Data overlap based on 1/2 is after M point filter tap coefficients, to mend M zero, then carries out the FFT that N is ordered, here N=2M.Make tap coefficient after zero padding after FFT, become carrying out:

$\hat{W}\left(k\right)=\mathrm{FFT}\left[\begin{array}{c}\hat{W}\left(k\right)\\ 0\end{array}\right]$

Wherein, for the vector of N * 1, the tap vector length of frequency domain is the twice of time domain tap vector.Responsively, for input data, carry out obtaining after FFT:

U(k)＝diag{FFT[x(kM-M),…,x(kM-1),x(kM),…,x(kM+M-1)]}

The matrix that the U here (k) is N * N, obtains after two continuous input block FFT by time domain.Utilize overlap-save method to carry out the filter frequency domain output vector that linear convolution obtains M * 1 dimension to be:

$\begin{array}{c}{y}^T\left(k\right)=[y\left(\mathrm{kM}\right),y(\mathrm{kM}+1),...,y(\mathrm{kM}+M-1)]\\ =\mathrm{last\; M\; elements\; of\; IFFT}\left[U\left(k\right)\hat{W}\left(k\right)\right]\end{array}$

According to the character of overlap-save method, in above formula, we get rear M the valid data of contrary FFT.

At tap new portion more, according to the form of time domain, obtain following steps.First, for k data block, the Expected Response vector sum error signal vector of definition M * 1 is as follows respectively:

d(k)＝[d(kM),d(kM+1),…,d(kM+M-1)] ^T

e(k)＝[e(kM),e(kM+1),…,e(kM+M-1)] ^T＝d(k)-y(k)

Due in formula, we have abandoned M data before output signal, therefore before error signal vector is carried out to FFT, need to before it, mend M individual zero, as follows:

$E\left(k\right)=\mathrm{FFT}\left[\begin{array}{c}0\\ e\left(k\right)\end{array}\right]$

The renewal of finally carrying out filter tap coefficients is as follows:

$\hat{W}(k+1)=\hat{W}\left(k\right)+\mathrm{\&mu;FFT}\left[\begin{array}{c}\hat{F}\left(k\right)\\ 0\end{array}\right]$

Wherein:

$\hat{F}\left(k\right)=\mathrm{first\; M\; elements\; of\; IFFT}\left[U^H\left(k\right)E\left(k\right)\right].$

In formula, μ represents the step factor of area block algorithm.X (n) represents n input signal vector constantly, x (n)=[x (n), x (n-1),, x (n-M+1)], M represents the length of filter, Expected Response vector when d (k) represents k piece, w (k) represents the time domain tap vector of k piece.

Claims (1)

1. a construction method for the sef-adapting filter based on NLMS algorithm, is characterized in that: the method concrete steps are as follows:

Step 1: determine parameter:

M=tap number is filter length, and μ (n)=self adaptation constant is step factor,

Wherein the algorithm of μ (n) is

$\mathrm{\&beta;}\left(n\right)=2-\frac{2\mathrm{\&epsiv;}}{\mathrm{\&epsiv;}+{\mathrm{\&sigma;}}^3\left(n\right)}$

$\mathrm{\&mu;}\left(n\right)=\left\{\begin{array}{cc}\frac{{\mathrm{\&mu;}}_{\max }}{\mathrm{\&delta;}+X^{T}X}& (\mathrm{\&beta;}\left(n\right)\&GreaterEqual;{\mathrm{\&mu;}}_{\max })\\ \frac{\mathrm{\&beta;}\left(n\right)}{\mathrm{\&delta;}+X^{T}X}& ({\mathrm{\&mu;}}_{\max }>\mathrm{\&beta;}\left(n\right))\end{array}\right.$

In formula, δ is steadiness parameter, and ε adjusts parameter, and X is input signal; σ (n)=λ σ (n-1)+(1-λ) | e (n) e (n-1) |

In iteration initial stage, | e (n) e (n-1) | be a larger value, thereby ε < σ (n) cause close to zero, cast out, β (n)=2, step factor is approximately

$\mathrm{\&mu;}\left(n\right)=\frac{2}{X^T\left(n\right)X\left(n\right)}$ Or $\mathrm{\&mu;}\left(n\right)=\frac{{\mathrm{\&mu;}}_{\max }}{X^T\left(n\right)X\left(n\right)}$

Therefore, at iteration initial stage step factor, remain in a higher level;

On the other hand, when evaluated error e (n) is smaller, ε > σ (n), $\mathrm{\&beta;}\left(n\right)=2-\frac{2\mathrm{\&epsiv;}}{\mathrm{\&epsiv;}+{\mathrm{\&sigma;}}^3\left(n\right)}\&ap;2-\frac{2\mathrm{\&epsiv;}}{\mathrm{\&epsiv;}},$ Can obtain $\mathrm{\&mu;}\left(n\right)\&ap;\frac{2-2}{\mathrm{\&delta;}+X^{T}X}=0$

Therefore, at converged state step factor, remain in a smaller level; Make to improve algorithm and reach good effect, must find a suitable adjustment parameter ε, make it at iteration starting stage ε < σ (n), and at converged state ε > σ (n);

Step 2: initialization:

If know tap weights vector priori, with it come for select suitable value; Otherwise order $\widehat{\mathrm{\&omega;}}\left(0\right)=0;$

Step 3: specified data:

A) given: x (n)=n time M * 1 tap input vector,

The Expected Response of d (n)=n time step;

B) to calculate:

According to overlapping storage method, carrying out the filter frequency domain output vector that linear convolution obtains M * 1 dimension is:

$\begin{array}{c}{y}^T\left(k\right)=[y\left(\mathrm{kM}\right),y(\mathrm{kM}+1),...,y(\mathrm{kM}+M-1)]\\ =\mathrm{last\; M\; elements\; of\; IFFT}\left[U\left(k\right)\hat{W}\left(k\right)\right]\end{array}$

Error signal vector is:

e(k)＝[e(kM),e(kM+1),…,e(kM+M-1)] ^T＝d(k)-y(k)

Filter tap weight coefficient upgrades:

$\hat{W}(k+1)=\hat{W}\left(k\right)+\mathrm{\&mu;FFT}\left[\begin{array}{c}\hat{F}\left(k\right)\\ 0\end{array}\right]$

Wherein:

$\hat{F}\left(k\right)=\mathrm{first\; M\; elements\; of\; IFFT}\left[U^H\left(k\right)E\left(k\right)\right]$

In formula, μ represents the step factor of area block algorithm, x (n) represents n input signal vector constantly, x (n)=[x (n), x (n-1),, x (n-M+1)], M represents the length of filter, Expected Response vector when d (k) represents k piece, w (k) represents the time domain tap vector of k piece.