CN106209701A - MFSK signal code rate-estimation method and device under Alpha Stable distritation noise circumstance - Google Patents

Abstract

The present invention relates to MFSK signal code rate-estimation method and device under a kind of Alpha Stable distritation noise circumstance, the present invention carries out nonlinear transformation first with nonlinear function to the MFSK signal received；Then the signal after nonlinear transformation is carried out frequency interval estimation, chooses wavelet scale according to frequency interval estimated value；And according to the wavelet scale chosen, the signal after nonlinear transformation is carried out twice wavelet transformation, to highlight symbol saltus step information；Data after twice wavelet transformation finally carrying out Fourier conversion, and carries out frequency spectrum search in positive frequencies, the frequency values corresponding to maximum sharpness searched is symbol rate estimation value.Pass through said process, the present invention can obtain MFSK signal code speed fast and accurately, solving the shallow sea underwater sound etc. to there is signal of communication character rate in the environment of impulsive noise and be difficult to the problem accurately estimated, the solution of this problem has important directive significance to follow-up demodulation, acquisition of information etc..

Description

Under Alpha Stable distritation noise circumstance MFSK signal code rate-estimation method and Device

Technical field

The present invention relates to MFSK signal code rate-estimation method and device under a kind of Alpha Stable distritation noise circumstance, Belong to signal of communication modulation parameter estimation technical field.

Background technology

Multi system frequency shift key control (MFSK) signal is widely applied in communication system with its preferable interference free performance, The modulation parameter of MFSK signal includes carrier frequency, frequency interval and character rate, in the fields such as spectrum monitoring, needs this A little parameters carry out high accuracy and estimate, differentiate or signal demodulation in order to realize signal attribute.Ionize at underwater sound communication or shortwave In layer communication, due to nature or anthropic factor, the spike noise being subject in signals transmission disturbs, and this kind of makes an uproar Sound obeys Alpha Stable distritation.Owing to Alpha Stable distritation has spiking characteristics so that be mixed with the signal of this noise There is not second order and above statistic thereof, existing method for parameter estimation based on second order or high-order statistic lost efficacy.Again due to The spike of Alpha Stable distritation noise makes signal transients characteristic be difficult to extract, and causes traditional based on wavelet transformation Symbol rate estimation algorithm lost efficacy.

Summary of the invention

It is an object of the invention to provide MFSK symbol rate estimation method and dress under a kind of Alpha Stable distritation noise circumstance Put, there is the problem that in the environment of impulsive noise, signal of communication character rate is difficult to accurately estimate solving the shallow sea underwater sound etc..

The present invention solves that above-mentioned technical problem provides MFSK signal code under a kind of Alpha Stable distritation noise circumstance Rate-estimation method, the step of this method of estimation is as follows:

1) structure nonlinear function, utilizes the nonlinear function of structure that the MFSK signal received is carried out non-linear change Change；

2) signal after nonlinear transformation is carried out frequency interval rough estimate, choose small echo chi according to frequency interval estimated value Degree；

3) according to step 2) in the wavelet scale chosen the signal after nonlinear transformation is carried out twice wavelet transform process, To highlight the saltus step information of symbol；

4) to step 3) in data after twice wavelet transformation carry out Fourier conversion, and carry out in positive frequencies Frequency spectrum is searched for, and the frequency values corresponding to maximum sharpness searched is symbol rate estimation value.

Described step 1) in structure nonlinear function be:

$f\left(r\right)=\frac{r}{\left|r\right|+\mathrm{\ϵ}}$

Wherein, r is pending data, ε →+0.

Step 2) in the process chosen of wavelet scale comprise the following steps:

A. the signal after nonlinear transformation is carried out power Spectral Estimation；

B. choose the power spectrum initial frequency corresponding more than the power spectrum of setting value and terminate frequency, and according to initial frequency Frequency interval estimated value is calculated with the difference and order of modulation terminating frequency；

The most empirically provide frequency interval and wavelet scale corresponding relation, according to institute in this corresponding relation selecting step B The wavelet scale that the frequency interval estimated value that obtains is corresponding.

Setting value in step B is the 1/2 of power spectrum peak-peak, and the computing formula of frequency interval estimated value is:

$\mathrm{\Δ}f=\frac{|f_{start}-f_{end}|}{M-1}$

Wherein Δ f is frequency interval estimated value, f_startFor initial frequency, f_endFor terminating frequency, M is order of modulation.

Step 3) in the expression formula of first time wavelet transformation be:

$CWT(a,n)=\frac{1}{\sqrt{a}}\underset{k}{\Σ}f\[r\left(k\right)\]{\mathrm{\ψ}}^{*}\left(\frac{k-n}{a}\right)$

Wherein r (k) is for receiving signal, and f [r (k)] is the signal after nonlinear transformation, and ψ (k) is mother wavelet function, ψ^*(k) Representing the conjugation of ψ (k), a is wavelet scale, and n is displacement.

Step 3) in the expression formula of second time wavelet transformation be:

$CWT(a_1,n_1)=\frac{1}{\sqrt{a_1}}\underset{n}{\Σ}\left|CWT\left(n\right)\right|{\mathrm{\ψ}}^{*}\left(\frac{n-n_1}{a_1}\right)$

Wherein | CWT (n) | is the envelope of first time wavelet transformation, and ψ (k) is mother wavelet function, ψ^*K () represents being total to of ψ (k) Yoke, a₁For wavelet scale, n₁For displacement.

Present invention also offers MFSK signal code rate estimates device under a kind of Alpha Stable distritation noise circumstance, should Estimation unit includes that nonlinear transformation module, wavelet scale choose module, wavelet transformation module and frequency spectrum search module,

Described nonlinear transformation module is used for constructing nonlinear function, and utilizes the nonlinear function of structure to receiving MFSK signal carry out nonlinear transformation；

Described wavelet scale chooses module for the signal after nonlinear transformation is carried out frequency interval rough estimate, foundation Frequency interval estimated value chooses wavelet scale；

Described wavelet transformation module is for choosing wavelet scale determined by module to non-linear change according to wavelet scale Signal after changing carries out twice wavelet transform process, to highlight symbol saltus step information；

Described frequency spectrum search module is used for carrying out the data after twice wavelet transformation Fourier conversion, and at positive frequency Carrying out frequency spectrum search in the range of rate, the frequency values corresponding to maximum sharpness searched is symbol rate estimation value.

The nonlinear function of nonlinear transformation module structure is:

$f\left(r\right)=\frac{r}{\left|r\right|+\mathrm{\ϵ}}$

Wherein, r is pending data, ε →+0.

Wavelet scale chooses module, and to choose the process of wavelet scale as follows:

A. the signal after nonlinear transformation is carried out power Spectral Estimation；

B. choose the power spectrum initial frequency corresponding more than the power spectrum of setting value and terminate frequency, and according to initial frequency Frequency interval estimated value is calculated with the difference and order of modulation terminating frequency；

The most empirically provide frequency interval and wavelet scale corresponding relation, according to institute in this corresponding relation selecting step B The wavelet scale that the frequency interval estimated value that obtains is corresponding.

Setting value in step B is the 50% of power spectrum peak-peak, and the computing formula of frequency interval estimated value is:

$\mathrm{\Δ}f=\frac{|f_{start}-f_{end}|}{M-1}$

Wherein Δ f is frequency interval estimated value, f_startFor initial frequency, f_endFor terminating frequency, M is order of modulation.

The invention has the beneficial effects as follows: first the present invention constructs nonlinear function, and utilizes the nonlinear function pair of structure The MFSK signal received carries out nonlinear transformation；Then the signal after nonlinear transformation is carried out frequency interval rough estimate, depend on Wavelet scale is chosen according to frequency interval estimated value；And according to the wavelet scale chosen, the signal after nonlinear transformation is carried out twice Wavelet transformation, to highlight symbol skip signal；Finally the data after twice wavelet transformation are carried out Fourier conversion, and just Carrying out frequency spectrum search in frequency range, the frequency values corresponding to maximum sharpness searched is symbol rate estimation value.Pass through Said process, the present invention solves the shallow sea underwater sound etc. and exists in the environment of impulsive noise in the application such as signal of communication supervision such as What effectively realizes MFSK signal code rate estimates problem, and the solution of this problem has weight to follow-up demodulation, acquisition of information etc. The directive significance wanted.

Accompanying drawing explanation

Fig. 1 is the flow chart of MFSK signal code rate-estimation method under Alpha Stable distritation noise circumstance of the present invention；

Fig. 2 is the flow chart of nonlinear transformation impulse noise mitigation；

Fig. 3 is that wavelet scale obtains flow chart；

Fig. 4 is wavelet transformation and the flow chart of frequency spectrum search.

Detailed description of the invention

Below in conjunction with the accompanying drawings the detailed description of the invention of the present invention is described further.

The embodiment of MFSK signal code rate-estimation method under Alpha Stable distritation noise circumstance of the present invention

The present invention carries out nonlinear transformation, impulse noise mitigation by structure nonlinear function, the docking collection of letters number；The most right Signal after nonlinear transformation carries out frequency interval rough estimate, chooses wavelet scale according to frequency interval estimated value；And according to choosing The wavelet scale taken carries out twice wavelet transformation to the signal after nonlinear transformation, highlights symbol saltus step information；Finally to twice Data after wavelet transformation carry out Fourier conversion, and carry out spectrum peak search in positive frequencies, the maximum point searched Frequency values corresponding to peak is the symbol rate estimation value required by the present invention, and the flow process of the method is as shown in Figure 1.Below with Characteristic index 1 ＜ α≤2 under Alpha Stable distritation noise circumstance, when mixing signal to noise ratio is more than 10dB, MFSK (M order of modulation) believes Number symbol rate estimation process illustrates.

1. structure nonlinear function, the docking collection of letters number carries out nonlinear transformation.

The reception signal model that the present invention relates to is:

R (k)=s (k)+n (k)

Wherein, k represents that sampled signal is counted, and s (k) is modulated fsk signal, and its form is as follows

$s\left(k\right)=e^{j2{\mathrm{\πf}}_{c}k/f_s}{e}^{j\mathrm{\θ}}\underset{i}{\Σ}{e}^{j(2{\mathrm{\πf}}_{i}k/f_s+{\mathrm{\φ}}_i)}g(k/f_s-iT)$

Wherein, r (k) is the MFSK signal received, and s (k) is modulated FSK, and T is symbol duration, R_b=T^-1Table Show character rate；G (k) is rectangular pulse functions；f_cFor carrier wave frequency deviation；θ is initial phase；f_sRepresent sampling rate；f_iWith φ_i Representing frequency and the phase place of fsk signal i-th symbol respectively, n (k) represents Alpha Stable distritation noise, uses mixing signal to noise ratioWherein,And γ_vRepresent variance and the Alpha Stable distritation noise n of signal s (k) respectively The coefficient of dispersion of (k).

Structure nonlinear function, docking is collected mail and number is carried out the flow process of nonlinear transformation as in figure 2 it is shown, what the present invention was constructed Nonlinear function is:

$f\left(r\right)=\frac{r}{\left|r\right|+\mathrm{\ϵ}}$

Wherein, r is pending data, ε →+0.

Signal r (k) received is carried out nonlinear transformation, i.e.

$f\[r\left(k\right)\]=\frac{r\left(k\right)}{\left|r\left(k\right)\right|+\mathrm{\ϵ}}$

In the present embodiment, ε is taken as 0.0001, owing to this nonlinear transformation can be by rational for the spike of impulsive noise It is mapped to limited scope (-1,1), such that it is able to play the effect of impulse noise mitigation.

2. the signal after pair nonlinear transformation carries out frequency interval estimation, chooses suitable wavelet transformation according to frequency interval Yardstick.This step realize flow process as it is shown on figure 3, to implement process as follows:

1). provide the wavelet scale empirical value at different frequency interval.

The present embodiment considers MFSK signal code speed range f to be estimated_d∈ [50Hz, 2000Hz], modulation index Scope h >=0.7, given frequency interval is as shown in table 1 with the relation of wavelet scale, and wherein a is first time continuous wavelet transform Yardstick, a₁Yardstick for second time continuous wavelet transform..

Table 1

2). the data after nonlinear transformation are carried out frequency interval rough estimate.

The present embodiment illustrates in order to as a example by power spectrum rough estimate frequency interval.

First the signal after nonlinear transformation being carried out power Spectral Estimation, its expression formula is as follows:

$G\left(f\right)=\frac{1}{M}\underset{m=0}{\overset{M-1}{\Σ}}\frac{1}{L}\left|\underset{k=1}{\overset{L}{\Σ}}f\right\{r\[m(L-L_p)+k\]\}{e}^{-j2\mathrm{\π}fk}{|}^2$

Wherein, M be segments andRepresent and round downwards, L_pFor data overlap length, L is point The length of segment data, N is total length of data, and f [r (k)] is the signal after nonlinear transformation.

Then power spectrum G (f) is carried out medium filtering and obtains Y (f), find peak-peak Y of Y (f)_max, and retain Y (f) Middle Y (f) ＞ 0.5Y_maxPart, is designated as Y_B(f)；Obtain Y_BF the initial frequency of () and termination frequency, be designated as f respectively_startWith f_end, The difference and order of modulation M that utilize initial frequency and terminate frequency realize frequency interval rough estimate, and expression is as follows:

$\mathrm{\Δ}f=\frac{|f_{start}-f_{end}|}{M-1}$

3). choose suitable wavelet scale according to the frequency interval estimated value Δ f synopsis 1 obtained.

Wavelet scale selected by this step includes continuous wavelet transform yardstick a and second time continuous wavelet transform for the first time Yardstick a₁。

3. according to the wavelet scale chosen in step 2, the signal after nonlinear transformation is carried out twice wavelet transformation.

It is to highlight symbol saltus step information that the present invention carries out the purpose of twice wavelet transformation to the data after nonlinear transformation, its As shown in Figure 4, detailed process is as follows for flow process；

1). according to the wavelet scale a chosen in step 2, the signal after nonlinear transformation is carried out continuous wavelet for the first time Conversion, its expression formula is:

$CWT(a,n)=\frac{1}{\sqrt{a}}\underset{k}{\Σ}f\[r\left(k\right)\]{\mathrm{\ψ}}^{*}\left(\frac{k-n}{a}\right)$

Wherein, r (k) is for receiving signal, and ψ (k) is mother wavelet function, and mother wavelet function ψ (k) in the present embodiment uses Haar small echo, its expression formula is:

ψ^*K () represents the conjugation of ψ (k), a is wavelet scale, and n is displacement.

2). according to wavelet transform dimension a chosen in step 2₁, the envelope of first time continuous wavelet transform is carried out again Continuous wavelet transform, i.e. second time continuous wavelet transform, its expression formula is:

$CWT(a_1,n_1)=\frac{1}{\sqrt{a_1}}\underset{n}{\Σ}\left|CWT\left(n\right)\right|{\mathrm{\ψ}}^{*}\left(\frac{n-n_1}{a_1}\right)$

Wherein | CWT (n) | represents continuous wavelet transform envelope, and ψ (k) is mother wavelet function, and in the present embodiment, second time connects Mother wavelet function ψ (k) of continuous wavelet transformation is also adopted by Haar small echo, and its expression formula is:

ψ^*K () represents the conjugation of ψ (k), a₁For the yardstick of second time continuous wavelet transform, and a₁More than first time in step A The yardstick a, n of continuous wavelet transform₁Displacement for second time continuous wavelet transform.

4. the data after pair twice continuous wavelet transform carry out Fourier conversion or chirp z transform, and in positive frequency In the range of carry out frequency spectrum search, the frequency values corresponding to maximum sharpness searched is symbol rate estimation value.

The present embodiment by Fourier convert as a example by illustrate, the real time process flow of this step as shown in Figure 4, first to step The result of rapid 3 carries out Fourier conversion, and calculation expression is:

$P\left(f\right)=\underset{n_1}{\Σ}\left|CWT(a_1,n_1)\right|e^{-j2{\mathrm{\πn}}_{1}f}$

Wherein, Fourier conversion is counted and is chosen for the length of continuous wavelet transform envelope.

Then in positive frequencies, carry out spectrum peak search, using the frequency values corresponding to amplitude spectrum P (f) maximum sharpness as Symbol rate estimation value, concrete estimation expression formula is:

${\hat{f}}_d=\arg \underset{f>0}{\max }\[\left|P\left(f\right)\right|\]$

By above-mentioned steps, the estimated value obtainedIt is under the Alpha Stable distritation noise circumstance required by the present invention MFSK signal code rate estimates.

The embodiment of MFSK signal code rate estimates device under Alpha Stable distritation noise circumstance of the present invention

The estimation unit of the present invention includes that nonlinear transformation module, wavelet scale choose module, wavelet transformation module and frequency Spectrum search module.Wherein, nonlinear transformation module is used for constructing nonlinear function, and utilizes the nonlinear function of structure to reception To MFSK signal carry out nonlinear transformation；Wavelet scale chooses module for carrying out the signal after nonlinear transformation between frequency Every rough estimate, choose wavelet scale according to frequency interval estimated value；Wavelet transformation module is for choosing module according to wavelet scale Determined by wavelet scale the signal after nonlinear transformation is carried out twice wavelet transform process, to highlight symbol saltus step information； Frequency spectrum search module for carrying out Fourier conversion to the data after twice wavelet transformation, and carries out frequency in positive frequencies Spectrum search, the frequency values corresponding to maximum sharpness searched is symbol rate estimation value.Each module can be by computer The corresponding module of middle design realizes, and the means that implement have been described in detail in the embodiment of method, the most superfluous State.

MFSK signal code speed can be obtained fast and accurately by the said process present invention, solve the shallow sea underwater sound etc. There is MFSK signal code speed in the environment of impulsive noise and be difficult to the problem accurately estimated, solving follow-up solution of this problem Tune, acquisition of information etc. have important directive significance.

Claims (10)

1. MFSK signal code rate-estimation method under 1.Alpha Stable distritation noise circumstance, it is characterised in that this method of estimation Step is as follows:

   1) structure nonlinear function, utilizes the nonlinear function of structure that the MFSK signal received is carried out nonlinear transformation；

   2) signal after nonlinear transformation is carried out frequency interval rough estimate, choose wavelet scale according to frequency interval estimated value；

   3) according to step 2) in the wavelet scale chosen the signal after nonlinear transformation is carried out twice wavelet transform process, with convex The saltus step information of aobvious symbol；

   4) to step 3) in data after twice wavelet transformation carry out Fourier conversion, and in positive frequencies, carry out frequency spectrum Search, the frequency values corresponding to maximum sharpness searched is symbol rate estimation value.
2. MFSK signal code rate-estimation method under Alpha Stable distritation noise circumstance the most according to claim 1, it is special Levy and be, described step 1) in the nonlinear function of structure be:

   $f\left(r\right)=\frac{r}{\left|r\right|+\mathrm{\ϵ}}$

   Wherein, r is pending data, ε →+0.
3. MFSK signal code rate-estimation method under Alpha Stable distritation noise circumstance the most according to claim 1, it is special Levy and be, step 2) in the process chosen of wavelet scale comprise the following steps:

   A. the signal after nonlinear transformation is carried out power Spectral Estimation；

   B. choose the power spectrum initial frequency corresponding more than the power spectrum of setting value and terminate frequency, and according to initial frequency and end Only difference and the order of modulation of frequency calculates frequency interval estimated value；

   The most empirically provide frequency interval and wavelet scale corresponding relation, obtained by this corresponding relation selecting step B Wavelet scale corresponding to frequency interval estimated value.
4. MFSK signal code rate-estimation method under Alpha Stable distritation noise circumstance the most according to claim 3, it is special Levying and be, the setting value in step B is the 1/2 of power spectrum peak-peak, and the computing formula of frequency interval estimated value is:

   $\mathrm{\Δ}f=\frac{|f_{start}-f_{end}|}{M-1}$

   Wherein Δ f is frequency interval estimated value, f_startFor initial frequency, f_endFor terminating frequency, M is order of modulation.
5. MFSK signal code rate-estimation method under Alpha Stable distritation noise circumstance the most according to claim 1, it is special Levy and be, step 3) in the expression formula of first time wavelet transformation be:

   $CWT(a,n)=\frac{1}{\sqrt{a}}\underset{k}{\Σ}f\[r\left(k\right)\]{\mathrm{\ψ}}^{*}\left(\frac{k-n}{a}\right)$

   Wherein r (k) is for receiving signal, and f [r (k)] is the signal after nonlinear transformation, and ψ (k) is mother wavelet function, ψ^*K () represents ψ K the conjugation of (), a is wavelet scale, and n is displacement.
6. MFSK signal code rate-estimation method under Alpha Stable distritation noise circumstance the most according to claim 1, it is special Levy and be, step 3) in the expression formula of second time wavelet transformation be:

   $CWT(a_1,n_1)=\frac{1}{\sqrt{a_1}}\underset{n}{\Σ}\left|CWT\left(n\right)\right|{\mathrm{\ψ}}^{*}\left(\frac{n-n_1}{a_1}\right)$

   Wherein | CWT (n) | is the envelope of first time wavelet transformation, and ψ (k) is mother wavelet function, ψ^*K () represents the conjugation of ψ (k), a₁ For wavelet scale, n₁For displacement.
7. 7. MFSK signal code rate estimates device under an Alpha Stable distritation noise circumstance, it is characterised in that this estimation fills Put and include that nonlinear transformation module, wavelet scale choose module, wavelet transformation module and frequency spectrum search module,

   Described nonlinear transformation module is used for constructing nonlinear function, and utilizes the nonlinear function of structure to receiving MFSK signal carries out nonlinear transformation；

   Described wavelet scale chooses module for the signal after nonlinear transformation carries out frequency interval rough estimate, according to frequency Interval estimated value chooses wavelet scale；

   Described wavelet transformation module is for choosing after determined by module, wavelet scale is to nonlinear transformation according to wavelet scale Signal carry out twice wavelet transform process, to highlight symbol saltus step information；

   Described frequency spectrum search module is used for carrying out the data after twice wavelet transformation Fourier conversion, and at positive frequency model Carrying out frequency spectrum search in enclosing, the frequency values corresponding to maximum sharpness searched is symbol rate estimation value.
8. MFSK signal code rate estimates device under Alpha Stable distritation noise circumstance the most according to claim 7, it is special Levying and be, the nonlinear function of nonlinear transformation module structure is:

   $f\left(r\right)=\frac{r}{\left|r\right|+\mathrm{\ϵ}}$

   Wherein, r is pending data, ε →+0.
9. MFSK signal code rate estimates device under Alpha Stable distritation noise circumstance the most according to claim 7, it is special Levying and be, wavelet scale chooses module, and to choose the process of wavelet scale as follows:

   A. the signal after nonlinear transformation is carried out power Spectral Estimation；

   B. choose the power spectrum initial frequency corresponding more than the power spectrum of setting value and terminate frequency, and according to initial frequency and end Only difference and the order of modulation of frequency calculates frequency interval estimated value；

   The most empirically provide frequency interval and wavelet scale corresponding relation, obtained by this corresponding relation selecting step B Wavelet scale corresponding to frequency interval estimated value.
10. MFSK signal code rate estimates device under Alpha Stable distritation noise circumstance the most according to claim 9, its Being characterised by, the setting value in step B is the 1/2 of power spectrum peak-peak, and the computing formula of frequency interval estimated value is:

    $\mathrm{\Δ}f=\frac{|f_{start}-f_{end}|}{M-1}$

    Wherein Δ f is frequency interval estimated value, f_startFor initial frequency, f_endFor terminating frequency, M is order of modulation.