CN103441975A - Two-phase coding signal parameter estimation method based on power spectrum - Google Patents

Abstract

The invention discloses a two-phase coding signal parameter estimation method based on the power spectrum. The two-phase coding signal parameter estimation method based on the power spectrum comprises the following steps that firstly, the fitting relation between the sub-pulse widths tau and the 3dB bandwidths B3dB which correspond to a two-phase coding signal when the two-phase coding signal has different code lengths is worked out; secondly, the power spectrum of the two-phase coding signal with the parameter to be estimated is detected, amplitude normalization is conducted on the power spectrum so that P(f) can be obtained, the P(f) is evenly sampled so that M points can be obtained, the P(f) are changed into a sequence P(m) with the length of M, discrete cosine transformation is conducted on the P(m) so that Ypre(P(m)) can be obtained, and threshold processing is conducted on the Ypre(P(m)) so that Y(P(m)) can be obtained; the upper envelope of the Y(P(m)) is worked out, the number n of the peak values of the upper envelope is calculated, and according to the relation between the signal code length N and the number n of the peak values, the signal code length N is worked out; discrete cosine inverse transformation is conducted on the Y(P(m)) so that Pi(m) can be obtained, and the carrier frequency fc, the 3dB bandwidth B3dB and the sub-pulse width tau of the Pi(m) are worked out. The two-phase coding signal parameter estimation method based on the power spectrum overcomes the defects that the influence of noise on a two-phase coding signal parameter estimation result is large and the calculated amount in the low signal-to-noise ratio environment is large in the prior art and achieves estimation of the two-phase coding signal parameter under the conditions that apriori information is not known.

Description

A kind of Coded Signals parameter estimation method based on power spectrum

Technical field

The present invention relates to a kind of Coded Signals parameter estimation method based on the power spectrum discrete cosine transform.

Background technology

Phase-coded signal, its phase modulation function is discrete limited state, belongs to discrete coded pulse compressed signal, because phase code adopts pseudo random sequence, therefore be called again the pseudorandomcode signal.Phase-coded signal is usually used in Doppler and changes less occasion.The pseudorandomcode signal can, by the classification of phase place value number, if phase place is only got two values, be called Coded Signals.

Coded Signals refers to that the signal phase modulating function is two discrete values, and phase code generally adopts pseudo random sequence, and time-domain expression is:

$s\left(t\right)=v\left(t\right)\⊗\underset{k=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_k\mathrm{\δ}(t-\mathrm{k\τ})$

Wherein, τ is the subpulse width, and N is code length, the subpulse function

$c_k=e^{j{\mathrm{\φ}}_k}=\±1.$

Coded Signals power spectrum expression formula is:

$P\left(f\right)={\mathrm{\τ}}^2\sin c^2\left[\mathrm{\τ}(f-f_c)\right]\{{\left[\underset{k=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_k\cos \left(2\mathrm{\πfk\τ}\right)\right]}^2+{\left[\underset{k=1}{\overset{N-1}{\mathrm{\Σ}}}{c}_k\sin \left(2\mathrm{\πfk\τ}\right)\right]}^2\}$

$={\mathrm{\τ}}^2\sin c^2\left[\mathrm{\τ}(f-f_c)\right]\{N-1+\frac{\sin \left[2\mathrm{N\π\τ}(f-f_c)\right]}{\sin \left[2\mathrm{\π\τ}(f-f_c)\right]}\}$

Coded Signals power spectrum characteristics are as follows:

1. power spectrum is about the centre frequency symmetry;

2. the peak or the paddy number that in bandwidth, present in multimodal, code length and bandwidth equate.

Due to the more general signal complexity of the Parameter Estimation Problem of Coded Signals, therefore become the difficult point of research.The parameter that Coded Signals is commonly used is as follows:

1. carrier frequency f _c;

2. three dB bandwidth B _3dB;

3. subpulse width τ, wide in the time of namely.

The mostly signal analysis based on time domain of existing Coded Signals parameter estimation method, method for parameter estimation commonly used has the time domain Phase difference, time frequency analysis and circulation spectrometry etc.Propose a kind of low rate BPSK burst bit rate method of estimation in disclosed patent CN101984613A on March 9th, 2011, utilized the method can obtain the bit rate of Coded Signals.2011, the people such as Cui Weiliang were published in the document " improved Cyclic Spectrum is estimated fast algorithm and performance evaluation " of " electronics and information journal ".2012, the people such as Xu Huifa were published in the document " several typical phase-coded signal based on FRFT detects and parameter Estimation " of " war industry's journal ".The amount of calculation of the Coded Signals parameter Estimation based on time frequency analysis and Cyclic Spectrum is very large, can't solve the contradiction between estimated accuracy and operand, and is not suitable for the low signal-to-noise ratio environment.

Summary of the invention

The object of the invention is: realize the valuation of the Coded Signals parameter under unknown prior information condition, overcome in prior art Coded Signals valuation the result large and large defect of amount of calculation affected by noise under the low signal-to-noise ratio environment.

Technical scheme of the present invention is: the invention provides a kind of Coded Signals parameter estimation method based on the power spectrum discrete cosine transform, it is characterized in that, the method comprises:

Step 1, corresponding subpulse width τ and three dB bandwidth B while obtaining Coded Signals different code length N _3dBthe matching relation, it specifically comprises:

Step a, establish Coded Signals code length N span for { N ₁, N ₂..., N _l..., N _r, l ∈ 1,2 ..., r}, set l=1;

Step b, to set described Coded Signals code length be N _l, subpulse width τ constant interval is [τ ₁, τ ₂], change step is △ τ;

Step c, in described τ constant interval, calculate described Coded Signals power spectrum corresponding to different τ values, establishing described power spectrum maximum is P _max, search for first value of described power spectrum for P _maxthe frequency f that/2 places are corresponding ₁with last, be worth for P _maxthe frequency f that/2 places are corresponding ₂, according to definition B _3dB=f ₂-f ₁calculate the three dB bandwidth B that each described power spectrum is corresponding _3dB, obtain τ-B one to one _3dBdata point;

Steps d, selection index function

to described τ-B _3dBdata point is carried out data fitting;

Step e, obtain respectively corresponding coefficient a, b of fitting function, obtain described subpulse width τ and described three dB bandwidth B _3dBthe matching relational expression, wherein, fitting function refers in steps d the fitting function that data fitting obtains;

Step f, make l add 1;

Step g, judge whether l equals r, if l equals r, execution step h, if l is not equal to r, return to step b;

Step h, draw different code length N described subpulse width τ and the described three dB bandwidth B of correspondence respectively _3dBthe matching relational expression.

Step 2, detect the power spectrum of Coded Signals to be valuated, described power spectrum is carried out to amplitude normalization and obtain P (f), to M point of described P (f) uniform sampling, the sequence P (m) that to become length be M, do discrete cosine transform to described P (m) and obtain Y _pre(P (m)), to described Y _pre(P (m)) carries out threshold process and obtains Y (P (m));

Step 3, ask the coenvelope of described Y (P (m)), calculate the peak value number n of described coenvelope, according to the relation of signal code length N and described peak value number n, obtain described signal code length N;

Step 4, described Y (P (m)) is carried out to inverse discrete cosine transform, obtain P _i(m), calculate described P _i(m) carrier frequency f _c, three dB bandwidth B _3dBwith subpulse width τ, it specifically comprises:

A, establish described P _i(m) maximum is P _max, search for described P _i(m) first value is P _maxthe frequency f that/2 places are corresponding ₁with last, be worth for P _maxthe frequency f that/2 places are corresponding ₂, according to definition

calculate described P _i(f) carrier frequency f _c;

B, according to the definition B _3dB=f ₂-f ₁calculate described P _i(f) three dB bandwidth B _3dB;

C, according to described subpulse width τ and described three dB bandwidth B _3dBthe matching relational expression obtain described subpulse width τ.

The invention has the beneficial effects as follows: the invention discloses a kind of Coded Signals parameter estimation method based on the power spectrum discrete cosine transform, the method comprises: corresponding subpulse width τ and three dB bandwidth B while obtaining the Coded Signals different code length _3dBthe matching relation; Detect the power spectrum of Coded Signals to be valuated, described power spectrum is carried out to amplitude normalization and obtain P (f), to M point of described P (f) uniform sampling, the sequence P (m) that to become length be M, do discrete cosine transform to described P (m) and obtain Y _pre(P (m)), to described Y _pre(P (m)) carries out threshold process and obtains Y (P (m)); Ask the coenvelope of described Y (P (m)), calculate the peak value number n of described coenvelope, according to the relation of signal code length N and described peak value number n, obtain described signal code length N; Described Y (P (m)) is carried out to inverse discrete cosine transform, obtain P _i(m), calculate described P _i(m) carrier frequency f _c, three dB bandwidth B _3dBwith subpulse width τ.The amount of calculation of the inventive method is mainly the complex multiplication amount of a FFT conversion and the amount of calculation of twice real number dct transform, overcome the current large defect of Time-Frequency Analysis Method amount of calculation commonly used, under the low signal-to-noise ratio environment, realize the accurate valuation of the Coded Signals parameter of unknown prior information condition.

The accompanying drawing explanation

Fig. 1 a kind of Coded Signals parameter estimation method flow diagram based on power spectrum disclosed by the invention;

Fig. 2 definite Coded Signals subpulse width τ disclosed by the invention and three dB bandwidth B _3dBconcern flow chart;

Fig. 3 selected threshold flow chart disclosed by the invention;

Fig. 4 Coded Signals code length disclosed by the invention N={5, subpulse width τ and three dB bandwidth B during 7,11,13} _3dBthe matched curve of relation;

When wherein, upper left is code length N=5; When upper right is code length N=7; When lower-left is code length N=11; When bottom right is code length N=13;

Signal root-mean-square error curve chart after noise reduction during different threshold value in Fig. 5 embodiment of the present invention;

Wherein,

while representing threshold value T=0.01max (Y (m)); While * representing threshold value T=0.02max (Y (m)); When △ represents threshold value T=0.03max (Y (m)); Zero while representing threshold value T=0.04max (Y (m)); When the dotted line representative is not got threshold value;

The root-mean-square error curve chart of signal after noise reduction during different parameters in Fig. 6 embodiment of the present invention;

Wherein,

representation parameter N=5, during τ=0.01 μ s;

representation parameter N=5, during τ=0.1 μ s; Zero representation parameter N=7, during τ=0.01 μ s; ▽ representation parameter N=7, during τ=0.1 μ s; representation parameter N=11, during τ=0.01 μ s; △ representation parameter N=11, during τ=0.1 μ s; * representation parameter N=13, during τ=0.01 μ s; representation parameter N=13, during τ=0.1 μ s;

The signal graph of Coded Signals power spectrum after discrete cosine transform in Fig. 7 embodiment of the present invention;

The envelope diagram of Coded Signals power spectrum signal after discrete cosine transform in Fig. 8 embodiment of the present invention;

The accuracy rate figure that in Fig. 9 embodiment of the present invention, the Coded Signals code length is estimated;

When wherein, * represents code length N=5; When △ represents code length N=7; When ◇ represents code length N=11; Zero while representing code length N=13.

Coded Signals power spectrum chart and Noise power spectrum chart not before and after experiment is processed in Figure 10 embodiment of the present invention;

Wherein, upper figure is power spectrum chart during Noise not; Power spectrum chart when middle figure is SNR=0dB; Figure below is the power spectrum chart of upper figure after the inventive method is processed.

The root-mean-square error figure of Coded Signals subpulse width valuation in Figure 11 embodiment of the present invention;

When wherein, * represents pulsewidth τ=0.01 μ s; When represents τ=0.05 μ s; Zero while representing pulsewidth τ=0.1 μ s;

The root-mean-square error figure of Coded Signals carrier frequency valuation in Figure 12 embodiment of the present invention.

When wherein, * represents pulsewidth τ=0.01 μ s; When represents τ=0.05 μ s; Zero while representing pulsewidth τ=0.1 μ s.

Embodiment

Hereinafter with reference to Fig. 1-12 pair embodiments of the present invention, describe.

As shown in Figure 1, the Coded Signals parameter estimation method that the embodiment of the present invention is carried out based on power spectrum comprises the following steps:

Step 1, corresponding subpulse width τ and three dB bandwidth B while obtaining Coded Signals different code length N _3dBthe matching relation, as shown in Figure 2, it specifically comprises:

Step a, establish Coded Signals code length N span for { N ₁, N ₂..., N _l..., N _r, l ∈ 1,2 ..., r}, set l=1;

Step b, to set described Coded Signals code length be N _l, subpulse width τ constant interval is [τ ₁, τ ₂], change step is △ τ;

Step c, in described τ constant interval, calculate described Coded Signals power spectrum corresponding to different τ values, establishing described power spectrum maximum is P _max, search for first value of described power spectrum for P _maxthe frequency f that/2 places are corresponding ₁with last, be worth for P _maxthe frequency f that/2 places are corresponding ₂, according to definition B _3dB=f ₂-f ₁calculate the three dB bandwidth B that each described power spectrum is corresponding _3dB, obtain τ-B one to one _3dBdata point;

Steps d, selection index function

to described τ-B _3dBdata point is carried out data fitting;

Step e, obtain respectively corresponding coefficient a, b of fitting function, obtain described subpulse width τ and described three dB bandwidth B _3dBthe matching relational expression;

Step f, make l add 1;

Step g, judge whether l equals r, if l equals r, execution step h, if l is not equal to r, return to step b;

Step h, draw different code length N described subpulse width τ and the described three dB bandwidth B of correspondence respectively _3dBthe matching relational expression.

Step 2, detect the power spectrum of Coded Signals to be valuated, described power spectrum is carried out to amplitude normalization and obtain P (f), to M point of described P (f) uniform sampling, the sequence P (m) that to become length be M, do discrete cosine transform to described P (m) and obtain Y _pre(P (m)), to described Y _pre(P (m)) carries out threshold process and obtains Y (P (m));

Wherein, in step 2, by following steps, obtain described Y (P (m)):

In Coded Signals power spectrum expression formula, making τ is the subpulse width, and N is code length, f _cfor carrier frequency, Coded Signals power spectrum expression formula is:

$P\left(f\right)={\mathrm{\τ}}^2\sin c^2\left[\mathrm{\τ}(f-f_c)\right]\{{\left[\underset{k=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_k\cos \left(2\mathrm{\πfk\τ}\right)\right]}^2+{\left[\underset{k=1}{\overset{N-1}{\mathrm{\Σ}}}{c}_k\sin \left(2\mathrm{\πfk\τ}\right)\right]}^2\}$

$={\mathrm{\τ}}^2\sin c^2\left[\mathrm{\τ}(f-f_c)\right]\{N-1+\frac{\sin \left[2\mathrm{N\π\τ}(f-f_c)\right]}{\sin \left[2\mathrm{\π\τ}(f-f_c)\right]}\}$

To M point of P (f) uniform sampling, the sequence P (m) that to become length be M, in wherein said discrete cosine transform formula $c\left(k\right)=\left\{\begin{array}{cc}\frac{1}{\sqrt{2}},& k=0\\ 1,& k=\mathrm{1,2},\·\·\·,M-1\end{array},,\right.$ Described discrete cosine transform formula is: $Y_{\mathrm{pre}}\left(P\left(m\right)\right)=\sqrt{\frac{2}{M}}c\left(k\right)\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}P\left(m\right)\cos \frac{(2m+1)\mathrm{k\π}}{M},k,m=\mathrm{0,1},\·\·\·,M-1$

And the actual signal of receiving is to be with noisyly, the signal after discrete cosine transform also can be subject to noise effect, therefore sets a threshold value T, by described Y _prethe part zero setting that (P (m)) value is (T, T) just obtains described Y (P (m)).

It should be noted that, as shown in Figure 3, the selecting step of threshold value is as follows:

A, described Y (P (m)) is done to inverse discrete cosine transform obtain signal P _i(m), set described P _i(m) with template signal P _nn(m) root-mean-square error threshold value is σ _r;

B, set thick scope (0, the △ of described threshold value T ₁), in described thick scope with 10 ^-n△ ₁for step-length, n=1 wherein;

C, calculate described root-mean-square error σ respectively _i, i=1,2,3,

D, select min{ σ _icorresponding threshold value T _a;

E, judge described min{ σ _iwhether be less than described σ _r, be, perform step h, no, perform step f;

F, reset threshold range (T _a-10 ^-n△ ₁, T _a+ 10 ^-n△ ₁), step-length is 10 ^-(n+1)△ ₁;

G, make n add 1, return to execution step c;

H, choose T _afor optimal threshold.

Wherein, in step a, P described in patent of the present invention _i(m) by inverse discrete cosine transform, calculate, its expression formula is as follows:

$P_i\left(m\right)=\sqrt{\frac{2}{M}}c\left(k\right)\underset{k=0}{\overset{M-1}{\mathrm{\Σ}}}Y\left(P\left(m\right)\right)\cos \frac{(2m+1)\mathrm{k\π}}{M},$ k、m=0,1,…,M-1；

It should be noted that template signal P described in patent of the present invention _nn(m) signal while being defined as Noise not;

It should be noted that P described in patent of the present invention _i(m) with described template signal P _nn(m) root-mean-square error is defined as follows:

Root-mean-square error is described P _i(m) with described template signal P _nn(m) square root of the variance between, its definition is:

$\mathrm{RMSE}=\sqrt{\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}{[P_{\mathrm{nn}}\left(m\right)-P_i\left(m\right)]}^2/M};$

Step 3, ask the coenvelope of described Y (P (m)), calculate the peak value number n of described coenvelope, according to the relation of signal code length N and described peak value number n, obtain described signal code length N;

Wherein, in step 3, the pass of signal code length N and described Y (P (m)) coenvelope peak value number n is:

N=2n+1

It should be noted that, in the present invention, coenvelope is defined as follows:

Peak point in described Y (P (m)) is linked to be to a curve, is the coenvelope of described Y (P (m));

It should be noted that, the peak value number determination methods of coenvelope is as follows:

Each point to described coenvelope judged, when estimative point is greater than the continuous point in 5, its continuous point in 5, left side and its right side simultaneously, just can judge that this point is peak point;

Step 4, described Y (P (m)) is carried out to inverse discrete cosine transform, obtain P _i(m), calculate described P _i(m) carrier frequency f _c, three dB bandwidth B _3dBwith subpulse width τ, it specifically comprises:

A, establish described P _i(m) maximum is P _max, search for described P _i(m) first value is P _maxthe frequency f that/2 places are corresponding ₁with last, be worth for P _maxthe frequency f that/2 places are corresponding ₂, according to definition

calculate described P _i(f) carrier frequency f _c;

B, according to the definition B _3dB=f ₂-f ₁calculate described P _i(f) three dB bandwidth B _3dB;

C, according to described subpulse width τ and described three dB bandwidth B _3dBthe matching relational expression obtain described subpulse width τ.

Coded Signals is take in the present invention, and as embodiment, the present invention is described in detail; The specific embodiment of the invention means Coded Signals with abbreviation BPSK, and with abbreviation, DCT means discrete cosine transform, and with abbreviation, IDCT means inverse discrete cosine transform, and with abbreviation, SNR means signal to noise ratio.Simulation parameter arranges: code length N={5, and 7,11,13}, subpulse width τ=0.05 μ s, carrier frequency is 500MHz.

The embodiment of the present invention can be applied to military electronic countermeasures and civilian frequency spectrum supervision field, estimate exactly signal parameter under the low signal-to-noise ratio environment, function and the purposes that can reflect radar, improve the positioning precision of sonar tracking system and improve tracking effect significant.

One, calculate τ-B corresponding to different code length _3dBthe matching relational expression;

As shown in Figure 4, and the goodness of fit all is greater than 99.5% to the matching relation curve, and fitting formula is:

1. 5 bpsk signal τ-B _3dBfitting formula:

τ=0.18604·B _3dB ^-0.9922

2. 7 bpsk signal τ-B _3dBfitting formula:

τ=0.82959·B _3dB ^-0.99148

3. 11 bpsk signal τ-B _3dBfitting formula:

τ=0.86469·B _3dB ^-0.98822

4. 13 bpsk signal τ-B _3dBfitting formula:

τ=0.21173·B _3dB ^-0.98466

Two, threshold value T's chooses;

If the signal maximum after DCT is max{Y (P (m)) }, set described σ _r=0.1, △ ₁=0.1max{Y (P (m)) }, according to the threshold value selection principle, when threshold value is taken as 0.02max{Y (P (m)) } time can meet threshold value and choose condition, setting the bpsk signal parameter is code length N=13, when SNR changes at-5dB～20dB, as shown in Figure 5, when parameter changes, described root-mean-square error curve as shown in Figure 6 for described root-mean-square error curve.

From Fig. 5-6, when taking threshold process, can make signal there is noise reduction, and be taken as 0.02max{Y (P (m)) when threshold value } time, described root-mean-square error all is less than 0.1, so patent of the present invention is taked threshold value T=0.02max{Y (P (m)) }.

Three, detect bpsk signal power spectrum P (f) to be valuated, and described bpsk signal is carried out to the code length estimation;

Described bpsk signal power spectrum is carried out to dct transform, after conversion, signal as shown in Figure 7, and do threshold process and obtain Y (P (m)), ask described after threshold process the coenvelope of signal, as shown in Figure 8, obtain peak value number n, so obtain the estimation of the code length N of described bpsk signal, when the SNR excursion is [5dB～20dB], carry out 100 Monte Carlo tests.

As shown in Figure 9, when be greater than-5dB of SNR, the bpsk signal code length estimates that accuracy rate is 100%, therefore can further realize the accurate valuation to subpulse width and the carrier frequency of described bpsk signal.

Four, described bpsk signal is carried out the valuation of carrier frequency and subpulse width;

Described Y (P (m)) is carried out to idct transform, obtain P _i(m), set SNR=0dB, as shown in figure 10, signal after treatment is closer to the signal of Noise not.

Bpsk signal when SNR in interval is [5dB, 20dB] carries out 100 Monte Carlo tests, calculates the root-mean-square error (RMSE) of described bpsk signal carrier frequency and subpulse width, and result is as shown in Figure 11 and Figure 12.

When the inventive method is [5dB, 20dB] at SNR the evaluated error of carrier frequency as shown in figure 11, and at SNR-evaluated error of carrier frequency all is less than 0.5MHz during 5dB.

When the inventive method is [5dB, 20dB] at SNR the evaluated error of subpulse width as shown in figure 12, and at SNR-evaluated error of subpulse width all is less than 0.032 μ s during 5dB.

Claims (1)

1. the Coded Signals parameter estimation method based on power spectrum, is characterized in that, the method comprises:

Step 1, corresponding subpulse width τ and three dB bandwidth B while obtaining Coded Signals different code length N _3dBthe matching relation, it specifically comprises:

Step a, establish Coded Signals code length N span for { N ₁, N ₂..., N _l..., N _r, l ∈ 1,2 ..., r}, set l=1;

Step b, to set described Coded Signals code length be N _l, subpulse width τ constant interval is [τ ₁, τ ₂], change step is △ τ;

Step c, in described τ constant interval, calculate described Coded Signals power spectrum corresponding to different τ values, establishing described power spectrum maximum is P _max, search for first value of described power spectrum for P _maxthe frequency f that/2 places are corresponding ₁with last, be worth for P _maxthe frequency f that/2 places are corresponding ₂, according to definition B _3dB=f ₂-f ₁calculate the three dB bandwidth B that each described power spectrum is corresponding _3dB, obtain τ-B one to one _3dBdata point;

Steps d, selection index function

to described τ-B _3dBdata point is carried out data fitting;

Step e, obtain respectively corresponding coefficient a, b of fitting function, obtain described subpulse width τ and described three dB bandwidth B _3dBthe matching relational expression, wherein, fitting function refers in steps d the fitting function that data fitting obtains;

Step f, make l add 1;

Step g, judge whether l equals r, if l equals r, execution step h, if l is not equal to r, return to step b;

Step h, draw different code length N described subpulse width τ and the described three dB bandwidth B of correspondence respectively _3dBthe matching relational expression;

Step 2, detect the power spectrum of Coded Signals to be valuated, described power spectrum is carried out to amplitude normalization and obtain P (f), to M point of described P (f) uniform sampling, the sequence P (m) that to become length be M, do discrete cosine transform to described P (m) and obtain Y _pre(P (m)), to described Y _pre(P (m)) carries out threshold process and obtains Y (P (m));

Step 3, ask the coenvelope of described Y (P (m)), calculate the peak value number n of described coenvelope, according to the relation of signal code length N and described peak value number n, obtain described signal code length N;

Step 4, described Y (P (m)) is carried out to inverse discrete cosine transform, obtain P _i(m), calculate described P _i(m) carrier frequency f _c, three dB bandwidth B _3dBwith subpulse width τ, it specifically comprises:

A, establish described P _i(m) maximum is P _max, search for described P _i(m) first value is P _maxthe frequency f that/2 places are corresponding ₁with last, be worth for P _maxthe frequency f that/2 places are corresponding ₂, according to definition

calculate described P _i(f) carrier frequency f _c;

B, according to the definition B _3dB=f ₂-f ₁calculate described P _i(f) three dB bandwidth B _3dB;

C, according to described subpulse width τ and described three dB bandwidth B _3dBthe matching relational expression obtain described subpulse width τ.

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