CN103607370A - Credibility assessment method of complex BPSK signal blind processing result - Google Patents

Abstract

The invention brings forward a credibility assessment method of a complex BPSK signal blind processing result. The method comprises: under the condition of no signal prior knowledge, first of all, constructing a reference signal according to a signal model corresponding to a modulation mode identification result, and on the basis of analyzing the curve characteristics of related accumulated die values of the sampling sequences of the reference signal and an observation signal, performing credibility determination on the complex BPSK signal blind processing result according to related coefficients and related coefficient symbols. The method provided by the invention can realize reliability examination of the complex BPSK signal blind processing result without signal prior information under the condition of a low signal-to-noise ratio.

Description

A kind of credibility assessment method of the multiple blind result of bpsk signal

Technical field

The present invention relates to a kind of multiple BPSK(Binary Phase Shift Keying, two-phase PSK) credibility assessment method of signal processing results, especially a kind of compared with the credibility assessment method of the blind result of multiple bpsk signal under Low SNR.

Background technology

Lacking under signal prior information and Low SNR, sample sequence to observation signal detects, Modulation Identification and parameter Estimation, electronic reconnaissance and cognitive radio signal (CR, Cognitive Radio) process the important step of front end, directly affect the handling property of follow-up signal processing links.In electronic reconnaissance, front end signal result will exert an influence to subsequent treatment links such as the sorting of signal, location and tracking, interference and individual radiation source identifications.In cognitive radio, front end frequency spectrum perception, result of spectrum analysis are the effectively prerequisites and basis of operation of the follow-up cognitive links such as frequency spectrum judging, spectrum management reliably.But under non-cooperation condition, to the Modulation Identification of the sample sequence of observation signal, parameter Estimation etc., can only carry out blind processing.Yet, less for whether correct, the believable Efficient Evaluation method of blind result.

The blind processing procedure of multiple bpsk signal comprises the links such as Modulation Mode Recognition and decoding.Obviously, the prerequisite being correctly decoded is that Modulation Mode Recognition is correct.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of credibility assessment method of effectively answering the blind result of bpsk signal, realizes the blind result of multiple bpsk signal is carried out to Credibility Assessment.

In order to address the above problem, the invention provides a kind of credibility assessment method of the multiple blind result of bpsk signal, the multiple blind processing procedure of bpsk signal comprises Modulation Mode Recognition and decoding, adopt hypothesis test to assess the credibility of the blind result of multiple bpsk signal, establish and in finite observation time, treat that the multiple bpsk signal of blind processing is:

$s\left(t\right)={\mathrm{Ae}}^{j(2\mathrm{\&pi;}{f}_{0}t+\mathrm{\&theta;})}\underset{k=1}{\overset{N_c}{\mathrm{\&Sigma;}}}{e}^{\mathrm{j\&pi;}{c}_k}{\mathrm{\&Pi;}}_{T_c}(t-{\mathrm{kT}}_c),0\&le;t<T$

Wherein, T is observation time, and A is signal amplitude, f ₀for signal carrier frequency, the initial phase that θ is signal, N _cfor the code length of signal, T _cfor the symbol width of signal, c _kbe k code word, value is 0 or 1;

Respectively the carrier frequency of multiple bpsk signal, code word, code length and symbol width are carried out to parameter Estimation, the estimates of parameters obtaining is respectively with

The superposeed sample sequence of observation signal of multiple bpsk signal of noise of foundation is:

$x\left(n\right)=s\left(n\right)+w\left(n\right)={\mathrm{Ae}}^{j(2\mathrm{\&pi;}{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA0000419978820000021.png,HDA0000419978820000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0\mathrm{n\&Delta;t}+\mathrm{\&theta;})}\underset{k=1}{\overset{N_c}{\mathrm{\&Sigma;}}}{e}^{\mathrm{j\&pi;}{c}_k}{\mathrm{\&Pi;}}_{T_c}(\mathrm{n\&Delta;t}-k{T}_c)+w\left(n\right),0\&le;n<N-1$

Wherein, in the sampling interval that Δ t is signal, s (n) is the sampled signal of multiple bpsk signal, and w (n) is return-to-zero average limit band white Gaussian noise, and N is number of samples, and the signal to noise ratio of signal is SNR=A ²/ 2 σ ², σ ²for sample variance;

First, suppose that Modulation Mode Recognition is correct and without decoding error, the modulation system of identifying is BPSK, and does not have decoding error in blind processing procedure, credibility assessment method comprises the following steps:

Step 1, builds corresponding reference signal according to the Modulation Mode Recognition result of hypothesis, and the relevant cumulative delivery of sample sequence with reference to signal to observation signal, obtains corresponding relevant cumulative mould value, and concrete steps are as follows:

(1-1) according to the reference signal of multiple bpsk signal structure, be:

$y_0\left(n\right)=e^{-j2\mathrm{\&pi;}{\hat{f}}_0\mathrm{n\&Delta;t}}\underset{k=1}{\overset{{\hat{N}}_c}{\mathrm{\&Sigma;}}}{e}^{-\mathrm{j\&pi;}{\hat{c}}_k}{\mathrm{\&Pi;}}_{{\hat{T}}_c}(\mathrm{n\&Delta;t}-k{\hat{T}}_c),0\&le;n\&le;N-1$

(1-2) with reference to signal y ₀(n) do relevant adding up to the sample sequence of observation signal, obtain relevant being accumulated as:

$z\left(n\right)=\underset{m=0}{\overset{n}{\mathrm{\&Sigma;}}}x\left(m\right)y_0\left(m\right)=s_0\left(n\right)+w_0\left(n\right),0\&le;n\&le;N-1$

Wherein, w ₀(n) be noise section, s ₀(n) be signal section,

$w_0\left(n\right)=\underset{m=0}{\overset{n}{\mathrm{\&Sigma;}}}w\left(m\right)y_0\left(m\right)$

$s_0\left(n\right)=\underset{m=0}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{Ae}}^{j(2\mathrm{\&pi;\&Delta;fn\&Delta;t}+\mathrm{\&theta;})}\underset{k=1}{\overset{{\hat{N}}_c}{\mathrm{\&Sigma;}}}{e}^{-\mathrm{j\&pi;}{\hat{c}}_k}{\mathrm{\&Pi;}}_{{\hat{T}}_c}[\mathrm{n\&Delta;t}-(k-1){\hat{T}}_c]\&CenterDot;\underset{k=1}{\overset{N_c}{\mathrm{\&Sigma;}}}{e}^{\mathrm{j\&pi;}{c}_k}{\mathrm{\&Pi;}}_{T_c}[\mathrm{n\&Delta;t}-(k-1)T_c]$

Wherein,

for carrier frequency evaluated error, when the value of Δ f trends towards 0, the approximation that obtains signal section is:

s ₀(n)≈A(n+1)e ^{j(πnΔfΔt+θ)}

(1-3), to relevant cumulative delivery, the relevant cumulative mould value obtaining is:

g(n)＝|z(n)|=|s ₀(n)+w ₀(n)|≈A(n+1)+ω'(n)

Wherein, A (n+1) is the certainty component of g (n), and ω ' is (n) the equivalent noise component(s) of g (n);

Step 2, extracts coefficient correlation feature C to relevant cumulative mould value ₁, concrete steps are:

(2-1) calculating the relevant correlation coefficient r that adds up mould value is:

$r=\frac{\mathrm{\&Sigma;ng}\left(n\right)}{\sqrt{\mathrm{\&Sigma;}{n}^2\mathrm{\&Sigma;}{g}^2\left(n\right)}}$

(2-2) correlation coefficient r is obtained as nonlinear transformation:

$p=0.5\ln \frac{1+r}{1-r}$

By nonlinear transformation, the distribution of correlation coefficient r is transformed between (∞ ,+∞) between (1,1), p is similar to Normal Distribution;

(2-3) the normal state side-play amount that calculating correlation coefficient r is done after nonlinear transformation is:

$Z=\frac{p-{\mathrm{\&zeta;}}_0}{{\mathrm{\&sigma;}}_z}$

Wherein, ζ ₀=0.5ln (1+ ρ ₀)/(1-ρ ₀), ρ herein ₀=0.99, standard deviation def (g (n)) is the degree of freedom;

(2-4) under level of significance α, 0.0001≤α≤0.01 herein, calculate threshold value and be:

Th＝-z _α

Wherein, z _αupper α quantile for standardized normal distribution, can obtain by query criteria gaussian distribution table, if Z < is Th, and coefficient correlation feature C ₁=1, otherwise C ₁=0;

Step 3, as coefficient correlation feature C ₁, in order further to determine in sampling interval whether have a bit-errors decoding, need to calculate coefficient correlation symbol consistency feature C at=1 o'clock ₂, concrete steps are:

(3-1) with starting point and terminal between Wavelet Transform misjudgment area decoder, the interval curve for relevant cumulative mould value g (n) of described decoded in error produces in decoded in error position to fracture and forms an interval forming with the starting point that fractures and terminal, establishing relevant Origin And Destination position of adding up mould value g (n) decoded in error interval and being respectively

with

its sectional is expressed as:

$g\left(n\right)=\left\{\begin{array}{c}{g}_{c_0}\left(n\right),0\&le;n_{e_0}-1\\ g_e\left(n\right),{\mathrm{<figure-callout\; id="0"\; label="n\; e"\; filenames="HDA0000419978820000021.png,HDA0000419978820000022.png"\; state="\{\{state\}\}">n</figure-callout>}}_{e_{}}\&le;n\&le;n_{e_1}\\ g_{c_1}\left(n\right),n_{e_1}+1\&le;n\&le;N-1\end{array}\right.$

Wherein, g _e(n) data in corresponding decoded in error interval,

with

corresponding to the data outside decoded in error interval;

(3-2) in three intervals of relevant cumulative mould value, calculate respectively coefficient correlation separately, obtain r _i, i=1 wherein, 2,3;

(3-3) symbolic vector of calculating coefficient correlation is: $s_i=\left\{\begin{array}{c}1,r_i>0\\ 0,r_i=0\\ -1,r_i<0\end{array}\right.,$ I=1 wherein, 2,3;

If (3-4) symbolic vector S ₁, S ₂and S ₃symbol identical, C ₂=1, if symbolic vector S ₁, S ₂and S ₃symbol different, C ₂=0;

Step 4, check assessment result: if C ₁=1 and C ₂=1, Modulation Mode Recognition correctly and without decoding error, hypothesis is set up, and the multiple blind result of bpsk signal is credible; If C ₁=0, Modulation Mode Recognition mistake, hypothesis is false, and the multiple blind result of bpsk signal is insincere; If C ₁=1 and C ₂=0, Modulation Mode Recognition is correct but have decoding error, and hypothesis is set up, but the multiple blind result of bpsk signal is insincere.

Adopt coefficient correlation feature C ₁with coefficient correlation symbol consistency feature C ₂judge the credibility of the blind result of multiple bpsk signal, work as C ₁=0 o'clock, the Modulation Mode Recognition mistake of signal, the blind result of bpsk signal is insincere again; Work as C ₁=1 o'clock, the Modulation Mode Recognition of signal was correct, can also further judge whether to exist decoding error, worked as C ₁=1 and C ₂=1 o'clock, the Modulation Mode Recognition of signal correctly and without decoding error, the blind result of bpsk signal is credible again; Work as C ₁=1 and C ₂=0 o'clock, the correct decoding error that still exists of Modulation Mode Recognition of signal, the blind result of bpsk signal is insincere again.

Beneficial effect of the present invention is: can carry out effective Credibility Assessment to the blind result of multiple bpsk signal, effectively tell that Modulation Mode Recognition mistake, Modulation Mode Recognition are correct but decoding error and Modulation Mode Recognition are correct and without these three kinds of situations of decoding error, thereby correspondingly determine that whether the multiple blind result of bpsk signal is credible.

Accompanying drawing explanation

Fig. 1 is the estimation flow figure of the credibility assessment method of the multiple blind result of bpsk signal of the present invention;

Fig. 2 is that multiple bpsk signal Modulation Mode Recognition of the present invention is correct and during without decoding error, relevant cumulative mould value g (n) and linear regression schematic diagram thereof;

When Fig. 3 is multiple bpsk signal Modulation Mode Recognition mistake of the present invention, mistake is known relevant cumulative mould value g (n) and the linear regression schematic diagram thereof for normal signal;

Fig. 4 is that multiple bpsk signal Modulation Mode Recognition of the present invention is correct but while having a bit-errors decoding, relevant cumulative mould value g (n) and linear regression schematic diagram thereof;

Fig. 5 (a) is that multiple bpsk signal Modulation Mode Recognition of the present invention is correct and during without decoding error, the statistic histogram of relevant cumulative mould value g (n) curve correlation coefficient;

When Fig. 5 (b) is multiple bpsk signal Modulation Mode Recognition mistake of the present invention, the statistic histogram of relevant cumulative mould value g (n) curve correlation coefficient;

Fig. 5 (c) for multiple BSPK signal Modulation Mode Recognition of the present invention correct but while there is a bit-errors decoding, the statistic histogram of relevant cumulative mould value g (n) curve correlation coefficient;

Fig. 6 is the interval schematic diagram of the multiple bpsk signal decoded in error of utilizing Second Wavelet Transform to obtain of the present invention.

Embodiment

As shown in Figure 1, the invention provides a kind of credibility assessment method of the multiple blind result of bpsk signal, the multiple blind processing procedure of bpsk signal comprises Modulation Mode Recognition and decoding, adopt hypothesis test to assess the credibility of the blind result of multiple bpsk signal, establish and in finite observation time, treat that the multiple bpsk signal of blind processing is:

$s\left(t\right)={\mathrm{Ae}}^{j(2\mathrm{\&pi;}{f}_{0}t+\mathrm{\&theta;})}\underset{k=1}{\overset{N_c}{\mathrm{\&Sigma;}}}{e}^{\mathrm{j\&pi;}{c}_k}{\mathrm{\&Pi;}}_{T_c}(t-{\mathrm{kT}}_c),0\&le;t<T$

Wherein, T is observation time, and A is signal amplitude, f ₀for signal carrier frequency, the initial phase that θ is signal, N _cfor the code length of signal, T _cfor the symbol width of signal, c _kbe k code word, value is 0 or 1;

Respectively the carrier frequency of multiple bpsk signal, code word, code length and symbol width are carried out to parameter Estimation, the estimates of parameters obtaining is respectively

with

The superposeed sample sequence of observation signal of multiple bpsk signal of noise of foundation is:

$x\left(n\right)=s\left(n\right)+w\left(n\right)={\mathrm{Ae}}^{j(2\mathrm{\&pi;}{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA0000419978820000021.png,HDA0000419978820000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0\mathrm{n\&Delta;t}+\mathrm{\&theta;})}\underset{k=1}{\overset{N_c}{\mathrm{\&Sigma;}}}{e}^{\mathrm{j\&pi;}{c}_k}{\mathrm{\&Pi;}}_{T_c}(\mathrm{n\&Delta;t}-k{T}_c)+w\left(n\right),0\&le;n<N-1$

Wherein, in the sampling interval that Δ t is signal, s (n) is the sampled signal of multiple bpsk signal, and w (n) is return-to-zero average limit band white Gaussian noise, and N is number of samples, and the signal to noise ratio of signal is SNR=A ²/ 2 σ ², σ ²for sample variance;

First, suppose that Modulation Mode Recognition is correct and without decoding error, the modulation system of identifying is BPSK, and does not have decoding error in blind processing procedure, credibility assessment method comprises the following steps:

Step 1, builds corresponding reference signal according to the Modulation Mode Recognition result of hypothesis, and the relevant cumulative delivery of sample sequence with reference to signal to observation signal, obtains corresponding relevant cumulative mould value, and concrete steps are as follows:

(1-1) according to the reference signal of multiple bpsk signal structure, be:

$y_0\left(n\right)=e^{-j2\mathrm{\&pi;}{\hat{f}}_0\mathrm{n\&Delta;t}}\underset{k=1}{\overset{{\hat{N}}_c}{\mathrm{\&Sigma;}}}{e}^{-\mathrm{j\&pi;}{\hat{c}}_k}{\mathrm{\&Pi;}}_{{\hat{T}}_c}(\mathrm{n\&Delta;t}-k{\hat{T}}_c),0\&le;n\&le;N-1$

(1-2) with reference to signal y ₀(n) do relevant adding up to the sample sequence of observation signal, obtain relevant being accumulated as:

$z\left(n\right)=\underset{m=0}{\overset{n}{\mathrm{\&Sigma;}}}x\left(m\right)y_0\left(m\right)=s_0\left(n\right)+w_0\left(n\right),0\&le;n\&le;N-1$

Wherein, w ₀(n) be noise section, s ₀(n) be signal section,

$w_0\left(n\right)=\underset{m=0}{\overset{n}{\mathrm{\&Sigma;}}}w\left(m\right)y_0\left(m\right)$

$s_0\left(n\right)=\underset{m=0}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{Ae}}^{j(2\mathrm{\&pi;\&Delta;fn\&Delta;t}+\mathrm{\&theta;})}\underset{k=1}{\overset{{\hat{N}}_c}{\mathrm{\&Sigma;}}}{e}^{-\mathrm{j\&pi;}{\hat{c}}_k}{\mathrm{\&Pi;}}_{{\hat{T}}_c}[\mathrm{n\&Delta;t}-(k-1){\hat{T}}_c]\&CenterDot;\underset{k=1}{\overset{N_c}{\mathrm{\&Sigma;}}}{e}^{\mathrm{j\&pi;}{c}_k}{\mathrm{\&Pi;}}_{T_c}[\mathrm{n\&Delta;t}-(k-1)T_c]$

Wherein,

for carrier frequency evaluated error, when the value of Δ f trends towards 0, the approximation that obtains signal section is:

s ₀(n)≈A(n+1)e ^{j(πnΔfΔt+θ)}

(1-3), to relevant cumulative delivery, the relevant cumulative mould value obtaining is:

g(n)＝|z(n)|=|s ₀(n)+w ₀(n)|≈A(n+1)+ω'(n)

Wherein, A (n+1) is the certainty component of g (n), and ω ' is (n) the equivalent noise component(s) of g (n);

Step 2, extracts coefficient correlation feature C to relevant cumulative mould value ₁, concrete steps are:

(2-1) calculating the relevant correlation coefficient r that adds up mould value is:

$r=\frac{\mathrm{\&Sigma;ng}\left(n\right)}{\sqrt{\mathrm{\&Sigma;}{n}^2\mathrm{\&Sigma;}{g}^2\left(n\right)}}$

(2-2) correlation coefficient r is obtained as nonlinear transformation:

$p=0.5\ln \frac{1+r}{1-r}$

By nonlinear transformation, the distribution of correlation coefficient r is transformed between (∞ ,+∞) between (1,1), p is similar to Normal Distribution;

(2-3) the normal state side-play amount that calculating correlation coefficient r is done after nonlinear transformation is:

$Z=\frac{p-{\mathrm{\&zeta;}}_0}{{\mathrm{\&sigma;}}_z}$

Wherein, ζ ₀=0.5ln (1+ ρ ₀)/(1-ρ ₀), ρ herein ₀=0.99, standard deviation

def (g (n)) is the degree of freedom;

(2-4) under level of significance α, 0.0001≤α≤0.01 herein, calculate threshold value and be:

Th＝-z _α

Wherein, z _αupper α quantile for standardized normal distribution, can obtain by query criteria gaussian distribution table, if Z < is Th, and coefficient correlation feature C ₁=1, otherwise C ₁=0;

Step 3, as coefficient correlation feature C ₁, in order further to determine in sampling interval whether have a bit-errors decoding, need to calculate coefficient correlation symbol consistency feature C at=1 o'clock ₂, concrete steps are:

(3-1) with starting point and terminal between Wavelet Transform misjudgment area decoder, the interval curve for relevant cumulative mould value g (n) of described decoded in error produces in decoded in error position to fracture and forms an interval forming with the starting point that fractures and terminal, establishing relevant Origin And Destination position of adding up mould value g (n) decoded in error interval and being respectively with its sectional is expressed as:

$g\left(n\right)=\left\{\begin{array}{c}{g}_{c_0}\left(n\right),0\&le;n_{e_0}-1\\ g_e\left(n\right),{\mathrm{<figure-callout\; id="0"\; label="n\; e"\; filenames="HDA0000419978820000021.png,HDA0000419978820000022.png"\; state="\{\{state\}\}">n</figure-callout>}}_{e_{}}\&le;n\&le;n_{e_1}\\ g_{c_1}\left(n\right),n_{e_1}+1\&le;n\&le;N-1\end{array}\right.$

Wherein, g _e(n) data in corresponding decoded in error interval,

with

corresponding to the data outside decoded in error interval;

(3-2) in three intervals of relevant cumulative mould value, calculate respectively coefficient correlation separately, obtain r _i, i=1 wherein, 2,3;

(3-3) symbolic vector of calculating coefficient correlation is: $s_i=\left\{\begin{array}{c}1,r_i>0\\ 0,r_i=0\\ -1,r_i<0\end{array}\right.,$ I=1 wherein, 2,3;

If (3-4) symbolic vector S ₁, S ₂and S ₃symbol identical, C ₂=1, if symbolic vector S ₁, S ₂and S ₃symbol different, C ₂=0;

Step 4, check assessment result: if C ₁=1 and C ₂=1, Modulation Mode Recognition correctly and without decoding error, hypothesis is set up, and the multiple blind result of bpsk signal is credible; If C ₁=0, Modulation Mode Recognition mistake, hypothesis is false, and the multiple blind result of bpsk signal is insincere; If C ₁=1 and C ₂=0, Modulation Mode Recognition is correct but have decoding error, and hypothesis is set up, but the multiple blind result of bpsk signal is insincere.

As shown in Figure 2, when the blind result of multiple bpsk signal is Modulation Mode Recognition while correctly and not there is decoding error, when calculating relevant cumulative mould value g (n), if the value of carrier frequency evaluated error Δ f trends towards at 0 o'clock, the approximation that can obtain g (n) is:

g(n)＝|z(n)|=|s ₀(n)+w ₀(n)|≈A(n+1)+ω'(n)

Wherein, A (n+1) is the certainty component of g (n), ω ' is (n) its equivalent noise component(s), relevant cumulative mould value g (n) obeys this distribution of Lay, when signal to noise ratio is higher, near approximate Gaussian distributed its average, therefore relevant cumulative mould value g (n) approximately equivalent is a straight line under noise background.

As shown in Figure 3, when multiple bpsk signal bandwidth is less or signal is disturbed generation distortion, the blind result of multiple bpsk signal may be Modulation Mode Recognition mistake, at receiving terminal, is likely judged to normal signal or other signal.Suppose the Modulation Mode Recognition mistake of multiple bpsk signal, bpsk signal is known for other signals by mistake again, if mistake is known, is normal signal, in like manner can construct reference signal according to normal signal and be:

$y_1\left(n\right)=e^{-j\left(2\mathrm{\&pi;}{\hat{f}}_0\mathrm{n\&Delta;t}\right)},0\&le;n\&le;N-1$

Again with reference to signal y ₁(n) do relevant adding up to the sample sequence of observation signal, obtain relevant being accumulated as:

$z\left(n\right)\underset{m=0}{\overset{n}{\mathrm{\&Sigma;}}}x\left(m\right)y_1\left(m\right)=s_1\left(n\right)+w_1\left(n\right),0\&le;n\&le;N-1$

Wherein, w ₁(n) be noise section, s ₁(n) be signal section,

Wherein,

for phase error function,

To relevant cumulative delivery, the relevant cumulative mould value obtaining is again:

g(n)＝|z(n)|=|s ₁(n)+w ₁(n)|。

Due to signal model mismatch and phase error function

existence, cause reference signal and the original signal of structure to carry out relevant cumulative mould value g (n) curve not linearly, by the coefficient correlation feature C of relevant mould value g (n) extraction that adds up ₁=0.

As shown in Figure 4, when Modulation Mode Recognition is correct, but the parameter estimating error of multiple bpsk signal is larger, likely because the accumulation of carrier frequency evaluated error or symbol width evaluated error is larger, or because the reason such as the estimation of code element figure place is wrong will cause decoding error.If there is a bit-errors decoding, at symbol decoding errors present, the curve of relevant cumulative mould value g (n) fractures generation, formation decoded in error is interval, and the interval curve for relevant cumulative mould value g (n) of this decoded in error produces in decoded in error position to fracture and forms one with the starting point that fractures and the interval of terminal formation.Now, relevant cumulative mould value g (n) curve is by several the rectilinear(-al)s that slope is different, and the data in decoded in error interval are carried out slope that linear regression obtains and the data outside decoded in error interval, and to carry out the slope symbol that linear regression obtains contrary.

As Fig. 5 (a), shown in 5 (b) and 5 (c), Fig. 5 (a) is Modulation Mode Recognition emulation statistic histogram correct and relevant cumulative mould value g (n) curve correlation coefficient during without decoding error, the emulation statistic histogram of the coefficient correlation of relevant cumulative mould value g (n) curve when Fig. 5 (b) is Modulation Mode Recognition mistake, Fig. 5 (c) is Modulation Mode Recognition emulation the statistic histogram correct but coefficient correlation of relevant cumulative mould value g (n) curve while there is a decoding error, the simulated conditions adopting is: the sample sequence model x (n) that supposes observation signal is the multiple bpsk signal being polluted by additive white Gaussian noise, signal to noise ratio is 3dB, carrier frequency is 10.05MHz, symbol width is 1 μ s, code sequence is 13 Barker codes, code sequence is [1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1], sample frequency f _sfor 100MHz, sample length is 1300 points, and the simulation times under three kinds of situations is all 1000 times.From Fig. 5 (a), when Modulation Mode Recognition is correct and during without decoding error, the coefficient correlation of relevant cumulative mould value g (n) curve all concentrates near 1, decentralization is less; From Fig. 5 (c), when Modulation Mode Recognition is correct but while there is a decoding error, the value of coefficient correlation is slightly less than 1, and all more than 0.95; From Fig. 5 (b), when Modulation Mode Recognition mistake, the phase relation numerical value of relevant cumulative mould value g (n) curve is dispersed between 0.3 to 0.95.So, we can utilize relevant mould value g (n) the curve correlation coefficient feature that adds up to distinguish Modulation Mode Recognition correctly and two kinds of situations of Modulation Mode Recognition mistake, cannot effectively distinguish debud mode and identify situation correct but that exist a bit-errors to decode.

As shown in Figure 6, while there is a bit-errors decoding if Modulation Mode Recognition is correct, first use the starting point n between Wavelet Transform misjudgment area decoder _e0with stop n _e1, in decoded in error interval, relevant cumulative mould value g (n) curve approximation is a linear function, after Second Wavelet Transform, in starting point and stop place, obtains respectively minimum and maximum, can determine the position in decoded in error interval.

Referring to table 1, the performance of the blind result certificate authenticity of multiple bpsk signal is added up to the multiple bpsk signal of the sample sequence x (n) that supposes the observation signal that receives for being polluted by additive white Gaussian noise, carrier frequency 10.05MHz, symbol width 1 μ s, code sequence is 13 Barker codes, code sequence is [1,1,1,1,1,0,0,1,1,0,1,0,1], sample frequency f _s=100MHZ, sample length is 1300 points, simulation times 1000 times, level of significance α gets respectively 0.01,0.001 and 0.0001.If definition: H ₀for Modulation Mode Recognition is correct and without decoding error, H ₁be defined as Modulation Mode Recognition mistake or Modulation Mode Recognition correct but have a decoding error, in table, n ₀₀represent that reality is H ₀, be judged as H ₀number of times; n ₀₁represent actual H ₀, be judged to H ₁number of times; n ₁₀represent that reality is H ₁, be judged to H ₀number of times; n ₁₁represent that reality is H ₁, be judged to H ₁number of times; Two class error probability sums are P _e=(n ₁₀+ n ₀₁)/1000.

As can be seen from Table 1, within the scope of appropriate signal to noise ratio, thresholding is selected when suitable, can effectively to the credibility of the blind result of multiple bpsk signal, assess.When signal to noise ratio is more than or equal to 0dB, in 1000 emulation, recognizer Modulation Mode Recognition used all correct and parameter Estimation is more accurate, without decoding error, two class error probabilities of check algorithm approach 0; When signal to noise ratio at-1dB between-2dB time, in 1000 emulation, all 2 Modulation Mode Recognition mistakes or decoding error all detect, and two class error probabilities are 0; When signal to noise ratio at-3dB between-4dB time, in blind processing, the number of times of Modulation Mode Recognition mistake or decoding error increases along with the minimizing of signal to noise ratio, utilize the certificate authenticity algorithm that the present invention proposes the major part in this situation can be identified, for example: signal to noise ratio-4dB, level of significance α gets 0.01, for the result that has Modulation Mode Recognition mistake or decoding error for 76 times, this algorithm can identify wherein 74 times, error detection rate is greater than 97.3%, but simultaneously, along with the minimizing of signal to noise ratio, in check, two class error probabilities also increase to some extent; When be less than-5dB of signal to noise ratio, due to the performance of the multiple blind processing method of bpsk signal used variation sharply, thereby cause in 1000 emulation, the number of times of Modulation Mode Recognition mistake or decoding error further increases, now, the error detection rate of this check algorithm reaches more than 95.3%.Therefore, the credibility assessment method of the blind result of multiple bpsk signal based on coefficient correlation that the present invention proposes, compared with still carrying out Credibility Assessment effectively to the blind result of multiple bpsk signal under Low SNR, possesses good error detection distinguishing ability.

Table 1

Claims (1)

1. the credibility assessment method of the multiple blind result of bpsk signal, the multiple blind processing procedure of bpsk signal comprises Modulation Mode Recognition and decoding, it is characterized in that: adopt hypothesis test to assess the credibility of the blind result of multiple bpsk signal, establish and in finite observation time, treat that the multiple bpsk signal of blind processing is:

$s\left(t\right)={\mathrm{Ae}}^{j(2\mathrm{\&pi;}{f}_{0}t+\mathrm{\&theta;})}\underset{k=1}{\overset{N_c}{\mathrm{\&Sigma;}}}{e}^{\mathrm{j\&pi;}{c}_k}{\mathrm{\&Pi;}}_{T_c}(t-{\mathrm{kT}}_c),0\&le;t<T$

Wherein, T is observation time, and A is signal amplitude, f ₀for signal carrier frequency, the initial phase that θ is signal, N _cfor the code length of signal, T _cfor the symbol width of signal, c _kbe k code word, value is 0 or 1;

Respectively the carrier frequency of multiple bpsk signal, code word, code length and symbol width are carried out to parameter Estimation, the estimates of parameters obtaining is respectively

with

The superposeed sample sequence of observation signal of multiple bpsk signal of noise of foundation is:

$x\left(n\right)=s\left(n\right)+w\left(n\right)={\mathrm{Ae}}^{j(2\mathrm{\&pi;}{f}_0\mathrm{n\&Delta;t}+\mathrm{\&theta;})}\underset{k=1}{\overset{N_c}{\mathrm{\&Sigma;}}}{e}^{\mathrm{j\&pi;}{c}_k}{\mathrm{\&Pi;}}_{T_c}(\mathrm{n\&Delta;t}-k{T}_c)+w\left(n\right),0\&le;n<N-1$

Wherein, in the sampling interval that Δ t is signal, s (n) is the sampled signal of multiple bpsk signal, and w (n) is return-to-zero average limit band white Gaussian noise, and N is number of samples, and the signal to noise ratio of signal is SNR=A ²/ 2 σ ², σ ²for sample variance;

First, suppose that Modulation Mode Recognition is correct and without decoding error, the modulation system of identifying is BPSK, and does not have decoding error in blind processing procedure, credibility assessment method comprises the following steps:

Step 1, builds corresponding reference signal according to Modulation Mode Recognition result, and the relevant cumulative delivery of sample sequence with reference to signal to observation signal, obtains corresponding relevant cumulative mould value, and concrete steps are as follows:

(1-1) according to the reference signal of multiple bpsk signal structure, be:

$y_0\left(n\right)=e^{-j2\mathrm{\&pi;}{\hat{f}}_0\mathrm{n\&Delta;t}}\underset{k=1}{\overset{{\hat{N}}_c}{\mathrm{\&Sigma;}}}{e}^{-\mathrm{j\&pi;}{\hat{c}}_k}{\mathrm{\&Pi;}}_{{\hat{T}}_c}(\mathrm{n\&Delta;t}-k{\hat{T}}_c),0\&le;n\&le;N-1$

(1-2) with reference to signal y ₀(n) do relevant adding up to the sample sequence of observation signal, obtain relevant being accumulated as:

$z\left(n\right)=\underset{m=0}{\overset{n}{\mathrm{\&Sigma;}}}x\left(m\right)y_0\left(m\right)=s_0\left(n\right)+w_0\left(n\right),0\&le;n\&le;N-1$

Wherein, w ₀(n) be noise section, s ₀(n) be signal section,

$w_0\left(n\right)=\underset{m=0}{\overset{n}{\mathrm{\&Sigma;}}}w\left(m\right)y_0\left(m\right)$

$s_0\left(n\right)=\underset{m=0}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{Ae}}^{j(2\mathrm{\&pi;\&Delta;fn\&Delta;t}+\mathrm{\&theta;})}\underset{k=1}{\overset{{\hat{N}}_c}{\mathrm{\&Sigma;}}}{e}^{-\mathrm{j\&pi;}{\hat{c}}_k}{\mathrm{\&Pi;}}_{{\hat{T}}_c}[\mathrm{n\&Delta;t}-(k-1){\hat{T}}_c]\&CenterDot;\underset{k=1}{\overset{N_c}{\mathrm{\&Sigma;}}}{e}^{\mathrm{j\&pi;}{c}_k}{\mathrm{\&Pi;}}_{T_c}[\mathrm{n\&Delta;t}-(k-1)T_c]$

Wherein, for carrier frequency evaluated error, when the value of Δ f trends towards 0, the approximation that obtains signal section is:

s ₀(n)≈A(n+1)e ^{j(πnΔfΔt+θ)}

(1-3), to relevant cumulative delivery, the relevant cumulative mould value obtaining is:

g(n)＝|z(n)|=|s ₀(n)+w ₀(n)|≈A(n+1)+ω'(n)

Wherein, A (n+1) is the certainty component of g (n), and ω ' is (n) the equivalent noise component(s) of g (n);

Step 2, extracts coefficient correlation feature C to relevant cumulative mould value ₁, concrete steps are:

(2-1) calculating the relevant correlation coefficient r that adds up mould value is:

$r=\frac{\mathrm{\&Sigma;ng}\left(n\right)}{\sqrt{\mathrm{\&Sigma;}{n}^2\mathrm{\&Sigma;}{g}^2\left(n\right)}}$

(2-2) correlation coefficient r is obtained as nonlinear transformation:

$p=0.5\ln \frac{1+r}{1-r}$

By nonlinear transformation, the distribution of correlation coefficient r is transformed between (∞ ,+∞) between (1,1), p is similar to Normal Distribution;

(2-3) the normal state side-play amount that calculating correlation coefficient r is done after nonlinear transformation is:

$Z=\frac{p-{\mathrm{\&zeta;}}_0}{{\mathrm{\&sigma;}}_z}$

Wherein, ζ ₀=0.5ln (1+ ρ ₀)/(1-ρ ₀), ρ herein ₀=0.99, standard deviation

def (g (n)) is the degree of freedom;

(2-4) under level of significance α, 0.0001≤α≤0.01 herein, calculate threshold value and be:

Th＝-z _α

Wherein, z _αupper α quantile for standardized normal distribution, can obtain by query criteria gaussian distribution table, if Z < is Th, and coefficient correlation feature C ₁=1, otherwise C ₁=0;

Step 3, as coefficient correlation feature C ₁, in order further to determine in sampling interval whether have a bit-errors decoding, need to calculate coefficient correlation symbol consistency feature C at=1 o'clock ₂, concrete steps are:

(3-1) with starting point and terminal between Wavelet Transform misjudgment area decoder, the interval curve for relevant cumulative mould value g (n) of described decoded in error produces in decoded in error position to fracture and forms an interval forming with the starting point that fractures and terminal, establishing relevant Origin And Destination position of adding up mould value g (n) decoded in error interval and being respectively

with its sectional is expressed as:

$g\left(n\right)=\left\{\begin{array}{c}{g}_{c_0}\left(n\right),0\&le;n_{e_0}-1\\ g_e\left(n\right),n_{e_0}\&le;n\&le;n_{e_1}\\ g_{c_1}\left(n\right),n_{e_1}+1\&le;n\&le;N-1\end{array}\right.$

Wherein, g _e(n) data in corresponding decoded in error interval,

with

corresponding to the data outside decoded in error interval;

(3-2) in three intervals of relevant cumulative mould value, calculate respectively coefficient correlation separately, obtain r _i, i=1 wherein, 2,3;

(3-3) symbolic vector of calculating coefficient correlation is: $s_i=\left\{\begin{array}{c}1,r_i>0\\ 0,r_i=0\\ -1,r_i<0\end{array}\right.,$ I=1 wherein, 2,3;

If (3-4) symbolic vector S ₁, S ₂and S ₃symbol identical, C ₂=1, if symbolic vector S ₁, S ₂and S ₃symbol different, C ₂=0;

Step 4, check assessment result: if C ₁=1 and C ₂=1, Modulation Mode Recognition correctly and without decoding error, hypothesis is set up, and the multiple blind result of bpsk signal is credible; If C ₁=0, Modulation Mode Recognition mistake, hypothesis is false, and the multiple blind result of bpsk signal is insincere; If C ₁=1 and C ₂=0, Modulation Mode Recognition is correct but have decoding error, and hypothesis is set up, but the multiple blind result of bpsk signal is insincere.

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