CN103607370B - A kind of credibility assessment method of the multiple blind result of bpsk signal - Google Patents

Abstract

The present invention proposes the credibility assessment method of a kind of multiple blind result of bpsk signal, the method is when no signal priori, first according to the signal model structure reference signal that Modulation Mode Recognition result is corresponding, analyzing on the basis of reference signal cumulative modulus value curve characteristic relevant to the sample sequence of observation signal, according to correlation coefficient and correlation coefficient symbol concordance feature, the credibility of the blind result of multiple bpsk signal is judged.The method that the present invention proposes is under relatively Low SNR, it may be achieved the certificate authenticity to the blind result of multiple bpsk signal, and without the prior information of signal.

Description

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

Technical field

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

Background technology

Under lacking signal prior information and Low SNR, the sample sequence of observation signal is detected, Modulation Identification and parameter estimation, it is electronic reconnaissance and cognitive radio signal (CR, CognitiveRadio) process the important step of front end, directly affect the process performance of follow-up signal processing links.In electronic reconnaissance, the subsequent treatment links such as the sorting of signal, location and tracking, interference and individual Radar recognition will be produced impact by front end signal result.In cognitive radio, reliable front end frequency spectrum perception, result of spectrum analysis are the premise effectively run of the follow-up cognitive link such as frequency spectrum judging, spectrum management and basis.But when non-cooperating, the Modulation Identification of sample sequence of observation signal, parameter estimation etc. can only be carried out blind process.But, whether correct effective appraisal procedure for blind result, believable be less.

The blind processing procedure of multiple bpsk signal includes the link such as Modulation Mode Recognition and decoding.Obviously, the premise 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 the credibility assessment method of a kind of effective blind result of bpsk signal again, it is achieved the blind result of multiple bpsk signal is carried out Credibility Assessment.

In order to solve the problems referred to above, the invention provides the credibility assessment method of a kind of multiple blind result of bpsk signal, the multiple blind processing procedure of bpsk signal includes Modulation Mode Recognition and decoding, adopt hypothesis testing method that the credibility of the blind result of multiple bpsk signal is estimated, if treating in finite observation time that the multiple bpsk signal of blind process is:

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

Wherein, T is observation time, and A is signal amplitude, f₀For signal carrier frequency, θ is the initial phase of signal, N_cFor the code length of signal, T_cFor the symbol width of signal, c_kFor kth code word, value is 0 or 1；

Respectively the carrier frequency of multiple bpsk signal, code word, code length and symbol width being carried out parameter estimation, the estimates of parameters obtained is respectivelyWith

The sample sequence of the observation signal setting up the multiple bpsk signal of superposition noise is:

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

Wherein, Δ t is the sampling interval of signal, and s (n) is the sampled signal of multiple bpsk signal, and w (n) limits band white Gaussian noise for return-to-zero average, and N is number of samples, and the signal to noise ratio of signal is SNR=A²/2σ², σ²For sample variance；

First, it is assumed that Modulation Mode Recognition is correct and without decoding error, the modulation system namely identified in blind processing procedure is BPSK, and is absent from decoding error, then credibility assessment method comprises the following steps:

Step 1, builds corresponding reference signal according to the Modulation Mode Recognition result assumed, Reference Signal cumulative delivery relevant to the sample sequence of observation signal, obtains corresponding relevant cumulative modulus value, specifically comprises the following steps that

(1-1) reference signal according to multiple bpsk signal structure is:

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

(1-2) Reference Signal y₀N () is made relevant cumulative to the sample sequence of observation signal, obtain relevant being accumulated as:

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

Wherein, w₀N () is noise section, s₀N () is signal section,

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

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

Wherein,For carrier frequency estimation difference, when the value of Δ f trends towards 0, the approximation obtaining signal section is:

s₀(n)≈A(n+1)e^{j(πnΔfΔt+θ)}

(1-3) to relevant cumulative delivery, the relevant cumulative modulus value obtained is:

G (n)=| z (n) |=| s₀(n)+w₀(n)|≈A(n+1)+ω'(n)

Wherein, the definitiveness component that A (n+1) is g (n), the noise component(s) of the equivalence that ω ' (n) is g (n)；

Step 2, extracts correlation coefficient eigenvalue C to relevant cumulative modulus value₁, concretely comprise the following steps:

(2-1) correlation coefficient r calculating relevant cumulative modulus 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:

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

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

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

Wherein,ρ herein₀=0.99, standard deviationDef (g (n)) is degree of freedom；

(2-4) under level of significance α, 0.0001≤α≤0.01 herein, calculating threshold value is:

Th=-z_α

Wherein, z_αFor the upper α quantile of standard normal distribution, can be obtained by query criteria gaussian distribution table, if Z < Th, then correlation coefficient eigenvalue C₁=1, otherwise C₁=0；

Step 3, as correlation coefficient eigenvalue C₁When=1, whether there is a bit-errors decoding in sampling interval to further determine that, it is necessary to calculate correlation coefficient symbol concordance feature C₂, concretely comprise the following steps:

(3-1) estimate, by Wavelet Transform, the beginning and end that decoded in error is interval, described decoded in error interval is that the curve of relevant cumulative modulus value g (n) produces in decoded in error position to fracture and form an interval constituted with the beginning and end fractureed, if the Origin And Destination position in relevant cumulative modulus value g (n) decoded in error interval is respectivelyWithThen its sectional is expressed as:

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

Wherein, g_eData in (n) corresponding decoded in error interval,WithCorresponding to the data outside decoded in error interval；

(3-2) in three intervals of relevant cumulative modulus value, calculate respective correlation coefficient respectively, obtain r_i, wherein i=1,2,3；

(3-3) symbolic vector calculating correlation coefficient is:Wherein i=1,2,3；

If (3-4) symbolic vector S₁、S₂And S₃Symbol identical, then C₂=1, if symbolic vector S₁、S₂And S₃Symbol different, then C₂=0；

Step 4, checks assessment result: if C₁=1 and C₂=1, then Modulation Mode Recognition is correct and without decoding error, it assumes that setting up, the multiple blind result of bpsk signal is credible；If C₁=0, then Modulation Mode Recognition mistake, it assumes that be false, the multiple blind result of bpsk signal is insincere；If C₁=1 and C₂=0, then correctly but there is decoding error in Modulation Mode Recognition, it assumes that is false, and the multiple blind result of bpsk signal is insincere.

Adopt correlation coefficient eigenvalue C1 and correlation coefficient symbol concordance feature C₂Judge the credibility of the blind result of multiple bpsk signal, work as C₁When=0, the Modulation Mode Recognition mistake of signal, then answer the blind result of bpsk signal insincere；Work as C₁When=1, the Modulation Mode Recognition of signal is correct, moreover it is possible to further determine whether there is decoding error, works as C₁=1 and C₂When=1, the Modulation Mode Recognition of signal is correct and without decoding error, then answer the blind result of bpsk signal credible；Work as C₁=1 and C₂But when=0, correctly there is decoding error in the Modulation Mode Recognition of signal, then answer the blind result of bpsk signal insincere.

The beneficial effects of the present invention is: the blind result of multiple bpsk signal can be carried out effective Credibility Assessment, effectively tell that Modulation Mode Recognition mistake, Modulation Mode Recognition be correct but decoding error and Modulation Mode Recognition is correct and without decoding error these three situation, thus to should determine that whether the blind result of multiple bpsk signal credible.

Accompanying drawing explanation

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

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

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

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

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

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

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

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

Detailed description of the invention

As shown in Figure 1, the invention provides the credibility assessment method of a kind of multiple blind result of bpsk signal, the multiple blind processing procedure of bpsk signal includes Modulation Mode Recognition and decoding, adopt hypothesis testing method that the credibility of the blind result of multiple bpsk signal is estimated, if treating in finite observation time that the multiple bpsk signal of blind process is:

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

Wherein, T is observation time, and A is signal amplitude, f₀For signal carrier frequency, θ is the initial phase of signal, N_cFor the code length of signal, T_cFor the symbol width of signal, c_kFor kth code word, value is 0 or 1；

Respectively the carrier frequency of multiple bpsk signal, code word, code length and symbol width being carried out parameter estimation, the estimates of parameters obtained is respectivelyWith

The sample sequence of the observation signal setting up the multiple bpsk signal of superposition noise is:

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

Wherein, Δ t is the sampling interval of signal, and s (n) is the sampled signal of multiple bpsk signal, and w (n) limits band white Gaussian noise for return-to-zero average, and N is number of samples, and the signal to noise ratio of signal is SNR=A²/2σ², σ²For sample variance；

First, it is assumed that Modulation Mode Recognition is correct and without decoding error, the modulation system namely identified in blind processing procedure is BPSK, and is absent from decoding error, then credibility assessment method comprises the following steps:

Step 1, builds corresponding reference signal according to the Modulation Mode Recognition result assumed, Reference Signal cumulative delivery relevant to the sample sequence of observation signal, obtains corresponding relevant cumulative modulus value, specifically comprises the following steps that

(1-1) reference signal according to multiple bpsk signal structure is:

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

(1-2) Reference Signal y₀N () is made relevant cumulative to the sample sequence of observation signal, obtain relevant being accumulated as:

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

Wherein, w₀N () is noise section, s₀N () is signal section,

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

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

Wherein,For carrier frequency estimation difference, when the value of Δ f trends towards 0, the approximation obtaining signal section is:

s₀(n)≈A(n+1)e^{j(πnΔfΔt+θ)}

(1-3) to relevant cumulative delivery, the relevant cumulative modulus value obtained is:

G (n)=| z (n) |=| s₀(n)+w₀(n)|≈A(n+1)+ω'(n)

Wherein, the definitiveness component that A (n+1) is g (n), the noise component(s) of the equivalence that ω ' (n) is g (n)；

Step 2, extracts correlation coefficient eigenvalue C to relevant cumulative modulus value₁, concretely comprise the following steps:

(2-1) correlation coefficient r calculating relevant cumulative modulus 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:

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

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

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

Wherein,ρ herein₀=0.99, standard deviationDef (g (n)) is degree of freedom；

(2-4) under level of significance α, 0.0001≤α≤0.01 herein, calculating threshold value is:

Th=-z_α

Wherein, z_αFor the upper α quantile of standard normal distribution, can be obtained by query criteria gaussian distribution table, if Z < Th, then correlation coefficient eigenvalue C₁=1, otherwise C₁=0；

Step 3, as correlation coefficient eigenvalue C₁When=1, whether there is a bit-errors decoding in sampling interval to further determine that, it is necessary to calculate correlation coefficient symbol concordance feature C₂, concretely comprise the following steps:

(3-1) estimate, by Wavelet Transform, the beginning and end that decoded in error is interval, described decoded in error interval is that the curve of relevant cumulative modulus value g (n) produces in decoded in error position to fracture and form an interval constituted with the beginning and end fractureed, if the Origin And Destination position in relevant cumulative modulus value g (n) decoded in error interval is respectivelyWithThen its sectional is expressed as:

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

Wherein, g_eData in (n) corresponding decoded in error interval,WithCorresponding to the data outside decoded in error interval；

(3-2) in three intervals of relevant cumulative modulus value, calculate respective correlation coefficient respectively, obtain r_i, wherein i=1,2,3；

(3-3) symbolic vector calculating correlation coefficient is:Wherein i=1,2,3；

If (3-4) symbolic vector S₁、S₂And S₃Symbol identical, then C₂=1, if symbolic vector S₁、S₂And S₃Symbol different, then C₂=0；

Step 4, checks assessment result: if C₁=1 and C₂=1, then Modulation Mode Recognition is correct and without decoding error, it assumes that setting up, the multiple blind result of bpsk signal is credible；If C₁=0, then Modulation Mode Recognition mistake, it assumes that be false, the multiple blind result of bpsk signal is insincere；If C₁=1 and C₂=0, then correctly but there is decoding error in Modulation Mode Recognition, it assumes that is false, and the multiple blind result of bpsk signal is insincere.

As shown in Figure 2, when the blind result of multiple bpsk signal is that Modulation Mode Recognition is correct and when being absent from decoding error, when calculating relevant cumulative modulus value g (n), if the value of carrier frequency estimation difference Δ f trends towards 0, then the approximation that can obtain g (n) is:

G (n)=| z (n) |=| s₀(n)+w₀(n)|≈A(n+1)+ω'(n)

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

As it is shown on figure 3, when multiple bpsk signal bandwidth is less or signal is disturbed when being distorted, the blind result of multiple bpsk signal is likely Modulation Mode Recognition mistake, is likely judged to normal signal or other signal at receiving terminal.Assuming the Modulation Mode Recognition mistake of multiple bpsk signal, namely answer bpsk signal and missed knowledge for other signals, if knowing is normal signal by mistake, then in like manner can construct reference signal according to normal signal is:

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

Reference Signal y again₁N () is made relevant cumulative to the sample sequence of observation signal, obtain relevant being accumulated as:

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

Wherein, w₁N () is noise section, s₁N () is signal section,

Wherein,For phase error function,

Again to relevant cumulative delivery, the relevant cumulative modulus value obtained is:

G (n)=| z (n) |=| s₁(n)+w₁(n)|。

Due to signal model mismatch and phase error functionExistence, cause that the reference signal of structure carries out relevant cumulative modulus value g (n) curve not linearly to original signal, namely add up modulus value g (n) the correlation coefficient eigenvalue C extracted by being correlated with₁=0.

As shown in Figure 4, when Modulation Mode Recognition is correct, but the parameter estimating error of multiple bpsk signal is bigger, it is possible to because the accumulation of carrier frequency estimation difference or symbol width estimation difference is bigger, or because the reason such as the estimation of code element figure place is wrong, decoding error will be caused.If there being a bit-errors decoding, then at symbol decoding errors present, generation is fractureed by the curve of relevant cumulative modulus value g (n), formation decoded in error is interval, and the curve that this decoded in error interval is relevant cumulative modulus value g (n) produces to fracture in decoded in error position and forms an interval constituted with the beginning and end fractureed.Now, relevant cumulative modulus value g (n) curve by the different rectilinear(-al) of several slopes, and the data in decoded in error interval carry out slope that linear regression obtains with decoded in error interval outside data to carry out the slope sign that linear regression obtains contrary.

nullSuch as Fig. 5 (a)、Shown in 5 (b) and 5 (c)，Correct for Modulation Mode Recognition and relevant cumulative modulus value g (n) curve correlation coefficient during without decoding error the emulation statistic histogram of Fig. 5 (a)，The emulation statistic histogram of the correlation coefficient of relevant cumulative modulus value g (n) curve when Fig. 5 (b) is for Modulation Mode Recognition mistake，Fig. 5 (c) for Modulation Mode Recognition is correct but the emulation statistic histogram of correlation coefficient of relevant cumulative modulus value g (n) curve when there is a decoding error，The simulated conditions adopted is: sample sequence model x (n) assuming observation signal is the multiple bpsk signal 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 without decoding error, the correlation coefficient of relevant cumulative modulus value g (n) curve all concentrates near 1, and dispersion is less；From Fig. 5 (c), when Modulation Mode Recognition is correct but when there is a decoding error, the value of correlation coefficient is slightly less than 1, and all more than 0.95；From Fig. 5 (b), when Modulation Mode Recognition mistake, the correlation coefficient value of relevant cumulative modulus value g (n) curve is dispersed between 0.3 to 0.95.Then, we can utilize relevant cumulative modulus value g (n) curve correlation coefficient feature correct in two kinds of situations of Modulation Mode Recognition mistake to distinguish Modulation Mode Recognition, but it is correct but there is the situation that a bit-errors decodes effectively to distinguish debud mode identification.

As shown in Figure 6, when if Modulation Mode Recognition is correct but existence one bit-errors decodes, first estimate, by Wavelet Transform, the starting point n that decoded in error is interval_e0With stop n_e1, in decoded in error interval, relevant cumulative modulus value g (n) curve approximation is a linear function, after Second Wavelet Transform, obtains minimum and maximum respectively in starting point and stop place, it may be determined that the position that decoded in error is interval.

Referring to table 1, the performance of the blind result certificate authenticity of multiple bpsk signal is added up, it is assumed that sample sequence x (n) of the observation signal received is the multiple bpsk signal polluted by additive white Gaussian noise, carrier frequency 10.05MHz, symbol width 1 μ s, code sequence is 13 Barker codes, and code sequence is [1,1,1,1,1,0,0,1,1,0,1,0,1], sample frequency f_s=100MH_Z, sample length is 1300 points, and simulation times 1000 times, level of significance α takes 0.01,0.001 and 0.0001 respectively.If definition: H₀Correct for Modulation Mode Recognition and without decoding error, H₁Be defined as Modulation Mode Recognition mistake or Modulation Mode Recognition correctly but exists a decoding error, then in table, n₀₀Represent that reality is H₀, it is judged that for H₀Number of times；n₀₁Represent actual H₀, it is judged to H₁Number of times；n₁₀Represent that reality is H₁, it is judged to H₀Number of times；n₁₁Represent that reality is H₁, it is judged to H₁Number of times；Two type error probabilities sum is P_e=(n₁₀+n₀₁)/1000。

As can be seen from Table 1, in appropriateness SNR ranges, when thresholding selects suitable, can effectively the credibility of the blind result of multiple bpsk signal be estimated.When signal to noise ratio is be more than or equal to 0dB, in 1000 emulation, recognizer Modulation Mode Recognition used is all correct and parameter estimation is calibrated, without decoding error, and the two type error probabilities of check algorithm is close to 0；When signal to noise ratio is between-1dB to-2dB, in 1000 emulation, all 2 Modulation Mode Recognition mistakes or decoding error all detect, and two type error probabilities is 0；When signal to noise ratio is between-3dB to-4dB, in blind process, the number of times of Modulation Mode Recognition mistake or decoding error increases along with the minimizing of signal to noise ratio, the certificate authenticity algorithm that the present invention proposes is utilized the major part in this situation to be identified, such as: signal to noise ratio-4dB, level of significance α takes 0.01, for there is the result of Modulation Mode Recognition mistake or decoding error for 76 times, 74 times therein can be identified by this algorithm, error detection rate is more than 97.3%, but simultaneously, along with the minimizing of signal to noise ratio, in inspection, two type error probabilities also increases to some extent；When signal to noise ratio is less than-5dB, owing to the performance of the multiple blind processing method of bpsk signal used is sharply deteriorated, thus causing that in 1000 emulation, the number of times of Modulation Mode Recognition mistake or decoding error increases further, 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 correlation coefficient that the present invention proposes, still the blind result of multiple bpsk signal being carried out Credibility Assessment effectively compared with under Low SNR, possess 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 includes Modulation Mode Recognition and decoding, it is characterized in that: adopt hypothesis testing method that the credibility of the blind result of multiple bpsk signal is estimated, if treating in finite observation time that the multiple bpsk signal of blind process is:

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

Wherein, T is observation time, and A is signal amplitude, f₀For signal carrier frequency, θ is the initial phase of signal, N_cFor the code length of signal, T_cFor the symbol width of signal, c_kFor kth code word, value is 0 or 1；

Respectively the carrier frequency of multiple bpsk signal, code word, code length and symbol width being carried out parameter estimation, the estimates of parameters obtained is respectivelyWith

The sample sequence of the observation signal setting up the multiple bpsk signal of superposition noise is:

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

Wherein, Δ t is the sampling interval of signal, and s (n) is the sampled signal of multiple bpsk signal, and w (n) limits band white Gaussian noise for return-to-zero average, and N is number of samples, and the signal to noise ratio of signal is SNR=A²/2σ², σ²For sample variance；

First, it is assumed that Modulation Mode Recognition is correct and without decoding error, the modulation system namely identified in blind processing procedure is BPSK, and is absent from decoding error, then credibility assessment method comprises the following steps:

Step 1, builds corresponding reference signal according to Modulation Mode Recognition result, Reference Signal cumulative delivery relevant to the sample sequence of observation signal, obtains corresponding relevant cumulative modulus value, specifically comprises the following steps that

(1-1) reference signal according to multiple bpsk signal structure is:

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

(1-2) Reference Signal y₀N () is made relevant cumulative 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, w₀N () is noise section, s₀N () is signal section,

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

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

Wherein,For carrier frequency estimation difference, when the value of Δ f trends towards 0, the approximation obtaining signal section is:

s₀(n)≈A(n+1)e^{j(πnΔfΔt+θ)}

(1-3) to relevant cumulative delivery, the relevant cumulative modulus value obtained is:

G (n)=| z (n) |=| s₀(n)+w₀(n)|≈A(n+1)+ω'(n)

Wherein, the definitiveness component that A (n+1) is g (n), the noise component(s) of the equivalence that ω ' (n) is g (n)；

Step 2, extracts correlation coefficient eigenvalue C to relevant cumulative modulus value₁, concretely comprise the following steps:

(2-1) correlation coefficient r calculating relevant cumulative modulus 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:

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

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

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

Wherein,ρ herein₀=0.99, standard deviationDef (g (n)) is degree of freedom；

(2-4) under level of significance α, 0.0001≤α≤0.01 herein, calculating threshold value is:

Th=-z_α

Wherein, z_αFor the upper α quantile of standard normal distribution, can be obtained by query criteria gaussian distribution table, if Z < Th, then correlation coefficient eigenvalue C₁=1, otherwise C₁=0；

Step 3, as correlation coefficient eigenvalue C₁When=1, whether there is a bit-errors decoding in sampling interval to further determine that, it is necessary to calculate correlation coefficient symbol concordance feature C₂, concretely comprise the following steps:

(3-1) estimate, by Wavelet Transform, the beginning and end that decoded in error is interval, described decoded in error interval is that the curve of relevant cumulative modulus value g (n) produces in decoded in error position to fracture and form an interval constituted with the beginning and end fractureed, if the Origin And Destination position in relevant cumulative modulus value g (n) decoded in error interval is respectivelyWithThen its sectional is expressed as:

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

Wherein, g_eData in (n) corresponding decoded in error interval,WithCorresponding to the data outside decoded in error interval；

(3-2) in three intervals of relevant cumulative modulus value, calculate respective correlation coefficient respectively, obtain r_i, wherein i=1,2,3；

(3-3) symbolic vector calculating correlation coefficient is:Wherein i=1,2,3；

If (3-4) symbolic vector S₁、S₂And S₃Symbol identical, then C₂=1, if symbolic vector S₁、S₂And S₃Symbol different, then C₂=0；

Step 4, checks assessment result: if C₁=1 and C₂=1, then Modulation Mode Recognition is correct and without decoding error, it assumes that setting up, the multiple blind result of bpsk signal is credible；If C₁=0, then Modulation Mode Recognition mistake, it assumes that be false, the multiple blind result of bpsk signal is insincere；If C₁=1 and C₂=0, then correctly but there is decoding error in Modulation Mode Recognition, it assumes that is false, and the multiple blind result of bpsk signal is insincere.