CN101572563A - Method for capturing pseudocode under non-Gaussian channel - Google Patents

Abstract

The invention provides a method for capturing pseudocode under a non-Gaussian channel, which comprises the following steps: after being processed by the operations of carrier wave striping and pseudocode dispreading treatment, a received signal is converted into two observed quantities Xi<i> and Xi<Q>of two I/Q branches; after being processed by the operation of squaring, the two observed quantities are added to the quadratic term gamma<2 >of a dispersion coefficient, and the obtained result is respectively divided by the two observed quantities of the I/Q branches to obtain reciprocal values so that the value of statistical quantity of each branch at a single time can be obtained; the values from 1 to M time (the variable of i) are sequentially processed by the steps of accumulation addition and square; and finally, the values of the two branches are added to each other to obtain and compare the statistical quantity with the threshold so as to judge whether a signal is captured or not, and the phase position of the local pseudocode is slid to carry out the operations of secondary judgment and comparison until the signal is captured under the circumstance that the statistical quantity is lower than the threshold. Proved by the result of comparison of performance simulation of the pseudocode capturing method of the invention and the traditional pseudocode capturing method, the detection performance of the pseudocode capturing method of the invention is drastically improved under the non-Gaussian noise environment, and the more obvious the pulse characteristic is, the more obvious the advantage of the detector designed by the invention can be.

Description

Method for acquiring pseudo code under a kind of non-Gaussian channel

(1) technical field

What the present invention relates to is a kind of signal processing method, specifically a kind of method for acquiring pseudo code.

(2) background technology

Many spread spectrum system receivers all will be in the face of how under the additivity jamming pattern, extract the problem of small-signal, spread spectrum is widely used in the army and the people's Communications And Navigation field because of advantages such as its antijamming capability is strong, good confidentiality, the declines of energy anti-multipath.But these advantages have only when local pseudo-code with receive pseudo-code and just can obtain when synchronous.The stationary problem of pseudo-code is the basic problem of spread spectrum.Be divided into synchronously thick synchronously and synchronously smart, promptly signal catching and following the tracks of.Catch and be meant that local pseudo-code sequence is aligned in certain scope (usually in half-chip) with receiving pseudo-code, catching is the prerequisite of following the tracks of.Resistant DS Spread Spectrum System (Direct-SequenceSpread-Spectrum, DS/SS) the most frequently used acquiring pseudo code structure is quadratic sum detector (the Squared-Sum Detector of incoherent inphase/orthogonal correlator in, the SS detector), this is because the quadratic sum detector is the optimal detection mode of direct sequence signal under the independent Gaussian channel.But in fact, the hypothesis of observation noise independence Gaussian Profile is invalid often.The noise that exists in many actual channel, artificial impulse disturbances as atmospheric noise and other various radio systems introducings, the probability density function that all causes observation noise is non-Gaussian Profile, therefore, under complicated non-Gaussian noise model, the quadratic sum detector that independent Gaussian noise hypothesis obtains down can not guarantee to reach the best capture performance, thereby is necessary to study the best capture method of directly-enlarging system under the non-Gaussian noise.

(3) summary of the invention

The object of the present invention is to provide a kind of method for acquiring pseudo code under a kind of non-Gaussian channel of the detection performance that can increase substantially system under the non-Gaussian channel.

The object of the present invention is achieved like this:

Received signal peeled off to connect expand to handle with pseudo-code by carrier wave become inphase quadrature two branch road observed quantity X _i ^IAnd X _i ^Q, to after this two observed quantities square with the quadratic term γ of the coefficient of dispersion ²Addition, be divided by with inphase quadrature two branch road observed quantities respectively again and get inverse, obtain the statistics value of each branch road of single point in time, then to i=M value addition constantly again square to i=1, at last the value addition of two branch roads is finally obtained statistic and with thresholding relatively, judge whether to capture signal, if less than thresholding, the local pseudo-code phase of then sliding judges that again comparison is until capturing signal, wherein choosing of thresholding can be referring to [Huang Qian, Chen Huimin. a kind of adaptive threshold control algolithm [J] based on coherent detection. Shanghai University's journal, 2002, (1): 11-14.].

The described statistic that finally obtains is with the detection statistic T under the non-Gaussian noise environment _LO(X ^I, X ^Q), ignore the detection statistic of diagonal entry, further it is carried out conversion, the available detection statistic T that under the non-Gaussian noise environment, simplifies _SLO(X ^I, X ^Q).

Received signal is obtained the non-Gaussian noise that adopts symmetrical α steady-state distribution to describe on DS/SS system received signal model based under the non-Gaussian channel.

The present invention proposes a kind of acquiring pseudo code structure under the non-Gaussian noise environment, this structure can detect the small-signal that is submerged in the strong jamming, and this method is equivalent to the hypothesis testing problem.Non-Gaussian noise is modeled as symmetrical α steady-state distribution usually, not only obeys the broad sense central-limit theorem because this noise model distributes, and is to have more universal significance.People such as Nikas research point out symmetrical α steady-state distribution be the extraordinary model of atmospheric noise is described can be referring to [Jingmin Xin, Nanning Zheng and Sano, A., " Simple andEfficient Nonparametric Method for Estimating the Number of SignalsWithout Eigendecomposition; " Signal Processing, 2007, Vol.55, pp.1405-1420.].

According to the binary hypothesis test theory, can be described as two kinds of situations for the input problem, first kind is H ₁Situation be that signal occurs, second kind of situation is H ₀Promptly there is not signal.

H ₁：z(t)＝r(t，θ)+w(t)

H ₀：z(t)＝w(t)

Wherein z (t) comprises interference in the received signal, and w (t) is a non-Gaussian noise, the signal that need to detect be r (t, θ)=s (t) cos (ω t+ θ), $s\left(t\right)=\sqrt{2E}d(t-{\mathrm{\&tau;T}}_c)c(t-{\mathrm{\&tau;T}}_c),$ θ is that obedience is equally distributed in [0,2 π] scope, and E is for receiving single chip energy; D (t) is emission data, T _cBe symbol width; τ is relative T _cThe normalization time delay; $c\left(t\right)={\mathrm{\&Sigma;}}_{-\&infin;}^{\&infin;}{c}_i{p}_{T_c}(t-{\mathrm{iT}}_c),$ C wherein _i∈ 1 ,+1} is to be i chip in the pseudo-code sequence of L in the cycle,

For interval [0, T _c] on the unit rectangular pulse; ω is the received signal carrier frequency, extracts base band integration composition and can get according to dualism hypothesis:

H ₁：x _i＝s _i?cos?θ+n _xi

y _i＝s _i?sin?θ+n _yi

H ₀：x _i＝n _xi

y _i＝n _yi

X wherein _iAnd n _XiBe respectively the observed quantity and the noise of in-phase branch, y _iAnd n _YiBe respectively the observed quantity and the noise of quadrature branch.Like this (I, Q) joint probability density of pairwise orthogonal branch road is: $f_{\mathrm{nn}}(x,y)=\underset{i=1}{\overset{N}{\mathrm{\&Pi;}}}{f}_{\mathrm{nn}}(x_i,y_i),$ Classical etection theory is under the mistake alarm probability of minimum, calculates likelihood ratio and thresholding relatively, and its likelihood ratio form is as follows:

$\frac{\frac{1}{2\mathrm{\&pi;}}\&Integral;\underset{i=1}{\overset{M}{\mathrm{\&Pi;}}}{f}_{\mathrm{nn}}(x_i-s_i\cos \mathrm{\&theta;},y_i-s_i\sin \mathrm{\&theta;})\mathrm{d\&theta;}}{\underset{i=1}{\overset{M}{\mathrm{\&Pi;}}}{f}_{\mathrm{nn}}(x_i,y_i)}\begin{array}{c}>\\ <\end{array}r$

Suppose r for setting thresholding, if likelihood ratio greater than thresholding then detect signal, otherwise then do not have signal, under the situation of small-signal, the joint probability density of two branch road noises is carried out Taylor expansion and is obtained:

$f(h+\mathrm{\&Delta;h})=f\left(h\right)+\underset{i=1}{\overset{2M}{\mathrm{\&Sigma;}}}\frac{\mathrm{\&delta;f}}{{\mathrm{\&delta;h}}_i}{\mathrm{\&Delta;h}}_i+\frac{1}{2}\underset{i=1}{\overset{2M}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{2M}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&delta;}}^{2}f}{{\mathrm{\&delta;h}}_i\mathrm{\&delta;}{h}_k}-\mathrm{\&Delta;}{h}_i{\mathrm{\&Delta;h}}_k$

H wherein ^T=[x ₁X _N, y ₁Y _N], Δ h ^T=[s ₁Cos θ ... s _NCos θ, y ₁Sin θ ... y _NSin θ], following formula is applied in the formula of likelihood ratio and decision threshold comparison and can obtains:

$[1-\frac{\frac{1}{2\mathrm{\&pi;}}\underset{0}{\overset{2\mathrm{\&pi;}}{\&Integral;}}[\cos \mathrm{\&theta;}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{s}_i{\mathrm{\&delta;f}}_{\mathrm{nn}}(x,y)/{\mathrm{\&delta;x}}_i+\sin \mathrm{\&theta;}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{s}_i{\mathrm{\&delta;f}}_{\mathrm{nn}}(x,y)/{\mathrm{\&delta;y}}_i]\mathrm{d\&theta;}}{f_{\mathrm{nn}}(x,y)}+\frac{\frac{1}{2\mathrm{\&pi;}}\&Integral;{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20091007208200111.png,A20091007208200112.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&theta;}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{s}_i{s}_k{\mathrm{\&delta;}}^2{f}_{\mathrm{nn}}(x,y)/{\mathrm{\&delta;x}}_i{\mathrm{\&delta;x}}_k\mathrm{d\&theta;}}{{2f}_{\mathrm{nn}}(x,y)}$

$+\frac{\frac{1}{2\mathrm{\&pi;}}\&Integral;{\sin }^2\mathrm{\&theta;}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{s}_i{s}_k{\mathrm{\&delta;}}^2{f}_{\mathrm{nn}}(x,y)/{\mathrm{\&delta;y}}_i{\mathrm{\&delta;y}}_k\mathrm{d\&theta;}}{{2f}_{\mathrm{nn}}(x,y)}+\frac{\frac{1}{2\mathrm{\&pi;}}\&Integral;\sin \mathrm{\&theta;}\cos \mathrm{\&theta;}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{s}_i{s}_k{\mathrm{\&delta;}}^2{f}_{\mathrm{nn}}(x,y)/{\mathrm{\&delta;y}}_i{\mathrm{\&delta;y}}_k\mathrm{d\&theta;}}{2f_{\mathrm{nn}}(x,y)}]\begin{array}{c}<\\ >\end{array}r$

Because θ be obey equally distributed, so cos θ, three of sin θ and sin θ cos θ, by being zero can eliminate in [0,2 π] upper integral, can simplify as follows for the item that adds up of the mixed partial derivative of two branch road joint probability densities in the following formula:

$\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&delta;}}^2{f}_{\mathrm{nn}}(x_i,y_i)}{{\mathrm{\&delta;x}}_i{\mathrm{\&delta;x}}_k}=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{k=1,i\&NotEqual;k}{\overset{M}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&delta;f}}_{\mathrm{nn}}(x_i,y_i)}{{\mathrm{\&delta;x}}_i}\frac{{\mathrm{\&delta;f}}_{\mathrm{nn}}(x_i,y_i)}{{\mathrm{\&delta;x}}_k}+\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&delta;}}^2{f}_{\mathrm{nn}}(x_i,y_i)}{{\mathrm{\&delta;x}}_i^2}$

When the detection signal signal to noise ratio hour, therefore the 1/M of detection limit when the detection limit in the formula of likelihood ratio during i=j is i ≠ j can ignore the detection statistic of diagonal entry, further it is carried out conversion, can get:

${[1/M\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{s}_i\frac{{\mathrm{\&delta;f}}_{\mathrm{nn}}(x_i,y_i)/\mathrm{\&delta;x}}{f_{\mathrm{nn}}(x_i,y_i)}]}^2+{[1/M\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{s}_i\frac{{\mathrm{\&delta;f}}_{\mathrm{nn}}(x_i,y_i)/\mathrm{\&delta;y}}{f_{\mathrm{nn}}(x_i,y_i)}]}^2\begin{array}{c}>\\ <\end{array}r-1$

The present invention compares acquiring pseudo code detection statistic and the thresholding that obtains under the non-Gaussian noise environment, obtain pseudo-code two dimension arresting structure under the non-Gaussian noise model,, further it is simplified for reducing computational complexity, obtain following formula and provided its implementation structure, as shown in Figure 2.

(4) description of drawings

Conventional quadratic sum (SS) detection architecture of Fig. 1;

The non-Gauss's pseudo-code of Fig. 2 detection architecture figure;

The following three kinds of detector acquisition performances contrast of Fig. 3 non-Gaussian noise;

Two kinds of detectors of Fig. 4 detect the relation of performance and α value;

(5) embodiment

For example the present invention is done description in more detail below in conjunction with accompanying drawing:

Acquiring pseudo code structure of the present invention is referring to shown in the accompanying drawing 2, received signal peeled off (as module 1) and pseudo-code by carrier wave connect to expand and handle (as module 2) and become inphase quadrature two branch road observed quantity X _i ^IAnd X _i ^Q, to after this two observed quantities square with the quadratic term γ of the coefficient of dispersion ²Addition, be divided by with inphase quadrature two branch road observed quantities respectively again and get inverse, obtain the statistics value of each branch road of single point in time, then i=1 is arrived i=M value square addition more constantly, value addition with two branch roads at last finally obtains statistic (as module 31), and, judge whether to capture signal this statistic and thresholding comparison.The model of this structure is to be based upon under the non-Gaussian channel to obtain on the DS/SS system received signal model based, the present invention adopts symmetrical α steady-state distribution to describe non-Gaussian noise, it is the noise profile that has more universal significance of obedience broad sense central-limit theorem, and the α steady-state distribution is to describe the extraordinary model of atmospheric noise.

Structure of the present invention realizes that concrete steps are as follows:

The first step can be expressed as DS/SS system received signal model under the non-Gaussian channel:

$r\left(t\right)=\sqrt{2E}d(t-{\mathrm{\&tau;T}}_c)c(t-{\mathrm{\&tau;T}}_c)\cos ({\mathrm{\&omega;}}_{c}t+\mathrm{\&phi;})+w\left(t\right)$

In the formula: E is for receiving single chip energy; D (t) is without loss of generality for the emission data, and the hypothesis modulating data is always 1 (i.e., d (t)=1) in the literary composition; T _cBe symbol width; τ is relative T _cThe normalization time delay; $c\left(t\right)={\mathrm{\&Sigma;}}_{-\&infin;}^{\&infin;}{c}_i{p}_{T_c}(t-{\mathrm{iT}}_c),$ C wherein _i∈ 1 ,+1} is to be i chip in the pseudo-code sequence of L in the cycle,

For interval [0, T _c] on the unit rectangular pulse; ω _cBe the received signal carrier frequency; φ is the received signal carrier phase, φ [0,2 π) in obey evenly and distribute, w (t) is a non-Gaussian noise.Carrier wave strip module 1 in the application drawing 1 and pseudo-code despreading module 2 are handled and are obtained quadrature two branch road observed quantity X _i ^IAnd X _i ^Q, with acquiring pseudo code corresponding to the hypothesis testing problem.Module 3 is statistical decision modules, major function is compute statistics and relatively judges whether to capture signal with thresholding, if greater than thresholding, then is judged as and captures signal, if less than thresholding, the local pseudo-code phase of then sliding judges that again comparison is until capturing signal.The present invention is divided into module 31 and module 32 to module 3 under the non-Gaussian noise environment, proposed a kind of algorithm of new statistic, and obtained a kind of new acquiring pseudo code structure referring to accompanying drawing 2.

Second step corresponding to the hypothesis testing problem, utilized the first step to obtain observed quantity X acquiring pseudo code _i ^IAnd X _i ^Q, at H ₀And H ₁Adjudicate under the two states, wherein, $H_0:|\mathrm{\&tau;}-\widehat{\mathrm{\&tau;}}|\&GreaterEqual;1$ Correspondence is trapped state not; $H_1:|\mathrm{\&tau;}-\widehat{\mathrm{\&tau;}}|<1$ Corresponding trapped state.At H ₀And H ₁Situation under, the observed quantity of inphase quadrature two branch roads can be expressed as respectively:

$H_0:(X_i^I=W_i^I,X_i^Q=W_i^Q),i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;M$

$H_1:(X_i^I=\mathrm{\&theta;}\cos \mathrm{\&phi;}+W_i^I,X_i^Q=\mathrm{\&theta;}\sin \mathrm{\&phi;}+W_i^Q),i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,M$

Wherein $\mathrm{\&theta;}=\sqrt{E}$ Be signal strength parameter; { W _i ^I} _I=0 ^M{ W _i ^Q} _I=0 ^MBe respectively homophase and quadrature two branch road non-Gaussian noise sampled values.

The noise that the 3rd step was mentioned second step carries out modeling and calculates its joint probability density, wherein two branch road noise samples W ^I, W ^QBe modeled as symmetrical α stable state (S α S) and distribute, it is a kind ofly to have more the probability density distribution of universal significance than Gaussian Profile, can keep the characteristic of natural noise process, is a kind of model of very well describing non-Gaussian noise.Its two-dimensional probability density function can obtain by the inverse-Fourier transform of finding the solution its characteristic function:

$f_{\mathrm{\&alpha;},\mathrm{\&gamma;},{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_2}\left(x_1{x}_2\right)=\frac{1}{{\left(2\mathrm{\&pi;}\right)}^2}\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}\exp \left[i({\mathrm{\&beta;}}_1{\mathrm{\&omega;}}_1+{\mathrm{\&beta;}}_2{\mathrm{\&omega;}}_2\right)$

$-\mathrm{\&gamma;}{({\mathrm{\&omega;}}_1^2+{\mathrm{\&omega;}}_2^2)}^{-\frac{\mathrm{\&alpha;}}{2}}]e^{-i(x_1{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="A20091007208200111.png,A20091007208200112.png"\; state="\{\{state\}\}">w</figure-callout>}}_1+x_2{w}_2)}{\mathrm{d\&omega;}}_1{\mathrm{d\&omega;}}_2$

Wherein α is a characteristic index, and γ is the coefficient of dispersion, β ₁And β ₂Be symmetric parameter.The span of characteristic index α is 0＜α≤2, and the α value is more little, the corresponding hangover that distributes thick more, so pulse characteristic is obvious more.Coefficient of dispersion γ is the tolerance of sample with respect to the degree of scatter of average, is similar to the variance in the Gaussian Profile.Symmetric parameter β ₁, β ₂Be used for determining the symmetry characteristic of distribution, what the present invention adopted is symmetrical α steady-state distribution, so β ₁=β ₂=0.But, for the expression formula that except α=1 (Cauchy's distribution) and α=2 (Gaussian Profile) two kinds of situations, does not have sealing in its two-dimensional probability density function.

$f_{\mathrm{\&alpha;},\mathrm{\&gamma;}}(x_1,x_2)=\left\{\begin{array}{cc}\frac{\mathrm{\&gamma;}}{{2\mathrm{\&pi;}(x_1^2+x_2^2+{\mathrm{\&gamma;}}^2)}^{\frac{3}{2}}},& \mathrm{\&alpha;}=1\\ \frac{1}{4\mathrm{\&pi;\&gamma;}}\exp (-\frac{x_1^2+x_2^2}{4\mathrm{\&gamma;}}),& \mathrm{\&alpha;}=2\end{array}\right.$

The present invention pays attention to analyzing the situation of α=1 o'clock, and its hangover is thicker, and pulse characteristic is apparent in view, therefore more can reflect the probability density distribution characteristic that other S α S distributes objectively.

For given phase, the sample sequence of noise process has formed mutually independently random vector.2M sampled point { X on the quadrature in-phase branch then _i ^I, X _i ^Q} _I=1 ^MThe observed quantity joint probability density function be:

$f_{X^I,X^Q}(X^I,X^Q)=E_{\mathrm{\&phi;}}\left\{\underset{i=1}{\overset{M}{\mathrm{\&Pi;}}}{f}_{W^I,W^Q}(W_i^I,W_i^Q)\right\}$

Finally obtain the joint probability density of quadrature two branch roads, wherein: E _φFor φ peek term is hoped.

Module 31 among the 4th step Fig. 2 is the methods in the application invention content, obtains new statistic T _SLO(X ^I, X ^Q).The statistic that the etection theory of at first utilization routine obtains:

$\frac{\frac{1}{2\mathrm{\&pi;}}\&Integral;\underset{i}{\overset{M}{\mathrm{\&Pi;}}}{f}_{X^I,X^Q}(X_i^I-\mathrm{\&theta;}\cos \mathrm{\&phi;},X_i^Q-\mathrm{\&theta;}\sin \mathrm{\&phi;})\mathrm{d\&phi;}}{\underset{i}{\overset{M}{\mathrm{\&Pi;}}}{f}_{X^I,X^Q}(X_i^I,X_i^Q)}$

Then top statistic is carried out Taylor expansion, can obtain the detection statistic T under the non-Gaussian noise environment _LO(X ^I, X ^Q) with the expression formula of thresholding r:

$\left[\frac{1}{2}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\right\{\frac{1}{f_{W^I,W^Q}(X_i^I,X_i^Q)}\&times;\frac{{\&PartialD;}^2{f}_{W^I,W^Q}(X_i^I,X_i^Q)}{{\&PartialD;\left(X_i^I\right)}^2}+\frac{1}{f_{W^I,W^Q}(X_i^I,X_i^Q)}\&times;\frac{{\&PartialD;}^2{f}_{W^I,W^Q}(X_i^I,X_i^Q)}{{\&PartialD;\left(X_i^Q\right)}^2}\}$

$+\frac{1}{2}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{j\&NotEqual;i,j=1}{\overset{M}{\mathrm{\&Sigma;}}}\left\{\right(\frac{1}{f_{W^I,W^Q}(X_i^I,X_i^Q)}\&times;\frac{{\&PartialD;f}_{W^I,W^Q}(X_i^I,X_i^Q)}{\&PartialD;X_i^I})\&CenterDot;(\frac{1}{f_{W^I,W^Q}(X_j^I,X_j^Q)}\&times;\frac{\&PartialD;f_{W^I,W^Q}(X_j^I,X_j^Q)}{{\&PartialD;X}_j^I})$

$+(\frac{1}{f_{W^I,W^Q}(X_i^I,X_i^Q)}\&times;\frac{{\&PartialD;f}_{W^I,W^Q}(X_i^I,X_i^Q)}{\&PartialD;X_i^Q})\&CenterDot;(\frac{1}{f_{W^I,W^Q}(X_j^I,X_j^Q)}\&times;\frac{\&PartialD;f_{W^I,W^Q}(X_j^I,X_j^Q)}{{\&PartialD;X}_j^Q})\left\}\right]\begin{array}{c}>\\ <\end{array}r$

Clearer in order to allow following formula express, use $h\left(X_i^b\right)=\frac{1}{f_{W^I,W^Q}(X_i^I,X_i^Q)}\&times;\frac{{\&PartialD;}^2{f}_{W^I,W^Q}(X_i^I,X_i^Q)}{\&PartialD;{\left(X_i^b\right)}^2}$ With $g\left(X_i^b\right)=\frac{1}{f_{W^I,W^Q}(X_i^I,X_i^Q)}\&times;\frac{{\&PartialD;f}_{W^I,W^Q}(X_i^I,X_i^Q)}{{\&PartialD;X}_i^b}$ Express following formula, b={I wherein, Q}, then:

$T_{\mathrm{LO}}(X^I,X^Q)=\frac{1}{2}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\{h\left(X_i^I\right)+h\left(X_i^Q\right)\}+\frac{1}{2}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{j\&NotEqual;i,j=1}{\overset{M}{\mathrm{\&Sigma;}}}\{g\left(X_i^I\right)g\left(X_j^I\right)+g\left(X_i^Q\right)g\left(X_j^Q\right)\}$

When the detection signal signal to noise ratio hour, therefore the 1/M of detection limit when the detection limit in the following formula during i=j is i ≠ j can ignore the detection statistic of diagonal entry, obtains the detection statistic T under the non-Gaussian noise environment _LO(X ^I, X ^Q):

$T_{\mathrm{LO}}(X^I,X^Q)=\frac{1}{2}{\left\{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}g\left(X_i^I\right)\right\}}^2+{\left\{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}g\left(X_i^Q\right)\right\}}^2+\frac{1}{2}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\{h\left(X_i^I\right)+h\left(X_i^Q\right)-g^2\left(X_i^I\right)-g^2\left(X_i^Q\right)\}$

$\&ap;\frac{1}{2}{\left\{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}g\left(X_i^I\right)\right\}}^2+{\left\{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}g\left(X_i^Q\right)\right\}}^2=T_{\mathrm{SLO}}(X^I,X^Q)$

Closed loop expression formula situation α=1 at there being α=1 in the S α S noise profile can obtain acquiring pseudo code detection statistic under the S α S noise model.When α=1, will $g\left(X_i^b\right)=\frac{{3X}_i^b}{{\left(X_i^I\right)}^2+{\left(X_i^Q\right)}^2+{\mathrm{\&gamma;}}^2}$ Bring formula T into _SLO(X ^I, X ^Q) in, finally obtain statistic T _SLO(X ^I, X ^Q):

$T_{\mathrm{SLO}}(X^I,X^Q)=9[{\left(\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\frac{X_i^I}{{\left(X_i^I\right)}^2+{\left(X_i^Q\right)}^2+{\mathrm{\&gamma;}}^2}\right)}^2+{\left(\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\frac{X_i^Q}{{\left(X_i^I\right)}^2+{\left(X_i^Q\right)}^2+{\mathrm{\&gamma;}}^2}\right)}^2]$

The 5th step is as Fig. 2 module 32, the statistic T that the local optimum algorithm is calculated _SLO(X ^I, X ^Q) and relatively can get with thresholding r:

$[9[{\left(\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\frac{X_i^I}{{\left(X_i^I\right)}^2+{\left(X_i^Q\right)}^2+{\mathrm{\&gamma;}}^2}\right)}^2+{\left(\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\frac{X_i^Q}{{\left(X_i^I\right)}^2+{\left(X_i^Q\right)}^2+{\mathrm{\&gamma;}}^2}\right)}^2]\begin{array}{c}>\\ <\end{array}r$

By statistic and thresholding are relatively judged whether to capture signal, if greater than thresholding, then be judged as and capture signal, if less than thresholding, the local pseudo-code phase of then sliding judges that again comparison is until capturing signal.Fig. 2 has provided detector arrangement figure of the present invention under the non-Gaussian channel.

In sum, the present invention has invented a kind of acquiring pseudo code structure under the non-Gaussian noise environment.Carry out Taylor expansion by detection statistic to routine, obtained the two-dimentional local optimum grabber SLOD of direct sequence signal under the non-Gaussian noise, and under the situation of α=1, this PN Code Phase Acquisition is carried out emulation, by the relatively conventional quadratic sum arresting structure of emulation and the performance of acquiring pseudo code structure of the present invention.

Adopt Meng Te-Carlow method that various different detector pseudo-codes are detected performance and carried out Computer Simulation, for sake of convenience, various different detectors are defined as follows: the quadratic sum detector that the SSD representative is traditional; SLOD represents acquiring pseudo code structure of the present invention.The pseudo-code employing sign indicating number cycle is 1023 m sequence in the emulation, and its primitive polynomial is 1+z ³+ z ¹⁰,, get M=50 for shortening simulation time.Detection threshold is P by the false alarm probability perseverance among Fig. 3 and Fig. 4 _Fa=10 ^-2Obtain, each simulated point independence simulation times gets 10 ⁶Inferior, the error that makes the gained detection probability is less than 1%.Advantage through comparative analysis PN Code Phase Acquisition of the present invention is as follows:

1. Fig. 3 has provided the relation curve of this two kinds of detectors acquisition probability and signal to noise ratio (snr) under the non-Gaussian noise environment, from figure, can find, in α=1 and α=1.5 o'clock, increase along with signal to noise ratio (snr), the corresponding increase of the acquisition probability of SLOD, and traditional SSD acquisition probability is very low, and remains unchanged substantially.

2. Fig. 4 has provided the relation of two kinds of detector acquisition performances and α value.From figure, can find, for most α values, the designed SLOD detector performance of the present invention is better than SSD, the α value is more little to be that pulse characteristic is obvious more, and the designed detector advantage of the present invention is obvious more, along with the increase of α value, the detection performance of SLOD decreases, when α approaches 2, when promptly ambient noise approached Gaussian Profile, traditional SSD detector detected performance and just is better than the designed SLOD detector of the present invention.

The acquiring pseudo code structure that the present invention proposes and traditional acquiring pseudo code structure have been carried out performance comparison such as Fig. 3 and Fig. 4, under the non-Gaussian noise environment, the designed more traditional quadratic sum detector detection performance of detector of the present invention has raising by a relatively large margin by comparative analysis.

Claims (3)

1, the method for acquiring pseudo code under a kind of non-Gaussian channel, comprise a carrier wave strip module, pseudo-code despreading module and statistical decision module, wherein the statistical decision module comprises a statistical module and a judging module, it is characterized in that: with the received signal of spread spectrum system receiver by carrier wave peel off handle with the pseudo-code despreading after, become inphase quadrature two branch road observed quantity X _i ^IAnd X _i ^Q, input is in statistical module, to two branch road observed quantity X _i ^IAnd X _i ^QAfter carrying out square with the quadratic term γ of the coefficient of dispersion ²Addition, be divided by with inphase quadrature two branch road observed quantities respectively again and get inverse, obtain the statistics value of each branch road of single point in time, then the statistics value of two branch roads being carried out quadratic sum handles and obtains statistic, in the input judging module, statistic and thresholding are compared, judge whether to capture signal, if less than thresholding, the local pseudo-code phase of then sliding judges that again comparison is until capturing signal.

2, the method for acquiring pseudo code under a kind of non-Gaussian channel according to claim 1, it is characterized in that: described received signal is obtaining on the DS/SS system received signal model based under the non-Gaussian channel, and adopts symmetrical α steady-state distribution to describe non-Gaussian noise.

3, the method for acquiring pseudo code under a kind of non-Gaussian channel according to claim 1, it is characterized in that: described statistical module is with the detection statistic under the non-Gaussian noise environment, the detection statistic of ignoring diagonal entry, further it is carried out conversion, obtain the detection statistic of under the non-Gaussian noise environment, simplifying.

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