CN101572564B - Locally optimal detector based method for capturing pseudocode under weakly dependent non-Gaussian environment - Google Patents

Abstract

The invention provides a locally optimal detector based method for capturing pseudocode under weakly dependent non-Gaussian environment, which comprises the following steps: a received signal passes through I/Q branches and is processed by the operations of carrier wave striping and pseudocode dispreading treatment to obtain the observed quantities Xi<i> and Xi<Q>; the statistical quantity obtained by calculating the joint probability density of the observed quantities of the two branches by the locally optimal algorithm is compared with the captured decision threshold so as to judge whether aDS signal is captured or not; under the circumstance that the statistical quantity is higher than the threshold, the signal is judged to be captured; and under the circumstance that the statistical quantity is lower than the threshold, the phase position of the local pseudocode is slid so as to repeat the operations of judgment and comparison until the signal is captured. Proved by the result ofcomparison 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 weakly dependent non-Gaussian noise environment, and the more obvious the non-Gaussian noise pulse characteristic is, the more outstanding the advantage of the designed detector can be.

Description

Under the weakly dependent non-Gaussian environment based on the method for acquiring pseudo code of locally optimal detector

(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, but, good confidentiality strong because of its antijamming capability of spread spectrum system, can the anti-multipath decline etc. advantage be widely used in the army and the people's Communications And Navigation field.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.In fact because the hypothesis of observation noise independence Gaussian Profile is invalid often.At first, the noise that exists in many actual channel, as the artificial impulse disturbances that the various radio systems of atmospheric noise and other are introduced, the probability density function that all causes observation noise is non-Gaussian Profile.Secondly, in the modern digital signal processing, because sampling rate is more and more higher, the noise contribution that is contained in the sampled value is no longer separate, but has certain correlation, needs to adopt correlated noise that it is carried out modeling.Therefore, under above-mentioned complicated dependent non-Gaussian noise model, the quadratic sum detector that general independent Gaussian noise hypothesis obtains down can not guarantee to reach the best capture performance, thereby is necessary to study the best capture structure of directly-enlarging system under the weakly dependent non-Gaussian noise.

Existing acquiring pseudo code structure brief analysis:

Resistant DS Spread Spectrum System (Direct-Sequence Spread-Spectrum, DS/SS) in the most frequently used acquiring pseudo code structure be the quadratic sum detector (Squared-SumDetector, SS detector) of incoherent inphase/orthogonal correlator, as shown in Figure 1.This is because the quadratic sum detector is the optimal detection mode of direct sequence signal under the independent Gaussian channel.Shortcoming: when this detector applies detected useful signal under non-Gaussian channel, performance can sharply descend.

(3) summary of the invention

The object of the present invention is to provide under a kind of weakly dependent non-Gaussian environment of the detection performance that can increase substantially system method for acquiring pseudo code based on locally optimal detector.

The object of the present invention is achieved like this:

At the acquiring pseudo code problem under the weakly dependent non-Gaussian channel, the present invention proposes a kind of acquiring pseudo code structure, and this method is equivalent to the hypothesis testing problem based on the local optimum detection statistic.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 [G.Samorodnitsky and M.S.Taqqu, Stable Non-GaussianRandom Processes:Stochastic Models with Infinite Variance.New York:Chapman﹠amp; Hall, 1994.].

DS/SS system received signal model can be expressed as under the weakly dependent non-Gaussian channel:

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

Wherein E receives single chip energy, and d (t) is without loss of generality for the emission data, supposes that modulating data is always 1, T _cBe symbol width, τ is relative T _cThe normalization time delay, $c\left(t\right)={\mathrm{\&Sigma;}}_{-\&infin;}^{\&infin;}{c}_i{p}_{T_c}(t-{\mathrm{iT}}_c),$

Be interval [0, T _c] on the unit rectangular pulse, ω _cBe the received signal carrier frequency, φ is the received signal carrier phase, and φ obeys evenly in [0,2 π] and distributes, and w (t) is the weakly dependent non-Gaussian noise.

Arresting structure of the present invention is that received signal is become quadrature two branch roads, with the observed quantity X of two branch roads _i ^IAnd X _i ^QCalculate statistic and compare to verify whether capture direct sequence signal by the local optimum algorithm with the prize judgment thresholding, 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 [Liu Naian, Deng. adaptive threshold technology and performance [J] thereof in the high-speed burst communication. electronic letters, vol, 1998,26 (1): 111-114.].

At first local optimum (LO) detector test statistics can be expressed as:

$T_{\mathrm{LO}}(Y^I,Y^Q)=\frac{1}{f_{X^I,X^Q}(Y^I,Y^Q){|}_{\mathrm{\&theta;}=0}}\&times;\frac{d^v{f}_{Y^I,Y^Q}(Y^I,Y^Q)}{d{\mathrm{\&theta;}}^v}{|}_{\mathrm{\&theta;}=0}$

Wherein:

Be the joint probability density of inphase quadrature two branch roads, v is

Exponent number at first non-zero derivative term at θ=0 place.Under weakly dependent non-Gaussian environment, the probability density function of noise is brought in the local optimum algorithm, can obtain the directly-enlarging system Capture Circle detection statistic that detects based on local optimum under the weakly dependent non-Gaussian noise circumstance:

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

$\frac{1}{2}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{j\&NotEqual;i,j=1}{\overset{M}{\mathrm{\&Sigma;}}}{C}_i{C}_j\{g\left(Y_i^I\right)g\left(Y_j^I\right)+g\left(Y_i^Q\right)g\left(Y_j^Q\right)\}$

Wherein:

$h\left(Y_i^b\right)=\frac{1}{f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_i^I,Y_i^Q)}\&times;\frac{{\&PartialD;}^2{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_i^I,Y_i^Q)}{\&PartialD;{\left(Y_i^b\right)}^2}$

$g\left(Y_i^b\right)=\frac{1}{f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_i^I,Y_i^Q)}\&times;\frac{\&PartialD;f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_i^I,Y_i^Q)}{\&PartialD;Y_i^b}$

In the formula: $C_i=\underset{j=0}{\overset{i-1}{\mathrm{\&Sigma;}}}{(-\mathrm{\&rho;})}^j;$ $Y_i^b=\underset{j=0}{\overset{i-1}{\mathrm{\&Sigma;}}}{(-\mathrm{\&rho;})}^j{X}_{i-j}^b,$ ρ is the coefficient correlation between the sampled value, b={I, the corresponding homophase of Q}, quadrature two branch roads.

When the detection signal signal to noise ratio hour, the 1/M of detection limit when the detection limit in the directly-enlarging system Capture Circle detection statistic that detects based on local optimum under the weakly dependent non-Gaussian noise circumstance during i=j is i ≠ j, therefore the detection statistic that can ignore diagonal entry, further this detection limit is carried out conversion, can get:

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

$\frac{1}{2}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{C}_i^2\{h\left(Y_i^I\right)+h\left(Y_i^Q\right)-g^2\left(Y_i^I\right)-g^2\left(Y_i^Q\right)\}$

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

So just, obtain the detection statistic simplified under the weakly dependent non-Gaussian noise circumstance, reduced computational complexity.

For existing the closed loop expression formula of α=1 situation to analyze in the two-dimentional S α S noise profile, obtain the two-dimentional local optimum arresting structure of directly-enlarging system under the relevant S α S noise model then.When α=1, will $g\left(Y_i^{I\left(Q\right)}\right)=\frac{{3Y}_i^{I\left(Q\right)}}{{\left(Y_i^I\right)}^2+{\left(Y_i^Q\right)}^2+{\mathrm{\&gamma;}}^2}$ Bring formula T into _LO(X ^I, X ^Q) in can get:

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

Under weak correlated noise environment,, do not considering { ρ because the correlation between the noise samples value is smaller in the actual directly-enlarging system ^k| k=2 ... wait under the situation of higher order term, can further obtain the more simple pseudo-code detector arrangement of structure T _FSLOThis simplification LO detector greatly reduces the implementation complexity of detector, and its detection statistic is:

$T_{\mathrm{FSLO}}(X^I,X^Q)=T_{\mathrm{SL}O}(X^I,X^Q){|}_{Y_i^b=X_i^b-\mathrm{\&rho;}{X}_{i-1}^b,C_i=1-\mathrm{\&rho;u}(i-2)}$ i＝(1，2…M)

In the formula, $X_0^b=0,u\left(i\right)$ Be the unit step response function, u (i)=0 when i＜0; U (i)=1 when i 〉=0.Fig. 2 has provided and has not considered { ρ ^k| k=2 ... wait the LO detector arrangement schematic diagram after simplifying under the situation of higher order term.

The present invention is for solving the acquiring pseudo code problem under the weakly dependent non-Gaussian noise circumstance, a kind of method for acquiring pseudo code based on the local optimum detection algorithm has been proposed, acquiring pseudo code is equivalent to the hypothesis testing problem, with the weakly dependent non-Gaussian noise modeling is single order moving average S α S noise model, utilize the local optimum detection algorithm to derive acquiring pseudo code detection statistic under the weakly dependent non-Gaussian noise circumstance, on this basis detection statistic is simplified, provided its implementation structure, and carried out the performance simulation contrast with traditional method for acquiring pseudo code, simulation result shows that catching method proposed by the invention detects performance by a relatively large margin raising is arranged under the weakly dependent non-Gaussian noise circumstance, and the non-Gaussian noise pulse characteristic is obvious more, and designed detector advantage is remarkable more.

(4) description of drawings

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

Fig. 2 local optimum detection architecture;

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

The relation of different following two kinds of detector acquisition probabilities of signal to noise ratio condition of Fig. 4 and ρ;

Two kinds of detectors of Fig. 5 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:

The first step handles 2 with received signal through carrier wave lift-off processing 1 and pseudo-code despreading as shown in Figure 1, obtains the observed quantity X of inphase/orthogonal two branch roads _i ^IAnd X _i ^QModule 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 promptly was applied in content of the present invention in the two-dimentional acquiring pseudo code structure based on the local optimum detection architecture and obtains statistic T as Fig. 2 module 31 _FSLO

1. at first 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, wherein τ is relative T _cThe normalization time delay, T _cBe symbol width.Sampled value according to the pairwise orthogonal branch road obtains two kinds of expression formulas under the hypothesis state:

$H_0:(X_i^I=W_i^I,X_i^Q=W_i^Q),$ i＝1，2，…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＝1，2，…，M

Wherein $\mathrm{\&theta;}=\sqrt{E}$ Be signal strength parameter.

2. according to top null hypothesis problem, the present invention analyzes the noise that receives, and obtains the joint probability density of quadrature two branch roads.{ W _i ^I} _I=0 ^M{ W _i ^Q} _I=0 ^MBe respectively the sampled value of the single order moving average noise of homophase and quadrature two branch roads, can be expressed as:

$W_i^I={\mathrm{\&Lambda;}}_i^I+\mathrm{\&rho;}{\mathrm{\&Lambda;}}_{i-1}^I$

$W_i^Q={\mathrm{\&Lambda;}}_i^Q+\mathrm{\&rho;}{\mathrm{\&Lambda;}}_{i-1}^Q$

Wherein, ρ is defined as the dependence parameter between adjacent two sampling instant noise sequences, when ρ=0, and noise sequence { W _i ^b} _I=1 ^MNeighbouring sample is constantly separate; The two-dimensional probability density function of its symmetrical α steady-state distribution can obtain by the inverse-Fourier transform of finding the solution its characteristic function:

$f_{\mathrm{\&alpha;},\mathrm{\&gamma;},{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_2}({\mathrm{<figure-callout\; id="1"\; label="x"\; filenames="H2009100720834E00021.png,H2009100720834E00022.png"\; state="\{\{state\}\}">x</figure-callout>}}_1,x_2)=\frac{1}{{\left(2\mathrm{\&pi;}\right)}^2}\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}\exp [i({\mathrm{\&beta;}}_1{\mathrm{\&omega;}}_1+{\mathrm{\&beta;}}_2{\mathrm{\&omega;}}_2)-\mathrm{\&gamma;}{({\mathrm{\&omega;}}_1^2+{\mathrm{\&omega;}}_2^2)}^{\frac{\mathrm{\&alpha;}}{2}}]e^{-i({\mathrm{<figure-callout\; id="1"\; label="x"\; filenames="H2009100720834E00021.png,H2009100720834E00022.png"\; state="\{\{state\}\}">x</figure-callout>}}_1{\mathrm{\&omega;}}_1+x_2{\mathrm{\&omega;}}_2)}d{\mathrm{\&omega;}}_{1}d{\mathrm{\&omega;}}_2$

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 when α=1st, Cauchy distributes, α=2nd, Gaussian Profile, and the α value is more little, the corresponding hangover that distributes thick more, so pulse characteristic is obvious more.Symmetric parameter β ₁, β ₂Be used for determining the symmetry characteristic of distribution, what adopt in this structure is symmetrical α steady-state distribution, so β ₁=β ₂=0, then its two-dimensional probability density function is:

$f_{\mathrm{\&alpha;},\mathrm{\&gamma;}}(x_1,x_2)=\frac{\mathrm{\&gamma;}}{2\mathrm{\&pi;}{(x_1^2+x_2^2+{\mathrm{\&gamma;}}^2)}^{\frac{3}{2}}},\mathrm{\&alpha;}=1$

This structure will pay attention to analyzing the situation of α=1 o'clock, and its hangover is thicker, and pulse characteristic is apparent in view, so more can reflect the probability density distribution characteristic of other symmetrical α steady-state distribution 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:

$f_{X^I,X^Q}(X^I,X^Q)=E_{\mathrm{\&phi;}}\left\{f_{W^I,W^Q}(X^I-\mathrm{\&theta;}\cos \mathrm{\&phi;},X^Q-\mathrm{\&theta;}\sin \mathrm{\&phi;})\right\}$

$=E_{\mathrm{\&phi;}}\{f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(X_1^I-\mathrm{\&theta;}\cos \mathrm{\&phi;},X_1^Q-\mathrm{\&theta;}\sin \mathrm{\&phi;})$

$\&times;f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(X_2^I-\mathrm{\&theta;}\cos \mathrm{\&phi;}-\mathrm{\&rho;}(X_1^I-\mathrm{\&theta;}\cos \mathrm{\&phi;}),X_2^Q-\mathrm{\&theta;}\sin \mathrm{\&phi;}-\mathrm{\&rho;}(X_1^Q-\mathrm{\&theta;}\sin \mathrm{\&phi;}))$

$...\&times;f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(X_M^I-\mathrm{\&theta;}\cos \mathrm{\&phi;}-\mathrm{\&rho;}(X_{M-1}^I-\mathrm{\&theta;}\cos \mathrm{\&phi;})+...+{(-\mathrm{\&rho;})}^{M-1}(X_1^I-\mathrm{\&theta;}\cos \mathrm{\&phi;}),$

$X_M^Q-\mathrm{\&theta;}\sin \mathrm{\&phi;}-\mathrm{\&rho;}(X_{M-1}^Q-\mathrm{\&theta;}\sin \mathrm{\&phi;})+...+{(-\mathrm{\&rho;})}^{M-1}(X_1^Q-\mathrm{\&theta;}\sin \mathrm{\&phi;})\}$

$=E_{\mathrm{\&phi;}}\left\{\underset{i=1}{\overset{M}{\mathrm{\&Pi;}}}{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_i^I-\mathrm{\&theta;}\cos \mathrm{\&phi;}{C}_i,Y_i^Q-\mathrm{\&theta;}\sin \mathrm{\&phi;}{C}_i)\right\}$

Wherein: E _φFor φ peek term is hoped; $C_i=\underset{j=0}{\overset{i-1}{\mathrm{\&Sigma;}}}{(-\mathrm{\&rho;})}^j;$ $Y_i^b=\underset{j=0}{\overset{i-1}{\mathrm{\&Sigma;}}}{(-\mathrm{\&rho;})}^j{X}_{i-j}^b,$ B={I, corresponding inphase quadrature two branch roads of Q}.Order $Y^I=(Y_1^I,Y_2^I,...Y_M^I),$ $Y^Q=(Y_1^Q,Y_2^Q,...Y_M^Q),$ Then Shang Mian dualism hypothesis becomes following form:

$H_0:(Y_i^I={\mathrm{\&Lambda;}}_i^I,Y_i^Q={\mathrm{\&Lambda;}}_i^Q),$ i＝1，2，…M

$H_1:(Y_i^I=\mathrm{\&theta;}\cos \mathrm{\&phi;}{C}_i+{\mathrm{\&Lambda;}}_i^I,Y_i^Q=\mathrm{\&theta;}\sin \mathrm{\&phi;}{C}_i+{\mathrm{\&Lambda;}}_i^Q),$ i＝1，2，…，M

Observed quantity { Y on homophase, quadrature two branch roads then _i ^I, Y _i ^Q} _I=1 ^MThe joint probability density function of 2M sampled point be:

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

3. above-mentioned noise model is used the local optimum detection algorithm and obtains new statistic, by the local optimum etection theory as can be known its statistic be:

$T_{\mathrm{LO}}(Y^I,Y^Q)=\frac{1}{f_{X^I,X^Q}(Y^I,Y^Q){|}_{\mathrm{\&theta;}=0}}\&times;\frac{d^v{f}_{Y^I,Y^Q}(Y^I,Y^Q)}{d{\mathrm{\&theta;}}^v}{|}_{\mathrm{\&theta;}=0}$

Wherein v is

First non-zero derivative order number at θ=0 place.When

First derivative at θ=0 place is:

$\frac{{\mathrm{df}}_{X^I,X^Q}(X^I,X^Q)}{\mathrm{d\&theta;}}{|}_{\mathrm{\&theta;}=0}=E_{\mathrm{\&phi;}}\left\{\underset{i=1}{\overset{N_b}{\mathrm{\&Sigma;}}}{f}_{N^I,N^Q}^{\&prime;}(N_i^I,N_i^Q)\underset{j=1,j\&NotEqual;i}{\overset{N_b}{\mathrm{\&Pi;}}}{f}_{N^I,N^Q}(N_j^I,N_j^Q){|}_{\mathrm{\&theta;}=0}\right\}$

Wherein:

$E_{\mathrm{\&phi;}}\left\{\frac{d{f}_{N^I,N^Q}(N_i^I,N_i^Q)}{\mathrm{d\&theta;}}{|}_{\mathrm{\&theta;}=0}\right\}=E_{\mathrm{\&phi;}}\{-\cos \mathrm{\&phi;}\frac{\&PartialD;f_{N^I,N^Q}(N_i^I,N_i^Q)}{\&PartialD;N_i^I}-\sin \mathrm{\&phi;}\frac{\&PartialD;f_{N^I,N^Q}(N_i^I,N_i^Q)}{\&PartialD;N_i^Q}\}=0$

So

First derivative at θ=0 place is 0.Therefore requirement Second dervative at θ=0 place:

$\frac{d^2{f}_{Y^I,Y^Q}(Y^I,Y^Q)}{d{\mathrm{\&theta;}}^2}{|}_{\mathrm{\&theta;}=0}=E_{\mathrm{\&phi;}}\left\{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\right[f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}^{\&prime;\&prime;}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)\underset{j=1,j\&NotEqual;i}{\overset{M}{\mathrm{\&Pi;}}}{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({{\mathrm{\&Lambda;}}^I}_j,{\mathrm{\&Lambda;}}_j^Q)$

$+f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}^{\&prime;}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)\underset{j=1,j\&NotEqual;i}{\overset{M}{\mathrm{\&Sigma;}}}{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}^{\&prime;}({{\mathrm{\&Lambda;}}^I}_j,{\mathrm{\&Lambda;}}_j^Q)\underset{k=1,k\&NotEqual;i,j}{\overset{M}{\mathrm{\&Pi;}}}{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({\mathrm{\&Lambda;}}_k^I,{\mathrm{\&Lambda;}}_k^Q)\left]\right\}$

Wherein:

$\frac{d^2{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)}{d{\mathrm{\&theta;}}^2}={\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="H2009100720834E00021.png,H2009100720834E00031.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&phi;}{\mathrm{<figure-callout\; id="2"\; label="C\; i"\; filenames="H2009100720834E00021.png,H2009100720834E00031.png"\; state="\{\{state\}\}">C</figure-callout>}}_i^{}\frac{{\&PartialD;}^2{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)}{{(\&PartialD;{\mathrm{\&Lambda;}}_i^I)}^2}+{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2009100720834E00021.png,H2009100720834E00031.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&phi;}{\mathrm{<figure-callout\; id="2"\; label="C\; i"\; filenames="H2009100720834E00021.png,H2009100720834E00031.png"\; state="\{\{state\}\}">C</figure-callout>}}_i^{}\frac{{\&PartialD;}^2{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)}{{(\&PartialD;{\mathrm{\&Lambda;}}_i^Q)}^2}$

$+\cos \mathrm{\&phi;}\sin \mathrm{\&phi;}{\mathrm{<figure-callout\; id="2"\; label="C\; i"\; filenames="H2009100720834E00021.png,H2009100720834E00031.png"\; state="\{\{state\}\}">C</figure-callout>}}_i^{}\frac{{\&PartialD;}^2{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)}{\&PartialD;{\mathrm{\&Lambda;}}_i^I\&PartialD;{\mathrm{\&Lambda;}}_i^Q}+\sin \mathrm{\&phi;}\cos \mathrm{\&phi;}{\mathrm{<figure-callout\; id="2"\; label="C\; i"\; filenames="H2009100720834E00021.png,H2009100720834E00031.png"\; state="\{\{state\}\}">C</figure-callout>}}_i^{}\frac{{\&PartialD;}^2{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)}{\&PartialD;{\mathrm{\&Lambda;}}_i^Q\&PartialD;{\mathrm{\&Lambda;}}_i^I}$

Then first of its second dervative is:

$E_{\mathrm{\&phi;}}\left\{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}^{\&prime;\&prime;}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)\underset{j=1,j\&NotEqual;i}{\overset{M}{\mathrm{\&Pi;}}}{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({{\mathrm{\&Lambda;}}^I}_j,{\mathrm{\&Lambda;}}_j^Q)\right\}{|}_{\mathrm{\&theta;}=0}=\frac{1}{2}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{C}_i^2\{h\left(Y_i^I\right)+h\left(Y_i^Q\right)\}\underset{j=1}{\overset{M}{\mathrm{\&Pi;}}}{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_j^I,Y_j^Q)$

Wherein:

$h\left(Y_i^b\right)=\frac{1}{f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_i^I,Y_i^Q)}\&times;\frac{{\&PartialD;}^2{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_i^I,Y_i^Q)}{\&PartialD;{\left(Y_i^b\right)}^2}$

B={I, the corresponding inphase quadrature branch road of Q}.

Equally

$f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}^{\&prime;}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}^{\&prime;}({{\mathrm{\&Lambda;}}^I}_j,{\mathrm{\&Lambda;}}_j^Q)={\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="H2009100720834E00021.png,H2009100720834E00031.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&phi;}{C}_i{C}_j\frac{\&PartialD;f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)}{\&PartialD;{\mathrm{\&Lambda;}}_i^I}\frac{\&PartialD;f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({{\mathrm{\&Lambda;}}^I}_j,{\mathrm{\&Lambda;}}_j^Q)}{\&PartialD;{{\mathrm{\&Lambda;}}^I}_j}$

$+{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2009100720834E00021.png,H2009100720834E00031.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&phi;}{C}_i{C}_j\frac{\&PartialD;f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)}{\&PartialD;{\mathrm{\&Lambda;}}_i^Q}\frac{\&PartialD;f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({{\mathrm{\&Lambda;}}^I}_j,{\mathrm{\&Lambda;}}_j^Q)}{\&PartialD;{{\mathrm{\&Lambda;}}^Q}_j}$

$+\cos \mathrm{\&phi;}\sin \mathrm{\&phi;}{C}_i{C}_j[\frac{{\&PartialD;f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)}{\&PartialD;{\mathrm{\&Lambda;}}_i^I}\frac{\&PartialD;f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({{\mathrm{\&Lambda;}}^I}_j,{\mathrm{\&Lambda;}}_j^Q)}{\&PartialD;{{\mathrm{\&Lambda;}}^Q}_j}+\frac{{\&PartialD;f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)}{\&PartialD;{\mathrm{\&Lambda;}}_i^Q}\frac{\&PartialD;f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({{\mathrm{\&Lambda;}}^I}_j,{\mathrm{\&Lambda;}}_j^Q)}{\&PartialD;{{\mathrm{\&Lambda;}}^I}_j}]$

Second of its second dervative is:

$E_{\mathrm{\&phi;}}\left\{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{j=1,j\&NotEqual;i}{\overset{M}{\mathrm{\&Sigma;}}}{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}^{\&prime;}({\mathrm{\&Lambda;}}_i^I,{\mathrm{\&Lambda;}}_i^Q)f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}^{\&prime;}({{\mathrm{\&Lambda;}}^I}_j,{\mathrm{\&Lambda;}}_j^Q)\underset{k=1,k\&NotEqual;i,j}{\overset{M}{\mathrm{\&Pi;}}}{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}({\mathrm{\&Lambda;}}_k^I,{\mathrm{\&Lambda;}}_k^Q)\right\}{|}_{\mathrm{\&theta;}=0}$

$=\frac{1}{2}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{j=1,j\&NotEqual;i}{\overset{M}{\mathrm{\&Sigma;}}}{C}_i{C}_j\{g\left(Y_i^I\right)g\left(Y_j^I\right)+g\left(Y_i^Q\right)g\left(Y_j^Q\right)\}\&times;\underset{k=1}{\overset{M}{\mathrm{\&Pi;}}}{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_k^I,Y_k^Q)$

Wherein:

$g\left(Y_i^b\right)=\frac{1}{f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_i^I,Y_i^Q)}\&times;\frac{\&PartialD;f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_i^I,Y_i^Q)}{\&PartialD;Y_i^b}$

Finally obtain the LO detector detection statistic under the weakly dependent non-Gaussian noise circumstance:

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

Wherein:

$h\left(Y_i^b\right)=\frac{1}{f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_i^I,Y_i^Q)}\&times;\frac{{\&PartialD;}^2{f}_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_i^I,Y_i^Q)}{\&PartialD;{\left(Y_i^b\right)}^2}$

$g\left(Y_i^b\right)=\frac{1}{f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_i^I,Y_i^Q)}\&times;\frac{\&PartialD;f_{{\mathrm{\&Lambda;}}^I,{\mathrm{\&Lambda;}}^Q}(Y_i^I,Y_i^Q)}{\&PartialD;Y_i^b}$

In the formula: $C_i=\underset{j=0}{\overset{i-1}{\mathrm{\&Sigma;}}}{(-\mathrm{\&rho;})}^j;$ $Y_i^b=\underset{j=0}{\overset{i-1}{\mathrm{\&Sigma;}}}{(-\mathrm{\&rho;})}^j{X}_{i-j}^b,$ B={I, the corresponding homophase of Q}, quadrature two branch roads.

4. reduce computation complexity.When the detection signal signal to noise ratio hour, the 1/M of detection limit when the detection limit in the LO detector detection statistic under the weakly dependent non-Gaussian noise circumstance during i=j is i ≠ j, therefore can ignore the detection statistic of diagonal entry, further it be carried out conversion, can get:

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

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

So just, obtain the detection statistic simplified under the weakly dependent non-Gaussian noise circumstance, reduced computational complexity.The situation of α=1 is analyzed in distributing at two-dimensional correlation symmetry α stable state stationary noise below, obtains the two-dimentional local optimum arresting structure and the reduced form thereof of directly-enlarging system under this noise model.In the time of α=1, will $g\left(Y_i^{I\left(Q\right)}\right)=\frac{{3Y}_i^{I\left(Q\right)}}{{\left(Y_i^I\right)}^2+{\left(Y_i^Q\right)}^2+{\mathrm{\&gamma;}}^2}$ Be brought in the LO detector detection statistic under the weakly dependent non-Gaussian noise circumstance, obtain the statistic under α=1 situation:

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

The LO detector that more than provides needs the individual memory space of 3 (M-1), takies multi-system resource, is difficult to practical application.Because the correlation in the actual directly-enlarging system between the noise samples value is smaller, is not considering { ρ ^k| k=2 ... wait under the situation of higher order term, only needing can obtain the simplification LO detector arrangement T of 3 memory spaces _FSLO:

$T_{\mathrm{FSLO}}(X^I,X^Q)=T_{\mathrm{LO}}(X^I,X^Q){|}_{Y_i^b=X_i^b-\mathrm{\&rho;}{X}_{i-1}^b,C_i=1-\mathrm{\&rho;u}(i-2)}i=(\mathrm{1,2}...M)$

In the formula, $X_0^b=0,u\left(i\right)$ Be the unit step response function, u (i)=0 when i＜0; U (i)=1 when i 〉=0.

The 3rd step: as Fig. 2 module 32, the statistic T that the local optimum algorithm is calculated _FSLO(X ^I, X ^Q) relatively judge whether to capture signal with thresholding r.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 the locally optimal detector structural representation.This detector greatly reduces the implementation complexity of detector, if do not consider all ρ ({ ρ ⁱ| i=1,2,3 ... M}), then can not needed the LO detector of memory space, be not difficult by analysis to find that the detector through after simplifying is consistent with detector arrangement under the irrelevant non-Gaussian noise environment.

In sum, under the weakly dependent non-Gaussian noise circumstance, invented a kind of acquiring pseudo code structure based on the local optimum detection algorithm.By utilizing the local optimum detection algorithm to provide the detection statistic that the pseudo-code two dimension is caught, obtained the two-dimentional local optimum grabber FSLOD of direct sequence signal under the weakly dependent non-Gaussian noise, and under the situation of α=1, conventional quadratic sum detector SSD and two kinds of PN Code Phase Acquisition of FSLOD are carried out emulation, compare their performance by emulation.

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; Local optimum (LO) detector of diagonal entry statistic is ignored in the FSLOD representative simultaneously.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, Fig. 4 and Fig. 5 _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 different detectors acquisition probability and signal to noise ratio under the dependent non-Gaussian noise circumstance, from figure, can find, in α=1 and α=1.5 o'clock, increase along with signal to noise ratio, the corresponding increase of the acquisition probability of FSLOD detector, and traditional SSD acquisition probability is very low, and remains unchanged substantially; When α=2, traditional SSD acquisition probability is better than FSLOD.

2. Fig. 4 has provided the relation curve of two kinds of detector acquisition probabilities and coefficient correlation ρ, and as seen from the figure, conventional SSD acquisition probability is lower, and does not change with the variation of ρ value; FS LOD detector acquisition probability reduces along with the increase of ρ value.

3. Fig. 5 has provided the relation of two kinds of detector acquisition performances and α value.From figure, can find, for most α values, the designed detector performance of this paper all is better than SSD, and having only when α approaches 2 is ambient noise when approaching Gaussian Profile, and traditional SSD detector detects performance and just is better than the designed FSLOD detector of the present invention; 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, and along with the increase of α value, the detection performance of FSLOD decreases.

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, under the dependent non-Gaussian noise circumstance, the designed more traditional quadratic sum detector detection performance of locally optimal detector of the present invention has raising by a relatively large margin by comparative analysis.

Claims (2)

1. Under the weakly dependent non-Gaussian environment based on the method for acquiring pseudo code of locally optimal detector, comprise a carrier wave strip module, a pseudo-code despreading module and a 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 through carrier wave peel off handle with the pseudo-code despreading after, become inphase/orthogonal two branch road observed quantity X _i ^IAnd X _i ^QObserved quantity X with two branch roads _i ^IAnd X _i ^QHandle through the statistical module that the local optimum algorithm is calculated, obtain statistic; In the statistic input judging module that obtains, statistic and prize judgment thresholding are compared to verify whether capture direct sequence signal,, then be judged as and capture signal if greater than thresholding, if less than thresholding, the local pseudo-code phase of then sliding judges that again comparison is until capturing signal.
2. 2. under the weakly dependent non-Gaussian environment according to claim 1 based on the method for acquiring pseudo code of locally optimal detector, 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.

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