[signal processing] weak signal detection in communication system based on the characteristics of high-order statistics with matlab code

1 Content introduction

Higher order statistics are widely used in radar 、 signal communication , biomedical science 、 Fault diagnosis in progress . Traditional signal detection methods have poor detection performance under low SNR and high dynamic . Bispectrum is insensitive to Gaussian white noise 、 High dynamic and low SNR are insensitive . High order statistics are used to detect weak signals with high dynamics and low signal-to-noise ratio , Under this condition, the higher-order statistics method obtains excellent performance . The experimental results under different dynamic and SNR conditions show excellent performance .​

2 Simulation code

% Bispectrum detectionclear allclose alln=100000;fs=n;t=0:1/fs:(fs-1)/fs;y=1*sin(2*pi*10000*t);yfft=abs(fftshift(fft(y)));f=(-length(yfft)/2:(length(yfft)-1)/2)*fs/length(yfft);%  Noise produces x1=normrnd(0,1,1,length(y));% Shot noise lamdac=2;Tmaxc=2000;ic=1;Tc(1)=random('exponential',lamdac);while(Tc(ic)<Tmaxc)    Tc(ic+1)=Tc(ic)+random('exponential',lamdac);    ic=ic+1;endTc(ic)=Tmaxc;xc=0:1:ic;wc(1)=0;for pc=1:ic    wc(pc+1)=Tc(pc);endtc=(1/fs:1/fs:1)*Tmaxc;ac=0.1;Wc=fs/Tmaxc*wc;Wc=floor(Wc);yc=zeros(length(Wc)-1,fs);for k1c=2:1:length(Wc);    kc=Wc(k1c);    t1c=1:1:fs;    ypc=exp(-(t1c-kc)*ac);    for kpc=1:1:kc-1        ypc(kpc)=0;    end    yc(k1c-1,:)=ypc;endx2=zeros(1,fs);for k2c=1:1:fs    x2(1,k2c)=sum(yc(:,k2c));end%  Gaussian colored noise p=0.5;f0=0.05;a1=-2*p*cos(2*pi*f0);a2=p^2;x3=zeros(1,length(y));for i=3:1:length(y);    x3(i)=a1*x3(i-1)-a2*x3(i-2)+x1(i);endy1=x2+y*0;[Bspec,waxis]=bispeci(y1,21,200,50,'unbiased',256);%  Three dimensional bispectrum figure(2)surf(abs(Bspec))%  Left view figure(3)surfl(abs(Bspec))view(0,0)%  Two dimensional slice B=abs(Bspec);B1=zeros(1,256);for i=1:1:255    B1(1,i)=max(B(i,:));endB1(1,256)=0;figure(4)plot(B1);% picturefigure(5)plot(t,y1)yfft=abs(fftshift(fft(y1)));figure(6)plot(f,yfft)% SNRsnr=0;ps=sum(sum((y-mean(mean(y))).^2));pn=sum(sum((y1-y).^2));snr=10*log10(ps/pn);

3 Running results

4 reference

[1] Zhai Yiqun , Huang Jianguo , Zhangqunfei , etc. . High dynamic weak signal detection based on high-order statistics [C]// Proceedings of the 7th National Conference on signal and intelligent information processing and Application . 2013.

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