lmseqdetecolor.m

具有检测FIR滤波器单位脉冲响应h[n]中零系数（zero tap detection）功能的LMS算法自适应均衡器

%Zero Tap Detection LMS Equalizer with Colored Inputs

%input generation and channel modeling
u =[zeros(1,35),randn(1,5000)];
H = [1,zeros(1,2),1,zeros(1,10),-2,zeros(1,10),3,zeros(1,10)];
C=0.8;
W=u;

u=filter(1,[1,-C],W);
u=sign(u);
figure(1);
plot(u);title ('Input u(k)');grid on;zoom on;
xlabel('Number of Sample Intervals');
ylabel('Sample Value');

mu=0.005;

N=length(W);
n=length(H);
He=zeros(1,N);
nn=randn(1,N)*0.1;
U=zeros(n,1);
Channel=zeros(n,N);
Est=zeros(n,N);
shift=diag(ones(1,n-1),-1);
HH=zeros(1,n);
U=zeros(n,1);
b=zeros(1,n);
a=ones(1,n)*0.01;
c=zeros(1,n);
g=zeros(1,n);
d=0;
sg=zeros(1,N);

for i=1:N,
    
    U=shift*U;
    U(1)=u(i);
    y(i)=H*U;
    v(i)=y(i)+nn(i);
    d=d+(v(i))^2;
    sigv=d/i;
    hv(i)=HH*U;
    e(i)=v(i)-hv(i);
    for k=1:n,
        if(k<i)&(i<=N)
            b(k)=b(k)+(v(i)*(u(i-k+1)));
            a(k)=a(k)+((u(i-k+1))^2);

            c(k)=((b(k))^2)/a(k);
            if c(k)>(sigv*log(i))
                g(k)=1;
            else
                g(k)=0;
            end;
            sg(i)=sum(g);
            HH(k)=g(k)*HH(k)+g(k)*mu*(u(i-k+1))*e(i);
        end;
    end;
    He(i)=(H-HH)*(H-HH)';
    Channel(:,i)= H';
    Est(:,i) = HH';
end;

%Channel Equalization
WV=zeros(n,1);
w=zeros(1,5035);

for i=36:5035,
    WV=shift*WV;
    w(i)=sign([1/HH(1)]*[v(i)-(HH(2:36)*WV(2:36))]);
    Q(i)=(u(i)-w(i))^2;
    WV(1)=w(i);
    
end;
figure(2);
plot (Q);title ('Equalizer');grid on;zoom on;
xlabel('Number of Sample Intervals');
ylabel('Squared Difference of u(k) and w(k)');

%plot results
figure(3);
plot (w);title ('Output w(k)');grid on;zoom on;
xlabel('Number of Sample Intervals');
ylabel('Sample Value');


figure(4);
subplot(2,1,1),plot(HH);
title ('Adaptive Filter Output-Standard LMS Algorithm with Zero Tap Detection');
xlabel('Number of Sample Intervals');
ylabel('Tap Weight');
grid on; zoom on;
subplot(2,1,2),plot(sg);
title('Sum of active taps-Standard LMS with Zero Tap Detection');
xlabel('Number of Sample Intervals');
ylabel('Number of Active Taps Detected');
grid on;zoom on;

figure(5);
subplot(2,1,1),semilogy(He);
title ('Adaptive Filter Output Asymptotic Error-Coloured Inputs');
xlabel('Number of Sample Intervals');
ylabel('Squared Euclidean Norm');
grid on; zoom on;
subplot(2,1,2),plot(sg);
ylabel('Number of Active Taps Detected');
xlabel('Number of Sample Intervals');
grid on; zoom on;