%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 該程序實現時域LMS算法，并用統計的方法仿真得出不同步長下的學習曲線
% W為信道參數，u為迭代步長
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function LMS(W,u)
% 初始化參數
g=200;                     %   統計仿真次數為g
N=1000;                    %   輸入信號抽樣點數N，也為迭代次數
M=11;                      %   時域抽頭LMS算法濾波器階數
d=6;                       %   信號延遲
ee=zeros(g,N-M+1);         %   將每次獨立循環的誤差結果存于矩陣ee中，以便后面對其平均
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  產生信道序列
h=zeros(1,3);              %   信道序列初始化
for n=1:3
    h(n)=0.5*(1+cos(2*pi/W*(n-2))); %   信道序列
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  獨立循環算法
for q=1:g                    
    out = randint(1,N);       %   產生隨機0、1序列
    I = (out-0.5).*2;         %   得到原始信號I
    xx=conv(h,I);             %   原始信號通過信道后的信號
    x=awgn(xx,30,'measured'); %   給信號加上方差為0.001的白噪聲
    xn=x(1:N);                %   被噪聲污染的輸入信號
    yd=zeros(1,N);            %   期望輸出信號yd初始化
    yd((d+1):N)=I(1:(N-d));   %   yd為I延遲7個單位
    w=zeros(1,M);             %   設置抽頭加權初值
    e=zeros(1,N);             %   誤差信號初始化
    % 用LMS算法迭代濾波
    for i=M:N
        XN=xn((i-M+1):(i));  
        y(i)=w*XN';
        e(i)=yd(i)-y(i);
        w=w+u*e(i)*XN;    
    end
    ee(q,:)=(e(M:N)).^2;      %   存儲誤差平方序列
end
for b=1:(N-M+1)
    bi(b)=sum((ee(:,b)))/g;   %   求誤差平方值的的統計平均
end
t=1:(N-M+1);
semilogy(t,bi);               %   平均學習曲線
title('MSE學習曲線');
xlabel('迭代次數');
ylabel('均方誤差');
hold on
%  EOF
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%