LMS,NLMS,RLS算法程序

%%%%%%%%%%%%%%%%%%%%LMS程序%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%ntr=9000;s=sign(2*rand(1,ntr)-1);%生成双极性码b=cos(pi/5)*[0.20.70.9];%b=[0.0050.0092-0.02420.8542-0.21820.0492-0.0162];a=1;%Transmissionchannelfilter传输通道滤波器channel=dfilt.df2t(b,a);%信道输出信号x(n)x=filter(b,a,s);%增加信道噪声snr=30;%信噪比u=awgn(x,snr,'measured');%AddwhiteGaussiannoise.即滤波器的输入向量%TrainedEqualizationM=11;%滤波器的抽头数%distrainingsignalisashiftedversionoftheoriginaltransmitted%d是训练信号%signals[n].d=[zeros(1,M)s(1:ntr-M+1)];mu=0.03;%收敛因子uw=zeros(1,M);%滤波器系数初始化%LMS算法fori=M:ntry(i)=w*u(i:-1:i-M+1)';e(i)=d(i)-y(i);w=w+2*mu*e(i)*u(i:-1:i-M+1);endfigure(1)subplot(4,1,1);stem(u(5000:5500),'r');title('均衡前信号u(n)');axis([150-22]);subplot(4,1,2);stem(y(5000:5500),'r');title('均衡后输出信号y(n)');axis([160-22]);subplot(4,1,3);stem(d(5000:5500),'r');title('期望输出d(n)');axis([150-22]);subplot(4,1,4);stem(e(5000:5500),'r');title('e(n)');axis([150-0.50.5]);figure(2)%subplot(2,1,1)plot(abs(e).^2);axis([-1006000-0.22]);%semilogy(abs(e).^2);xlabel('迭代数量');ylabel('均方误差')title('LMS算法SNR=30u=0.03M=11');%%%%%%%%%%%%%%%%%NLMS程序%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%clearallcloseallntr=9000;s=sign(2*rand(1,ntr)-1);%生成双极性码b=cos(pi/5)*[0.20.70.9];a=1;channel=dfilt.df2t(b,a);snr=30;%信噪比x=filter(b,a,s);u=awgn(x,snr);%在信号x中加入高斯白噪声%在系统中插入一个均衡器，抵消系统的码间串扰%NLMS算法%distrainingsignalisashiftedversionoftheoriginaltransmitted%signals[n].d=[zeros(1,10)s(1:ntr-10)];%期望响应%TrainedEqualizationM=9;%滤波器的抽头数c=0.001;mu=0.2;%收敛因子w=zeros(1,M);%滤波器系数初始化fori=M:ntry(i)=w*u(i:-1:i-M+1)';e(i)=d(i)-y(i);w=w+2.*mu.*e(i).*u(i:-1:i-M+1)/(c+u(i:-1:i-M+1)*u(i:-1:i-M+1)');end%训练误差figure(1)subplot(3,1,1);stem(u(5000:5500));title('均衡前信号u(n)');axis([160-1.51.5]);%由u(n)可看出系统中已发生码间串扰subplot(3,1,2);stem(d(5000:5500));title('期待输出信号d（n）');axis([160-1.51.5]);subplot(3,1,3);stem(y(5000:5500));title('均衡后信号y（n）');axis([160-1.51.5]);figure(2)plot(abs(e).^2);axis([-1006000-0.22.5]);xlabel('迭代数量');%Numberofiterationsylabel('均方误差')title('NLMS算法SNR=30u=0.2M=9')%%%%%%%%%RLS程序%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%clcclearallcloseallhidden%%初始化参数设置（用户可根据需要修改此处参数）nFrame=1;%仿真发送的帧数（可作为蒙特卡洛仿真次数）ntr=8000;%每帧的发送的数据点数step=0.001;%学习步长snr=30;%dB=25;%信噪比e=zeros(1,ntr);%瞬时计算误差E=zeros(1,ntr);%统计均方误差（为平滑用）%h=[0.18,0.3,1,0.18];%ISI信道参数%h=h/norm(h);M=11;%均衡器阶数%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%d=sign(2*rand(1,ntr)-1);LP=ntr-M%移掉几个数据避免负或零下标X=zeros(M+1,LP);%组织均衡器输入矩阵b=cos(pi/5)*[0.20.70.9];a=1;channel=dfilt.df2t(b,a)%snr=30;x=filter(b,a,d);u=awgn(x,snr);%循环开始（迭代次数=nFrame*nPacket）%forkk=1:nFrame%此处修改蒙特卡洛次数W=zeros(M+1,1);fori=1:LPX(:,i)=u(i+M:-1:i).';end%%RLS迭代算法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%初始化RLS相关参数%lambda=0.9;%遗忘因子,最大为1beta=std(u)^2;%信号功率P=1/beta*eye(M+1,M+1);%初始化相关矩阵%开始均衡器参数调整fori=1:LPK=(lambda^(-1)*P*X(:,i))/(1+lambda^(-1)*(X(:,i))'*P*X(:,i));%计算增益矢量e(i)=W'*X(:,i)-d(i);%误差W=W-conj(K)*e(i);%权值更新%P=lambda^(-1)*P-lambda^(-1)*K*(X(:,i))'*P;%相关矩阵更新E(i)=E(i)+e(i)^2;%均方误差值end%计算误码y=W'*X;%均衡后信号figure(1)subplot(3,1,1)stem(u(300:350),'r');axis([150-22]);title('u(n)均衡前信号')subplot(3,1,2)stem(d(300:350),'r');axis([150-22]);title('d(n)期望信号')subplot(3,1,3)stem(y(300:350),'r');axis([150-22]);title('y(n)均衡后信号')figure(2)plot(abs(e).^2);axis([-2008000-0.23]);title('误差平方（收敛曲线）')