ofdm.rar_OFDMOMP算法_OMP估计_OMP信道估计_estimationOMP_压缩信道

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OFDM（Orthogonal Frequency Division Multiplexing，正交频分复用）是一种高效的数据传输技术，广泛应用于现代无线通信系统，如Wi-Fi、4G/5G移动通信等。本资料包聚焦于OFDM系统中的信道估计问题，并探讨了使用压缩感知（Compressed Sensing, CS）中的OMP（Orthogonal Matching Pursuit，正交匹配追踪）算法来实现这一目标。通过与传统的LS（Least Squares，最小二乘）算法进行比较，我们可以深入理解这两种方法的优劣。在OFDM系统中，信号在多个正交子载波上同时传输，这极大地提高了频谱效率。然而，由于无线信道的多径传播，每个子载波上的信号会受到不同幅度和相位的衰落，因此准确的信道估计是确保系统性能的关键。 OMP算法是压缩感知理论中的一种恢复算法，它通过迭代寻找最相关的原子（在这里是信道响应的频率样本）来重建原始信号。在OFDM的信道估计中，OMP算法可以显著减少所需的测量数量，这对于资源有限的无线通信系统尤其有利。它通过与已知训练序列的匹配，逐步构建出信道响应的近似值。相比之下，LS算法是一种简单的线性估计算法，它通过最小化实际接收信号与期望信号之间的均方误差来估计信道响应。虽然LS算法实现简单，但当信道条件复杂或训练序列不足时，其性能可能会下降。在OFDM系统中，OMP算法的信道估计通常包括以下步骤： 1. 生成训练符号：在OFDM符号中插入已知的训练序列。 2. 接收并预处理：接收带有噪声的信号，执行快速傅里叶变换（FFT）。 3. 建立观测矩阵：将预处理后的信号与训练序列的复共轭相乘，形成观测矩阵。 4. 迭代过程：初始化空的原子集合，选择与观测向量最相关的一项加入集合，更新残差，并重复此过程直到达到预定的迭代次数。 5. 信道估计：根据选取的原子重构信道响应。通过对比OMP和LS算法，我们可以发现： - OMP在稀疏环境下（信道响应大部分为零）具有优势，因为它能精确地找出非零元素。 - LS算法对噪声敏感，而OMP在噪声环境中可能表现更稳定。 - OMP的计算复杂度相对较高，需要更多的计算资源，而LS算法则较为简单。在实际应用中，工程师会根据系统的需求和资源限制来选择合适的信道估计方法。理解并掌握这两种算法对于优化OFDM系统的性能至关重要。本压缩包文件可能包含OFDM系统模型、OMP和LS算法的实现代码、信道估计的仿真结果以及相关论文，这些资源可以帮助你深入学习和比较这两种信道估计方法。通过实践和分析，你可以更好地理解OFDM系统中的压缩信道估计，并为实际通信系统设计提供理论支持。

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ofdm.rar （2个子文件）

ofdm

OMP_ofdm.m 2KB

OFDM.m 18KB

clear all; clc; carrier_count=2047;%总的子载波数 bits_per_symbol=2;%用4进制调制 symbols_per_carrier=1; I=6; pilot_index=[1:I:2047];%导频坐标 N=2047;%总载波数 [M_M M]=size(pilot_index);%导频子载波数 N_number=carrier_count*symbols_per_carrier*bits_per_symbol;%总二进制数 fd=0.01;%假设多普勒频移为0 ts=1;%采样周期 CP=100;%保护时间 C=5;%符号数 circle=1;%循环次数取平均 SNR_number=7;%SNR数量 err_rate=ones(C,SNR_number); err_rate_ls=ones(C,SNR_number); ERR_RATE=ones(circle,SNR_number); ERR_RATE_ls=ones(circle,SNR_number); averr=ones(1,SNR_number); averr_ls=ones(1,SNR_number); mse=ones(circle,SNR_number); arrmse=ones(1,SNR_number); mse_ls=ones(circle,SNR_number); arrmse_ls=ones(1,SNR_number); h=zeros(N,1); for time=1:circle; h_sv=[]; h_sv_ls=[]; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%生成信道 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% K=6;%稀疏度为6 delay=[1 10 30 60 90 99];%各径延迟 % h(delay,1)=1+1*1i; a=[1 -0.9 -4.9 -8.0 -7.8 -23.8]; %多径的幅度 RLchannel=rayleighchan(ts,fd,delay,a); RLchannel.StorePathGains=1; test = ones(C,1);%测试向量 filter(RLchannel,test); h_RL=RLchannel.PathGains;%提取瑞利信道 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%生成信号 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for ii=[1 C 2 3 4];%循环次数 %X_bit=randint(N_number,1);%产生随机2进制信号 X_msg=randint(N,1,4); %%%%%%%%%%%%%%%QPSK调制%%%%%%%%%%%%%%%%%%%% X=pskmod(X_msg,4); % X_qpsk=(X_bit.*2-1)/sqrt(2); % Xreal=X_qpsk(1:2:N_number); % Ximage=X_qpsk(2:2:N_number); % X=Xreal+j.*Ximage;%待发射信号 x0=ifft(X);%待传输信号 for i=1:carrier_count; x(i+CP,1)=x0(i,1); end for i=1:CP; x(i,1)=x0(i+carrier_count-CP,1); end %加CP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%信道 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for hh=1:K; h(1+delay(hh))= h_RL(ii,hh);%信道的冲击响应 end H=fft(h); y_r=filter(h,1,x);%收到的信号 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for SNR_index=1:SNR_number;%信噪比7个点 y = awgn(y_r,(SNR_index-1)*5,'measured');%加噪声; %y=y_r; %%%%%%%%%%%% % symbol_power=[norm(CP+carrier_count)]^2/(length(CP+carrier_count));%信号的符号功率 % %bit_power=var(Tx_data); % noise_power=10*log10((bit_power/(10^(snr_db/10))));%噪声功率 % noise=wgn(CP+carrier_count,1,noise_power,'complex');%产生GAUSS白噪声信号 %%%%%%%%%%%% y0=y(CP+1:CP+carrier_count,1);%去CP Y=fft(y0); if ii==1||ii==C %Y2=X.*H;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 % y2=ifft(Y2); %norm(Y-Y2)/norm(Y) X_pilot=X(pilot_index,1); Y_pilot=Y(pilot_index,1); H_R=Y_pilot./X_pilot; % H2=H(pilot_index); % ttttt=norm(H2-H_R)/norm(H2) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%CS信道估计%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fai=fft(eye(2047)); phi=Fai(pilot_index,:); %check=max(abs(H_R-phi*h)) v=H_R; m=K; %[h_esti lamda]=omp1(phi,2048,v,m); h_esti=OMP_ofdm(v,phi,K); mse(time,SNR_index)=sum(abs(h-h_esti).^2); H_esti=fft(h_esti); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%LS信道估计%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% H_esti_ls=zeros(N,1); H_esti_ls(1)=H_R(1); lsm=1; for lsn=2:N; if lsn<pilot_index(lsm)||lsn==pilot_index(lsm) H_esti_ls(lsn)=H_R(lsm-1)+(lsn-pilot_index(lsm-1))/I*(H_R(lsm)-H_R(lsm-1)); elseif lsm==M H_esti_ls(lsn)=H_R(lsm); else lsm=1+lsm; H_esti_ls(lsn)=H_R(lsm-1)+(lsn-pilot_index(lsm-1))/I*(H_R(lsm)-H_R(lsm-1)); end end h_esti_ls=ifft(H_esti_ls) ; mse_ls(time,SNR_index)=sum(abs(h-h_esti_ls).^2); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% X_esti=Y./H_esti;%%估计的导频加信号的值 X_esti_ls=Y./H_esti_ls; % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %QPSK解调 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % X_msg_esti=pskdemod(X_esti,4); % [err_number,err_rate(ii,SNR_index)]=symerr(X_msg,X_msg_esti); h_sv=[h_sv h_esti]; h_sv_ls=[h_sv_ls h_esti_ls]; else h_esti=h_sv(:,SNR_index)+(h_sv(:,SNR_index+SNR_number)-h_sv(:,SNR_index))*(ii-1)/(C-1);%线性插值 H_esti=fft(h_esti); X_esti=Y./H_esti;%%估计的导频加信号的值 h_esti_ls=h_sv_ls(:,SNR_index)+(h_sv_ls(:,SNR_index+SNR_number)-h_sv_ls(:,SNR_index))*(ii-1)/(C-1);%线性插值 H_esti_ls=fft(h_esti_ls); X_esti_ls=Y./H_esti_ls;%%估计的导频加信号的值 end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %QPSK解调 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% X_msg_esti=pskdemod(X_esti,4); X_msg_esti_ls=pskdemod(X_esti_ls,4); [err_number,err_rate(ii,SNR_index)]=symerr(X_msg,X_msg_esti); [err_number_ls,err_rate_ls(ii,SNR_index)]=symerr(X_msg,X_msg_esti_ls); end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for kk=1:SNR_number; ERR_RATE(time,kk)=mean(err_rate(:,kk)); ERR_RATE_ls(time,kk)=mean(err_rate_ls(:,kk)); end end for kk=1:SNR_number; averr(kk)=mean(ERR_RATE(:,kk)); averr_ls(kk)=mean(ERR_RATE_ls(:,kk)); avmse(kk)=mean(mse(:,kk)); avmse_ls(kk)=mean(mse_ls(:,kk)); end t=0:5:5*(SNR_number-1); figure(1); semilogy(t,averr,'-.r'); hold on; xlabel('SNR(单位：dB)'); ylabel('SER'); grid on; figure(3); semilogy(t,averr_ls,'-.g'); hold on; xlabel('SNR(单位：dB)'); ylabel('SER'); grid on; %legend('CS Channel Estimation SER Internal=6','LS Channel Estimation SER Internal=6'); figure(2); semilogy(t,avmse,'-or'); hold on; xlabel('SNR(单位：dB)'); ylabel('MSE'); grid on; figure(4); semilogy(t,avmse_ls,'-og'); hold on; xlabel('SNR(单位：dB)'); ylabel('MSE'); grid on; %legend('CS Estimation MSE Internal=6','LS Estimation MSE Internal=6'); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 clear all; clc; carrier_count=2047;%总的子载波数 bits_per_symbol=2;%用4进制调制 symbols_per_carrier=1; I=12; pilot_index=[1:I:2047];%导频坐标 N=2047;%总载波数 [M_M M]=size(pilot_index);%导频子载波数 N_number=carrier_count*symbols_per_carrier*bits_per_symbol;%总二进制数 fd=0.01;%假设多普勒频移为0 ts=1;%采样周期 CP=100;%保护时间 C=5;%符号数 circle=1000;%循环次数取平均 SNR_number=7;%SNR数量 err_rate=ones(C,SNR_number); err_rate_ls=ones(C,SNR_number); ERR_RATE=ones(circle,SNR_number); ERR_RATE_ls=ones(circle,SNR_number); averr=ones(1,SNR_number); averr_ls=ones(1,SNR_number); mse=ones(circle,SNR_number); arrmse=ones(1,SNR_number); mse_ls=ones(circle,SNR_number); arrmse_ls=ones(1,SNR_number); h=zeros(N,1); for time=1:circle; h_sv=[]; h_sv_ls=[]; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%生成信道 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% K=6;%稀疏度为6 delay=[1 10 30 60 90 99];%各径延迟 % h(delay,1)=1+1*1i; a=[1 -0.9 -4.9 -8.0 -7.8 -23.8]; %多径的幅度 RLchannel=rayleighchan(ts,fd,delay,a); RLchannel.StorePathGains=1; test = ones(C,1);%测试向量 filter(RLchannel,test); h_RL=RLchannel.PathGains;%提取瑞利信道 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%生成信号 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for ii=[1 C 2 3 4];%循环次数 %X_bit=randint(N_number,1);%产生随机2进制信号 X_msg=randint(N,1,4); %%%%%%%%%%%%%%%QPSK调制%%%%%%%%%%%%%%%%%%%% X=pskmod(X_msg,4); % X_qpsk=(X_bit.*2-1)/sqrt(2); % Xreal=X_qpsk(1:2:N_number); % Ximage=X_qpsk(2:2:N_number); % X=Xreal+j.*Ximage;%待发射信号 x0=ifft(X);%待传输信号 for i=1:carrier_count; x(i+CP,1)=x0(i,1); end for i=1:CP; x(i,1)=x0(i+carrier_count-CP,1); end %加CP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%信道 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for hh=1:K; h(1+delay(hh))= h_RL(ii,hh);%信道的冲击响应 end H=fft(h); y_r=filter(h,1,x);%收到的信号 %%%%