日志
OFDM系统的整体性仿真
| |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%文件说明
%函数说明：这是一个比较完整的OFDM系统，我在发送端做了比较简单的QPSK调制映射生成OFDM 符号，
% 经串并转换后插入导频Pilot和循环前缀CP，再进行并串转换加噪声送入多径瑞利信道。
% 在接收端，先进行串并转换；然后去掉循环前缀，提取导频信息进行LS估计，最后经过并串
% 转换，QPSK解码还原信息
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%参数说明
%Ｘ：欲发送的二进制比特流
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all;
clc;
IFFT_bin_length=128; % IFFT和FFT的点数 128
carrier_count=100; % 子载波个数 100
bits_per_symbol=2; % 每符号上的比特数 2
symbols_per_carrier=12; % 每桢的OFDM符号数 12
LI=7 ; %导频之间的间隔
Np=ceil(carrier_count/LI)+1; %导频数加1 使最后一列也是导频，即有16个导频子信道
N_number=carrier_count*symbols_per_carrier*bits_per_symbol; %总共发送的信息比特数
% 100*12*2=2400
carriers=1:carrier_count+Np;
GI=8; % 保护间隔长度
N_snr=40; % 每比特信息上的信噪比
snr=8; %信噪比间隔
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%发送端变量初始化
X=zeros(1,N_number); %Ｘ：欲发送的二进制比特流
X1=[]; %原始的二进制数据流每2个一组进行QPSK映射编码得到X1
X2=[]; %X1串并转换后得到X2
X3=[]; %X2插入导频后得到X3
X4=[]; %IFFT变换后得到X4
X5=[];
X6=[]; %加入循环前缀后得到X6
X7=[]; %并串转换后得到X7
%接收端变量初始化
Y1=[]; %X1的估计值
Y2=[]; %提取数据信道上的信息
Y3=[];
Y4=[]; %Y5经FFT变换后得到Y4
Y5=[]; %Y6去掉循环前缀后得到Y5
Y6=[]; %Y7并串转换后得到Y6
Y7=[]; %接收端从信道上得到的信号，即信道输出Y7
XX=zeros(1,N_number);
dif_bit=zeros(1,N_number);
dif_bit1=zeros(1,N_number);
dif_bit2=zeros(1,N_number);
dif_bit3=zeros(1,N_number);
X=randint(1,N_number);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%QPSK调制：(1 1)->pi/4;(0 1)->3*pi/4;(0 0)->-3*pi/4;(1,0)->-pi/4;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
s=(X.*2-1)/sqrt(2);
sreal=s(1:2:N_number); % 将原信息比特流每两个为一组编码
simage=s(2:2:N_number); %前后比特分别编码为OFDM符号的实，虚部
X1=sreal+j.*simage ; % 进行QPSK映射编码（复数形式）
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%产生随机导频信号
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
train_sym=randint(1,2*symbols_per_carrier);
t=(train_sym.*2-1)/sqrt(2); % 将导频序列也进行QPSK调制映射
treal=t(1:2:2*symbols_per_carrier);
timage=t(2:2:2*symbols_per_carrier);
training_symbols1=treal+j.*timage; % 构成两组相同的
training_symbols2=training_symbols1.' ; % 训练序列用于信道估计
training_symbols=repmat(training_symbols2,1,Np);
%将training_symbols2作为一个子矩阵，生成12行，Np=16列大型矩阵
disp(training_symbols) % 显示训练序列的内容，共16列
pilot=1:(LI+1):(carrier_count+Np);
%以LI+1=8 为间隔，标注导频子载波，即每8个子载波，第1个传导频，其余7个传数据
if length(pilot)~=Np
pilot=[pilot,carrier_count+Np];
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%串并转换
X2=reshape(X1,carrier_count,symbols_per_carrier).';
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%插入导频
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
signal=1:carrier_count+Np;
signal(pilot)=[];
X3(:,pilot)=training_symbols; % 在导频子载波上填入导频符号
X3(:,signal)=X2; %在数据子载波上填入数据
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%OFDM调制
IFFT_modulation=zeros(symbols_per_carrier,IFFT_bin_length);
IFFT_modulation(:,carriers)=X3;
X4=ifft(IFFT_modulation,IFFT_bin_length,2);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%加保护间隔（循环前缀）
for k=1:symbols_per_carrier;
for i=1:IFFT_bin_length;
X6(k,i+GI)=X4(k,i);
end
for i=1:GI;
X6(k,i)=X4(k,i+IFFT_bin_length-GI); % 加CP：将每个符号最后的GI位复制到最前端
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%并串转换
X7=reshape(X6.',1,symbols_per_carrier*(IFFT_bin_length+GI));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%信道模型:带多普勒频移的瑞利衰落信道
fd=100; %多普勒频移
r=6; %多径数
a=[0.12 0.3 0.4 0.5 0.7 0.8]; %多径的衰落幅度
d=[2 3 4 5 7 6]; %各径的延迟
T=1; %系统采样周期
th=[90 0 72 144 216 288]*pi./180; % 各径的相移
h=zeros(1,carrier_count);
hh=[];
for k=1:r
h1=a(k)*exp(j*((2*pi*T*fd*d(k)/carrier_count)));%各径的响应函数
hh=[hh,h1];
end
h(d+1)=hh;
%6条信道模拟多径
channel1=zeros(size(X7));
channel1(1+d(1):length(X7))=hh(1)*X7(1:length(X7)-d(1));
channel2=zeros(size(X7));
channel2(1+d(2):length(X7))=hh(2)*X7(1:length(X7)-d(2));
channel3=zeros(size(X7));
channel3(1+d(3):length(X7))=hh(3)*X7(1:length(X7)-d(3));
channel4=zeros(size(X7));
channel4(1+d(4):length(X7))=hh(4)*X7(1:length(X7)-d(4));
channel5=zeros(size(X7));
channel5(1+d(5):length(X7))=hh(5)*X7(1:length(X7)-d(5));
channel6=zeros(size(X7));
channel6(1+d(6):length(X7))=hh(6)*X7(1:length(X7)-d(6));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Tx_data=X7+channel1+channel2+channel3+channel4+channel5+channel6; %发送端送入信道的符号，即信道输入
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%加高斯白噪声
Error_ber=[]; %误比特率
Error_ber1=[];
Error_ber2=[];
Error_ber3=[];
for snr_db=0:snr:N_snr %在每比特数据上加噪声
code_power=0;
code_power=[norm(Tx_data)]^2/(length(Tx_data)); % 符号功率
bit_power=code_power/bits_per_symbol; %比特功率
noise_power=10*log10((bit_power/(10^(snr_db/10))));%噪声功率
noise=wgn(1,length(Tx_data),noise_power,'complex');%产生高斯白噪声
Y7=Tx_data+noise; % 接收端从信道上得到的信息，即信道输出
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%接收端
%串并变换
Y6=reshape(Y7,IFFT_bin_length+GI,symbols_per_carrier).';
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%去保护间隔（CP）
for k=1:symbols_per_carrier;
for i=1:IFFT_bin_length;
Y5(k,i)=Y6(k,i+GI);
end
end
Y4=fft(Y5,IFFT_bin_length,2);
Y3=Y4(:,carriers);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% LS信道估计
H=[];
Y2=Y3(:,signal); %提取数据信息
Rx_training_symbols=Y3(:,pilot); % 提取导频信道上的导频信息
Rx_training_symbols0=reshape(Rx_training_symbols,symbols_per_carrier*Np,1);
training_symbol0=reshape(training_symbols,1,symbols_per_carrier*Np);
training_symbol1=diag(training_symbol0);
training_symbol2=inv(training_symbol1);
Hls=training_symbol2*Rx_training_symbols0; % LS估计量的公式H=X’Y
Hls1=reshape(Hls,symbols_per_carrier,Np);
HLs=[];
HLs1=[];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if ceil(carrier_count/LI)==carrier_count/LI
for k=1:Np-1 % 依此得到各个信道上的响应估计量
HLs2=[];
for t=1:LI
HLs1(:,1)=(Hls1(:,k+1)-Hls1(:,k))*(t-1)./LI+Hls1(:,k);
HLs2=[HLs2,HLs1];
end
HLs=[HLs,HLs2];
end
else
for k=1:Np-2
HLs2=[];
for t=1:LI
HLs1(:,1)=(Hls1(:,k+1)-Hls1(:,k))*(t-1)./LI+Hls1(:,k);
HLs2=[HLs2,HLs1];
end
HLs=[HLs,HLs2];
end
HLs3=[];
for t=1:mod(carrier_count,LI)
HLs1(:,1)=(Hls1(:,Np)-Hls1(:,Np-1))*(t-1)./LI+Hls1(:,Np-1);
HLs3=[HLs3,HLs1];
end;
HLs=[HLs,HLs3];
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Y1=Y2./HLs;
% Hls是导频位置上获得的信道响应估计量，由于采用慢变信道，所以将它也看作数据
% 子信道的响应估计量，用该估计量估计出实际接发送的信号Y1，即Y1是X1的估计值
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%并串变换
%通过采用估计和不采用对比体现采用信道估计可以提升OFDM系统的通信质量
YY=reshape(Y2.',1,N_number/bits_per_symbol); %不采用信道估计未解码符号
YY1=reshape(Y1.',1,N_number/bits_per_symbol); %采用LS估计的未解码符号
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%QPSK解码
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
y_real=sign(real(YY)); %通过符号函数进行解码
y_image=sign(imag(YY));
y_re=y_real./sqrt(2);
y_im=y_image./sqrt(2); %未进行估计的
y_real1=sign(real(YY1));
y_image1=sign(imag(YY1));
y_re1=y_real1./sqrt(2);
y_im1=y_image1./sqrt(2); %进行了LS估计的
r00=[];
r01=[];
r10=[];
r11=[];
% 反映射还原信息比特流
for k=1:length(y_re);
r01=[r01,[y_re(k),y_im(k)]];
end;
for k=1:length(y_re1);
r11=[r11,[y_re1(k),y_im1(k)]];
end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%计算在不同信噪比下的误比特率
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
dif_bit=s-r01; %s是发送端的输入比特流经编码后得到的符号
dif_bit1=s-r11; %r01是未进行估计，解码得到的符号
%r11是进行估计后，解码得到的符号
%它们进行比较判断误比特
ber_snr=0; %记录误比特数
for k=1:N_number;
if dif_bit(k)~=0;
ber_snr=ber_snr+1;
end
end;
ber_snr1=0; %记录误比特数
for k=1:N_number;
if dif_bit1(k)~=0;
ber_snr1=ber_snr1+1;
end
end
Error_ber=[Error_ber,ber_snr];
Error_ber1=[Error_ber1,ber_snr1];
end
BER=zeros(1,length(0:snr:N_snr));
BER1=zeros(1,length(0:snr:N_snr));
BER=Error_ber./N_number; %未进行估计的BER
BER1=Error_ber1./N_number; %进行LS估计的BER
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%作图比较未进行信道估计和进行LS估计后的误比特（BER）性能
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
i=0:snr:N_snr;
semilogy(i,BER,'-*r');
grid on;
xlabel('SNR in dB');
ylabel('Bit Error Rate');
hold on;
semilogy(i,BER1,'-ob');
grid on;
xlabel('SNR in dB');
ylabel('Bit Error Rate');
title('BER性能比较');
legend('No Channel Estimation','LS Channel Estimation');
微信：HuangL1121
邮箱：1224848052@qq.com
微信扫一扫：
/1 
eetop公众号
创芯大讲堂
创芯人才网