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OFDM系统的整体性仿真

上一篇 / 下一篇  2018-10-29 14:55:16

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%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');

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