%OFDM Channel Estimation Based on Comb Pilot
%IFFT_bin_length: IFFT和FFT的點數
%carrier_count: 子載波個數
%bits_per_symbol: 每符號上的比特數
%symbols_per_carrier: 每楨的OFDM符號數
%Ｘ：欲發送的二進制比特流

clear all;
clc;
IFFT_bin_length=128;%ifft長度
carrier_count=100;%子載波數
bits_per_symbol=2;%每符號比特數
symbols_per_carrier=12;%一楨符號數
LI=7 ; %導頻之間的間隔
Np=ceil(carrier_count/LI)+1;%16 導頻數加1的原因：使最后一列也是導頻

N_number=carrier_count*symbols_per_carrier*bits_per_symbol;%2400一禎比特數
carriers=1:carrier_count+Np;%116 子載波加導頻

GI=8;             % guard interval length
N_snr=40;          % 每比特信噪比
snr=8;             %信噪比間隔
%------------------------------------------------------------
% vector initialization


X=zeros(1,N_number);%2400個bit
X1=[];
X2=[];
X3=[];
X4=[];
X5=[];
X6=[];
X7=[];
Y1=[];
Y2=[];
Y3=[];
Y4=[];
Y5=[];
Y6=[];
Y7=[];
XX=zeros(1,N_number);%2400
dif_bit=zeros(1,N_number);%2400
dif_bit1=zeros(1,N_number);%2400
dif_bit2=zeros(1,N_number);%2400
dif_bit3=zeros(1,N_number);%2400
X=randint(1,N_number);%產生二進制隨即序列（非0即1）2400
%--------------------------------------------------------
%QPSK調制：(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);
simage=s(2:2:N_number);
X1=sreal+j.*simage;%已調信號bit流0.7071 - 0.7071i   0.7071 - 0.7071i   0.7071 + 0.7071i。。。。。（1*1200）

%---------------------------------------------------------
%產生隨機導頻信號
%--------------------------------------------------------
train_sym=randint(1,2*symbols_per_carrier);%1*24
t=(train_sym.*2-1)/sqrt(2);
treal=t(1:2:2*symbols_per_carrier);
timage=t(2:2:2*symbols_per_carrier);
training_symbols1=treal+j.*timage;% 0.7071 - 0.7071i  -0.7071 - 0.7071i  -0.7071 - 0.7071i   1*12
training_symbols2=training_symbols1.';%12*1
training_symbols=repmat(training_symbols2,1,Np);%12*16 復制第一列變成16列

%disp(training_symbols)
pilot=1:LI+1:carrier_count+Np;%導頻插入位置序號1     9    17    25    33    41    49    57    65    73    81    89    97   105  113
if length(pilot)~=Np
    pilot=[pilot,carrier_count+Np];%最后一列變成導頻1     9    17    25    33    41    49    57    65    73    81    89    97   105  113   116
end
%--------------------------------------------------------
%串并轉換
X2=reshape(X1,carrier_count,symbols_per_carrier).';%12*100，12個復信號符號，100列載波
%---------------------------------------------------------
%插入導頻
signal=1:carrier_count+Np;%1*116
signal(pilot)=[];%1*100
X3(:,pilot)=training_symbols;%先放入16列導頻
X3(:,signal)=X2;%再放入12*100，100列子載波，共12*116
%X3=cat(1,training_symbols,X2);
IFFT_modulation=zeros(symbols_per_carrier,IFFT_bin_length);%12*128
IFFT_modulation(:,carriers)=X3;%116列后補12列全0子載波，12*128
%IFFT_modulation(:,conjugate_carriers)=conj(X3);
X4=ifft(IFFT_modulation,IFFT_bin_length,2);%每個符號128點ifft
%X5=X4.';
%加保護間隔（循環前綴）
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);    
   end
end
%---------------------------------------------------------
%并串轉換
X7=reshape(X6.',1,symbols_per_carrier*(IFFT_bin_length+GI));%12*136先轉置，再變成1*1632復信號流

%---------------------------------------------------------
%信道模型:帶多普勒頻移的瑞利衰落信道

fd=100; %多普勒頻移
r=6;   %多徑數
a=[0.123 0.3 0.4 0.5 0.7 0.8]; %多徑的幅度
d=[2 3 4 5 9 13]; %各徑的延遲
T=1;  %系統采樣周期
th=[90 0 72 144 216 288]*pi./180;%相移
h=zeros(1,carrier_count);%1*100
hh=[];
    for k=1:r
        %deta=[zeros(1,d(k)-1),1,zeros(1,carrier_count-d(k))];
        h1=a(k)*exp(j*((2*pi*T*fd*d(k)/carrier_count)));
        %h1=a(k)*exp(j*((2*pi*T*fd*d(k)/carrier_count)));
        hh=[hh,h1];
    end
    h(d+1)=hh;%3 4 5 6 10 14處有多徑效應
%noise=randn(1,length(X7))+j.*randn(1,length(X7)); 
%--------------------------------------------------------

channel1=zeros(size(X7));%1*1632
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;%4徑干擾后的數據流1*1632
%---------------------------------------------------------------


%---------------------------------------------------------------
%----------------------------------------------------------------
%加高斯白噪聲
Error_ber=[];%誤比特率
Error_ber1=[];
Error_ber2=[];%誤比特率
Error_ber3=[];
%Error_ser=[];%誤符號率
for snr_db=0:snr:N_snr %0:8:40

    code_power=0;
    code_power=[norm(Tx_data)]^2/(length(Tx_data));%信號的符號功率
    %bit_power=var(Tx_data);
    bit_power=code_power/bits_per_symbol;%比特功率 
    noise_power=10*log10((bit_power/(10^(snr_db/10))));%噪聲功率
    noise=wgn(1,length(Tx_data),noise_power,'complex');%產生GAUSS白噪聲信號
    
    Y7=Tx_data+noise;

%-------------------------------------------------------
  %串并變換
   Y6=reshape(Y7,IFFT_bin_length+GI,symbols_per_carrier).';%先變成136*12，再轉置成12*136，恢復成行為符號，列為載波
   
  %去保護間隔
    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);%每行的符號進行128點fft  12*128
     Y3=Y4(:,carriers);%去掉尾部12列原補零點， 12*116
 %-------------------------------------------------------------   
 %LS信道估計
  H=[];
  Y2=Y3(:,signal);
  Rx_training_symbols=Y3(:,pilot);
  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);
  %disp(training_symbols)
  training_symbol2=inv(training_symbol1);
  Hls=training_symbol2*Rx_training_symbols0;
  Hls1=reshape(Hls,symbols_per_carrier,Np);
  HLs=[];
  HLs1=[];
 if ceil(carrier_count/LI)==carrier_count/LI
     for k=1:Np-1
        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
  %Hls1=Hls.';
  %H=repmat(Hls1,symbols_per_carrier,1);%將導頻擴展成symbols_per_carrier*carrier_count矩陣
  Y1=Y2./HLs;
  
  
%-------------------------------------------------------------------

 
 
 
     
             
             
%-------------------------------------------------------------
  %并串變換
  YY=reshape(Y2.',1,N_number/bits_per_symbol);
  YY1=reshape(Y1.',1,N_number/bits_per_symbol);
 
%------------------------------------------------------------
%QPSK解調
   y_real=sign(real(YY));
   y_image=sign(imag(YY));
   y_re=y_real./sqrt(2);
   y_im=y_image./sqrt(2); 
   y_real1=sign(real(YY1));
   y_image1=sign(imag(YY1));
   y_re1=y_real1./sqrt(2);
   y_im1=y_image1./sqrt(2); 
 
   r00=[];
   r01=[];
   r10=[];
   r11=[];
 
  for k=1:length(y_real);
     r00=[r00,[y_real(k),y_image(k)]];
  end;
  for k=1:length(y_real1);
     r10=[r10,[y_real1(k),y_image1(k)]];
  end;
 
 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;

    XX(find(r01>0))=1;
%-------------------------------------------------------------
%計算在不同信噪比下的誤比特率并作圖

 dif_bit=s-r01; 
 dif_bit1=s-r11; 

 ber_snr=0;    %紀錄誤比特數
    for k=1:N_number;
       if dif_bit(k)~=0;
         ber_snr=ber_snr+1;
       end
   end;
 ber_snr1=0;    %紀錄誤比特數
    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;
BER1=Error_ber1./N_number;
%-------------------------------------------------------------
%-------------------------------------------------------------
 i=0:snr:N_snr;
semilogy(i,BER,'-*r');

hold on;
semilogy(i,BER1,'-og');
hold on;

grid on;

legend('No Channel Estimation','LS Channel Estimation');
hold off