ofdm_cfo1.m

OFDM信号的频偏校正程序

%% generate the OFDM data using for blind timing estimation;

clear all;

close all;

clc;

%% load the original state of random squence;
load randn_set_file_y5

%% the original state of uniform distribution;
randn('state',sn_set_y2);

%% the original state of Gaussian distribution;
rand('state',s_set_y2);

%% the bandwidth of OFDM systems;
BW=20e6;

%% the original sampling period, which is also the reciprocal of bandwidth;
Ts=1/BW;

%% the oversampling factor;
J1=40;

%% the downsampling factor;
os=20;

%% the oversampling factor;
J2=2;

%% the oversampling period;
Tss=Ts/J2;

%% the length of one OFDM symbol;
sym_l=128; 

%% the length of the prefix;
pre_l=12;

%% the sub-carrier interval;
SBW=BW/sym_l;

%% the transmitted rate of input data;
Fd=1;

%% the transmitted rate of output data;
Fs=1;

%% the number of overall OFDM blocks;
b_n=10; 

%% exploit M-ary modulation style;
M=4;

%% the number of the array elements;
arr_l=4;

%% exploit half-wavelength spacing;
sidelength=0.5;

%% generate M-ary random sequence as modulated information;
xs=randint(sym_l*b_n,1,M);

%% modulate the user information;
xs_mod0=modmap(xs,Fd,Fs,'qam',M);

%% the modulated data by combining the real part with image part;
xs_mod=xs_mod0(:,1)+j*xs_mod0(:,2);

%% generate four M-ary random sequences as interference data;
xi=randint(sym_l*b_n,1,M);

%% modulate the interference data;
xi_mod0=modmap(xi,Fd,Fs,'qam',M);

%% the modulated interference data by combining the real part with image part;
xi_mod=xi_mod0(:,1)+j*xi_mod0(:,2);

clear xs xs_mod0 xi xi_mod0;
%% save the signal data;
x_s=[];

%% save the interference data;
x_i=[];

%% assign each OFDM block to each column of the matrix;
for i1=1:b_n
    
    x_s=[x_s xs_mod((i1-1)*sym_l+1:i1*sym_l,:)];
    
    x_i=[x_i xi_mod((i1-1)*sym_l+1:i1*sym_l,:)];
    
end

%% normlize the signal mean power;
x_s=sym_l^0.5/2^0.5*J1.*x_s;

%% normlize the interference mean power;
x_i=sym_l^0.5/2^0.5*J1.*x_i;

%% padding zeros in the middle of the modulated signal;
xs_ifft=ifft([x_s(1:sym_l/2,:);zeros(sym_l*(J1-1),b_n);x_s(sym_l/2+1:sym_l,:)],sym_l*J1,1);

%% padding zeros in the middle of the modulated interference;
xi_ifft=ifft([x_i(1:sym_l/2,:);zeros(sym_l*(J1-1),b_n);x_i(sym_l/2+1:sym_l,:)],sym_l*J1,1);

% clear xs_mod xi_mod x_s x_i;
%% insert perfix to form OFDM blocks of signal;
xs_pre=[xs_ifft((sym_l-pre_l)*J1+1:sym_l*J1,:);xs_ifft];

%% insert perfix to form OFDM blocks of interference;
xi_pre=[xi_ifft((sym_l-pre_l)*J1+1:sym_l*J1,:);xi_ifft];

%% save the series data stream of signal;
x_s=[];

%% save the series data stream of interference;
x_i=[];

% break;


for i2=1:b_n
    
    x_s=[x_s;xs_pre(:,i2)];
    
    x_i=[x_i;xi_pre(:,i2)];
    
end

% break;

f_cfo=0.3*SBW;%% the frequency offset;

ph_r=exp(j*2*pi*f_cfo*[1:length(x_s)].'*Ts/J1);

x_s=x_s.*ph_r;

% clear xs_ifft xi_ifft xs_pre xi_pre;
%% the length of the series data stream;
yl=length(x_s);

%% raised cosine filter;
f_t0=rcosflt(1,1,40,'norm',0.05,3);

%% cut the front 241 points;
ft=f_t0(1:241,:);

%% filter the  OFDM signal by raised cosine filter;
x_fs=filter(ft,1,x_s);

%% cut the front 121 points;
xs=x_fs(121:yl,:);

% break;

% clear x_s x_fs;
%% the length of the received data;
yyl=length(xs);

%% the OFDM signal mean power;
s_mp=norm(xs)^2/yyl;

%% the received interference passing by raised cosine filter;
x_fi=filter(ft,1,x_i);

%% cut the front 241 points;
xi=x_fi(121:yl,:);

clear x_i x_fi;
%% the interference signal mean power;
i_mp=norm(xi)^2/length(xi);

%% the addtive white gaussian noise;

G_noise_0=1/2^0.5*(randn(yl,arr_l)+j*randn(yl,arr_l));
    
%% filter the noise using raised cosine filter;
G_noise_1=filter(ft,1,G_noise_0);

clear G_noise_0;
%% cut the front 121 points of the filtered noise ;
G_noise=G_noise_1(121:yl,:);

clear G_noise_1;
%% the recieved noise of the first antenna;
noise1=G_noise(:,1);

%% the mean power of the noise;
g_mp=norm(noise1)^2/yyl;

clear noise1;
%% normlized SNR equals zero;
xss=(1/(s_mp/g_mp)^0.5).*xs;

%% normlized INR equals zero;
xii=(1/(i_mp/g_mp)^0.5).*xi;

clear xs xi;
% the signal to noise ratio of the first ray;
SNR=10;

%% the interference to noise ratio of the first ray;
INR=5;

%% the amplified signal amplitude;
sig_a=10^(SNR/20);

%% the amplified interference amplitude;
inf_a=10^(INR/20);

% after adjusting the SNR, the signal vector;
xss=sig_a.*xss;

%% after adjusting the INR, the interference signal vector;
xii=inf_a.*xii;

%% the original sampling position;
Lorig=(sym_l+2*pre_l)*J1;

%%the sampling starting position;
L1=Lorig+1;

%% the terminal sampling position;
lr=yyl;

%% the number of multipath rays;
L_rays=4;

%% the arrival angle of multipath OFDM signals;
ths=[52.4;47.8;57.5;63.4];;

%% the arrival angle of multipath interference signals;
thi=[-35.5;-29.6;-39.6;-43.5];

%% the time delay of multipath OFDM signals;
ds_soi = [0;24;58;98];

%% the time delay of multipath interference signals;
di_soi=[0;58;91;120];

%% the propogation loss of multipath OFDM signals;
Ksis = [0.98+0.21j;0.69+0.16j;0.34+0.19j;0.09-0.08j];

%% the propogation loss of multipath interference signals;
Ksii=[-0.17+0.98j;0.31-0.46j;-0.43+0.11j;-0.06-0.16j];

 for i3=1:L_rays
    
  %% save the multipath rays of OFDM signals;
  s_soi(:,i3)=xss(L1-ds_soi(i3):os:lr-ds_soi(i3),:);
  
  %% save the multipath rays of interference signals;
  i_soi(:,i3)=xii(L1-di_soi(i3):os:lr-di_soi(i3),:);
  
   
 end

 clear xss xii;
 
 for i4=1:L_rays 
 
  %% the array manifold of the OFDM signals;
  bs_soi(:,i4)=Ksis(i4)*steering(ths(i4),arr_l,sidelength);
  
  %% the array manifold of the interference signals;
  bi_soi(:,i4)=Ksii(i4)*steering(thi(i4),arr_l,sidelength);

 end
 
%% the received user signal of a single ray of the antenna array;
%  arr_s=bs_soi(:,[1])*s_soi(:,[1]).';

%% the received user signal of multipath rays of the antenna array;
arr_s=bs_soi*s_soi.';

%% the received interference signal of a single ray of the antenna array;
% arr_i=bi_soi(:,[1])*i_soi(:,[1]).';
 
%% the received interference signal of multipath rays of the antenna array;
arr_i=bi_soi*i_soi.';

%% the received noise of the antenna array;
arr_n=G_noise(L1:os:lr,:).';

clear s_soi i_soi G_noise;

% the array output data with interference signal;
% arr_X=(arr_s+arr_i+arr_n);

%% the array output data without interference signal;

arr_X=arr_s+arr_n;

% arr_X=arr_s;

b_mm=5;

iik=[1:sym_l/2 sym_l*3/2+1:sym_l*J2];

% iik=[-sym_l+1:-sym_l/2 sym_l/2+1:sym_l];


% % 
% % Wp=[];
% % 
% % for k=1:sym_l
% %     
% %     Wp=[Wp exp(j*2*pi*(iik(k)-1)*SBW*[1:sym_l*J2].'*Tss)];
% %     
% % end
% % 

Wp = exp(j*2*pi*[1:256]'*(iik-1)/256);

b_m=40;

f=zeros(1*b_m+1,1);

index=0;


% break;

for ii=0:40
    
    ii
    
    index=index+1;
    
    fre_e=ii*0.1*SBW;

%      fre_e = 2.3*SBW;
    
    Z=diag(exp(j*2*pi*fre_e*Tss*[0:sym_l*J2-1].'));
    
    R=zeros(arr_l,arr_l);
   
    for k=1:b_mm
        
    Y=arr_X(:,(sym_l+pre_l)*(k-1)*J2+1:(sym_l+pre_l)*(k-1)*J2+sym_l*J2).';

    R=R+Y'*Z*(eye(sym_l*J2,sym_l*J2)-Wp*Wp'./(sym_l*J2))*conj(Z)*Y;
    
    end
    
%     clear Y Z;

    [V_R,d_R]=eig(R);
    
%     [min_v,min_ind]=min(real(diag(d_R)));
    
    Wopt=V_R(:,1);
    
    f(index)=Wopt'*R*Wopt;
    
%     clear R;
    
end

plot([0:b_m],abs(f),'r');

grid;


%% save the state information of random sequences;
  sn_set_y2=randn('state');

  s_set_y2=rand('state');

save randn_set_file_y5 sn_set_y2 s_set_y2;