Gardner定时恢复

%File:timing_syn.m timing synchronization
clc
clear
Data_Len = 2000;

Fs = 3840000*8;                  % Sampling Frequency
Fd = 3840000;                  % Symbol Frequency 四倍采样速率
SNR = 30;                   % S/N Ratio for Chanel Simulatioin 
RolloffCoef = 0.22;         % Roll Off Coeff.
T_Gain = 0.02;              % TED Loop Gain

Ratio = Fs/Fd/2;            % = Ts/Td/2 每个符号输出两个采样点
Offset = 32;                % 

timing_error = 0;
datalen = Fs / Fd * (Data_Len - Offset);
displaysize  = 128;
ted_out = zeros(1,displaysize);
Interp_Pos = 2*Ratio + Ratio;
Rec_out = zeros(1,displaysize);

disp('1 Data Send');
%1+++++++++++++Data Source+++++++++++++++++++
disp('  1.1 Data Source');
x = (-1).^(rand(1,Data_Len)>0.5) + j * (-1).^(rand(1,Data_Len)>0.5);

figure(1)
plot(x,'r*');
xlabel('real')
ylabel('image')
xlim([-2.0 2.0]);
ylim([-2.0 2.0]);
title('Sending Conset')
grid on;

%+++++++++++++pulse shaping+++++++++++++++++++
%        Using Rolloff Setting
%+++++++++++++++++++++++++++++++++++++++++++++
disp('  1.2 Pulse Shaping');
x_t=rcosflt(x,Fd,Fs,'sqrt',RolloffCoef);

%+++++++++++++channel simulation++++++++++++++
%   Add White Offsetoise Using SOffsetR Setting        
%+++++++++++++++++++++++++++++++++++++++++++++
disp('2 Channel Simulation');
c_t = awgn(x_t,SNR,'measured');

%++++++++++++++++++receive++++++++++++++++++++
disp('3 Receive');

%4++++++++++Matching Filter++++++++++++++++++++
disp('  3.1 Matching Filter');
%matched_data=rcosflt(r_t,Fd,Fs,'sqrt/Fs',RolloffCoef);
r_t=rcosflt(c_t,Fd,Fs,'sqrt/Fs',RolloffCoef);
matched_data=[r_t(Offset+1:end-Offset)];

%++++++++++++Timing Recovery+++++++++++++++++++
% =======Gardner Timing Recovery=============== 
%  TE(k)={Y[(k-1)Td]-Y[kTd])*Y[(kTd-Td/2]
% =======Parabolic Interpolation=============== 
%     C_2 =  0.5 * mu^2 - 0.5 * mu;
%     C_1 = -0.5 * mu^2 + ( 0.5 + 1 ) * mu;
%     C0  = -0.5 * mu^2 + ( 0.5 - 1 ) * mu + 1;
%     C1  =  0.5 * mu^2 - 0.5 * mu;
%+++++++++++++++++++++++++++++++++++++++++++++++
disp('  3.2 Timing Recovery');
C_2 = inline('0.5*u^2-0.5*u');
C_1 = inline('-0.5*u^2+1.5*u');
C0  = inline('-0.5*u^2-0.5*u+1');
C1  = inline('0.5*u^2-0.5*u');

ted_data1 = matched_data(Offset);
ted_data2 = matched_data(Offset+Ratio);

% hp = timing_prefilter(T,Ti,2,beta);
k = 1;
count = 0;

while(  Interp_Pos < ( datalen - 6 ) )
    %++++++++++++The first half++++++++++++++++++
    mk = floor(Interp_Pos);         % Integer Part
    uk = Interp_Pos-mk             % Fraction Part
    
    C_2u = C_2(uk);
    C_1u = C_1(uk);
    C0u  = C0(uk);
    C1u  = C1(uk);
    
    %+++++++++++++++Get Sampling Data+++++++++++++
%     data1 = matched_data(mk);
%     data2 = matched_data(mk+1);
%     data3 = matched_data(mk+2);
%     data4 = matched_data(mk+3);
    
    data1 = matched_data(mk-1);
    data2 = matched_data(mk);
    data3 = matched_data(mk+1);
    data4 = matched_data(mk+2);
    
    %+++++++++++++Interpolation+++++++++++++++++++
    % out = C_2 * in_i(4) + C_1 * in_i(3) + C0 * in_i(2) + C1 * in_i(1);
    %+++++++++++++++++++++++++++++++++++++++++++++
    Interp_data = C_2u * data4 + C_1u * data3 + C0u * data2 + C1u * data1;
    Rec_out(k) = Interp_data;
    ted_data3 = Interp_data;

    Interp_Pos = Interp_Pos + Ratio + timing_error;% 
      
    %++++++++++++++Gardner TED+++++++++++++++++++
    % temp= ( ted_data1 - ted_data3 ) * ted_data2;
    %++++++++++++++++++++++++++++++++++++++++++++
    temp = ( ted_data1 - ted_data3 ) * conj(ted_data2);

    %++++++++++++++Loop Filter++++++++++++++++++
    timing_error = real(temp) * T_Gain;
    %timing_error = timing_error + real(temp) * T_Gain;
    
    ted_out(k) = timing_error;
  
    %+++++++++++++The second half+++++++++++++++
    mk = floor(Interp_Pos);
    uk = Interp_Pos-mk
    
    C_2u = C_2(uk);
    C_1u = C_1(uk);
    C0u  = C0(uk);
    C1u  = C1(uk);
    
    %+++++++++++++++Get Sampling Data++++++++++++++
%     data1 = matched_data(mk);
%     data2 = matched_data(mk+1);
%     data3 = matched_data(mk+2);
%     data4 = matched_data(mk+3);
    
    data1 = matched_data(mk-1);
    data2 = matched_data(mk);
    data3 = matched_data(mk+1);
    data4 = matched_data(mk+2);
    %+++++++++++++++++++Interpolation++++++++++++++
    % out = C_2 * in_i(4) + C_1 * in_i(3) + C0 * in_i(2) + C1 * in_i(1);
    %++++++++++++++++++++++++++++++++++++++++++++++
    Interp_data = C_2u * data4 + C_1u * data3 + C0u * data2 + C1u * data1;
 
    %+++Update Sampling Position(NCO Process)++++
    %  NewPosition = OldPosition + Fs/Fd/2 + TED 
    %++++++++++++++++++++++++++++++++++++++++++++
    Interp_Pos = Interp_Pos + Ratio + timing_error;

    ted_data1 = ted_data3;
    ted_data2 = Interp_data;  

    k = k + 1;
    count = count + 1;
    if count==displaysize
        count = 0;
        k = 1;
        figure(2);
        plot(Rec_out,'r*');
        xlabel('real')
        ylabel('image')
        xlim([-2.0 2.0]);
        ylim([-2.0 2.0]);
        title('Receiving Conset')
        grid on;

        figure(3);
        plot(ted_out,'r+');
        ylim([-0.2 0.2]);
        title('TED Error')
        grid on;
        pause(0.1);
    end
end
figure(3);
stem(Rec_out);
grid;