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

Fs?=?3840000*8;??????????????????%?Sampling?Frequency
Fd?=?3840000;??????????????????%?Symbol?Frequency?四倍采樣速率
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?每個符號輸出兩個采樣點
Offset?=?32;????????????????%?

timing_error?=?0;
datalen?=?Fs?/?Fd?*?（Data_Len?-?Offset）;
displaysize??=?1280;
ted_out?=?zeros（1displaysize）;
Interp_Pos?=?2*Ratio?+?Ratio;
Rec_out?=?zeros（1displaysize）;

disp（‘1?Data?Send‘）;
%1+++++++++++++Data?Source+++++++++++++++++++
disp（‘??1.1?Data?Source‘）;
x?=?（-1）.^（rand（1Data_Len）>0.5）?+?j?*?（-1）.^（rand（1Data_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（xFdFs‘sqrt‘RolloffCoef）;

%+++++++++++++channel?simulation++++++++++++++
%???Add?White?Offsetoise?Using?SOffsetR?Setting????????
%+++++++++++++++++++++++++++++++++++++++++++++
disp（‘2?Channel?Simulation‘）;
c_t?=?awgn（x_tSNR‘measured‘）;

%++++++++++++++++++receive++++++++++++++++++++
disp（‘3?Receive‘）;

%4++++++++++Matching?Filter++++++++++++++++++++
disp（‘??3.1?Matching?Filter‘）;
%matched_data=rcosflt（r_tFdFs‘sqrt/Fs‘RolloffCoef）;
r_t=rcosflt（c_tFdFs‘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（TTi2beta）;
k?=?1;
m=1;
count?=?0;

while（??Interp_Pos?????%++++++++++++The?first?half++++++++++++++++++
????mk?=?floor（Interp_Pos）;?????????%?Integer?Part
????uk?=?Interp_Pos-mk;?????????????%?Fraction?Part
????u（m）=uk;
??