How does the nr-prach receiver detect the relationship between prembleid and Ta

PRACH Is to make use of ZC Two characteristics of sequences ：

1.ZC The sequence has a constant amplitude , after DFT After that, the amplitude is also constant ,
This limits the influence of peak to average ratio on the boundary and time flatness of other users , In the calculation process, only the phase needs to be considered , There is no need to consider the amplitude , This simplifies the calculation .
2.ZC Sequences have ideal autocorrelation properties , The property of zero cross-correlation , The sequence length is L_RA, The peak value after autocorrelation is L_RA, After cross-correlation, the value is assigned as close 0, This makes it easy to detect .

The first feature （ Mainly for you to know ）

%%%%%%test dft Amplitude after %%%%%%%%%%
L_RA =839
for  i = 1:1:L_RA
      x_u(i) = exp(-1i*pi*26*i*(i+1)/L_RA);
end
DFT_fre =  abs(fft(x_u,839));
plot(DFT_fre);
title('ZC Sequence DFT The latter is of constant amplitude ');

The second feature determines how to parse preambleid and TA value

We know prach Maximum support 64 Users access at the same time , Because we have 64 individual preamid have access to .

First of all, our husband became 64 Different preambleid Sequence

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Time ：2021.01.16
%%% Briefly ：matalb Simulation prach The detection mechanism of , And then introduce ZC Characteristics of sequences 
%%% author ： Communication pawn 
%%% Modify the record ： 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clc
clear all
filename_u ='F:\4G5G\CDSN\nr-prach\table_6_3_3_1_3.xls';
filename_ncs ='F:\4G5G\CDSN\nr-prach\table_6_3_3_1_5.xls';
%TABLE_6_3_3_1_3 = 
[TABLE_6_3_3_1_3,txt_u,num_u] = xlsread(filename_u);
[TABLE_6_3_3_1_5,txt_ncs,num_ncs] = xlsread(filename_ncs);
L_RA =839;

ZC_zonecfg = 5;% Subcarrier spacing in unrestricted format 1.25khz For example 
N_CS= TABLE_6_3_3_1_5(ZC_zonecfg+1,1);
%%% Find out how many u To satisfy 64 individual preambleid
%%% This example C_v=v*NCS
logic_index_i =50  ;% Take the long sequence as an example , use i Find out u
seq_num =0;
for u_loop = 1:1:64
      if(seq_num<64)
              seq_num = u_loop.*floor(L_RA/N_CS);
      else
          u_loop =u_loop -1;
          break;
      end
end
%%% Get enough u
for   u_loop_init = 1:1:u_loop 
      [row_u ,column_u] = size(TABLE_6_3_3_1_3);
      row_u_x =floor( (logic_index_i+u_loop_init)/column_u)+1;
      column_u_y = mod(logic_index_i+u_loop_init-(row_u_x-1)*column_u,column_u);
      u(1,u_loop_init) = TABLE_6_3_3_1_3(row_u_x,column_u_y);
end
%%%% Generate 64 individual preamble Sequence 
%%% Except for the last one u, Use other u obtain preamble Sequence 
seq_index =0;
 for   u_loop_init = 1:1:u_loop-1 
         %%%% Generate ZC Sequence 
        for  i = 1:1:L_RA
               x_u(i) = exp(-1i*pi*u(1,u_loop_init)*i*(i+1)/L_RA);
        end
        %%% For each u Corresponding preamble Sequence 
        for seq_index = seq_index :1:(seq_index+floor(L_RA/N_CS)-1)
              Cv = N_CS*mod(seq_index+1,floor(L_RA/N_CS));
              for n = 0:1:L_RA-1
              preamble_seq(seq_index+1,n+1) = x_u(mod((n+Cv),L_RA)+1);
              end
        end
 end
 %%% the last one u Generated preamble Sequence 
 seq_remain = 64-(u_loop-1)*floor(L_RA/N_CS);
 for  i = 1:1:L_RA
        x_u(i) = exp(-1i*pi*u(1,u_loop)*i*(i+1)/L_RA);
end
%%% For each u Corresponding preamble Sequence 
for seq_index = seq_index+1 :1:(seq_index+seq_remain)
              Cv = N_CS*mod(seq_index+1,floor(L_RA/N_CS));
              for n = 0:1:L_RA-1
              preamble_seq(seq_index+1,n+1) = x_u(mod((n+Cv),L_RA)+1);
              end
 end
%%% Generated 64 individual preamble Sequence 

Be careful Here I import 211 Two of the agreements excel form

table_6_3_3_1_3 In order to determine u,table_6_3_3_1_5 In order to determine NCS Of
You can go 38.211 Go inside , Easy to find , The picture is too big, it seems excel Can't import , I'll cut a small picture , Let's find it by ourselves .

preable The sequence is autocorrelated

Peak size and location ： The peak position is at the first point , The peak is 839（ Divide by 839）

%%% Test the same preambleid The position of the peak at the time of autocorrelation %%%
%%% Time domain correlation is equal to frequency domain conjugate multiplication %%%%%%

test_com_id_fre = fft(preamble_seq(1,:),839).*conj(fft(preamble_seq(1,:),839));
test_com_id_time = abs(ifft(test_com_id_fre,839))./L_RA;
figure(1);
plot(test_com_id_time);
title(' The same preamble The sequence autocorrelation detects the originator preambleid');
[y_max,x_max] = max(test_com_id_time);
text(x_max,y_max,['(',num2str(x_max),',',num2str(y_max),')'],'color','r');

Different preamble Sequences are correlated

The beginning preamble id yes 1 For receiving 4 To test

The detected delay should be NCS3 =263=78

%%%%%%%% The same u Different preambleid Detection delay %%%%%%%%%
%%%preambleid 1 and preambleid 3%%%
test_com_id_fre = fft(preamble_seq(1,:),839).*conj(fft(preamble_seq(4,:),839));
test_com_id_time = abs(ifft(test_com_id_fre,839))./L_RA;
figure(2);
plot(test_com_id_time);
title(' The same u Different preambleid Detection delay ');
[y_max,x_max] = max(test_com_id_time);
text(x_max,y_max,['(',num2str(x_max),',',num2str(y_max),')'],'color','r');
[y_min,x_min] = min(test_com_id_time);
text(x_min,y_min,['(',num2str(x_min),',',num2str(y_min),')'],'color','r');

The receiving end uses the same preamble Sequence , But the originator must have a delay

Here we simulate 4 Time delay of points , How much delay does each point represent 839 A point of time and our agreement with format0 For example ,24576K The time taken is consistent , Just push it yourself .

%%%%%%%% testing preamble Internal delay %%%%%%%%%%%%%
preamble_seq_delay =[preamble_seq(1,4:839),[0 0 0]]
test_com_id_fre = fft(preamble_seq(1,:),839).*conj(fft(preamble_seq_delay,839));
test_com_id_time = abs(ifft(test_com_id_fre,839))./L_RA;
figure(4);
plot(test_com_id_time);
title(‘ The same preamble The sequence originator has a delay measurement delay ’);
[y_max,x_max] = max(test_com_id_time);
text(x_max,y_max,[’(’,num2str(x_max),’,’,num2str(y_max),’)’],‘color’,‘r’);

The originator is preambleid yes 4 and 5（ Two ue Access at the same time ）, For receiving 4 Deconstruction

Can solve the original preamble yes 4, This also shows the difference preamble Sequence superposition does not affect each other .

%%%%%% The originator is preambleid  yes 4 and 5（ Two ue Access at the same time ）, For receiving 4 Deconstruction 
%%% Correlation can resolve the corresponding preambleid
for n = 0:1:L_RA-1
send_seq(1,n+1) = preamble_seq(4,n+1)+preamble_seq(5,n+1);
end
test_com_id_fre = fft(send_seq(1,:)).*conj(fft(preamble_seq(4,:),839));
test_com_id_time = abs(ifft(test_com_id_fre,839))./L_RA;
figure(6);
plot(test_com_id_time);
title('preambleid  yes 4 and 5（ Two ue Access at the same time ）, The receiving end detects 4');
[y_max,x_max] = max(test_com_id_time);
text(x_max,y_max,['(',num2str(x_max),',',num2str(y_max),')'],'color','r');

Different one u Corresponding preamble The sequence cannot detect the time delay

%%%%%%%% Different one u Different preambleid Nothing can be detected %%%%%%,
%%%preambleid 1 and preambleid 40%%%
test_com_id_fre = fft(preamble_seq(1,:),839).*conj(fft(preamble_seq(40,:),839));
test_com_id_time = abs(ifft(test_com_id_fre,839))./L_RA;
figure(3);
plot(test_com_id_time);
title(' Different one u Different preambleid Nothing can be detected ');
[y_max,x_max] = max(test_com_id_time);
text(x_max,y_max,['(',num2str(x_max),',',num2str(y_max),')'],'color','r');

Finally, the previous correlation is realized by conjugate multiplication in the frequency domain , Of course, the time domain itself can be directly turned off first

The number of time domain direct correlation points becomes 2N-1, Just look on the right ,865-839=26, Time delay detected .

%%%%%% Time domain correlation %%%%%%%%%%%%%%
test_com_id_time = abs(xcorr(preamble_seq(40,:),preamble_seq(41,:)))./L_RA;
figure(5);
plot(test_com_id_time);
title(' Different preamble Time domain autocorrelation of sequences ');
[y_max,x_max] = max(test_com_id_time);
text(x_max,y_max,['(',num2str(x_max),',',num2str(y_max),')'],'color','r');