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Commit 249e6715 authored by Matthieu Kanj's avatar Matthieu Kanj
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add synchro fucntions for NPSS and NSSS signal for NB-IoT

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openair1/PHY/LTE_REFSIG/first_synchro_NB_IoT.m 0 → 100644
View file @ 249e6715
function [ theta_estim, estim_CFO ] = Fc_first_synchro( observation, L_frame, L_sub_frame, FFT_size, L_symbol, N_subframe_observation, L_CP, SNR, type_first_estim )
% This function performs the estimation of the beginning of symbols as well
% as the estimation of CFO. It allows for a coarse synchronization
gamma = zeros(1,L_frame);
epsilon = zeros(1,L_frame);
for n = 1 : 1 : length(gamma)
gamma(n) = sum(observation(n:n+L_CP-1).*conj(observation(n+FFT_size:n+FFT_size+L_CP-1)));
epsilon(n) = sum(abs(observation(n:n+L_CP-1)).^2 + abs(observation(n+FFT_size:n+FFT_size+L_CP-1)).^2);
end
rho = 10^(SNR/20)/(10^(SNR/20)+1);
theta = 2*abs(gamma)-rho*(epsilon);
% Estimation of the symbol start and the corresponding CFO
theta_reshape = reshape(theta,L_symbol,N_subframe_observation*L_sub_frame);
% gamma_reshape = reshape(gamma,L_symbol,N_subframe_observation*L_sub_frame); % useful for estimation of CFO
[~,index_max] = max(theta_reshape); % where theta is max symbol by symbol
switch type_first_estim
case 1
%estimation by mean
theta_estim = sum(index_max)/length(index_max); % estimation by mean
estim_CFO = -1/(2*pi)*atan(imag(gamma(round(theta_estim)))/real(gamma(round(theta_estim))));
case 2
%estimation by majority
counter_index = zeros(1,L_symbol);
for k = 1 : 1 : length(index_max)
counter_index(index_max(k)) = counter_index(index_max(k)) + 1; % add the number of index_max
end
[~,theta_estim] = max(counter_index); % get the max of index max -> theta estim
% index_index_max = find(index_max == theta_estim);
% estim_CFO = -1/(2*pi)*atan(imag(gamma(round(theta_estim)))/real(gamma(round(theta_estim))));
estim_CFO_vec = -1/(2*pi)*atan(imag(gamma(round(theta_estim:L_symbol:end)))./real(gamma(round(theta_estim:L_symbol:end))));
% estim_CFO_vec2 = -1/(2*pi)*atan(imag(gamma_reshape(theta_estim,index_max(index_index_max)))./real(gamma_reshape(theta_estim,index_max(index_index_max))));
estim_CFO = sum(estim_CFO_vec)/length(estim_CFO_vec);
% estim_CFO_2 = sum(estim_CFO_vec2)/length(estim_CFO_vec2);
otherwise
print('error: type of estimation not defined')
end
openair1/PHY/LTE_REFSIG/main_synchro_NPSS_NB_IoT.m 0 → 100644
View file @ 249e6715
clear all
close all
% description: test synchro using CP for time-freq. synchro
% and ZC sequence for beginning of the radio frame estimation
% date : 09/03/2017
% author : Vincent Savaux, b<>com, Rennes, France
% email: vincent.savaux@b-com.com
% Parameters
u = 5; % root of ZC sequence
size_RB = 12; % number of sub-carrier per RB
N_ZC = size_RB-1;
L_sub_frame = 14;
j = 1i;
CFO = 0.1; % normalized CFO
N_frames = 4; % at least 3
N_sub_frame = 10*N_frames; % how many simulated sub_frame you want
FFT_size = 128;
N_zeros = (FFT_size-size_RB)/2; % Number of zero subcarriers in upper and lower frequencies
L_CP = round(4.6875/(66.7)*FFT_size); % Number of samples of the CP
L_symbol = (FFT_size + L_CP);
L_frame = (FFT_size + L_CP)*L_sub_frame*10;
L_signal = (FFT_size + L_CP)*L_sub_frame*N_sub_frame;
normalized_time = 0 : 1 : L_signal-1;
SNR_start = 0; % in dB
SNR_end = 30; % in dB
N_subframe_observation = 10; % length of observation for syncronization
N_loop = 1000; % number of runs, for good statistics
type_first_estim = 2; % 1 -> estimation by mean, 2-> estimation by majority
matrix_error_theta_1 = zeros(N_loop,SNR_end-SNR_start+1);
matrix_error_theta_2 = zeros(N_loop,SNR_end-SNR_start+1);
matrix_error_angle_1 = zeros(N_loop,SNR_end-SNR_start+1);
matrix_error_angle_2 = zeros(N_loop,SNR_end-SNR_start+1);
matrix_error_angle_3 = zeros(N_loop,SNR_end-SNR_start+1);
matrix_error_BOF = zeros(N_loop,SNR_end-SNR_start+1);
for SNR = SNR_start : 2 : SNR_end
for loop = 1 : N_loop
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Creation of the signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ZC sequence in frequency domain
vec_n = 0:N_ZC-1;
f_ZC_sequence = exp(-j*pi*u*vec_n.*(vec_n+1)/N_ZC);
f_NPSS_symbol = [f_ZC_sequence.';0]; % one NPSS symbol
f_NPSS_frame = [zeros(size_RB,3),kron(ones(1,L_sub_frame-3),f_NPSS_symbol)];
% OFDM sub_frame in frequency domain -> modulation : QPSK
%random QPSK elements:
f_OFDM_frames = (2*randi([0,1],size_RB,L_sub_frame*N_sub_frame)-1) + j*(2*randi([0,1],size_RB,L_sub_frame*N_sub_frame)-1);
%replace the k*6th subframes by f_NPSS_frame:
f_LTE_frames = f_OFDM_frames;
for k = 0 : N_frames-1
N_index = k*10*L_sub_frame + 85;
f_LTE_frames(:,N_index:N_index+13) = f_NPSS_frame;
end
% IFFT: get frames in time domain (Parralel representation)
f_zero_carriers = zeros(N_zeros,L_sub_frame*N_sub_frame);
f_ups_LTE_frames = [f_zero_carriers;f_LTE_frames;f_zero_carriers]; % add zero carriers up and down the symbols
t_P_LTE_frames = ifft(f_ups_LTE_frames,FFT_size);
% Add CP (Parralel representation)
t_P_LTE_frames_CP = [t_P_LTE_frames(end-L_CP+1:end,:);t_P_LTE_frames];
% Parralel to series conversion
t_S_LTE_frames = reshape(t_P_LTE_frames_CP,1,[]);
% Add a channel frequency offset (CFO)
t_S_received_frames = t_S_LTE_frames.*exp(j*2*pi*CFO*normalized_time/FFT_size);
% Add noise
P_signal = sum(abs(t_S_received_frames).^2)/length(t_S_received_frames);
P_noise = P_signal*10^(-SNR/20);
init_noise = randn(size(t_S_received_frames));
normalized_noise = init_noise/sqrt(sum(abs(init_noise).^2)/length(init_noise));
noise = sqrt(P_noise)*normalized_noise;
t_S_noisy_frames = t_S_received_frames + noise;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Time and frequency synchronization
% The principle is based on the croos-correlation between the received
% sequence and the transmitted SC sequence.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Get an observation, the duration of which is one frame length. The
% beginning of the stored samples is at 1 frame +- 0.5 frame
index_start = L_frame + randi([-L_frame/2,L_frame/2],1);
observation = t_S_noisy_frames(index_start:index_start+1.5*L_frame-1);
f_oversampl_NPSS_symbol = [f_zero_carriers(:,1);f_NPSS_symbol;f_zero_carriers(:,1)];
t_NPPS_unit = ifft(f_oversampl_NPSS_symbol,FFT_size);
t_NPPS_correl = [t_NPPS_unit(end-L_CP+1:end);t_NPPS_unit];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Estimation of start of the symbols and the CFO
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[ theta_estim, estim_CFO ] = first_synchro( observation, L_frame, L_sub_frame, FFT_size, L_symbol, N_subframe_observation, L_CP, SNR, type_first_estim );
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Time and frequency synchronization
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
new_index_start = index_start + theta_estim - 1;
new_vec_time = new_index_start-1 : 1 : new_index_start+1.5*L_frame-2;
new_observation = t_S_noisy_frames(new_index_start:new_index_start+1.5*L_frame-1).*exp(-j*2*pi*estim_CFO*new_vec_time/FFT_size);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Second synchronization: beginning of frame (BOF)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[ BOF ] = second_synchro( new_observation, f_NPSS_symbol , L_frame, L_symbol, FFT_size, L_CP, N_zeros );
exact_index = L_symbol - rem(index_start,L_symbol) + 2;
[error_theta_1,ind_error1] = min([abs(exact_index - theta_estim-L_symbol), abs(exact_index - theta_estim),abs(exact_index - theta_estim+L_symbol)]);
% [error_theta_2,ind_error2] = min([abs(exact_index - theta_estim_2-137), abs(exact_index - theta_estim_2),abs(exact_index - theta_estim_2+137)]);
error_CFO_1 = CFO - estim_CFO;
% error_CFO_2 = CFO - estim_CFO_1;
% error_CFO_3 = CFO - estim_CFO_2;
vec_exact_index = 85 : 140 : N_frames*140;
estim_BOF = ceil((index_start-1)/L_symbol) + BOF ;
error_BOF = min(abs(estim_BOF-vec_exact_index));
matrix_error_theta_1(loop,SNR-SNR_start+1) = error_theta_1;
% matrix_error_theta_2(loop,SNR-SNR_start+1) = error_theta_2;
matrix_error_angle_1(loop,SNR-SNR_start+1) = error_CFO_1;
% matrix_error_angle_2(loop,SNR-SNR_start+1) = error_CFO_2;
% matrix_error_angle_3(loop,SNR-SNR_start+1) = error_CFO_3;
matrix_error_BOF(loop,SNR-SNR_start+1) = error_BOF;
end
end
plot(SNR_start:2:SNR_end,sqrt(sum(abs(matrix_error_theta_1(:,1:2:SNR_end+1)).^2)/N_loop))
hold
% plot(SNR_start:2:SNR_end,sqrt(sum(abs(matrix_error_theta_2(:,1:2:SNR_end+1)).^2)/N_loop))
figure
plot(SNR_start:2:SNR_end,sqrt(sum(abs(matrix_error_angle_1(:,1:2:SNR_end+1)).^2)/N_loop))
hold
% plot(SNR_start:SNR_end,sum(abs(matrix_error_angle_2(:,1:31)))/N_loop)
% plot(SNR_start:SNR_end,sum(abs(matrix_error_angle_3(:,1:31)))/N_loop)
% plot(SNR_start:2:SNR_end,sqrt(sum(abs(matrix_error_angle_2(:,1:2:SNR_end+1)).^2)/N_loop),'s')
% plot(SNR_start:2:SNR_end,sqrt(sum(abs(matrix_error_angle_3(:,1:2:SNR_end+1)).^2)/N_loop),'d')
figure
plot(SNR_start:2:SNR_end,sqrt(sum(abs(matrix_error_BOF(:,1:2:SNR_end+1)).^2)/N_loop))
hold
save
openair1/PHY/LTE_REFSIG/second_synchro_NB_IoT.m 0 → 100644
View file @ 249e6715
function [ BOF ] = Fc_second_synchro( new_observation, f_NPSS_symbol , L_frame, L_symbol, FFT_size, L_CP , N_zeros )
%UNTITLED2 Summary of this function goes here
% Detailed explanation goes here
% new_obs_reshape = reshape(new_observation(1:L_frame), L_symbol, []);
new_obs_reshape = reshape(new_observation, L_symbol, []);
t_new_obs_CP_remov = new_obs_reshape(L_CP+1:end,:);
f_new_symbols = fft(t_new_obs_CP_remov,FFT_size);
for n = 1 : length(f_new_symbols(1,:))
corr(:,n) = xcorr(f_new_symbols(N_zeros+1:N_zeros+12,n),f_NPSS_symbol);
mean = sum(abs(corr(:,n)));
mm(n) = sum((abs(corr(:,n))-mean).^2);
end
for k = 1 : length(mm) - 13
min_var(k) = sum(mm(k:k+13));
end
[~,BOF] = min(min_var);
end
openair1/PHY/LTE_TRANSPORT/nsss_gen_NB_IoT.m 0 → 100644
View file @ 249e6715
clear all
% nsss_gen / matlab
% Copyright 2016 b<>com. All rights reserved.
% description: generation of NSSS subframe
% Reference: 3GPP TS36.211 release 13
% author: Vincent Savaux, b<>com, Rennes, France
% email: vincent.savaux@b-com.com
% Input : \
% Output : matrix NSSS_frame
% Parameters
% frame_number = 100;
% cellID = 200;
% % % Mapping results to estimated u-3
SNR_start = -10;
SNR_end = 2;
vec_SNR = SNR_start : 2 : SNR_end;
N_loop = 40;
Proba_fail = zeros(1,length(vec_SNR));
mat_bn = zeros(4,128); % mat_bn contains the 4 possible Hadamard sequences defined in the standard
mat_bn(1,:) = ones(1,128);
mat_bn(2,:) = [1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 ...
-1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 ...
1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 ...
-1 1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 -1 ...
1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 ...
-1 1 1 -1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 ...
1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1];
mat_bn(3,:) = [1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 ...
-1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 ...
-1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 ...
1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 ...
1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 ...
-1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 ...
-1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1];
mat_bn(4,:) = [1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 ...
-1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 ...
-1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 ...
1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 1 ...
-1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 ...
1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 ...
1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1];
mat_bn = [mat_bn,mat_bn(:,1:4)]; % see the definition of m in stadard
mat_theta_f = zeros(4,132); % mat_bn contains the 4 possible phase sequences defined in the standard
mat_theta_f(1,:) = ones(1,132);
mat_theta_f(2,:) = repmat([1,-j,-1,j],1,33);
mat_theta_f(3,:) = repmat([1,-1],1,66);
mat_theta_f(4,:) = repmat([1,j,-1,-j],1,33);
mat_16_theta = round(kron(mat_theta_f,ones(4,1))); % mat_bn contains the 4x4=16 possible pseudo-random sequences
mat_16_bn = repmat(mat_bn,4,1);
mat_16 = mat_16_theta.*mat_16_bn;
corresponding_values = zeros(16,2); % first column for q, second for theta_f
corresponding_values(:,1) = repmat([0;1;2;3],4,1); % mapping column to q
corresponding_values(:,2) = kron([0;1;2;3],ones(4,1)); % mapping column to theta_f
for k = 1 : length(vec_SNR) % loop on the SNR
N_fail = 0;
for loop = 1 : N_loop
SNR = vec_SNR(k);
frame_number = 2*randi([0,3],1);
cellID = randi([0,503],1);
% function NSSS_subframe = nsss_gen(frame_number,cellID)
theta_f = 33/132*mod(frame_number/2,4); % as defined in stadard
u = mod(cellID,126) + 3; % root of ZC sequence, defined in standard
q = floor(cellID/126);
size_RB = 12; % number of sub-carrier per RB
N_ZC = 131;
L_sub_frame = 14; % number of OFDM symbols per subframe
j = 1i;
vec_n = 0:N_ZC;
vec_n1 = mod(vec_n,131);
vec_bq = mat_bn(q+1,:);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Creation of the signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ZC sequence in frequency domain
ZC_sequence = exp(-j*pi*u*vec_n1.*(vec_n1+1)/N_ZC);
had_sequence = exp(-j*2*pi*theta_f*vec_n);
vec_bq_had = vec_bq.*had_sequence;
P_noise = 10^(-SNR/10); % SNR in dB to noise power
noise = sqrt(P_noise/2)*randn(1,132)+sqrt(P_noise/2)*j*randn(1,132);
vec_d = vec_bq.*had_sequence.*ZC_sequence + noise;
mat_NSSS = flipud(reshape(vec_d,size_RB,L_sub_frame-3));
NSSS_subframe = [zeros(size_RB,3),mat_NSSS];
% end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Exhaustive cell ID research
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
sequence_r = repmat(vec_d,16,1).*conj(mat_16); % this remove the phase component
vec_u = 3 : 128;
mat_u = repmat(vec_u.',1,length(vec_n1));
mat_n1 = repmat(vec_n1,126,1);
sequence_ZC = exp(-j*pi*mat_u.*mat_n1.*(mat_n1+1)/N_ZC);
matrix_max_correl = zeros(126,16); % this will be filled by the maximum of correlation value
for s_ = 1 : 16
seq_ref = sequence_r(s_,:);
for u_ = 1 : 126
correl = xcorr(seq_ref,sequence_ZC(u_,:));
[val_max,ind_max] = max(abs(correl));
matrix_max_correl(u_,s_) = val_max;
end
end
max_correl = max(max(matrix_max_correl)); % get the max of all correlation values
index_max = find(matrix_max_correl==max_correl);
estim_u_ = mod(index_max,126)-1;
index_column = (index_max-mod(index_max,126))/126+1;
estim_q_ = corresponding_values(index_column);
estim_cell_ID = q*126 + estim_u_;
if cellID ~= estim_cell_ID
N_fail = N_fail + 1;
end
end
Proba_fail(k) = N_fail/N_loop;
end
plot(vec_SNR,Proba_fail)
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