ofdm.m

基于训练序列的OFDM的信道估计

% ZC = conj(Z) returns the complex conjugate of the elements of Z. 
% AlgorithmIf Z is a complex array: conj(Z) = real(Z) - i*imag(Z)
%－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
time_wave_matrix = ifft(IFFT_modulation');                                     % 进行IFFT操作
time_wave_matrix = time_wave_matrix';                                          % 进行矩阵转置
cp_add = zeros(4 + symbols_per_carrier + 1,cp_length);
 for i = 1:4 + symbols_per_carrier + 1
    cp_add(i,:) = time_wave_matrix(i,(IFFT_bin_length - cp_length + 1) : IFFT_bin_length);
end
time_wave_matrix_cp = [cp_add,time_wave_matrix];
for i = 1: 4 + symbols_per_carrier + 1                     % windowed_time_wave_matrix(i,:) = real(time_wave_matrix(i,:)) .* hamming(IFFT_bin_length)';
    windowed_time_wave_matrix_cp(i,:) = real(time_wave_matrix_cp(i,:));
end
%－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
% Serialize the modulating waveform
%   - sequentially take each row of windowed_time_wave_matrix and construct a row vector
%   - the row vector will be the modulating signal
%   - note that windowed_time_wave_matrix is transposed, this is to account for the way the
%     Matlab 'reshape' function works (reshape takes the columns of the target matrix and 
%     appends them sequentially) 
% get the real part of the result of IFFT
% 这一步可以省略，因为IFFT结果都是实数
% 由此可以看出，只是取了IFFT之后载波上的点，并未进行CP的复制和添加end
%－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
ofdm_modulation = reshape(windowed_time_wave_matrix_cp', 1, (IFFT_bin_length + cp_length)*(4 + symbols_per_carrier+1));   % P2S operation
%－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Tx_data = ofdm_modulation;
%－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
%                                  信道模拟                                    
%－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
% The channel model is Gaussian (AWGN) only 
%   - Rayleigh fading would be a useful addition
%－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
d1 = 40; a1 = 0.2; d2 = 50; a2 = 0.3; d3 = 60; a3 = 0.4; 
%d4 = 160; a4 = 0.9;
copy1 = zeros(size(Tx_data)) ;
for i = 1 + d1: length(Tx_data)
copy1(i) = a1*Tx_data( i - d1) ;
end
copy2 = zeros(size(Tx_data) ) ;
for i = 1 + d2: length( Tx_data)
copy2(i) = a2*Tx_data( i - d2) ;
end
copy3 = zeros(size(Tx_data) ) ;
for i = 1 + d3: length(Tx_data)
copy3(i) = a3*Tx_data ( i - d3) ;
end
copy4 = zeros(size(Tx_data) ) ;
for i = 1 + d4: length( Tx_data)
copy4(i) = a4*Tx_data(i - d4) ;
end
Tx_data = Tx_data + copy1 + copy2 + copy3 + copy4;           % 4 multi-paths
Tx_signal_power = var(Tx_data);
%-------------------------------------------------------------------------
% 函数说明：
%  VAR Variance.
%     For vectors, Y = VAR(X) returns the variance of the values in X.  For
%     matrices, Y is a row vector containing the variance of each column of
%     X.
%-------------------------------------------------------------------------
linear_SNR = 10^(SNR/10);
noise_sigma = Tx_signal_power/linear_SNR;
noise_scale_factor = sqrt(noise_sigma);
%
noise = randn(1, length(Tx_data))*noise_scale_factor;
Rx_Data = Tx_data + noise;
%Rx_Data = Tx_data;
%-------------------------------------------------------------------------
% 函数说明：产生正态分布的随机函数
% Y = randn(m,n) or Y = randn([m n]) returns an m-by-n matrix of random
% entries.
% The randn function generates arrays of random numbers whose elements are
% normally distributed with mean 0 and variance 1.
%-------------------------------------------------------------------------
% --------------------------------------------- %
%                  信号接收                      %
% --------------------------------------------- %
%-------------------------------------------------------------------------
Rx_Data_matrix_cp = reshape(Rx_Data, IFFT_bin_length + cp_length, 4 + symbols_per_carrier + 1);
Rx_Data_matrix_cp = Rx_Data_matrix_cp';
Rx_Data_matrix = zeros(4 + symbols_per_carrier + 1,IFFT_bin_length);
for i = 1:4 + symbols_per_carrier + 1
    Rx_Data_matrix(i,:) = Rx_Data_matrix_cp(i,(cp_length + 1):(IFFT_bin_length + cp_length));
end
Rx_Data_matrix = Rx_Data_matrix';
%-------------------------------------------------------------------------
% Transform each symbol from time to frequency domain
%   - take the fft of each column
%-------------------------------------------------------------------------
Rx_spectrum = fft(Rx_Data_matrix);
%-------------------------------------------------------------------------
%  Suppose precise synchronazition between Tx and Rx
Rx_carriers = Rx_spectrum(carriers,:)';
Rx_training_symbols = Rx_carriers( (1: 4) , : ) ;
Rx_carriers = Rx_carriers((5: 55), : ) ;
% --------------------------------------------- %
%                    信道估计                    %
% --------------------------------------------- %
Rx_training_symbols = Rx_training_symbols./ training_symbols;
Rx_training_symbols_deno = Rx_training_symbols.^2;
Rx_training_symbols_deno = Rx_training_symbols_deno(1,:)+Rx_training_symbols_deno(2,:)+Rx_training_symbols_deno(3,:)+Rx_training_symbols_deno(4,:) ;
Rx_training_symbols_nume = Rx_training_symbols(1, : ) +Rx_training_symbols(2, : ) + Rx_training_symbols(3, : ) +Rx_training_symbols(4, : ) ;
Rx_training_symbols_nume = conj(Rx_training_symbols_nume) ;
%-------------------------------------------------------------------------
% 取4个向量的导频符号是为了进行平均优化
% 都是针对 “行向量”即单个的OFDM符号 进行操作
% 原理：寻求1/H，对FFT之后的数据进行频域补偿
% 1/H = conj(H)/H^2 because H^2 = H * conj(H) 
%-------------------------------------------------------------------------
Rx_training_symbols = Rx_training_symbols_nume./Rx_training_symbols_deno;
Rx_training_symbols_2 = cat(1, Rx_training_symbols,Rx_training_symbols) ;
Rx_training_symbols_4 = cat(1, Rx_training_symbols_2,Rx_training_symbols_2) ;
Rx_training_symbols_8 = cat(1, Rx_training_symbols_4,Rx_training_symbols_4) ;
Rx_training_symbols_16 = cat(1, Rx_training_symbols_8, Rx_training_symbols_8) ;
Rx_training_symbols_32 = cat(1, Rx_training_symbols_16, Rx_training_symbols_16) ;
Rx_training_symbols_48 = cat(1, Rx_training_symbols_32, Rx_training_symbols_16) ;
Rx_training_symbols_50 = cat(1, Rx_training_symbols_48, Rx_training_symbols_2) ;
Rx_training_symbols = cat(1, Rx_training_symbols_50,Rx_training_symbols) ;
Rx_carriers = Rx_training_symbols.*Rx_carriers;
%-------------------------------------------------------------------------
% 进行频域单抽头均衡
%-------------------------------------------------------------------------
Rx_phase = angle(Rx_carriers)*(180/pi);
phase_negative = find(Rx_phase < 0);
%-------------------------------------------------------------------------
% 函数说明：找出非零元素的索引号
%     FIND   Find indices of nonzero elements.
%     I = FIND(X) returns the linear indices of the array X that are nonzero.
%     X may be a logical expression. Use IND2SUB(I,SIZE(X)) to calculate
%     multiple subscripts from the linear indices I.
%---------------------------------------------------------------------------
Rx_phase( phase_negative );
Rx_phase(phase_negative) = rem(Rx_phase(phase_negative) + 360, 360) ;
% 把负的相位转化为正的相位
Rx_decoded_phase = diff(Rx_phase) ;
%  这也是为什么要在前面加上初始相位的原因 
% “Here a row vector of zeros is between training symbols and data symbols!!!”
%-------------------------------------------------------------------------
% 函数说明：
%     DIFF Difference and approximate derivative.
%     DIFF(X), for a vector X, is [X(2)-X(1)  X(3)-X(2) ... X(n)-X(n-1)].
%     DIFF(X), for a matrix X, is the matrix of row differences,
%        [X(2:n,:) - X(1:n-1,:)].
%------------------------Test Codes --------------------------------------
%  a = [1 2 3; 4 5 6; 7 8 9; 10 11 12];
%  b = a;
%      for i = 2:4
%        b(i,:) = b(i-1,:) + b(i,:);
%      end
%  c = diff(b);
%-----------------------Test Result --------------------------------------
%  a =                  Modulating signal
%      1     2     3
%      4     5     6
%      7     8     9
%     10    11    12
%  b =                  Modulated signal
%      1     2     3
%      5     7     9
%     12    15    18
%     22    26    30
%  c =                  Recovered signal
%      4     5     6
%      7     8     9
%     10    11    12
% ----------------------------------------------------------------------------
%   Name                   Size                    Bytes  Class
%   Rx_phase              51x200                   81600  double array
%   Rx_decoded_phase      50x200                   80000  double array
% ---------------------------------------------------------------------------- 
phase_negative = find(Rx_decoded_phase < 0) ;
Rx_decoded_phase(phase_negative)= rem(Rx_decoded_phase(phase_negative) + 360, 360) ;
% ---------------------------------------------------------------------------- 
% Extract phase differences (from the differential encoding)
%   - the matlab diff( ) function is perfect for this operation
%   - again, normalize the result to be between 0 and 359 degrees
% 再次把负的相位转化为正的相位
% ---------------------------------------------------------------------------- 
% --------------------------------------------- %
%                   QDPSK解调                   %
% --------------------------------------------- %
base_phase = 360 /2^bits_per_symbol;
delta_phase = base_phase /2;
Rx_decoded_symbols = zeros(size(Rx_decoded_phase,1),size(Rx_decoded_phase,2)) ;
%
for i = 1: (2^bits_per_symbol - 1)
center_phase = base_phase*i;
plus_delta = center_phase + delta_phase;  % Decision threshold 1
minus_delta = center_phase - delta_phase; % Decision threshold 2
decoded = find((Rx_decoded_phase <= plus_delta)&(Rx_decoded_phase > minus_delta)) ;
Rx_decoded_symbols(decoded) = i;
end
% ---------------------------------------------------------------------------- 
%  仅仅对三个区域进行判决
%  剩下的区域就是零相位的空间了
%  这个区域在定义解调矩阵时已经定义为零
% ---------------------------------------------------------------------------- 
Rx_serial_symbols = reshape(Rx_decoded_symbols',1,size(Rx_decoded_symbols, 1)*size(Rx_decoded_symbols,2)) ;
for i = bits_per_symbol: -1: 1
if i ~= 1
Rx_binary_matrix(i, : ) = rem(Rx_serial_symbols, 2) ;
Rx_serial_symbols = floor(Rx_serial_symbols/2) ;
else
Rx_binary_matrix( i, : ) = Rx_serial_symbols;
end
end                                                             % Integer to binary
baseband_in = reshape(Rx_binary_matrix, 1,size(Rx_binary_matrix, 1)*size(Rx_binary_matrix, 2) ) ;
% --------------------------------------------- %
%                   误码率计算                   %
% --------------------------------------------- %
bit_errors = find(baseband_in ~= baseband_out) ;            % find的结果 其每个元素为满足逻辑条件的输入向量的标号，其向量长度也就是收发不一样的bit的个数
bit_error_count = size(bit_errors, 2) ;
total_bits = size( baseband_out, 2) ;
bit_error_rate = bit_error_count/ total_bits;
fprintf ( '%f \n',bit_error_rate) ;