Question

哪位有基于Matlab的OFDM系统仿真中，不同信道下误码率曲线的代码？万分感谢！！！

Answer 1

拿去把 信道估计，有BER曲线

clear all;
close all;
fprintf( '\n OFDM仿真\n \n') ;
% --------------------------------------------- %
% 参数定义 %
% --------------------------------------------- %
IFFT_bin_length = 1024;
carrier_count = 200;
bits_per_symbol = 2;
symbols_per_carrier = 50;
% 子载波数 200
% 位数/ 符号 2
% 符号数/ 载波 50
% 训练符号数 10
% 循环前缀长度 T/4（作者注明） All-zero CP
% 调制方式 QDPSK
% 多径信道数 2、3、4（缺省）
% 信道最大时延 7 (单位数据符号)
% 仿真条件 收发之间严格同步
%SNR=input('SNR='); % 输入信噪比参数
SNR=3:14;%定义信噪比范围
BER=zeros(1,length(SNR));
baseband_out_length = carrier_count * symbols_per_carrier * bits_per_symbol;% 计算发送的二进制序列长度
carriers = (1: carrier_count) + (floor(IFFT_bin_length/4) - floor(carrier_count/2)); % 坐标： (1 to 200) + 156 , 157 -- 356
conjugate_carriers=IFFT_bin_length-carriers+2; % 坐标 ：1024 - (157:356) + 2 = 1026 - (157:356) = (869:670)
% 构造共轭时间－载波矩阵，以便应用所谓的RCC，Reduced Computational Complexity算法，即ifft之后结果为实数
% Define the conjugate time-carrier matrix
% 也可以用flipdim函数构造对称共轭矩阵
% --------------------------------------------- %
% 信号发射 %
% --------------------------------------------- %
%out = rand(1,baseband_out_length);
%baseband_out1 = round(out) ;
%baseband_out2 = floor(out*2) ;
%baseband_out3 = ceil(out*2)-1 ;
%baseband_out4 = randint(1,baseband_out_length);
% 四种生成发送的二进制序列的方法，任取一种产生要发送的二进制序列
%if (baseband_out1 == baseband_out2 & baseband_out1 == baseband_out3 )
% fprintf('Transmission Sequence Generated \n \n');
% baseband_out = baseband_out1 ;
%else
% fprintf('Check Code!!!!!!!!!!!!!!!!!!!!! \n \n');
%end
% 验证四种生成发送的二进制序列的方法
baseband_out=round( rand(1,baseband_out_length));
convert_matrix = reshape(baseband_out,bits_per_symbol,length(baseband_out)/bits_per_symbol);
for k = 1length(baseband_out)/bits_per_symbol),
modulo_baseband(k) = 0;
for i = 1:bits_per_symbol
modulo_baseband(k) = modulo_baseband(k) + convert_matrix(i,k)* 2^(bits_per_symbol - i);
end
end
% 每2个比特转化为整数 0至3
% 采用'left-msb'方式
%-------------------------------------------------------------------------
% Test by lavabin
% A built-in function of directly change binary bits into decimal numbers
%-------------------------------------------------------------------------
%convert_matrix1 = zeros(length(baseband_out)/bits_per_symbol,bits_per_symbol);
%convert_matrix1 = convert_matrix' ;
%Test_convert_matrix1 = bi2de(convert_matrix1,bits_per_symbol,'left-msb');
%Test_convert_matrix2 = bi2de(convert_matrix1,bits_per_symbol,'right-msb');
% 函数说明：
% BI2DE Convert binary vectors to decimal numbers.
% D = BI2DE(B) converts a binary vector B to a decimal value D. When B is
% a matrix, the conversion is performed row-wise and the output D is a
% column vector of decimal values. The default orientation of thebinary
% input is Right-MSB; the first element in B represents the least significant bit.
%if (modulo_baseband == Test_convert_matrix1')
% fprintf('modulo_baseband = Test_convert_matrix1 \n\n\n');
%else if (modulo_baseband == Test_convert_matrix2')
% fprintf('modulo_baseband = Test_convert_matrix2 \n\n\n');
% else
% fprintf('modulo_baseband ~= any Test_convert_matrix \n\n\n');
% end
%end
% we get the result "modulo_baseband = Test_convert_matrix1".
%-------------------------------------------------------------------------
carrier_matrix = reshape(modulo_baseband,carrier_count,symbols_per_carrier)';
% 生成时间－载波矩阵
% --------------------------------------------- %
% QDPSK调制 %
% --------------------------------------------- %
carrier_matrix = [zeros(1,carrier_count); carrier_matrix]; % 添加一个差分调制的初始相位，为0
for i = 2symbols_per_carrier + 1)
carrier_matrix(i, = rem(carrier_matrix(i, + carrier_matrix (i-1,, 2^bits_per_symbol) ; % 差分调制
end
carrier_matrix = carrier_matrix*((2*pi)/(2^bits_per_symbol)) ; % 产生差分相位
[X, Y]=pol2cart(carrier_matrix, ones(size(carrier_matrix,1),size(carrier_matrix,2))); % 由极坐标向复数坐标转化 第一参数为相位 第二参数为幅度
% Carrier_matrix contains all the phase information and all the amplitudes are the same‘1’.
complex_carrier_matrix = complex(X, Y) ;
% 添加训练序列 `
training_symbols = [ 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 ...
-j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 ...
1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 ...
-1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j ...
-1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 1 j j 1 -1 -j -j -1 ]; % 25 times "1 j j 1" , 25 times "-1 -j -j -1", totally 200 symbols as a row
training_symbols = cat(1, training_symbols, training_symbols) ;
training_symbols = cat(1, training_symbols, training_symbols) ; % Production of 4 rows of training_symbols
complex_carrier_matrix = cat(1, training_symbols, complex_carrier_matrix) ; % 训练序列与数据合并
% block-type pilot symbols
IFFT_modulation = zeros(4 + symbols_per_carrier + 1,IFFT_bin_length) ;
% Here a row vector of zeros is between training symbols and data symbols!!! 
% 4 training symbols and 1 zero symbol
% every OFDM symbol takes a row of "IFFT_modulation"
IFFT_modulation(: , carriers) = complex_carrier_matrix;
IFFT_modulation(: , conjugate_carriers) = conj(complex_carrier_matrix) ;
%-------------------------------------------------------------------------
% Test by lavabin -- Find the indices of zeros
%index_of_zeros = zeros(symbols_per_carrier,IFFT_bin_length - 2*carrier_count);
%IFFT_modulation1 = zeros(4 + symbols_per_carrier + 1,IFFT_bin_length);
%IFFT_modulation2 = zeros(4 + symbols_per_carrier + 1,IFFT_bin_length);
%IFFT_modulation1(6:symbols_per_carrier+5, = IFFT_modulation(6:symbols_per_carrier+5,==0 ;
%for i = 1:symbols_per_carrier
%index_of_zeros(i, = find(IFFT_modulation1(i+5,==1);
%end
%-------------------------------------------------------------------------
time_wave_matrix = ifft(IFFT_modulation') ; % 进行IFFT操作
time_wave_matrix = time_wave_matrix'; % If X is a matrix, ifft returns the inverse Fourier transform of each column of the matrix.
for i = 1: 4 + symbols_per_carrier + 1
windowed_time_wave_matrix( i, : ) = real(time_wave_matrix( i, : )) ;
end
% 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',1, IFFT_bin_length*(4 + symbols_per_carrier + 1) ) ;
% P2S operation
%-------------------------------------------------------------------------
% Test by lavabin
% Another way of matrix transition
%ofdm_modulation_tmp = windowed_time_wave_matrix.';
%ofdm_modulation_test = ofdm_modulation_tmp(';
%if (ofdm_modulation_test == ofdm_modulation)
% fprintf('ofdm_modulation_test == ofdm_modulation \n\n\n');
%else
%fprintf('ofdm_modulation_test ~= ofdm_modulation \n\n\n');
%end
% We get the result "ofdm_modulation_test == ofdm_modulation" .
%-------------------------------------------------------------------------
Tx_data=ofdm_modulation;
% --------------------------------------------- %
% 信道模拟 %
% --------------------------------------------- %
d1= 4; a1 = 0.2; d2 = 5; a2 = 0.3; d3 = 6; a3 = 0.4; d4 = 7; a4 = 0.5; %信道模拟
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);
for idx=1:length(SNR)%monte carlo 仿真模拟

linear_SNR = 10^( SNR(idx) /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;
% --------------------------------------------- %
% 信号接收 %
% --------------------------------------------- %
Rx_Data_matrix = reshape(Rx_Data, IFFT_bin_length, 4 + symbols_per_carrier + 1) ;
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 = 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) ;
%----------------------Test of Using "rem"---------------------------------
%Rx_phase1 = Rx_phase;
%Rx_phase2 = Rx_phase;
%Rx_phase1(phase_negative) = rem(Rx_phase1(phase_negative) + 360, 360) ;
%Rx_phase2(phase_negative) = Rx_phase2(phase_negative) + 360 ;
%if Rx_phase2(phase_negative) == Rx_phase1(phase_negative)
%fprintf('\n There is no need using rem in negative phase transition.\n')
%else
% fprintf('\n We need to use rem in negative phase transition.\n')
%end
%-------------------------------------------------------------------------
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!!!”
phase_negative = find(Rx_decoded_phase < 0) ;
Rx_decoded_phase(phase_negative)= rem(Rx_decoded_phase(phase_negative) + 360, 360) ; % 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(idx) = 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(idx) = size(bit_errors, 2) ;
%total_bits = size( baseband_out, 2) ;
%bit_error_rate = bit_error_count/ total_bits;
%fprintf ( '%f \n',bit_error_rate) ;
[number_err(idx),BER(idx)] = biterr(baseband_out,baseband_in ) ;
end
semilogy(SNR,BER,'r*');

legend('OFDM BER-SNR');
xlabel('SNR (dB)'); ylabel('BER');
title('OFDM');
grid on;
% --------------------------------------------- %
% The END %
% --------------------------------------------- %
%
% 1. 该程序进行了简单的LMS信道估计，没有加入与MMSE等其他信道估计算法的比较；
%
%2. 仿真条件为系统处于理想同步情况下。

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