Matlab简单的OFDM仿真,信道估计,有BER曲线

clear all; close all; fprintf( ' OFDM仿真\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 '); %   baseband_out = baseband_out1 ; %else %   fprintf('Check Code!!!!!!!!!!!!!!!!!!!!! '); %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 '); %else if (modulo_baseband == Test_convert_matrix2')      %    fprintf('modulo_baseband = Test_convert_matrix2 '); %    else %    fprintf('modulo_baseband ~= any Test_convert_matrix '); %    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。 继续阅读