关于qpsk的ofdm

% 5 Appendix % 5.1 OFDM Transmission %DVB-T 2K Transmission %The available bandwidth is 8 MHz %2K is intended for mobile services clear all; close all; %DVB-T Parameters Tu=224e-6; %useful OFDM symbol period T=Tu/2048; %baseband elementary period G=0; %choice of 1/4, 1/8, 1/16, and 1/32 delta=G*Tu; %guard band duration Ts=delta+Tu; %total OFDM symbol period Kmax=1705; %number of subcarriers Kmin=0; FS=4096; %IFFT/FFT length q=10; %carrier period to elementary period ratio fc=q*1/T; %carrier frequency Rs=4*fc; %simulation period t=0:1/Rs:Tu; %Data generator (A) M=Kmax+1; rand('state',0); a=-1+2*round(rand(M,1)).'+i*(-1+2*round(rand(M,1))).'; A=length(a); info=zeros(FS,1); info(1:(A/2)) = [ a(1:(A/2)).']; %Zero padding info((FS-((A/2)-1)):FS) = [ a(((A/2)+1):A).']; %Subcarriers generation (B) carriers=FS.*ifft(info,FS); tt=0:T/2:Tu; figure(1); subplot(211); stem(tt(1:20),real(carriers(1:20))); % 12 subplot(212); stem(tt(1:20),imag(carriers(1:20))); figure(2); f=(2/T)*(1:(FS))/(FS); subplot(211); plot(f,abs(fft(carriers,FS))/FS); subplot(212); pwelch(carriers,[],[],[],2/T); % D/A simulation L = length(carriers); chips = [ carriers.';zeros((2*q)-1,L)]; p=1/Rs:1/Rs:T/2; g=ones(length(p),1); %pulse shape figure(3); stem(p,g); dummy=conv(g,chips(:)); u=[dummy(1:length(t))]; % (C) figure(4); subplot(211); plot(t(1:400),real(u(1:400))); subplot(212); plot(t(1:400),imag(u(1:400))); figure(5); ff=(Rs)*(1:(q*FS))/(q*FS); subplot(211); plot(ff,abs(fft(u,q*FS))/FS); subplot(212); pwelch(u,[],[],[],Rs); [b,a] = butter(13,1/20); %reconstruction filter [H,F] = FREQZ(b,a,FS,Rs); figure(6); plot(F,20*log10(abs(H))); uoft = filter(b,a,u); %baseband signal (D) figure(7); subplot(211); plot(t(80:480),real(uoft(80:480))); subplot(212); plot(t(80:480),imag(uoft(80:480))); figure(8); subplot(211); plot(ff,abs(fft(uoft,q*FS))/FS); subplot(212); pwelch(uoft,[],[],[],Rs); %Upconverter s_tilde=(uoft.').*exp(1i*2*pi*fc*t); s=real(s_tilde); %passband signal (E) figure(9); plot(t(80:480),s(80:480)); figure(10); subplot(211); % 13 %plot(ff,abs(fft(((real(uoft).').*cos(2*pi*fc*t)),q*FS))/FS); %plot(ff,abs(fft(((imag(uoft).').*sin(2*pi*fc*t)),q*FS))/FS); plot(ff,abs(fft(s,q*FS))/FS); subplot(212); %pwelch(((real(uoft).').*cos(2*pi*fc*t)),[],[],[],Rs); %pwelch(((imag(uoft).').*sin(2*pi*fc*t)),[],[],[],Rs); pwelch(s,[],[],[],Rs); % 5.2 OFDM Reception %DVB-T 2K Reception clear all; close all; Tu=224e-6; %useful OFDM symbol period T=Tu/2048; %baseband elementary period G=0; %choice of 1/4, 1/8, 1/16, and 1/32 delta=G*Tu; %guard band duration Ts=delta+Tu; %total OFDM symbol period Kmax=1705; %number of subcarriers Kmin=0; FS=4096; %IFFT/FFT length q=10; %carrier period to elementary period ratio fc=q*1/T; %carrier frequency Rs=4*fc; %simulation period t=0:1/Rs:Tu; tt=0:T/2:Tu; %Data generator sM = 2; [x,y] = meshgrid((-sM+1):2:(sM-1),(-sM+1):2:(sM-1)); alphabet = x(:) + 1i*y(:); N=Kmax+1; rand('state',0); a=-1+2*round(rand(N,1)).'+i*(-1+2*round(rand(N,1))).'; A=length(a); info=zeros(FS,1); info(1:(A/2)) = [ a(1:(A/2)).']; info((FS-((A/2)-1)):FS) = [ a(((A/2)+1):A).']; carriers=FS.*ifft(info,FS); %Upconverter L = length(carriers); chips = [ carriers.';zeros((2*q)-1,L)]; p=1/Rs:1/Rs:T/2; g=ones(length(p),1); dummy=conv(g,chips(:)); u=[dummy; zeros(46,1)]; [b,aa] = butter(13,1/20); uoft = filter(b,aa,u); delay=64; %Reconstruction filter delay s_tilde=(uoft(delay+(1:length(t))).').*exp(1i*2*pi*fc*t); 14 s=real(s_tilde); %OFDM RECEPTION %Downconversion r_tilde=exp(-1i*2*pi*fc*t).*s; %(F) figure(1); subplot(211); plot(t,real(r_tilde)); axis([0e-7 12e-7 -60 60]); grid on; figure(1); subplot(212); plot(t,imag(r_tilde)); axis([0e-7 12e-7 -100 150]); grid on; figure(2); ff=(Rs)*(1:(q*FS))/(q*FS); subplot(211); plot(ff,abs(fft(r_tilde,q*FS))/FS); grid on; figure(2); subplot(212); pwelch(r_tilde,[],[],[],Rs); %Carrier suppression [B,AA] = butter(3,1/2); r_info=2*filter(B,AA,r_tilde); %Baseband signal continuous-time (G) figure(3); subplot(211); plot(t,real(r_info)); axis([0 12e-7 -60 60]); grid on; figure(3); subplot(212); plot(t,imag(r_info)); axis([0 12e-7 -100 150]); grid on; figure(4); f=(2/T)*(1:(FS))/(FS); subplot(211); plot(ff,abs(fft(r_info,q*FS))/FS); grid on; subplot(212); pwelch(r_info,[],[],[],Rs); %Sampling r_data=real(r_info(1:(2*q):length(t)))... %Baseband signal, discretetime +1i*imag(r_info(1:(2*q):length(t))); % (H) figure(5); subplot(211); stem(tt(1:20),(real(r_data(1:20)))); axis([0 12e-7 -60 60]); grid on; 15 figure(5); subplot(212); stem(tt(1:20),(imag(r_data(1:20)))); axis([0 12e-7 -100 150]); grid on; figure(6); f=(2/T)*(1:(FS))/(FS); subplot(211); plot(f,abs(fft(r_data,FS))/FS); grid on; subplot(212); pwelch(r_data,[],[],[],2/T); %FFT info_2N=(1/FS).*fft(r_data,FS); % (I) info_h=[info_2N(1:A/2) info_2N((FS-((A/2)-1)):FS)]; %Slicing for k=1:N, a_hat(k)=alphabet((info_h(k)-alphabet)==min(info_h(k)-alphabet)); % (J) end; figure(7) plot(info_h((1:A)),'.k'); title('info-h Received Constellation') axis square; axis equal; figure(8) plot(a_hat((1:A)),'or'); title('a_hat 4-QAM') axis square; axis equal; grid on; axis([-1.5 1.5 -1.5 1.5]); 16 5.3 Eq. (2.1.4) vs. IFFT %DVB-T 2K signal generation Eq. (2.1.4) vs. 2N-IFFT clear all; close all; Tu=224e-6; %useful OFDM symbol period T=Tu/2048; %baseband elementary period G=0; %choice of 1/4, 1/8, 1/16, and 1/32 delta=G*Tu; %guard band duration Ts=delta+Tu; %total OFDM symbol period Kmax=1705; %number of subcarriers Kmin=0; FS=4096; %IFFT/FFT length q=10; %carrier period to elementary period ratio fc=q*1/T; %carrier frequency Rs=4*fc; %simulation period a=-1+2*round(rand(M,1)).'+i*(-1+2*round(rand(M,1))).'; A=length(a); info = [ a.']; tt=0:1/Rs:Ts; TT=length(tt); k=Kmin:Kmax; for t=0:(TT-1); % Eq. (2.1.4) phi=a(k+1).*exp((1j*2*(((t*(1/Rs))-delta))*pi/Tu).*((k-(Kmax- Kmin)/2))); s(t+1)=real(exp(1j*2*pi*fc*(t*(1/Rs))).*sum(phi)); end infof=zeros(FS,1); infof(1:(A/2)) = [ a(1:(A/2)).']; infof((FS-((A/2)-1)):FS) = [ a(((A/2)+1):A).']; carriers=FS.*ifft(infof,FS); % IFFT %Upconverter L = length(carriers); chips = [ carriers.';zeros((2*q)-1,L)]; p=1/Rs:1/Rs:T/2; g=ones(length(p),1); dummy=conv(g,chips(:)); u=[dummy(1:TT)]; [b,a] = butter(13,1/20); uoft = filter(b,a,u); s_tilde=(uoft.').*exp(1i*2*pi*fc*tt); sf=real(s_tilde); figure(1); plot(tt,s,'b',tt,sf,'g'); figure(2); pwelch(s,[],[],[],Rs); hold on; pwelch(sf,[],[],[],Rs); hold off;