基于离散傅里叶变换和逆离散傅里叶变换的OFDM信号生成和恢复

clear;

K=10; N=2\*K; Ts=25; T=N\*Ts;

a=rand(1,(K-1)\*4);  % k-1符号，1个保护间隔0

a=sign(a-0.5);

b=reshape(a,K-1,4);

XXX=2\*b(:,1)+b(:,2)+j\*(2\*b(:,3)+b(:,4));    % 随机声称9个16点QAM星座点

XX=XXX';

X=[0 XX 0 conj(XX(K-1:-1:1))];    % X长度为20，等于N

xt=zeros(1,T+1);

for t=0:T   % 载波分辨力

  for k=0:N-1   % 载波数量

     xt(t+1)=xt(t+1)+1/sqrt(N)\*X(k+1)\*exp(j\*2\*pi\*k\*t/T);

  end

end

xn=zeros(1,N);

for n=0:N-1

  for k=0:N-1

    xn(n+1)=xn(n+1)+1/sqrt(N)\*X(k+1)\*exp(j\*2\*pi\*n\*k/N);

  end

end

xn1=ifft(X,N)\*sqrt(N);

plot([0:T],real(xt),'r',[0:T/N:T-T/N],xn,'.b',[0:T/N:T-T/N],xn1,'og'),grid

legend('连续信号','采样信号','IFFT信号\*4.5')

hold on % 画出每个子载波波形

    for ii=[10,12]

        plot([0:T],1/sqrt(N)\*X(ii)\*exp(j\*2\*pi\*(ii-1)\*[0:T]/T),':')

    end

hold off

for n=0:N-1

  d(n+1)=xt(T/N\*n+1)-xn(1+n);

end

e=norm(d);

Y=zeros(1,K);

for k=0:K-1

  for n=0:N-1

    Y(k+1)=Y(k+1)+1/sqrt(N)\*xn(n+1)\*exp(-j\*2\*pi\*k\*n/N);

  end

end

Y1=fft(xn1,N)/sqrt(N);

dd=Y(1:K)-X(1:K);

dd1=Y1(1:K)-X(1:K);

ee=norm(dd)

ee2=norm(dd1)