CCS

Spectral Characteristics of OFDM Signals

The signals transmitted on the subcarriers of an OFDM system are mutually orthogonal in the time domain; that is,

However, these signals have significant overlap in the frequency domain.

This can be observed by computing the Fourier transform of the signal for several values of k.

Matlab Coding

Note the large spectral overlap of the main lobes of each I Uk (j) I.

Also note that the first sidelobe in the spectrum is only 13 dB down from the main lobe.

Therefore, there is a significant amount of spectral overlap among the signals transmitted on different subcarriers.

Nevertheless, these signals are orthogonal when transmitted synchronously in time.

 1 % MATLAB script for Illustrative Problem 8.5
 2 
 3 T = 1;
 4 k = 0 : 5;
 5 f_k = k/T;
 6 f = 0 : 0.01*4/T : 4/T;
 7 U_k_abs = zeros(length(k),length(f));
 8 for i = 1 : length(k)
 9     U_k_abs(i,:) = abs(sqrt(T/2)*(sinc((f-f_k(i))*T) + sinc((f+f_k(i))*T)));
10     U_k_norm(i,:) = U_k_abs(i,:)/max(U_k_abs(i,:));
11 end
12 U_k_dB = 10*log10(U_k_norm);
13 plot(f,U_k_dB(1,:),'black',f,U_k_dB(2,:),'black',f,U_k_dB(3,:),'black',...
14     f,U_k_dB(4,:),'black',f,U_k_dB(5,:),'black',f,U_k_dB(6,:),'black')
15 axis([min(f) max(f) -180 20])
16 xlabel('f')
17 ylabel('|U_k(f)| (dB)')


Simulation Result

Reference,

　　1. <<Contemporary Communication System using MATLAB>> - John G. Proakis