Multicarrier Modulation and OFDM

In this chapter, we describe the transmission of digital information on multiple
carriers. In multicarrier modulation, the available channel bandwidth is subdivided into
a number of equal-bandwidth subchannels,

Matlab Coding

 1 % MATLAB script for Illustrative Problem 8.1
 

 2 
 3 M = 50;
 4 m = 0:M-1;
 5 phi_k = 2*pi*rand;
 6 phi_j = 2*pi*rand;

 7 % The sampled signals:
 8 x_k = sin(4*pi*m/5+phi_k);

 9 n = 1;
10 x_j_1 = sin(4*pi*m/5+2*pi*m*n/M+phi_j);
11 n = 2 ;
12 x_j_2 = sin(4*pi*m/5+2*pi*m*n/M+phi_j);
13 n = 3 ;
14 x_j_3 = sin(4*pi*m/5+2*pi*m*n/M+phi_j);

15 % Investigating the orthogonality of the sampled signals:
 
16 Sum1 = sum(x_k.*x_j_1);
17 % Displaying the results:
18 disp(['The result of the computation for n=1 is:    ',num2str(Sum1)])
19 Sum2 = sum(x_k.*x_j_2);
20 disp(['The result of the computation for n=2 is:    ',num2str(Sum2)])
21 Sum3 = sum(x_k.*x_j_3);
22 disp(['The result of the computation for n=3 is:    
 
',num2str(Sum3)])


Outputs

The result of the computation for n=1 is: -4.3743e-14

The result of the computation for n=2 is: 5.6066e-15

The result of the computation for n=3 is: -2.9976e-14

Reference,

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