Signals and Systems - Electrical Engineering

738 CHAPTER 12: Applications of Discrete-Time Signals and Systems

n Robustness to interference from other users:Assuming no noise or jammer, if the received baseband

signal comes from two users—that is,

ˆr(t)=m 1 (t)c 1 (t)+m 2 (t)c 2 (t) (12.25)

where the codesc 1 (t)andc 2 (t)are the corresponding codes for the two users, andm 1 (t)andm 2 (t)

their messages. At the receiver of user 1, despreading using codec 1 (t)we get

ˆr(t)c 1 (t)=m 1 (t)c^21 (t)+m 2 (t)c 2 (t)c 1 (t)≈m 1 (t) (12.26)

since the codes are generated so thatc^21 (t)=1 andc 1 (t)andc 2 (t)are not correlated. Thus, we

detect the message corresponding to user 1. The same happens when there is interference from

more than one user.

Simulation of direct sequence spread spectrum. In this simulation we consider that the mes-

sage is randomly generated and that the spreading code is also randomly generated (our code does

not have the same characteristics as the one used to generate the code for spread-spectrum systems).

To generate the train of pulses for the message and the code we use filters of different length (recall the

spreading code changes more frequently than the message). The spreading makes the transmitting

signal have a wider spectrum than that of the message (see Figure 12.13).

The binary transmitting signal modulates a sinusoidal carrier of frequency 100 Hz. Assuming the

communication channel does not change the transmitted signal and perfect synchronization at the

analog receiver is possible, the despread signal coincides with the sent message. In practice, the effects

of multipath in the channel, noise, and possible jamming would not make this possible.

%%%%%%%%%%%%%%%%

% Simulation of

% spread spectrum

%%%%%%%%%%%%%%%%

clear all; clf

% message

m1 = rand(1,12)>0.9;m1 = (m1-0.5)∗2;

m = zeros(1,00);

m(1:9:100) = m1

h = ones(1,9);

m = filter(h,1,m);

% spreading code

c1 = rand(1,25)>0.5;c1 = (c1-0.5)∗2;

c = zeros(1,100);

c(1:4:100) = c1;

h1 = ones(1,4);

c = filter(h1,1,c);

Ts = 0.0001; t = [0:99]∗Ts;

s = m.∗c;

figure(1)