Application to Digital Communications 737

12.4 Application to Digital Communications 737

When transmitting over a radio link the baseband signal x(t) modulates an analog carrier to obtain the transmitting signal s(t). At the receiver, if no interference occurred in the transmission, the received signal r(t) = s(t), and after demodulation using the analog carrier frequency, the spread signal x(t) is obtained. If we multiply it by c(t) we get

(12.22) since c 2 ( t) = 1 for all t. See Figure 12.12.

x(t)c(t) 2 =c ( t)m(t) = m(t)

Two significant advantages of direct-sequence spread spectrum are:

Robustness to noise and jammers: The above detection or despreading is idealized. The received signal will have interferences due to channel noise, interference from other users, and even, in military applications, intentional jamming. Jamming attempts to corrupt the sent message by adding to it either a narrowband or a wideband signal. If at the receiver, the spread signal con- tains additive noise η(t) and a jammer j(t), it is demodulated by the BPSK system. The received baseband signal is

(12.23) where the noise and the jammer have been affected by the demodulator.

ˆr(t) = x(t) + ˆη(t) + ˆj(t)

Multiplying it by c(t) gives

(12.24) or the desired message with a spread noise and jammer. Thus, the transmitted signal is resistant

ˆr(t)c(t) = m(t) + ˆη(t)c(t) + ˆj(t)c(t)

to interferences by spreading them over all frequencies.

Spreader BPSK Modulator

A cos(Ω c t )

(t ) = s(t) + η(t) + j(t) Despreader m ∧ (t )

BPSK Demodulator

spread-spectrum system.

A cos(Ω c t )

c (t )

C H A P T E R 12: Applications of Discrete-Time Signals and Systems

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 codes c 1 ( t) and c 2 ( t) are the corresponding codes for the two users, and m 1 ( t) and m 2 ( t)

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

ˆr(t)c 2

(12.26) since the codes are generated so that c 2 1 ( t) = 1 and c 1 ( t) and c 2 ( t) are not correlated. Thus, we

1 ( t) =m 1 ( t)c 1 ( t) +m 2 ( t)c 2 ( t)c 1 ( t) ≈m 1 ( t)

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)