Signals and Systems - Electrical Engineering

12.4 Application to Digital Communications 737

When transmitting over a radio link the baseband signalx(t)modulates an analog carrier to obtain

the transmitting signals(t). At the receiver, if no interference occurred in the transmission, the received

signalr(t)=s(t), and after demodulation using the analog carrier frequency, the spread signalx(t)is

obtained. If we multiply it byc(t)we get

x(t)c(t)=c^2 (t)m(t)=m(t) (12.22)

sincec^2 (t)=1 for allt. See Figure 12.12.

Two significant advantages of direct-sequence spread spectrum are:

n 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 noiseη(t)and a jammerj(t), it is demodulated by the BPSK system. The received

baseband signal is

ˆr(t)=x(t)+ ˆη(t)+ˆj(t) (12.23)

where the noise and the jammer have been affected by the demodulator.

Multiplying it byc(t)gives

ˆr(t)c(t)=m(t)+ ˆη(t)c(t)+ˆj(t)c(t) (12.24)

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

to interferences by spreading them over all frequencies.

FIGURE 12.12
Direct-sequence
spread-spectrum system.

Spreader BPSK Modulator

× LPF ×

× ×

BPSK Demodulator

Despreader

m(t)

A cos(Ωct)

A cos(Ωct)

c(t)

r(t)=s(t)+η(t)+j(t)

c(t)

s(t)

m∧(t)