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ST2115
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(c)
Convolution of spectra of the (a) data signal with the (b) PN code signal
Figure 8
The product signal u ( t ) c ( t ), also illustrated in figure 8, is used to amplitude modulate
the carrier A
c
cos 2p f
c
t and, thus, to generate the DSB-SC signal
( ) ( ) ( ) cos 2
c c
u t A t c t f t
υ π =
Since u ( t ) c ( t ) = ±1 for any t , it follows that the carrier-modulated transmitted signal
may also be expressed as
[ ]
( ) cos 2 ( )
c c
u t A f t t
π θ = +
where q ( t ) = 0 when u ( t ) c ( t ) = 1 and q ( t ) = p when u ( t ) c ( t ) = –1. Therefore, the
transmitted signal is a binary PSK signal.
The rectangular pulse p ( t ) is usually called a chip and its time duration T
c
is called the
chip interval . The reciprocal 1/ T
c
is called the chip rate and corresponds
(approximately) to the bandwidth W of the transmitted signal. The ratio of the bit
interval T
b
to the chip interval T
c
is usually selected to be an integer in practical spread
spectrum systems. We denote this ratio as
b
c
c
T
L
T
=
Hence, L
c
is the number of chips of the PN code sequence/information bit. Another
interpretation is that L
c
represents the number of possible 180° phase transitions in the
transmitted signal during the bit interval T
b
.
For demodulation of the signal, received signal is first multiplied by a replica of the
waveform
c ( t ) generated by the PN code sequence generator at the receiver, which is
synchronized to the PN code in the received signal. This operation is called
(spectrum)
despreading , since the effect of multiplication by c ( t ) at the receiver is to
undo the spreading operation at the transmitter. Thus, we have
2
( ) ( ) cos 2 ( ) cos 2
c c c c
A t t f t A t f t
υ π υ π =
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