Spread Spectrum
Whereas conventional modulation
techniques strive to achieve greater power and bandwidth efficiency and minimize
the required transmission bandwidth, spread spectrum technique employ a
transmission bandwidth that is several orders of magnitude greater than the
minimum required signal bandwidth, while this system is very bandwidth
inefficiency for a signal user, the advantage of spread spectrum is that many
users can share the same bandwidth without significantly interfering with one
another. In a multiple-user, multiple access interference environment, spectrum
system become very bandwidth efficiency.
Apart from occupying a very large
bandwidth, spread spectrum signals are pseudorandom and have nose-like
properties. The spreading waveform is controlled by a PN sequence or PN code.
Spread spectrum signals are demodulated at the receiver through
cross-correlation with a locally-generated version of the PN carrier.
Cross-correlation with the correct PN sequence despreads the spread spectrum
signal and restores the modulated message in the same narrow band as the
original data, whereas cross-correlating the signal from an undesired user
results in a very small amount of wideband noise at the receiver.
Since each user is assigned a unique PN
code which is approximately orthogonal to the codes of other users, the receiver
can separate each user based on their codes.
GO BACK TO TOP
Direct Sequence spreading, spread
spectrum signal(DS-SS)
An end-to-end direct sequence spread spectrum system is
illustrated in Figure 1-1. The multiplication by
and
the carrier 
could
be done in opposite order as well: downconverting prior to despreading allows
the code synchronization and despreading to be done digitally, but complicates
carrier phase tracking since it must be done relative to the wideband spread
signal. For simplicity we only illustrate the receiver for in-phase signaling, a
similar structure is used for the quadrature signal component. The data symbols
are
first linearly modulated to form the baseband modulated signal
,
where 
is
the modulator shaping pulse, 
is
the symbol time, and
is
the symbol transmitted over the lth symbol time. Linear modulation is
used since DSSS is a form of phase modulation and therefore works best in
conjunction with a linearly modulated data signal. The modulated signal is then
multiplied by the spreading code
with
chip time
,
and then upconverted through multiplication by the carrier
.
The spread signal passes through the channel
which
also introduces additive noise
and
narrowband interference
.
DSSS Systen Model
Assume the channel introduces
several multipath components
The input to the matched filter is
given by
Without
multipath and interference, i.e. for
and
since
.
If 
is
sufficiently wideband then
has
approximately the same statistics as
.The
matched filter output over a symbol time will thus be
The interference signal
I(t)
at the carrier frequency
fc,
which can be modeled as
for
some narrowband baseband signal
.
Multiplication by the spreading
signal perfectly synchronized to the incoming signal is
The demodulator output is then
given by
The spread interference
is
a wideband signal with bandwidth of roughly
,
and the integration acts as a lowpass filter with bandwidth of roughly
,
thereby removing most of the interference power.
Now consider ISI rejection. Assume
a multipath channel with one delayed component:
.
For simplicity, assume
is
an integer multiple of the symbol time. Suppose that the first multipath
component is stronger than the second:
,
and that the receiver synchronizes to the first component (
in
Figure 1-1). Then, in the absence of narrowband interference (),
after despreading we have
Since
the
ISI just corresponds to the signal transmission of the
(l
−
k)th
symbol, i.e.
.
The demodulator output over the
lth
symbol time is then given by
where, as in the case of
interference rejection,
and
correspond
to the data symbol and noise output of a standard demodulator without spreading
or despreading and the approximation assumes
The
middle term
comes
from the following
integration:
where 
is
the autocorrelation of the spreading code at delay
over
a symbol time.
GO BACK TO TOP
Spreading Codes for ISI
Rejection: Pseudorandom and m-Sequences
Apart from occupying a very large
bandwidth, spread spectrum signals are pseudorandom and have nose-like
properties. The spreading waveform is controlled by a PN sequence or PN code.
Spread spectrum signals are demodulated at the receiver through
cross-correlation with a locally-generated version of the PN carrier.
Cross-correlation with the correct PN sequence despreads the spread spectrum
signal and restores the modulated message in the same narrow band as the
original data, whereas cross-correlating the signal from an undesired user
results in a very small amount of wideband noise at the receiver. One type of PN
code generator is said to generate a maximum-length sequence, or m-sequence
waveform. These sequences
have the maximum period
that
can be generated by a shift register of length n, so the sequence repeats every
seconds.
Generation of Spreading
Codes
Properties of Maximum-Length Sequences:
1.
In one period, the number of 1’s is always one more than the number of
0’s.
2.
The modulo-2 sum of any m-sequence, when summed chip by chip with a
shifted version of the same sequence, produces another shifted verson of the
same sequence.
3.
If a window of width r is slid along the sequence of N shifts, then all
possible r-bit words will appear exactly once, except for the all 0 r-bit word.
4.
If the 0’s and 1’s are represented by -1 and +1V, the autocorrelation of
the sequence is
where 
is
the autocorrelation of the sequence and
Autocorrelation of Maximal
Linear Code
Autocorrelation
has Period T=NTc
Moreover, since the spreading code
is periodic with
period
,
the autocorrelation is also periodic with the same period, as shown in Figure
1-4. Thus, if
is
not within a chip time of
for
any integer
，
.
By making
sufficiently
large, the impact of multipath at delays that are not within a chip
time of
can
be mostly removed.
GO BACK TO TOP