Transcript Spread Spectrum

Corso di Comunicazioni Mobili
TECNICHE DI TRASMISSIONEDATI DIGITALI BASATE SUL
CONCETTO DI
SPREAD SPECTRUM
Prof. Carlo Regazzoni
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Bibliografia
1.
R. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of SpreadSpectrum Communications – A Tutorial”, IEEE Transactions on
Communications, Vol. COM-30, No. 5, Maggio 1982, pp. 855-884.
2.
K. Pahlavan, A.H. Levesque, “Wireless Information Networks”, Wiley:
New York 1995.
3.
A.J. Viterbi, “CDMA: Principles of Spread Spectrum Communications”:
Addison Wesley: 1995.
4.
J.G. Proakis, “Digital Communications”, (Terza Edizione), McGraw-Hill:
1995.
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The concept of
Spread Spectrum
Spread Spectrum is a Digital transmission technique, which spreads the
signal using a bandwidth larger than the original one, in order to obtain
very low power per frequency unit (Watt/Hertz).
To measure the spreading a Process Gain is defined as the ratio
between the bandwidth of Spread Spectrum signal (W) and the narrow
bandwidth of the original signal (R)
P 
W
R
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SS System Architecture
D ati
M odulaz io ne
digita le
a banda
stretta
S pread ing
del se gna le
C odice d i
spreading
T rasm ettitore SS
De S pread ing
D eM odulaz io ne
digita le
a banda
stretta
D ati
C odice d i
spreading
R icevitore SS
4/31
Properties and Advantages
(1/5)
1. High protection against illegal access
2. Low probability of random interception
3. High safety against intentional jamming
4. Multiple Access to the channel with multi
user interference reduction
5. Multi path interference attenuation
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Properties and Advantages
(2/5)
High protection against illegal access
The signal is spread in a wide band, by using a pseudo-random
pattern. This sequence (Chip Sequence) is only known by transmitter
and receiver. If this ‘key’ is not available, it is difficult to obtain the
narrow-band signal and then to demodulate it.
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Properties and Advantages
(3/5)
Low Probability of random Interception (LPI)
The power spectrum density of the signal is very low, then for a
random receiver it is not distinguished from thermal noise and very
hard to be detected.
High safety against jamming
By using pseudo-sequences the jamming is reduced and, in some
case, eliminated. Due to this reason SS techniques have been
extensively used in Second World War.
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Properties and Advantages
(4/5)
Multiple Access to the channel with multi-user
interference reduction
By using different chip sequences for each user it is possible to share the
radio channel. This technique is called CDMA (Code Division Multiple
Access) and it is a powerful alternative of TDMA and FDMA.
Trough SS-CDMA Multi-User Interference (MUI) is strongly reduced due
to low transmission power and orthogonal spreading codes.
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Properties and Advantages
(5/5)
Multipath Interference Reduction
Due to multi-path effect the transmitted signal is delayed in time and
shifted in frequency.
Spread Spectrum techniques reduce this effect obtaining better results
than narrow band modulations.
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Applications
• Cellular Networks
• Wireless LAN
• Train-Ground communications
• Remote Video-Surveillance
Application
Carrier
User
Bandwidth
Cellular Networks, WLAN
902–928 MHz
1.25 MHz (IS-95)
Wireless Multimedia, 3G (UMTS)
1.85-2.2 GHz
350MHz
Remote Video Surveillance, WLAN
2.4–2.4835 GHz
26 MHz (IEEE
802.11)
WLAN
5.725–5.850 GHz
Non standard
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Main Techniques
Two methods are mainly used and implemented:
• DIRECT SEQUENCE (DS)
• FREQUENCY HOPPING (FH)
Hybrid methodologies have been also implemented
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Direct Sequence (DS)
The Direct Sequence Spread Spectrum (DS-SS) is based on the direct
multiplication between based-band signal and wideband signal (chip
sequence). The chip sequence is called PSEUDO-NOISE signal.
The pseudo-noise sequence
is composed by rectangular
pulses of Tc (chip time)
seconds.
The auto-correlation function and frequency spectrum are reported in these
figures:
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Direct Sequence
Transmitter
S (t)
X (t)
g (t)
c (t ) 
2 P cos( 2  f 0 t   )
PN
S equence
S p re a d in g
D ig ita l M o d u la to r B P S K
The source signal X(t) is a binary digital signal with period T. It is multiplied by the
PN sequence, g(t), whose period is:
T
Tc 
N
Once the signal is spread, it is then modulated through a multiplication by a
carrier c(t) with frequency f0 and phase 
.
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Direct Sequence
Receiver
r(t)
D em o d u la to r
BPSK
(1/2)
V (t)
T
D e te c to r
 dt
0
t = T
Y
g (t)
c (t ) 
2 P cos( 2  f 0 t   )
PN
S equence
D e s p re a d in g
The receiver signal r(t) is composed by the transmitted S(t) corrupted by
noise. With Additive White Gaussian Noise (AWGN) the received signal is
r (t )  S (t )  n (t )
where n(t) is the Gaussian Noise with spectral density N0. The complete
formula is given by:
r ( t )  2 P X ( t ) g ( t ) cos( 2 f 0 t   )  n ( t )
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Direct Sequence
Receiver
(2/2)
The first step is the BPSK demodulation: the signal is multiplied by a copy of
the carrier used in transmission and then filtered to remove the image
frequency (2f0). The signal is now:
V (t ) 
P
2
X ( t ) g ( t )  n lp ( t )
Where nlp(t) is the low-pass equivalent of n(t) with the same mean value and
variance.
The dispreading module, called matched filter receiver, is based on a
synchronised copy of the PN sequence. The synchronization is very difficult
but very important in DS-SS, in order to perform a correct detection of the
signal.
P
Y

Tb 0  
The output of matched filter in t=T is:
2
Where b0 is the transmitted bit in [0,T) and  is the filtered Gaussian noise
with zero mean value and variance
The detector is an hard limiter which chooses +1 if the input is positive or -1 if
the input is negative.
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Frequency Hopping (FH)
The transmitter changes continuously carrier frequency among an a-priori
known group of values. The time during which the signal has the same
carrier is called Hop Time (Th).
For instance, if the narrow band signal has a bandwidth of 100 KHz and the SS bandwidth is 100
MHz, the transmitter could change carrier frequency among 1000 different values.
In relation to a comparison between the Th and the period Tb of the original
signal, it is possible to identify two different kind of FH:
•
SLOW FH (SFH) (right) if more bits can be transmitted in the same
carrier, Tb<Th .
•
FAST FH (FFH) (left) if one bit is divided in one or more carriers Tb>Th,
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Frequency Hopping
Transmitter
The transmitter is composed by:
Data modulator : it is a BPSK modulator whose initial frequency is the carrier
frequency.
Code Generator : it generates the pseudo-random number (k) that represents
the frequency hop which will be used.
Frequency
Synthesizer
:
it
converts the previous number in a
frequency offset  f N
used to
modulate the carrier generator
obtaining a frequency f 0   f N
.
The signal has this frequency for an
interval called Hop Time.
Highpass filter used to shape the
signal in the correct band.
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Frequency Hopping
Receiver
The receiver is composed by:
Image Reject Filter is used to remove inferring signals in image frequencies.
The Code Generator and the Frequency Synthesizer are the same of
transmission part.
Band Pass Filter to reject
non useful information in
different bands.
Demodulator: it is used to
de-modulate the signal and
extract the transmitted data.
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DS-SS vs FH-SS
• The bandwidth for DS-SS is 2 f chip
, where f chip is the chip frequency.
To obtain high bandwidth (i.e. high P, then increase the inference reduction)
it is necessary to use high chip frequencies; the drawback of this solution is
the synchronization and timing procedures and the power consumption.
• In FH-SS, wide bandwidth is related to the range within the frequencies
can change.
This means that it is simpler than DS-SS to obtain large
bandwidth.
• The time and synchronization procedure is more difficult in DS than FH
In fact in FH hops can change in a range of few thousands per seconds,
whereas for DS the chip frequency reaches several MHz.
• The DS-SS is really a wide-band signal, whereas the FH-SS is a narrowband signal continuously moved in a wide range.
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DS-SS Performances in Noisy
Environment
White Gaussian Noise
Let’s consider the signal r ( t )  s ( t )  n ( t ),where the first term is the transmitted
signal by using the architecture presented in the previous slides and n(t) is
the AWGN. The amplitude of r(t) output of the matched filter is:
s0  
AT
2
T
The noise after the matched filter is: n 0 
 n ( t ) p ( t ) cos 2 f t dt
c
0
Its auto-correlation function is:
Its variance:
R n ( )  E n ( t ) n ( t   ) 
N0
2
 

2
 T


N 0T


2
var( n 0 ) E n 0   E   n ( t ) p ( t ) cos  2 f c t dt   
4
 
  0



It is worth mentioning that the P has no inferences on the previous values.
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DS-SS Performances in Noisy
Environment
Now it is possible to define the Signal to Noise Radio (SNR):
2
SNR
out

2
s0
2
E (n0 )

A T
4
2
4
N 0T
2

A T
N0
2
Eb
N0
The result shows that SNR with DS-SS with BPSK and AWGN has the
same performance of a simple narrow band BPSK system.
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DS-SS Performances in Noisy
Environment
Narrow Band Noise (Jamming)
Hp: jammer only present in the system
The jammer signal is defined as: J ( t )  S J ( t ) cos  2 f 1 t   
Where Sj(t) is stationary, zero mean, pass-band random process and ψ
is a random variable uniformly distributed between (0,2π).
The noisy component due to the jammer output from the matched filter is:
T
j0 
S
J
( t ) p ( t ) cos  2 f 1 t    cos  2 f c t dt
0
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DS-SS Performances in Noisy
Environment
The autocorrelation function is:
R J ( )  E J ( t ) J ( t   ) 
Where R ( ) is the correlation of
power of the process, i.e. P .
SJ
S J (t )
1
2
R SJ   cos  2 f 1 t 
. Its value in the origin is the mean
SJ
Now it is possible to obtain the variance of j0. It can be noticed that the
variance is strictly related to the process gain.
With these values the SNR is:
2
SNR

out
2
s0
2
E ( j0 )

A T
4
2
4P
PSJ T
2

A
2
PSJ
S 
P  P 
 I  narrowband
In this case an increase of Process Gain P has a direct inference in the
SNR.
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DS-SS Performances in Noisy
Environment
Broad Band Noise
In this case another wide band signal (namely another DS user) is present in the
same band. Another hypothesis is that the amplitude of the two signal are the same.
The received signal is now composed by: r ( t )  s ( t )  J ( t )  Ac ( t ) p ( t ) cos  2 f c t  
Ac ( t   ) p ( t   ) cos 2 f c t  
'
'
'
'
'

The interfering signal output of the matched filter is:
T

j 0  A  c ( t   ) p ( t   ) p ( t ) cos 2  f c t  
'
'
'
'
'
 cos 2 f t dt
c
0
 1
cos   
2
T

AT
 
'

'

p ( t   ) p ( t ) dt 
'
'
1
T
0
T


'

A
2
T
  c ( t  
cos 
'
'
'
) p ( t   ) p ( t ) dt 
'
'
0

'
'
p ( t   ) p ( t ) dt 

The previous value is called Single-User Interference. Several terms of that
type make the Multiple Access Interference – MAI
2
Its variance is :
var( j 0 ) 
A T
4
2

F P , R p p ( )
'

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DS-SS Performances in
Multipath Environment
The received signal is composed by the direct component (LOS) and
reflected copies of it. As hypothesis only one replica is here considered.
It can be proved that the noise generated by the replica can be rejected if its
delay t’ is larger than the chip time Tc, i.e. t’ > Tc.
This means that if it could be possible to estimate the minimum delay of the
copies of the signal and consider a chip time lower than it, then the autoinference could be complete removed.
This can be carried out in indoor channel where the delay changes between
200-500 nsec. Unfortunately in several environments it is not possible to
obtain a measure of the minimum delay.
The solution is the Rake Receiver.
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Rake Receiver
In the Rake Receiver a tapped delay line extracts the energy for each replica.
In particular the signal goes through a delay line, where each module delays
the input of D seconds. Usually D=Tc or D=Tc/2, whereas in new version of
Rake Receivers the delay D is dynamically computed.
The relation between the delay of each replica and the SS bandwidth allows
1
 Tc
one to evaluate the performances of Rake Receiver:  k   l 
B ss
Where  k and  l are the delays of the copy k and l. The larger the difference
between k and l, the higher the number of replicas can be ‘solved’.
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FH-SS Performances in
Multipath Environment
Also by using the FH-SS good performances can be obtained. A typical
frequency response of the multipath channel is plotted in the figure.
This frequency selectivity is due to the features of the multipath in the time
domain. It is possible to avoid those particular frequency, strongly hit by
multipath effect, reducing the hop time.
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FH-SS Performances in
Multipath Environment
•
In case of Slow FH, one or more bits are completely corrupted by
multipath producing an high Bit Error Rate (BER). By using FEC coding
or interleaving this problem can be reduced.
•
In case Fast FH, only parts of bits are corrupted, namely those parts
corresponding to those hops strongly hit by multipath. This means better
performances than Slow-FH.
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PN Sequences
The pseudo noise sequences are usually generated by a r-stages shift
register as reported in figure:
1
C1
2
C2
3
C3
… … … … … … … ..
r – 1
C r-1
r
b n 
Cr
M icro – sw itch
(C i= 1 connessione)
The output of the register is a sequence bn: b n  C 1 b n  1  C 2 b n  2  .......  C r b n  r
The coefficients Cr can be 0 or 1 in order to command the relative module.
NB: r is the length of the shift register and NOT of the sequence.
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PN Sequences
From a user point of view the PN sequence can be seen as completely
random. In fact can be proved that:
Pr( b n  1) 
Where
1
(1  s )
2
Pr( b n   1) 
1
(1  s )
2
1
s ˆ
2
r 1
is the statistical displacement.
Without s the values of chip have the same probability. The dependence from
s can be reduced increasing r and can be completely left out with r
sufficiently large.
The output of the model presented in previous figure is a sequence
composed by values (0,1) and in order to obtain a bipolar (+1,-1) sequence a
PAM codec is inserted.
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PN Sequences
The presented sequences are also called periodic. The period L is the
length of PN sequence and it is usually identify by L or N.
The equality L  N  2 r  1 is obtained when the characteristic polynomial
2
P ( x )  1  C 1 x  C 2 x  ......  C r x
r
is primitive and when the initial conditions are:
( b10 ,......, b r 0 )  ( 0 , 0 ,......, 01 )
In this case the PN sequence is called maximal length sequence (m –
sequence).
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