1/31

Corso di Comunicazioni Mobili

Prof. Carlo Regazzoni

TECNICHE DI TRASMISSIONE-DATI DIGITALI BASATE SUL CONCETTO DI SPREAD SPECTRUM

2/31

Bibliografia

1. R. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of

Spread-Spectrum 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.

3/31

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)R

WP

4/31

SS System Architecture

Modulazionedigitalea bandastretta

Spreadingdel segnale

Dati

Codice dispreading

De-Modulazione

digitalea bandastretta

De -Spreading

Codice dispreading

Dati

Trasmettitore SS Ricevitore SS

5/31

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

6/31

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.

7/31

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.

8/31

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.

9/31

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.

10/31

Applications• Cellular Networks

• Wireless LAN

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

• Train-Ground communications

• Remote Video-Surveillance

11/31

Main Techniques

Two methods are mainly used and implemented:

• DIRECT SEQUENCE (DS)

• FREQUENCY HOPPING (FH)

Hybrid methodologies have been also implemented

12/31

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 auto-correlation function and frequency spectrum are reported in these

figures:

The pseudo-noise sequence is composed by rectangular pulses of Tc (chip time) seconds.

13/31

Direct Sequence Transmitter

X ( t )

P N S e q u e n c e

g ( t ) )2cos(2)( 0 tfPtc

S ( t )

S p r e a d i n g

D i g i t a l M o d u l a t o 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:

Once the signal is spread, it is then modulated through a multiplication by a carrier c(t) with frequency f0 and phase .

N

TTc

14/31

Direct Sequence

Receiver (1/2)

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

where n(t) is the Gaussian Noise with spectral density N0. The complete formula is given by:

r(t) De- modulator BPSK

)2cos(2)( 0 tfPtc

PN Sequence

g(t)

T

dt0

Detector

t = T

V(t)

Y

Despreading

)()()( tntStr

)()2cos()()(2)( 0 tntftgtXPtr

15/31

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:

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.

The output of matched filter in t=T is:

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.

02Tb

PY

)()()(2

)( tntgtXP

tV lp

16/31

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,

17/31

Frequency Hopping

TransmitterThe 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 used to modulate the carrier generator obtaining a frequency . The signal has this frequency for an interval called Hop Time.

Highpass filter used to shape the signal in the correct band.

Nff 0

Nf

18/31

Frequency Hopping

ReceiverThe 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.

19/31

DS-SS vs FH-SS• The bandwidth for DS-SS is , where 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 narrow-

band signal continuously moved in a wide range.

chipf2 chipf

20/31

DS-SS Performances in Noisy Environment

White Gaussian Noise

Let’s consider the signal ,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:

)()()( tntstr

20

ATs

T

c dttftptnn0

0 2cos)()( The noise after the matched filter is:

Its auto-correlation function is: 2

)()()( 0NtntnERn

Its variance: 4

2cos)()()var( 0

2

0

200

TNdttftptnEnEn

T

c

It is worth mentioning that the P has no inferences on the previous values.

21/31

DS-SS Performances in Noisy Environment

00

2

0

22

20

20 2

4

4)( N

E

N

TA

TN

TA

nE

sSNR b

out

Now it is possible to define the Signal to Noise Radio (SNR):

The result shows that SNR with DS-SS with BPSK and AWGN has the same performance of a simple narrow band BPSK system.

22/31

DS-SS Performances in Noisy Environment

Narrow Band Noise (Jamming)

Hp: jammer only present in the system

The jammer signal is defined as: tftStJ J 12cos)()(

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

cJ dttftftptSj0

10 2cos2cos)()(

23/31

DS-SS Performances in Noisy Environment

The autocorrelation function is: tfRtJtJER SJJ 12cos2

1)()()(

)(tSJWhere is the correlation of . Its value in the origin is the mean power of the process, i.e. .

)(SJR

SJP

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:

narrowbandSJSJ

out I

SPP

P

A

TP

PTA

jE

sSNR

2

2

22

20

20 4

4)(

In this case an increase of Process Gain P has a direct inference in the SNR.

24/31

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:

The interfering signal output of the matched filter is:

''''' 2cos)()(

2cos)()()()()(

tftptAc

tftptActJtstr

c

c

T

TT

cc

dttptpT

dttptpT

AT

dttptptcA

dttftftptptcAj

'

'

)()(1

)()(1

cos2

)()()(cos2

2cos2cos)()()(

''

0

'''

0

'''''

0

'''''0

)(,4

)var( '

22

0 pp

RPFTA

j

The previous value is called Single-User Interference. Several terms of that type make the Multiple Access Interference – MAI

Its variance is :

25/31

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 auto-

inference 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.

26/31

Rake ReceiverIn 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 one to evaluate the performances of Rake Receiver: c

sslk T

B

1

kWhere and 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’.

l

27/31

FH-SS Performances in Multipath EnvironmentAlso 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.

28/31

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.

29/31

PN Sequences

1 2 3 ………………….. r – 1 r

C1 C2 C3 Cr-1 Cr

nb

Micro – switch(Ci= 1 connessione)

The pseudo noise sequences are usually generated by a r-stages shift register as reported in figure:

The output of the register is a sequence bn:

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.

rnrnnn bCbCbCb .......2211

30/31

PN Sequences

From a user point of view the PN sequence can be seen as completely

random. In fact can be proved that:

Where 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.

)1(2

1)1Pr( sbn )1(

2

1)1Pr( sbn

12

1ˆ

rs

31/31

PN SequencesThe 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 is obtained when the characteristic polynomial

is primitive and when the initial conditions are:

In this case the PN sequence is called maximal length sequence (m –

sequence).

12 rNL

rr xCxCxCxP ......1)( 2

21

)01,......,0,0(),......,( 010 rbb