Spread Spectrum Techniques - PowerPoint Presentation

Slide1

Spread Spectrum Techniques

Frequency HoppingDirect Sequence

1Slide2

Shannon’s Theorem and

Nyquist’s Theorem

channel capacity,

[bps]. channel bandwidth, [Hz]. SNR is the signal-to-Noise ratio [Unitless].Shannon’s theorem has some interesting implications:For a given capacity, :There is no limit to how small the bandwidth can be, provided that SNR is sufficiently large.There is no limit to how small the SNR can be, provided that the bandwidth is sufficiently large.For a given Bandwidth, :There is no limit to the capacity provided that SNR is sufficiently large.There is no limit to how small SNR can be, provided that the Capacity is reduced accordingly.

2Slide3

Cont.

Rearranging Shannon’s equation gives:

For large

:

3Slide4

Graph C/B vs. SNR (dB)

4

SNR (dB)

C/BSlide5

Negative SNR

Shannon’s theorem acknowledges the possibility that the noise power can be at a higher level than the signal’s power, this situation does not make data transmission impossible.

Considering the equation, data transmission is possible as long as

is positive, that is when there is some signal power.

Shannon’s theorem therefore tells us that data transmission is possible under these conditions.

For negative values of however, will be less than 1. e.g., for an SNR of -30 dB, a bandwidth of 714 kHz would be required to carry data at 1 kbps.  5Slide6

Nyquist’s

Theorem Although Shannon’s theorem places a limit on the data that can be carried, it is not the only limit.Nyquist’s

theorem places an absolute limit on the symbol (baud) rate for a channel of a particular bandwidth regardless of noise levels.According to Nyquist’s theorem a channel of bandwidth

can carry a maximum of

symbols per second.

 6Slide7

Example

It is required to transmit data at a rate of 9600 bps over a channel of bandwidth 2000 Hz. Use Shannon’s theorem to determine the minimum signal to noise ratio required and, referring to Nyquist’s theorem. Comment on a suitable modulation scheme.

Solution:

Therefore a SNR of at least 14.3 dB is required.The bandwidth 2000 Hz limits the baud rate to 4000 Baud

Thus there must be at least 3 bits per symbol.

7Slide8

Spread Spectrum

Spread spectrum is a communication technique that spreads a

narrowband communication signal over a wide range of frequencies for transmission then de-spreads it into the original data bandwidth at the receive. Makes jamming and interception harder

Two Techniques:

Frequency hoping

Signal broadcast over seemingly random series of frequenciesDirect SequenceEach bit is represented by multiple bits in transmitted signalChipping (spreading) code/sequence8Slide9

Spread Spectrum Concept

Input fed into channel encoder Produces narrow bandwidth signal around central frequencySignal modulated using sequence of digits

Spreading code/sequenceTypically generated by pseudonoise/pseudorandom number generator (PN)Increases bandwidth significantly

Spreads spectrum

Receiver uses same sequence to demodulate signal

Demodulated signal fed into channel decoder9Slide10

General Model of Spread Spectrum System

10Slide11

11

Spread spectrum

ConceptSlide12

12Slide13

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Frequency Hopping Spread Spectrum (FHSS)

Signal broadcast over seemingly random series of frequenciesReceiver hops between frequencies in sync with transmitterEavesdroppers hear unintelligible blips

Jamming on one frequency affects only a few bits

Hedy

Lamarr15Slide16

16

 Slide17

17

 Slide18

Basic Operation

Typically 2k carriers frequencies forming 2k channelsChannel spacing corresponds with bandwidth of inputEach channel used for fixed interval

300 ms in IEEE 802.11Some number of bits transmitted using some encoding schemeMay be fractions of bit (see later)

Sequence dictated by spreading code

18Slide19

FHSS

19

Frequency

Time

f4

f3

f2

f1

Repeating period

Spreading Factor

 Slide20

FHSS

20

Frequency

Time

f4

f3

f2

f1

Repeating periodSlide21

Multiplexing

21

Frequency

Time

f4

f3

f2

f1

Repeating period

User1

User2Slide22

Multiplexing

22

Frequency

Time

f4

f3

f2

f1

Repeating period

User1

User2Slide23

Frequency Hopping Spread Spectrum System

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Frequency Hopping Spread Spectrum System

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Slow and Fast FHSS

Frequency shifted every Tc secondsDuration of signal symbol is TM

secondsSlow FHSS has Tc  T

M

Fast FHSS has

Tc < TMGenerally fast FHSS gives improved performance in noise (or jamming)25Slide26

Slow Frequency Hop Spread Spectrum Using MFSK (M=4, k=2)

26

 Slide27

Fast Frequency Hop Spread Spectrum Using MFSK (M=4, k=2)

27

 Slide28

Direct Sequence Spread Spectrum (DSSS)

Each bit represented by multiple bits using spreading (chipping

)code/sequence. This process

is called

Processing

Gain.The bits resulting from combining the information bits with the chipping code are called chips - the result- which is then transmitted.Spreading code spreads signal across wider frequency bandIn proportion to number of bits used10 bit spreading code spreads signal across 10 times bandwidth of 1 bit code  Processing Gain Spreading Factor (SF) =10SF is the number of chips within each symbol duration , let be the chip duration

: chipping rate,

: Baud rate.

One method

:Combine input with spreading code using XORInput bit 1 inverts spreading code bitInput zero bit doesn’t alter spreading code bitData rate equal to original spreading codePerformance similar to FHSS 28Slide29

Direct Sequence Spread Spectrum Example

: XOR

29Slide30

Another method (polar)

30

 Slide31

Approximate Spectrum of

DSSS Signal

The BW of

is

BW:

31Slide32

Direct Sequence Spread Spectrum Transmitter

32Slide33

Direct Sequence Spread Spectrum Receiver

Spread Signal

Original Signal

33Slide34

34

DSSS Overall Transmit/Receive

user data

chipping

sequence

modulator

radio

carrier

spread

spectrum

signal

transmit

signal

transmitter

demodulator

received

signal

radio

carrier

chipping

sequence

lowpass

filtered

signal

receiver

integrator

products

decision

data

sampled

sums

correlator

X

X

PN generator

PN generator

: we can look at it as a pulse shaping

 Slide35

DSSS Using BPSK

Multiply BPSK signal,

by

[takes values +1, -1] to get

amplitude of signal

carrier frequency

digital baseband signal

pulse shaping signal

bit duration

At receiver, incoming signal multiplied by

Since,

, original signal is recovered

35Slide36

Direct Sequence Spread Spectrum Using BPSK Example

36Slide37

37

Narrowband

vs.

Spread Spectrum

Frequency

Power

Spread Spectrum

(Low Peak Power)

Narrowband

(High Peak Power)

The bandwidth increases with spreading but spectral power density necessary for transmission decreases. Spread spectrum needs only very small power densities, often below the level of natural background noise.Slide38

Gains

Immunity from various noise and multipath distortionIncluding jammingCan hide/encrypt signals

Only receiver who knows spreading code can retrieve signalAdvantagesreduces frequency selective fading

in cellular networks

base stations can use the

same frequency rangeseveral base stations can detect and recover the signalsoft handoverDisadvantagesprecise power control necessary38Slide39

39

Gains (cont.)

Problem of radio transmission: frequency dependent fading can wipe out narrow band signals for duration of the interference

Solution: spread the narrow band signal into a broad band signal using a special code - protection against narrow band interference

detection at

receiver

Interference

or noise

spread signal

signal

spread

Interference or noise

f

f

power

power

frequency

channel

quality

1

2

3

4

5

6

Narrowband signal

guard space

narrowband channels

2

2

2

2

2

frequency

channel

quality

1

spread

spectrum

spread spectrum channelsSlide40

40

Effects of spreading

on noise and interference

+

x

Rx

The noise is spreadSlide41

41

Effects of spreading and interference

PSD

f

i)

PSD

f

ii)

sender

PSD

f

iii)

PSD

f

iv)

receiver

f

v)

user signal

broadband interference

narrowband interference

PSDSlide42

Code Division Multiple Access (CDMA)

Multiplexing Technique used with spread spectrum

Start with data signal rate

Buad

rate (symbols per second)

Break each symbol into SF chips according to fixed pattern specific to each user (User’s spreading code)SF is the number of chips within each symbol duration , let be the chip duration New channel has chip data rate chips per second (cps). Spreading code repetition period (code length)

:

Short code:

an exact pattern of the PN will repeat each data symbol.

Long code:

 Slide43

Short vs. Long Code

43

Short

Long

1 0 1 1 0 1 0 01 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 1 01 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 1Slide44

CDMA Example

e.g. SF=6, three users (A,B,C) communicating with base receiver RCode for A = <1,-1,-1,1,-1,1>

Code for B = <1,1,-1,-1,1,1>Code for C = <1,1,-1,1,1,-1>

Short codeSlide45

CDMA Explanation

Consider A communicating with baseBase knows A’s codeAssume communication already synchronized

A wants to send a 1Send chip pattern <c1, c2, c3, c4, c5, c6>, e.g.<1,-1,-1,1,-1,1>

A’s code

A wants to send 0

Send chip pattern <-c1, -c2, -c3, -c4, -c5, -c6>, e.g.<-1,1,1,-1,1,-1>Complement of A’s codeReceiver knows sender’s code and performs electronic decode function<d1, d2, d3, d4, d5, d6> = received chip pattern<c1, c2, c3, c4, c5, c6> = sender’s codeDecoder ignores other sources when using A’s code to decodeOrthogonal codes45Slide46

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CDMA Example

User A code = <1,

–

1,

–1, 1, –1, 1>To send a 1 bit = <1, –1, –1, 1, –1, 1>To send a 0 bit = <–1, 1, 1, –1, 1, –1>User B code = <1, 1, –1, – 1, 1, 1>To send a 1 bit = <1, 1, –1,

–1, 1, 1>To send a 0 bit = <

–1,–1, 1, 1,

–

1,

–1>Receiver receiving with A’s code(A’s code) x (received chip pattern)User A ‘1’ bit: 6 1User A ‘0’ bit: -6 0User B ‘1’ bit: <1, –1, –1, 1, –1,

1>X<1, 1, –1, –1, 1, 1>=0

unwanted signal ignored

 Slide47

CDMA for DSSS

n users each using different orthogonal PN sequenceModulate each users data streame.g. Using BPSKMultiply by spreading code of user

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CDMA in a DSSS Environment

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Seven Channel CDMA Encoding and Decoding

49Slide50

50

demodulator

received

signal

radio

carrier

chipping

sequence

lowpass

filtered

signal

receiver

integrator

products

decision

data

sampled

sums

correlator

X

PN generator

 Slide51

Multiple Access Interference (MAI)

51

integrator

X

integrator

X

integrator

X

.

.

.

X

X

X

.

.

.

Channel

Compute the interference at the output of one receiver caused by the remaining M-1 users.

Focus on the time interval

and the

k

th

symbol of all users.

The

th

user transmit one symbol

over the time interval

.

Each user receives the

k

th

symbol of all users within

.

The

i

th

user’s transmitted power is

.

The

i

th

user’s channel has a gain

.

 Slide52

MAI

Where

Is the time-varying cross-correlation between two spreading codes.

For short code

are periodic and the period is

, the spreading codes are identical over each interval

the cross correlation between two spreading codes is a constant (does not change with

k

)

52Slide53

MAI

Where

is the MAI

When

the spreading codes are selected to be orthogonal i.e.

So

53Slide54

Pseudorandom Numbers

Also called Pseudonoise(PN) because the autocorrelation of it resembles that of a white noise (an impulse).

Generated by algorithm using initial seedDeterministic algorithmNot actually randomIf algorithm good, results pass reasonable tests of randomness

Need to know algorithm and seed to predict sequence

Pseudonoise

(PN) sequence chosen so that its autocorrelation is very narrow PSD is very wide, in order to make the correlation between a code and a shifted version of it approximately zero.Concentrated around t < Tc toCross-correlation between two codes is very small, if it is zero Orthogonal. 54Slide55

PN Sequence Generation

Codes are periodic and generated by a shift register and XOR

Maximum-length (ML) shift register sequences (m-sequence), m-stage shift register, length:

bits

-

1/L

T

c

t

-

LT

c

LT

c

Output

1

-

T

c

D

Delay tap by

(shift register)

D

D

D

…

D

D

XOR (Modulo-2 adder)

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Generating PN Sequences

Take m=2

L=3cn

=[1,1,0,1,1,0, . . .], usually written as bipolar

cn=[1,1,-1,1,1,-1, . . .] DD

+

Output

00

01

10

11

1

1

0

Finite State Machine (FSM)

Dead state

Slide

56Slide57

Properties of

m-sequencesThe cross correlation between an m-sequence and noise is low

This property is useful to the receiver in filtering out noiseThe cross correlation between two different m-sequences is low

This property is useful for CDMA applications

Enables a receiver to discriminate among spread spectrum signals generated by different m-sequences

Easy to guess connection setup in 2m samples so not too secureIn practice, Gold codes or Kasami sequences which combine the output of m-sequences are used.57Slide58

Gold Codes

Gold sequences constructed by the XOR of two m-sequences with the same clocking

Codes have well-defined cross correlation propertiesOnly simple circuitry needed to generate large number of unique codes

58Slide59

59

Orthogonal Variable Spreading Factor Codes (OVSF)

C

ch

,

i

,j

selected from this tree

Notes:

1) For fixed chip rate, desired information

rate determines length of spreading

sequence and therefore processing gain.

2) When a specific code is used, no other

code on the path from that code to the root

and

on

the

subtree

beneath that

code may be used.

3) All the codes at any depth into the tree

are the set of Walsh Sequences.

4) Code phase is synchronous with

information symbols.

5) FDD UL processing gain between 256 and 4

FDD DL processing gain between 512 and 4

TDD UL/DL processing gain between 16 and 1

6)

Multicode

used only for SF = 4

(

,

)

(

,

)

Walsh-

Hadamard

codes

,

,

integer,

Are perfect orthogonal such that:

,

,

Requires tight synchronization, Cross correlation between different shifts of Walsh sequences is not zero