Spread Spectrum

TUNALI Data Communication 1

Spread Spectrum

Chapter 9

TUNALI Data Communication 2

Spread Spectrum• Can be used to transmit either analog or digital

data• Analog signal• Spread data over wide bandwidth• Makes jamming and interception harder• Frequency hoping

—Signal broadcast over seemingly random series of frequencies

• Direct Sequence—Each bit is represented by multiple bits in transmitted

signal—Chipping code

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Spread Spectrum Concept• Input fed into channel encoder

—Produces narrow bandwidth analog signal around central frequency

• Signal modulated using sequence of digits —Spreading code/sequence—Typically generated by pseudonoise/pseudorandom

number generator

• Increases bandwidth significantly—Spreads spectrum

• Receiver uses same sequence to demodulate signal

• Demodulated signal fed into channel decoder

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General Model of Spread Spectrum System

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Gains• Immunity from various noise and

multipath distortion—Including jamming

• Can hide/encrypt signals—Only receiver who knows spreading code can

retrieve signal

• Several users can share same higher bandwidth with little interference—Cellular telephones—Code division multiplexing (CDM)—Code division multiple access (CDMA)

TUNALI Data Communication 6

Pseudorandom Numbers• Generated by algorithm using initial seed• Deterministic algorithm

—Not actually random—If algorithm is good, results pass reasonable

tests of randomness

• Need to know algorithm and seed to predict sequence

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Frequency Hopping Spread Spectrum (FHSS)• Signal broadcast over seemingly random

series of frequencies• Receiver hops between frequencies in

sync with transmitter• Eavesdroppers hear unintelligible blips• Jamming on one frequency affects only a

few bits

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Basic Operation• Typically 2k carriers frequencies forming 2k

channels• Channel spacing between carrier

frequencies corresponds with bandwidth of input

• Each channel used for fixed interval—300 ms in IEEE 802.11—Some number of bits transmitted using some

encoding scheme—Sequence dictated by spreading code

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Frequency Hopping Example

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Frequency Hopping Spread Spectrum System (Transmitter)

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Frequency Hopping Spread Spectrum System (Receiver)

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Spread Spectrum Math 1• FSK input to the FHSS

—sd(t) = A cos(2(f0+0.5(bi+1)f)t) iT<t<(i+1)T

—A = amplitude of signal

—f0 = base frequency

—bi = value of the ith bit of data f = frequency separation—T = bit duration

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Spread Spectrum Math 2• Product signal during i th bit

—p(t)= sd(t)c(t)= A cos(2(f0+0.5(bi+1)f)t) cos(2fit)

—Using cos(x)cos(y)=1/2(cos(x+y)+cos(x-y)

—p(t)=0.5A[ cos(2(f0+0.5(bi+1)f + fi)t + cos(2(f0+0.5(bi+1)f - fi)t ]

—Using a bandpass filter difference frequency can be blocked yielding

—s(t)=0.5A cos(2(f0+0.5(bi+1)f + fi) t

• At the receiver, s(t) is multiplied by c(t). We again use the above trigonometric identity. This time sum frequency is blocked to obtain the original signal.

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FHSS Using MFSK• Transmitted signal

—si (t) = A cos 2 f i t 1 ≤ i ≤ M

—f i =f c + (2i -1-M) f d

—f d = denotes difference frequency

—M = number of different signal elements = 2 L

—L = number of bits per signal element

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Slow and Fast FHSS• Frequency shifted every Tc seconds

• Duration of signal element is Ts seconds

• Slow FHSS has Tc Ts

• Fast FHSS has Tc < Ts

• Generally fast FHSS gives improved performance in noise (or jamming)

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

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

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FHSS Performance Considerations• Typically large number of frequencies used

—Improved resistance to jamming—Suppose that we have an MFSK transmitter with

• bandwidth Wd

• Noise jammer with same bandwidth and fixed power Sj on the signal carrier frequency

—Then the signal energy per bit to noise power density per Hertz is

j

db

j

b

S

WE

N

E

•If frequency hopping is used, the jammer must jam all 2k frequencies reducing jamming power at a frequency to Sj/2k. Processing (Signal to noise ratio) gain is 2k = Ws/Wd

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Direct Sequence Spread Spectrum (DSSS)• Each bit represented by multiple bits using

spreading code• Spreading code spreads signal across wider

frequency band—In proportion to number of bits used—10 bit spreading code spreads signal across 10 times

bandwidth of 1 bit code

• One method:—Combine input with spreading code using XOR—Input bit 1 inverts spreading code bit—Input zero bit doesn’t alter spreading code bit—Data rate equal to original spreading code

• Performance similar to FHSS

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Direct Sequence Spread Spectrum Example

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DSSS Using BPSK• Use +1 and -1• The signal is )2cos()()( tftAdts cd

Where

A= amplitude of the signal

fc = carrier frequency

d(t)= discrete function converting 1 to +1 and 0 to -1

With c(t) being the previous spreading signal

)()2cos()()()( tstftctAdts dc At the receiver, since c(t)c(t)=1

)()2cos()()()()()( tstftctctAdtcts dc

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Direct Sequence Spread Spectrum Transmitter

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Direct Sequence Spread Spectrum Receiver

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Direct Sequence Spread Spectrum Using BPSK Example

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ApproximateSpectrum of DSSS Signal

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DSSS Performance Considerations 1• Let the jamming

signal be of the form)2cos(2)( tfSts cjj

The received signal is )()()()( tntststs jr

where

s(t)=transmitted signal

sj(t)=jamming signal

n(t)=additive white noise

Sj=jamming signal power

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DSSS Performance Considerations 2• The signal component

due to jamming signal is

)2cos()(2)( tftcSty cjj

This is BPSK modulation of the carrier tone and carrier power Sj is spread over a bandwidth of 2/Tc. BPSK demodulator has bandpass filter of 2/T width, thus most of the jamming power is filtered. Passing jamming power

)/()/2/()/2( TTSTTSS cjcjjF

Gain in signal to noise ratio is T/Tc= Rc/R which is approximately Ws/Wd

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Code Division Multiple Access (CDMA)• Multiplexing Technique used with spread spectrum• Start with data signal rate D

—Called bit data rate

• Break each bit into k chips according to fixed pattern specific to each user—User’s code

• New channel has chip data rate kD chips per second

• E.g. k=6, three users (A,B,C) communicating with base receiver R

• Code 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>

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CDMA Example

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CDMA Explanation• Consider A communicating with base• Base knows A’s code• Assume communication already synchronized• A wants to send a 1

—Send chip pattern <1,-1,-1,1,-1,1>• A’s code

• A wants to send 0—Send chip pattern <-1,1,1,-1,1,-1>

• Complement of A’s code

• Decoder ignores other sources when using A’s code to decode—Orthogonal codes—SA(sA)+ SA(sB) = SA(sA)

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CDMA for DSSS• n users each using different orthogonal PN

sequence• Modulate each users data stream

—Using BPSK

• Multiply by spreading code of user

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CDMA in a DSSS Environment

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Required Reading• Stallings chapter 9