Spread Spectrum - Islamic University of Gaza

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© Ammar Abu-Hudrouss Islamic University Gaza

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Spread SpectrumSpread Spectrum

Slide 2Wireless Communications

Spread Spectrum

Input is fed into a channel encoder Produces analog signal with narrow bandwidth

Signal is further modulated using sequence of digits

Spreading code or spreading sequence Generated by pseudonoise, or pseudo-random number generator

Effect of modulation is to increase bandwidth of signal to be transmitted

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On receiving end, digital sequence is used to demodulate the spread spectrum signal

Signal is fed into a channel decoder to recover data


Spread spectrum is typically implemented in one of two forms: direct sequence (DS) or frequency hopping (FH).

In direct sequence spread spectrum (DSSS) modulation, the modulated data signal s (t ) is multiplied by a wideband spreading signal or code sc (t ),

sc (t ) has rate of 1/ Tc where Tc called Chip rate and it has two values: ±1.

Tc is much smaller than Ts (the symbol duration) where Ts /Tc = G (the processing gain)

Thus, the transmitted signal s (t)sc (t) has frequency response S(f ) ∗ Sc(f), which has a bandwidth of roughly Bc + B.

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Spread spectrum signal


Direct Sequence Spread Spectrum (DSSS)

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For an AWGN channel the received spread signal is s (t )sc(t ) + n (t ).

If the receiver multiplies this signal by a synchronized replica of the spreading signal

Moreover n’(t) = n (t)sc(t ) has approximately the same statistics as n(t) if sc(t) is zero mean and sufficiently wideband.

)(')(2 tntststntsts cc


consider narrowband interference I (t), Neglecting noise, we see that the receiver input consists of the spread modulated signal S(f) ∗ Sc(f) and the narrowband interference I (f ).

The despreading in the receiver recovers the data signal S(f). But receiver despreading has the effect of distributing the interference power over the bandwidth of the spreading code.

The interference power is reduced by the processing gain G ≈ Bc/B

Immunity to jamming

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Suppose the spread signal s (t )sc (t) is transmitted through a two-path channel with impulse response.

Receiver input in the absence of noise equal

If the receiver multiplies this signal by a synchronized replica of the spreading signal

Immunity to multipath interference

tststststhtsts ccc )(*

tstststs cc

ttth )(


Direct Sequence Spread Spectrum (DSSS)

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Since the second multipath component

includes the product of asynchronized copies of sc(t), it remains spread out over the spreading code bandwidth, and the demodulation process will remove most of its energy.

tsts c


spread-spectrum transmission

Three advantages over fixed spectrum Spread-spectrum signals are highly resistant to noise and interference. The process of re-collecting a spread signal spreads out noise and interference, causing them to recede into the background.

Spread-spectrum signals are difficult to intercept

Spread-spectrum transmissions can share a frequency band with many types of conventional transmissions with minimal interference. The spread-spectrum signals add minimal noise to the narrow-frequency communications, and vice versa. As a result, bandwidth can be utilized more efficiently.

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In the previous system model, assume rectangular pulse is used

The signal stream can be represented as

x (t) is multiplied by sc (t) and then modulated by the carrier frequency fc.

The channel impulse response is given by

DSSS system model

ss TtTtg 0,/2

l sl lTtgstx

1100 ttth


The input to the matched filter is given by

If we assume no delay and no interference and receiver synchronize at = 0

The output of the matched filter is

cccc ftstItnthftstxtx 2cos)()()(*2cosˆ

cccc ftstnftstxtx 2cos))(2cosˆ

lll nss ˆ

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We now consider the interference signal I (t) at the carrier frequency fc, which can be modeled as

The input to the matched filter is given by

The modulator output is given by

As the power of I’ (t) is spreaded by sc (t ), the lowpass filtering will result on Il with very small power compared to the power of I (t).

cftItI 2cos'

cccc ftstIftstnftxtx 2cos)(2cos)(2cosˆ 2'22

llll Inss ˆ


Now, assume that there is multi-path component at 1 = KTS or the channel response is given by

Assume I (t ) = 0, 0 >> 1 and the receiver synchronize at = 0, the output of the matched filter will be

Where c is the auto-correlation function given by

NT = T / Tc

110 ttth

lccklll nfsss 1110 2cosˆ

s TT N

n scscT

ccs

c nTsnTsN

dttstsT 0 1

11

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It can be shown that ρc(τ ) is a symmetric function with maximum value at τ = 0.

Moreover, if sc(t ) is periodic with period T, then the autocorrelation depends only on the time difference of the spreading codes, i.e.

If T = Ts and ρc(τ) = δ(τ ), the despreading process removes all ISI.

sT

cccs

dttstsT 0 01011

Slide 18Wireless CommunicationsEE 552/452 Spring 2007

PN Sequence Generator

Pseudorandom sequenceRandomness and noise propertiesWalsh, M-sequence, Gold, Kasami, Z4Provide signal privacy

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It has approximately an equal number of zero and ones (balance properties)

It does not have a long run of zeros or ones. (run Property)

For N very large half of the runs are of length 1, ¼ of length two , 1/8 of length 3,…..

If the sequence shifted by any nonzero number of elements, the resulting sequence have half of its elements different from the original and the other half is the same.

Properties of PN sequence

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PN Sequences

PN generator produces periodic sequence that appears to be random

PN Sequences Generated by an algorithm using initial seedSequence isn’t statistically random but will pass many test of randomnessSequences referred to as pseudorandom numbers or pseudonoise sequencesUnless algorithm and seed are known, the sequence is impractical to predict


Definitions

Correlation The concept of determining how much similarity one set of data has with anotherRange between –1 and 1 1 The second sequence matches the first sequence 0 There is no relation at all between the two sequences -1 The two sequences are mirror images

Cross correlation The comparison between two sequences from different sources rather than a shifted copy of a sequence with itself

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Advantages of Cross Correlation

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

This property is useful to the receiver in filtering out noise

The 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


The autocorrelation of m-sequence over a full period T = NTc is given by

Autocorrelation function

c

cCc

TN

TT

N

/1

/111

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1) there are a small number of maximum length codes of a given length N, (at most N users can share the same channel)

2) M-sequences have relatively poor cross-correlation properties.

Other codes such as Gold, Kasami are used due to superior cross-correlation properties.

Pitfalls of M-sequence codes


If the channel response is

The autocorrelation is done over one period T = NTcOf the spreading code, the output of the Correlator will be

Synchronization

At the receiver we assume that phase recovery assure coherence in face between transmitter and receiver.

0)( tth

05.0)( cisw

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The synchronization circuits shown shift the spreading code generator in step of τ in increment of Tc until maximum w (τ) is achieved (coarse synchronization)

The next step that the control feed back make fine adjustment to τ to achieve the exact delay. (fine synchronization)

By this method the receiver will detect the first multipath component arrived (this may be not the strongest components)

Synchronization


Rake Receiver

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The rake receiver assume that there are multipath component at each multiple integer of the chip time.

It is another way of achieving diversity as multipath components separated by multiple of Tc can be viewed as independent (why?)

The larger number of multipath component, the larger is the improvement in the received snr.

Spreading spectrum is not used mainly for diversity as it requires large bandwidth.

Rake receiver


Frequency Hoping Spread Spectrum (FHSS).

Signal is broadcast over seemingly random series of radio frequencies

A number of channels allocated for the FH signalWidth of each channel corresponds to bandwidth of input signal

Signal hops from frequency to frequency at fixed intervals

Transmitter operates in one channel at a timeBits are transmitted using some encoding schemeAt each successive interval, a new carrier frequency is selected

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Frequency Hoping Spread Spectrum


Frequency Hoping Spread Spectrum

Channel sequence dictated by spreading code Receiver, hopping between frequencies in

synchronization with transmitter, picks up message

AdvantagesEavesdroppers hear only unintelligible blipsAttempts to jam signal on one frequency succeed only at knocking out a few bits

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The chip time Tc dictates the time between hops,

The hop time can exceed a symbol time, Tc = kTs for some integer k, which is called slow frequency hopping (SFH)

The carrier can be changed multiple times per symbol, Tc = Ts /k for some integer k, which is called fast frequency hopping (FHS)


FHSS Using MFSK

MFSK signal is translated to a new frequency every Tc seconds by modulating the MFSK signal with the FHSS carrier signal

For data rate of R:duration of a bit: T = 1/R secondsduration of signal element: Ts = LT seconds

Tc Ts - slow-frequency-hop spread spectrum Tc < Ts - fast-frequency-hop spread spectrum

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FHSS Performance Considerations

Large number of frequencies used Results in a system that is quite resistant to jamming

Jammer must jam all frequenciesWith fixed power, this reduces the jamming power in any one frequency band


If the multipath components have delay exceed the hoping time the FH does not exhibit fading

The impact of narrow band interference is very hard to anlyzaeand depends on the structure of the interfering signal.

We will focus on symbol error probability of SFH system without coding. The interference if presents is constant over the symbol time.

Assume a SFH system with M out of the N frequency bands occupied by a narrowband interferer.

The signal hops are assumed uniformly over the entire frequency band.

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The probability of any given hop being in the same band as an interferer is then M/N.

The probability of symbol error is obtained by conditioning on the presence of an interferer over the given symbol period:

Ps = p(symbol error| no interference)p(no interference) + p(symbol error| interference)p(interference)

If the interfering is assume as a partial noise jammer with additive noise power Nj, the effective snr in presence of interference become

INTs

AWGNss P

NMP

NMNP

Js

INTs NBN

BN

0

0


Or

Suppose now that the interference consists of a tone at the hopped carrier frequency with some offset phase. Then

the demodulator output is given by

The impact of the additional interference term Il will depend on the modulation. For example, with coherent MPSK, assuming ∠sl= 0,

INTs

INTs

INTs P

lllll Insas ˆ

MInsapP lllls /1

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