Modulation Schemes

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UNIVERSITY OF WOLLONGONG


ECTE465 L.4

ECTE465 L.4

ECTE465Lecture 4

Assoc. Prof. Tadeusz A Wysocki (Tad)

[email protected]

tel: (02) 4221 3413

10/3/2006 Dr Tad Wysocki 2



ECTE465 L.4

ECTE465 L.4

Contents

Digital Modulation Schemes PSK QAM MSK GMSK

Spread Spectrum Communications




ECTE465 L.4

ECTE465 L.4

Introduction

A digital modulator is a device that maps digital

information onto analog waveforms.

This is done to:

minimize the effect of channel

minimize the energy per transmitted symbol

minimize the bandwidth

facilitate distinction between different symbols.




ECTE465 L.4

ECTE465 L.4

Digital Modulation Schemes

Factors influencing the choice of a modulation scheme:

power efficiency (sometimes referred to as energyefficiency) P, often expressed as the ratio of the signalenergy per bit to noise power spectral density Eb/N0required at the receiver input for a certain probability of

error (e.g. 10-6),

bandwidth efficiency B describing the ability of amodulation scheme to accommodate data within the given

bandwidth; if R is data rate, and B is the bandwidth

occupied by the modulated signal, thenB = R/B bps/Hz.


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ECTE465 L.4

ECTE465 L.4

Digital Modulation Schemes

Factors influencing the choice of a modulation scheme(ctd.): cost and complexity of mobile terminal,

performance of a modulation scheme under mobile channelimpairments, like Rayleigh and Rician fading, multipathpropagation (resulting in time dispersion), given aparticular implementation of the demodulator,

performance of a modulation scheme in an interferenceenvironment,

sensitivity to Doppler spread (due to movements of mobile

terminals), sensitivity to detection of timing jitter, caused by time-

varying channels.




ECTE465 L.4

ECTE465 L.4

Examples of Modulation Schemes Example of digital modulation schemes used in wireless

communication systems:

BPSK

QPSK

mQAM

Linear

FSK

GMSK

CPM

Frequency

Hopping

DirectSequence

Spread

Spectrum

Digital Modulation

Schemes




ECTE465 L.4

ECTE465 L.4

BPSK (1)

Binary Phase Shift Keying (BPSK)

The phase of a constant amplitude carrier is switchedbetween two values according to the modulating data m1and m2 corresponding to binary 1 and 0 or +1 and -1.

To obtain the best error performance, the two phases are

separated by 180o.

For the sinusoidal carrier of the amplitude Ac, the energy

per bit is given by:

Eb= 0.5Ac2Tb, which gives

b

bc T

EA 2=




ECTE465 L.4

ECTE465 L.4

BPSK (2)

The transmitted BPSK signal is either:

for binary +1,

or

for binary -1.

bccb

bBPSK TtfTEts


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ECTE465 L.4

ECTE465 L.4

BPSK (3)

0 1 2 3 4 5 6- 2

- 1

0

1

2

0 1 2 3 4 5 6- 2

- 1

0

1

2

t/Tb

Data

BP

S

K

Example plots for BPSK signalling.




ECTE465 L.4

ECTE465 L.4

BPSK (4)

The 90% of the BPSK signal energy is contained within abandwidth of approximately 1.6Rb.

- 3 - 2 - 1 0 1 2 3- 7 0

- 6 0

- 5 0

- 4 0

- 3 0

- 2 0

- 1 0

0

(f - fc)Tb

Norm

alized

PSD

[dB]




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BPSK (5)

To improve spectral performance of BPSK, it is convenient tointroduce pulse shaping, and such a generalized BPSK signal

can be expressed as:

where the pulse m(t)is chosen to have a raised cosinespectrum with the rolloff factor = 0.5.

)cos(2

)()( ccb

bBPSK T

Etmts +=

- 3 - 2 - 1 0 1 2 3-0.2

0

0.2

0.4

0.6

0.8

1

1.2

t/Tb

Magnitude




ECTE465 L.4

ECTE465 L.4

QPSK (1)

Quaternary PSK (QPSK) sometimes referred to asQuadrature PSK, has twice the bandwidth efficiency of

BPSK, as 2 bits are transmitted in a single modulationsymbol.

To minimize the error probability, the phase of the carriertakes on 1 of 4 equally spaced values, such as 0, /2, ,3/2, with each phase value corresponding to a unique pair ofmessage symbols.

The QPSK signal, for this set of phases, can be expressed as

[ ]

bs

s

cssQPSK

TTkTt

ktTEts

24,3,2,10

)1(5.0cos2)(

==


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UNIVERSITY OF WOLLONGONGUNIVERSITY OF WOLLONGONG

ECTE465 L.4ECTE465 L.4

QPSK (2)

Using a simple trigonometric identity, we can write:

Assuming two orthogonal basis functions:

are defined over the interval [0,Ts), then we can writesQPSK(t) in a form:

[ ]

[ ] )sin()1(5.0sin2

)cos()1(5.0cos2)(

tkTE

tkTEts

css

cssQPSK

=

)sin(2)(),cos(2)( 21 tTttTt cscs ==

[ ] [ ]

4,3,2,1

)()1(5.0sin)()1(5.0cos)( 21

=

=

k

tkEtkEts ssQPSK




QPSK (3)

The latest formula leads to the graphical representation ofQPSK signalsQ

IsE

I

Q

QPSK constellations:left -- the carrier phases are: 0, /2, , 3/2,right-- the carrier phases are: /4, 3/4, 5/4, 7/4.




BER for Coherent BPSK and QPSK




From QPSK to QAM (1)

Quadrature Amplitude Modulation (QAM) is ageneralization of QPSK signalling.

Contrary to PSK, it allows for both phase and amplitudemodulation.

Each modulated signal symbol is characterized by a pairof amplitude Ak, and phase k, or more often as a pairof two amplitudes Ik and Qk.


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From QPSK to QAM (2)

Using the previously two orthogonal basis functions,0


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Other Digital Phase Modulation Schemes

In order to improve performance of digital modulationused in wireless communication systems, severalmodifications to BPSK and QPSK have been proposed,and successfully applied.

Some of these schemes are: Differential BPSK -- DBPSK

Offset QPSK -- OQPSK

/4 QPSK




Differential /4 QPSK

I

Q

- /410-3/4003/401/411

Phasedifference

Bitsequence




Types of QPSK

Conventional QPSK has transitions through zero ( ie. 180o phasetransition) . Highly linear amplifier required.

In Offset QPSK, the transitions on the I and Q channels arestaggered. Phase transitions are therefore limited to 90o.

In /4- QPSK the set of constellation points are toggled eachsymbol, so transitions through zero cannot occur. This schemeproduces the lowest envelope variations.

All QPSK schemes require linear power amplifiers.




General QAM Modulator

PulseGenerator

PulseGenerator

S/PConverter

CarrierGenerator

90o PhaseShifter

Data

I(t)

Q(t)

Acos(ct)

-Asin(ct)

sQAM(t)


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MSK (1)

Minimum Shift Keying (MSK) is a special type of ContinuousPhase-Frequency Shift Keying (CP-FSK), in which the peakfrequency deviation is equal to the half of bit rate.

MSK is equivalent to CP-FSK with a modulation index

hFSK= (2f)/Rbequal to 0.5. Here, 2f is the peak-to-peak frequency shift.

A modulation index hFSK= 0.5, corresponds to the minimumfrequency spacing between upper and lower frequencies in

FSK, required for two FSK signals to be orthogonal.




MSK (2)

MSK is spectrally efficient modulation scheme, and thereforeit is attractive for wireless and mobile applications.

In addition, MSK is: a constant envelope signalling,

characterized with good BER performance (because of theorthogonality),

a self-synchronizing signal.

MSK can be regarded as a special form of OQPSK where the

rectangular baseband pulses are replaced with half-sinusoidalpulses.




Break




GMSK (1)

Gaussian Minimum Shift Keying (GMSK) is a derivative ofMSK.

By passing the modulating NRZ data waveform through apremodulation Gaussian pulse-shaping filter, the sidelobelevels of the spectrum are significantly reduced, comparedwith MSK.

The premodulation Gaussian filtering introduces inter-symbolinterference (ISI) but it is not severe for the 3-dBbandwidth-bit duration product (BTb) of the filter not lowerthan 0.5.

GMSK with BTb = 0.3 is used in GSM.


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GMSK (2)

The GMSK filter has an impulse response given by:

BtthG

2ln2,exp)( 2

2

2

=

=

- 3 - 2 - 1 0 1 2 30

0 .0 5

0 .1

0 .1 5

0 .2

0 .2 5

0 .3

0 .3 5

0 .4

0 .4 5

0 .5

Magnitude

N o rm a lize d tim e t /T

BT=0.3




GMSK (3)

In MSK , the BT is infinity andthis allows the square bittransients to directly modulatethe VCO.

In GMSK, low values of BTcreate significant intersymbolinterference ( ISI) . In thediagram, the portion of thesymbol energy acts as ISIfor adjacent symbols.

If BT is less than 0.3, someform of combating the ISI isrequired.




GMSK Spectra

GMSK has a main lobe 1.5 times that of QPSK.

GMSK generally achieves a bandwidth efficiency less than 0.7 bitsper second per Hz ( QPSK can be as high as 1.6 bits per second perHz) .




Spread Spectrum (SS) - (1)

A spread spectrum (SS) signal is generated by modulating adata signal onto a wideband carrier, resulting in transmitted

signal having bandwidth being much larger than the datasignal.

The bandwidth of SS signal is relatively insensitive to thedata signal.

A spread spectrum transmitter.


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The most widely applied SS signals are as follows: Direct Sequence (DS) Signal with chip time Tc,

Frequency Hopping (FH) Signal with hop time Th:

fast hopping Th < Tb,

slow hopping Th > Tb,

Time Hopping (TH),

Chirp Signals (CS).





The main advantages of SS signals (from the viewpointof mobile communications) are:

resists intentional and non-intentional interference -- animportant feature for mobile communications,

has the ability to eliminate or alleviate the effect ofmultipath propagation, which can be a big obstacle inurban communication,

under some conditions can share the same frequency band(as an overlay) with other users; because of its noise-like signal characteristics,

it is permitted to operate unlicensed SS systems withlimited RF-power in the ISM frequency bands.





Processing gain:

One of the most important parameters of the SS systemsis the processing gain Gp.

It is defined as a ratio of the spread spectrum bandwidth

WSS to the baseband bandwidth required for data Wd:

Gp = WSS/Wd

Value of the Gp, usually expressed in dB, determines theinterference rejection capabilities of the SS system.




ISI and Interference Rejection

Narrowband Interference Rejection (1/K)

Multipath Rejection (Autocorrelation r(t))

S(f) S(f)I(f)S(f)*Sc(f)

Info. Signal Receiver Input Despread Signal

I(f)*Sc(f)

S(f)S(f)

S(f)*Sc(f)[(t)+(t-)]

Info. Signal Receiver Input Despread Signal

S(f)


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Direct Sequence (DS) SS combined with BPSK as a data modulation isone of the most commonly considered SS scheme.

The transmitted DS BPSK signal is given by:

s(t) = Ag(t)b(t)cos(0t + c)g(t) - physical implementation of a spreading sequence

b(t) - physical representation of bipolar data.

Block diagram of DS BPSK transmitter.





Alternative transmitter for DS BPSK SS allows forperforming spreading in the baseband.

Baseband spreading DS BPSK transmitter.





Example signals for the DS BPSK transmitter with basebandspreading.

{gn(j )} = (0, 0, 1, 1, 1, 0, 1)





DS BPSK demodulator recovers the data signal b(t),and finally, the sequence of data symbols {bk} from the

received signal (t). Because of the propagation delay , the received signal

can be expressed as:

(t) = s(t-) + n(t)=Ab(t-)g(t-)cos[0(t-) + 0] + n(t)

where n(t) is the noise from the channel and the front-end of the receiver.


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The block diagram of a conventional DS BPSK receiver.





After despreading, the resulting narrowband signal w(t) isthen demodulated using a conventional BPSK demodulator.

To perform a successful demodulation, the receiver needs toknow the phase , the carrier frequency, 0, as well as thebeginning of each bit.

Example signals for DS BPSK receiver.




DS QPSK

Apart from BPSK, and its differential form DBPSK, onlyQuadrature Phase-Shift Keying (QPSK) is a modulation

scheme commonly discussed in conjunction with DS SSsystems.

Functional diagram of a DS QPSK transmitter.




DS QPSK - (2)

Functional diagram of a DS QPSK receiver.


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DS QPSK - Advantages

The bandwidth of modulated signals sI

(t) and sQ

(t) are thesame, and therefore equal to the bandwidth of the aggregatesignal s(t).

Because, the data rates of bI(t) and bQ(t) are equal to halfthe rate of b(t), the bandwidth occupied by a DS QPSKsignal equals to the half of the bandwidth occupied by anequivalent DS BPSK signal.

Alternatively, a DS QPSK system can transmit twice as muchdata as a DS BPSK sys-tem that uses the same bandwidthand has the same processing gain and signal to noise ratio.




DS QPSK - Disadvantages

A disadvantage of a DS QPSK system is a higher complexitythan that of a DS BPSK system.

In addition, if the two carriers used for demodulation at thereceiver are not truly orthogonal, then there will be a crosstalk between the in-phase and quadrature channels, which cansignificantly impair the system performance.





There are many families of spreading sequences, alsoknown as pseudo-noise (PN) codes.

The sequences should possess low mutual cross-correlation for any relative delay.

Some examples: m-sequences,

Walsh sequences,

Gold codes,

Kassami sequences,

FZC sequences,

Walsh-Chirp sequences.




16-chip Walsh Sequences


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15-chip Gold-like Sequences

There are 16 Gold-likesequences of length 15.

The actual spreadingsequences are bipolarsequences, obtained usingthe formula:

}1,0{

}1,1{)1(

+=

n

gn

g

g n




Frequency Hopping

Spreading codes used to generate a (slow or fast) hoppingcarrier frequency for d(t).

Channel bandwidth determined by hopping range - bandwidthneed not be continuous.

Channel introduces noise, ISI, narrowband and MAIinterference. Hopping has no effect on AWGN No ISI if d(t) narrowband, but channel nulls affect certain hops. Narrowband interference affects certain hops. MAI users collide on some hops.

NonlinearModulation.

(FSK,MSK)

d(t)

Sci(t)

FH Modulator

s(t) ChannelNonlinear

Demod.

FH Demodulator

VCO

Mixer

VCO

Mixer

Sci(t)




Spectral Properties

Di(f-fc)

Dj(f-fc)

1 3 2 4

1 2 34




Slow vs. Fast Hopping

Fast Hopping - hop on every symbol NB interference, MAI interference, and channel nulls affect

just one symbol. Correct using error-control coding

Slow Hopping - hop after several symbols NB interference, MAI interference, and channel nulls affect

many symbols.

Correct using error-control coding and interleaving.


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Documents

Modulation Schemes