Mobile Communication Systems

Professor Z Ghassemlooy

Electronics & IT DivisionScholl of Engineering, Sheffield Hallam University

U.K.www.shu.ac.uk/ocr

Professor Z Ghassemlooy

Electronics & IT DivisionScholl of Engineering, Sheffield Hallam University

U.K.www.shu.ac.uk/ocr

Part 5- Modulation Techniques

Contents

SignalsModulation – Why?Types of Modulation TechniquesBER PerformanceAdvance Modulation Techniques

Signals

Signals can be:– Deterministic: value at any instant can be

expressed exactly with a mathematic formula (eg. Sine wave)

– Probabilistic: future values can be estimated, based on past values

• Random: a probabilistic function where all values within a range are equally likely to occur

Most telecom signals are probabilistic:– Estimation of a sample value is the best we

can do.

Signals

Is physical representation of information (voice, data,..)Is function of time and locationHas parameters, which represent the value of information Types: Time Value

Continuous Analogue signalDiscrete Digital signal

Disceret

• Sine wave as special periodic signal used as a Carrier:s(t) = A sin(2 π f t + ϕ)

Peak amplitude frequency Phase

Signal - Periodical

1

0t

Harmonic components

)2cos()2sin(21)(

11

nftbnftactgn

nn

n ππ ∑∑∞

=

∞

=

++=

DC AC components

1

0t

ideal periodic signal

T

f = 1/T

Signal - Representation

Amplitude domain

ϕ

A [V]

t[s]

Frequency domainf [Hz]

A [V]

phase state diagram (amplitude M and phase ϕin polar coordinates)

ϕ

I = M cos ϕ

Q = M sin ϕ

Noise

White noise: all frequencies at equal power– Many sources (thermal noise, combination sources)– Not possible in practical circuits, so we get …

Band-limited white noise: constant power spectral density over a finite range of frequencies– Corrupts digital signals when decision thresholds are

crossed

Modulation - Why?

Smaller antennas (e.g., λ/4)Multiplexing Ability to manipulate the signalTo fully utilise the medium characteristicsImprove the performance…….

System Block Diagram

Digitalmodulation

Digitalmodulation

Digitaldata

101101001

Analogmodulation

Analogmodulation

RadiocarrierRadiocarrier

AerialAnaloguebase-band

signal

fm

fc >fm

ModulatedRF signal

Transmitter

Decisioncircuit

Decisioncircuit

Analogdemodulation

Analogdemodulation

Analogbase-band

signal

ReceiverRadiocarrierRadiocarrier

Digitaldata

101101001

Noise

Analogue Modulation

Where the center frequency of base-band signal shifted up to the radio carrier frequency by means of:– Amplitude modulation (AM)– Frequency modulation (FM)– Phase modulation (PM)

Digital Modulation

Digital data is translated into an analogue carrier signal by means of Passband Digital Modulation (typically bits encoded in amplitude)

))(2cos()()( ttftAts ncn

n θπ += ∑∞

−∞=

Passband digital modulation has form

Bits encoded in amplitude An, phase θn, or frequency θn=2p(fn-fc)t, which are constant over a bit time Tb.

Digital Modulation - Types

Amplitude Shift Keying(ASK)Frequency Shift Keying (FSK)Phase Shift Keying (PSK)

Multi-levels Schemes

ASK

• The most basic and simple• Low bandwidth• Ssusceptible to interference

⎩⎨⎧

==π

=π=0012

2)()()cos(

)cos()()(b

bccccASK nTm

nTmtfAtfAtmts

Information

Carrier frequency

1 0 1

t

Data m(t)

Bit durationTb

Ac

ASK - Vector & Constellation Diagrams

0

A

cos ωctVector diagram

Q

I0

A Constellation diagram:• The x axis is a reference for symbol that are in-phase (I) with the carrier,

• The y axis is the quadrature (Q) carrier Components (i.e. sin ωct)

PSK

⎩⎨⎧

−=π+π=π

=π=12

122

)()cos()()cos(

)cos()()(bcc

bccccPSK nTmtfA

nTmtfAtftmAts

1 0 1Data m(t)

t

Ac

Bit durationTb

PSK - Implementation

Carrier(cos ωct)Carrier

(cos ωct)

Inverter Data

PSK

• Basic

Carrier(cos ωct)Carrier

(cos ωct)

PSKXInputdata

Inputdata

Pulse shapingfilter

Pulse shapingfilter

• Advanced

PSK - Constellation Diagrams

Q

I-A

A

cos ωct

cos ωct

It display antipodal signalling. I.e. symbols are equal and Opposite to each other, unlike ASK.

PSK - Spectrum

BPSK represented in a complex envelope form:

{ }tfjcBPSK

cc eetmAS πθ= 2))((ReComplex envelope

The power spectral density of the complex envelope is:

22

⎟⎟⎠

⎞⎜⎜⎝

⎛ππ

=−b

bcBPSKce fT

fTAfP sin)(

PSK - Spectrum - contd.

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−−π−−π

+⎟⎟⎠

⎞⎜⎜⎝

⎛−π−π

=222

4 bc

bc

bc

bccBPSK Tff

TffTff

TffAfP)(

)(sin)(

)(sin)(

fcfc+Rbfc-Rb

fc+2Rbfc-2Rb

Pow

er sp

ectra

l den

sity

Frequency

ASK/PSK – Non-Coherent Demodulation

Similar to AM but only requires to choose between one of two values

s(t) ×

cos(2πfct)

∫ ⋅bT

dt0

)(

Decision device determines which of r0 or r1 that r(iTb) is closest to– Noise immunity ∆N is half the distance between r0 and r1– Bit errors occur when noise exceeds this immunity

nTb

Decision Device

“1” or “0”r(nTb)

r0

r1

∆NSampler

A coherent demodulator for BPSK

P. M. Shankar

FSK

The instantaneous frequency of the carrier signal is switched between two (or more) values by the modulating digital data signal.

⎩⎨⎧

<<ω

<<ω=

''cos''cos

)(0010

ForTttnAForTttmA

tSbcc

bccFSK

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

δω+ω= ∫t

ccFSK dttmAtS0

)]()([cos)(

Data

FSK – contd.

Data 1 0 1 1

FSK

Ac cos (2πfc1t)Ac cos (2πfc1t)

Ac cos (2πfc2t)Ac cos (2πfc2t)FSK

Data

VoltageControlledoscillator

VoltageControlledoscillator

Inputdata

Inputdata

FSK

FSK - Spectrum

Am

plitu

de

fc1

fc1 +Rbfc1 -Rb

fc1 +3Rbfc1 -3Rbfc2

fc2 +Rbfc2 -Rb

fc2 +3Rbfc2 -3Rb

Frequencyfc

δ f δf

δf = Frequency deviation = (fc2 - fc1)/2

FSK bandwidth = 2δf

FSK - Demodulation - Non-coherent

Envelopedetector

Envelopedetector

∑∑

Envelopedetector

Envelopedetector

+

-

DecisionthresholdDecisionthreshold

Dataoutput

BPF@fc1

BPF@fc1

BPF@fc2

BPF@fc2

S FSK(t) + n(t)

FSK - Demodulation - Coherent

× LPFLPF

VCO@fc1

VCO@fc1

× LPFLPF

VCO@fc2

VCO@fc2

∑∑+

-

DecisionthresholdDecisionthreshold

Dataoutput

SFSK(t) + n(t)

Bit Error Rate (BER) - ASK/PSK

Probability of bit error: Pb=p(|N(nTb)|>∆N)N(nTb) is a Gaussian RV

s(t) ×

cos(2πfct)

∫bT

0

nTb

r(nTb)+N(nTb)

“1” or “0”+

N(t)Channel

∆N

Receiver

BER – ASK/PSK contd.

The expression for BER (or probability of error) normally contains the energy-to-noise ratio (E/No)The unit energy is:

E = ST Energy/bit

S = Signal power = Ac2/2, Assume R = 1 Ohm

o

b

o NST

NE

=Or in terms of signal to noise ratio (SNR)

Bit rate R = 1/Tb, thusRN

SNE

oo=

BER – ASK/PSK contd.

..,,)cos()( 2122

=π= ifortfTE

tS cb

ASK

ASK & PSK can be represented as:

}b

cb

cb

PSK Ttbiaryfortf

TE

biaryfortfT

E

tS <<

⎪⎪

⎩

⎪⎪

⎨

⎧

π−

π

= 0022

122

"")cos(

"")cos()(

BER – ASK

erfc = Complementary error function, and one needs to use a

standard table.

⎟⎟⎠

⎞⎜⎜⎝

⎛=−

oCASKs N

EerfcP2

5.0

• Coherent

• Non-Coherent

⎟⎟⎠

⎞⎜⎜⎝

⎛= −

−o

NENCASKs N

EerfceP2

5.05.0 )4/(

BER – PSK

Coherent

⎟⎟⎠

⎞⎜⎜⎝

⎛∆=− φcos5.0)(

oCPSKs N

EerfctP

Differential

05.0)( NE

DPSKs etP−

− =

BER Vs. Signal -to-Noise Ratio

C-ASK

NC-ASK

E/No (dB)

CPSK BER Vs. Signal-to-Noise Ratio

Various phase difference

P. M. Shankar

BER - FSK

The average energy / bit is given as:

∫∫ =ω==bb T

bc

cc

T

FSK TAdttAdttSE0

222

0

2

2)(sin)(

⎟⎟⎠

⎞⎜⎜⎝

⎛=−

oCFSKe N

EQP2

Coherent

oNE

NCFSKe eP 2

21 −

− =

Non-coherent

BER – FSK, ASK, and PSK

C-ASK & C-FSK

NC-ASK

NC-FSK

E/No (dB)

• Equal E

M-ARY Modulation Schemes

In ASK, PSK, and FSK each modulated carrier is capable of transmitting one bit of information.To increase the bit transmission rate one could allow each carrier signal to transmit more than one bit of information. This is called M-ARYModulation Schemes.For example M = 4, there are four basic symbols (or carriers). Therefore a sequence of two binary bits can be transmitted by just 4-ary symbols.

M-Ary Modulation

Digital-to-analogue converter(l -bits)

Digital-to-analogue converter(l -bits)

ModulatorModulator

M-level modulated outputBinary data

Rb bits/sec

M = 2l levelmulti-level

digital signal

Rs =Rb/l

Quadrature Amplitude Modulation (QAM)

Combines amplitude and phase modulationOne symbol is used to represent n bits using one symbolBER increases with n, Offers improved BER compared to comparable PSK schemes

QAM – Example : 16 - QAM

n = 4 bits = 1 symbol0011 and 0001 have the same phase, but different amplitude. 0000 and 1000 have different phase, but same amplitude.

0000

0001

0011

1000

Q

I

0010

Used in standard 9600 bit/s modems

Binary Phase Shift Keying (BPSK)

Bit 0 : sin ωtBit 1 : - sin ωtBasic PSKLow spectral efficiencyRobust, used in satellite communication systems

Q

I0

1

Quadrature PSK (QPSK)

2 bits coded as one symbolSymbol shift of sine waveLess bandwidth then BPSKMore complex

Q

I

11

01

10

00

Relative, rather than the absolute phase shift could also be used: •Differential QPSK

Quadrature PSK (QPSK)

The two QPSK constellations. Note that they differ by п /4. When going from (1,1) to (-1, -1), the phase is shifted by п. When going from (1, -1) to (1,1), the phase shifts by п /2. Thus, depending on the incoming symbol, transitions from (1,1) can occur to (1,1), (1,-1), (-1, 1), or (-1, -1) or vice versa, leading to phase shifts of 0, ± п /2, or ± п in QPSK. I and Q represent the in-phase and quadrature bits, respectively. Arrows show all possible transitions.

Main Points

Most information today is in bits

Digital baseband modulation uses simple techniques to encode bits into baseband analog signal.

Digital passband modulation encodes binary bits into the amplitude, phase, or frequency of the carrier.

Decision device in receiver uses threshold to determine which bit was sent.

Bits errors occur when noise exceeds noise immunity threshold.

BER in AWGN is a function of Eb/N0