chapter 6 modulation techniques for mobile radio

ECE 8708 Wireless Communications : Modulation Techniques

Chapter 6Chapter 6Modulation Techniques for Mobile RadioModulation Techniques for Mobile Radio

Yimin Zhang, Ph.D.Department of Electrical & Computer Engineering

Villanova UniversityVillanova Universityhttp://yiminzhang.com/ECE8708

Yimin Zhang, Villanova University 1


OutlinesOutlines

Concept of Modulation

Power and Spectral Efficiency

Pulse Shaping

Digital ModulationsDigital Modulations

Linear – BPSK, QPSK, DPSK, OQPSK, π/4 QPSK

Nonlinear – FSK, MSK, GMSKo ea S , S , G S

M-ary ASK, M-ary PSK, M-ary FSK

Coherent and Noncoherent Detection



Concept of Modulation and DemodulationConcept of Modulation and Demodulation

Modulation is the process of encoding information from a message source in a manner suitable for transmission.

It generally involves translating a baseband message signal (called the source) to a bandpass signal at frequencies that are very high compared to the baseband frequency.compared to the baseband frequency.

The bandpass signal is called modulated signal and the baseband signal is called modulating signal.

Demodulation is the process of extracting the baseband message from the carrier so that it may be processed and interpreted by the y p p yintended receiver.



Modulation TechniquesModulation Techniques

ModulationModulation

Analog ModulationAnalog Modulation Digital ModulationDigital Modulationgg(First Generation(First Generation

Mobile Radio)Mobile Radio)

gg(Present & Future(Present & Future

Systems)Systems)

Amplitude modulation

A l d l ti

Amplitude shift keying (ASK)

F hift k i (FSK)Angle modulation (Frequency & phase modulations)

Frequency shift keying (FSK)

Phase shift keying (PSK)

Quadrature amplitude


pmodulation (QAM)


AM and FM Modulations

AM and FM signalsAM and FM signals produced by a single tone.

(a) Carrier wave(a) Carrier wave.

(b) Sinusoidal modulating signal.signal.

(c) Amplitude-modulated signal.

(d) Frequency-modulated signal.


g


Frequency Modulation vs. Amplitude Modulation

FM signals have all their information in phase or frequency of th ithe carrier

AM signals have all their information in the amplitude of the carriercarrier

FM has better noise immunity when compared to amplitude modulation

AM signals are able to occupy less bandwidth as compared to FM signals

FM exhibits a so-called capture effect characteristic



Amplitude Modulation

• AM signal can be represented as

)2cos()](1[)( tftmAts ccAM π+=

• For a sinusoidal modulating signal )2cos()/()( tfAAtm π=• For a sinusoidal modulating signal

the modulation index is given by

A

)2cos()/()( tfAAtm mcm π=

c

m

AAk =

The spectr m of an AM signal can be sho to be• The spectrum of an AM signal can be show to be

)]()()()([21)( cccccAM ffMffffMffAfS ++++−+−= δδ


2




1





Angle Modulationg

• The two most important classes of angle modulation are frequencymodulation and phase modulation

• Frequency modulation (FM) can be represented as

⎤⎡ t

⎥⎦

⎤⎢⎣

⎡+=+= ∫

∞−

t

fccccFM dmktfAttfAtS ηηππθπ )(22cos)](2cos[)(

Ac : amplitude of the carrier c pfc : carrier frequencykf : frequency deviation constant

• Phase modulation (PM) can be represented as

)](2cos[)( tmktfAtS ccPM θπ +=


kθ : phase deviation constant


FM Modulation Methods – Direct Method

• Direct methodThe carrier frequency is directly

varied in accordance with the input modulating signal.



FM Modulation Methods – Indirect Method

• Indirect method4A narrowband FM signal is generated using a balanced modulator and

frequency multiplication is used to increase both the frequency deviation and the carrier frequency to the required lever.


tftAtfAtS ccccFM πθπ 2sin)(2cos)( −≈


FM Detection Techniqueq

• Slope Detector

• Zero-crossing Detector

• PLL for FM Detection

Q d t D t ti• Quadrature Detection



Digital Modulation TechniquesDigital Modulation Techniques



Why Using Digital Modulations?Why Using Digital Modulations?Advantages

Higher transmission efficiencyg y

Noise immunity

Robustness to channel impairments

Easier multiplexing (voice, data, image)

Greater security

C t ffi i & i i i tiCost efficiency & minimization

Software implementation for flexibility

Error control codes (for error detection and correction)

Source coding, encryption


Equalizations


Basics of Digital Communications

• In digital wireless communication systems, the message (mod lating signal) is represented as a time seq ence of s mbols(modulating signal) is represented as a time sequence of symbols or pulses.

• Each symbol has m finite states

Example m=16Each symbol represents n bits of information

n = log2m =4 bits/symbol



Power and Bandwidth EfficienciesPower and Bandwidth Efficiencies

Performance of modulation is often measured by

power efficiencyThe ability of a modulation technique to preserve the fidelity ofthe digital message at low power levels.

pη

Expressed in Eb/N0 (ratio of signal energy per bit to noise power spectral density) required at the receiver output for a certain error probability.certain error probability.

bandwidth efficiencyThe ability of modulation scheme to accommodate data within

li it d b d idth

Bη

a limited bandwidth.

Expressed as the ratio of throughput data rate per Hz. R


bps/HzBR

B =η



Fundamental upper bound on achievable bandwidth efficiency(Shannon’s channel coding theorem)

For AWGN (additive white Gaussian noise) non-fading channels

⎞⎛ SC

C / W [bits/s/Hz]

Unattainablei

C: channel capacity (bps)

bps/Hz1log2max ⎟⎠⎞

⎜⎝⎛ +==

NS

WC

Bηregion

p y ( p )W: RF signal bandwidth (Hz)S/N: signal-to-noise power ratio (SNR) Practical region

There is a tradeoff between bandwidth efficiency and power efficiency.

C i li l t W d i l ith

SNR [dB]


C increases linearly to W, and in logarithm to SNR (for high SNR).



Examples :

For US digital cellular standard, R = 48.6 kbpsRF bandwidth = 30 KHzF SNR 20 dB 100For SNR = 20 dB 100C = 30000 * log2(1 + S/N)

= 30000 * log2(1 + 100) = 199.75 kbpsg2( ) p

For GSM standard, R = 270.833 kbpsC = 1 99 Mbps for S/N = 30 dBC = 1.99 Mbps for S/N = 30 dB

> For most exiting systems, the actual data rate is much lower than th it b d


the capacity bound.


Shannon’s LimitShannon’s Limit

⎟⎟⎞

⎜⎜⎛+=

CEC b1log⎟⎠⎞

⎜⎝⎛ +=

NSWC 2 1log

⎟⎟⎠

⎜⎜⎝+=

WNW 02 1log

⎩⎨⎧

==

WNNCES b

0

[dB]6169301

:get we,0or As

≈→

→∞→

EWCW

b Shannon limit[dB] 6.1693.0log 20

−≈=→eN

b

– There exists a limiting value of Eb/N0 below which there can be no error-free communication at any information rate.

– By increasing the bandwidth alone, the capacity cannot be increased to any desired value.


Q: How to increase Eb/N0 in a highly noisy environment?



R>C

R / W [bits/s/Hz]

R=C

M=256Unattainable region

Bandwidth limited M=8

M=16

M=64

M=256

R<CPractical regionM=2

M=4

M 8

M=2M=4M=8

M=16

Power limited

Shannon limit MPSKMQAMMFSK

510−=BP


[dB] / 0NEb


Power Spectral DensityPower Spectral Density

The power spectral density (PSD) of a random signal w(t) is define asas

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

∞→ TfW

fp T

Tw

2)(

lim)(

⎩⎨⎧ <<−

=⇔elsewhere

2/2/0

)()()(

TtTtwtwfW TT

The power of the signal in a given frequency band can be calculated

⎩

by integrating over positive and negative frequencies,

∫∫−

+= 12 )()(ff

dffpdffpP


∫∫ −+=

21

)()(f wf w dffpdffpP


BandwidthBandwidth

Bandwidth

• Absolute bandwidth

• Null-to-null bandwidth

• Half-power bandwidth (3 dB bandwidth)

• Occupied bandwidth (defined by FCC; contains99% of signal power)99% of signal power)

• Bandwidth with PSDoutside the band is under


certain stated level


Line CodingLine Coding

• Line codes are used to id ti lprovide particular

spectral characteristics of a pulse train.

• Most commonly used – Return-to-zero (RZ)– Non-return-to-zero

(NRZ)– Manchester Code

• Uni-polar (0,V) or Bipolar (-V, V )


Bipolar ( V, V )


Pulse Shaping techniques Pulse Shaping techniques

BandlimitedChannelChannel

• ISI – Inter Symbol Interference ⇒ errors in transmission of symbols• Pulse shaping techniques ⇒ reduces the inter-symbol effects

> The objective of pulse shaping is to design causal pulse waveforms that yields no or negligible ISI for propagation in band-limited channels


channels.


Nyquist Criterion for ISI Cancellation Nyquist Criterion for ISI Cancellation



Nyquist Criterion for ISI Cancellation Nyquist Criterion for ISI Cancellation

Transmitter Channel Receiverpulse shape of the channel impulse receiver impulse

heff(t)

p psymbol p(t)

presponse hc(t)

receiver impulse response hr(t)

• Mathematical analysis of Nyquist criterion)(*)(*)(*)()(eff ththtptth rcδ=

* denotes convolution operationTwo important considerations• h (t) should have fast decay with a small magnitude near the• heff(t) should have fast decay with a small magnitude near the

sample values for n ≠ 0.• for a ideal channel, hc(t) = δ(t), it should be possible to realize or

closely approximate shaping filters at both receiver and


closely approximate shaping filters at both receiver and transmitter to produce the desired heff(t).


Pulse Shaping Techniques

• Rectangular “brick-wall” filter0.8

1

s

s

TtTtth

/)/sin()(eff π

π=

0.4

0.6

h eff(t)

⎟⎟⎠

⎞⎜⎜⎝

⎛=

ss ff

ffH rect1)(eff

-0.2

0

0.2h

-20 -10 0 10 20-0.4

t/Ts

)( fH

It satisfies Nyquist’s criterion, but the filter is not causal (not buildable).

f

)(eff fH

Decay at 1/t. An error in the sampling time will cause


fs-fs

sampling time will cause significant ISI.


Pulse Shaping Techniques• Alternative

The following filter also

)(/

)/sin()(eff tzTt

Ttth s

ππ

=

satisfy Nyquist’s criterion.

)(rect1)(eff fZff

ffH

ss

⊗⎟⎟⎠

⎞⎜⎜⎝

⎛=

/Tt sπ

ff ss ⎠⎝

)()( fZfZ −=

sTfffZ

21for 0)( 0 =≥=



Raised Cosine Rolloff FIlter

• Raised cosine rolloff filter

⎪⎪

⎪⎪⎨

⎧

+>+≤<−

−≤≤

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +−

+= ss

ss

RC

TfTfT

TffTfH

2/)1(||2/)1(||2/)1(

2/)1(||0

21||2(cos1

21

1

)(α

ααα

ααπ

⎪⎪⎩

+> sTf 2/)1(||0 α

⎟⎟⎞

⎜⎜⎛⎟⎠⎞

⎜⎝⎛= 2

)/cos()/sin()( ssRC

TtTtth παπ⎟⎟⎠

⎜⎜⎝ −⎟⎠

⎜⎝ 2))2/(4(1

)(s

RC Ttt απ

Most popular pulse shaping filter used in mobile communications

As the value of α (rolloff factor) increases,

- the bandwidth of the filter also increases


- the time sidelobe levels decrease.








Geometric Representation of Digital Modulation Signalsp g g

• Modulation signal set S = {S (t) S (t) S (t)}S = {S1(t), S2(t),..... SM(t)}

M =2: BinaryM >2 : M-ary

• Number of bits of information possible = log2M bits/symbol



Types of Digital Modulation

Linear Non-Linear Spread Spectrum

Amplitude of transmitted signal s(t) varies linearly

Amplitude of carrier is constant

Transmission bandwidth >> minimum required

with message signal m(t)

signal bandwidth

Bandwidth efficient- Higher bandwidth Inefficient for single useful for accommodating more users in a li it d t

but high immunity against random FM noise.

user but efficient for multi-users

limited spectrumQPSKOQPSK

FSKGMSK(Gaussian

min. Shift keying)


π/4 QPSK MFSK


Linear Modulation Techniques

• Digital modulation techniques are classified as linear and nonlinear.

• For linear modulations, the amplitude of transmitted signal, s(t),varies linearly with the modulating digital signal, m(t).

)]2()()2()([ )]2()([)(

tfsintmtfcostmAtfjexptAmRets

cIcR

c

πππ−=

=)]()()()([ tfsintmtfcostm cIcR ππ

amplitudethe:A

signalmodulatedthe:)()()(frequencycarier the:

amplitude the:

tjmtmtmfA

IR

c

+=


signalmodulated the: )()()( tjmtmtm IR +


Binary Phase Shift Keying (BPSK)

• The information of the transmitted signal is modulated into the phase of the carrier signal.

)2(cos2)( ccb

bBPSK tf

TEtS θπ +=

)1binary (0 Tt b≤≤

2

)2(cos2)( ccb

bBPSK

E

tfTEtS θππ ++=

)y(b

)2(cos2 ccb

b tfTE θπ +−=

)0binary (0 Tt b≤≤

⎥⎤

⎢⎡

⎟⎟⎞

⎜⎜⎛ −−

+⎟⎟⎞

⎜⎜⎛ −

22)(sin)(sin bcbcb TffTffEP ππ )2(cos2)()( cc

bBPSK tfEtmtS θπ +=


⎥⎥⎦⎢

⎢⎣

⎟⎟⎠

⎜⎜⎝ −−

+⎟⎟⎠

⎜⎜⎝ −

=)()(2 bc

bc

bc

bcbBPSK TffTff

Pππ

)()()( ccb

BPSK fT


Coherent BPSK Receiver with Carrier Recovery Circuits

The received BPSK signal ( ) ( ) 1cos22cos 2 −= xx ( ) ( )[ ]12cos21cos2 += xx

)2(cos2)()( chθθπ ++= tfEtmtS ccb

BPSK

)2(cos2)(

)2(cos)()( ch

θπ

θθπ

+=

++

tfTEtm

tfT

tmtS

cb

b

ccb

BPSK

b



Coherent BPSK Receiver

The bit error rate in an AWGN channel

)|( 1srP)|( 2srP

⎤⎡

= ∫∞−

0 2

0

11,

)(1

)|()|(

Er

drsrpseP BPSKe

⎥⎤

⎢⎡−=

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−=

∫

∫−

∞−

/2 2

00

exp1

)(exp1

0

dxx

drN

ErN

NE

b

b

π

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎥

⎦

⎤⎢⎣

⎡−=

⎥⎦

⎢⎣

=

∫

∫∞

∞−

0/2

2 22

exp21

2exp

2

NEQdxx

dx

b

NEπ

π

bEbE−

⎠⎝⎦⎣ 0/2 0NEb

⎟⎞

⎜⎛ 2)|()()|()( EQPPPPP b


⎟⎟⎠

⎜⎜⎝

=+=0

2,21,1, )|()()|()(N

QsePsPsePsPP bBPSKeBPSKeBPSKe


Coherent BPSK Receiver

The bit error rate in an AWGN channel ⎟⎟⎠

⎞⎜⎜⎝

⎛=

0,

2NEQP b

BPSKe

10-1

100

10-2

10-4

10-3

BE

R

10-6

10-5


0 2 4 6 8 10 1210

Eb/N0 (dB)


Quadrature Phase shift keying (QPSK)

• 2 bits are transmitted at a signal modulation symbol.• Therefore QPSK has twice the bandwidth efficiency of BPSK• Therefore, QPSK has twice the bandwidth efficiency of BPSK.

.4,3,2,1 0 )2

)1(2(cos2)( s =≤≤−+= iTtitfTEtS c

sQPSK

ππ2Ts



Quadrature Phase shift keying (QPSK)

• BPSK BBS TRRBW /222 ===

• QPSK

BBS

BBS TRRBW /12 ===

• Quadrature Phases = 0, π/2, π, 3π/2

BBS

• Average probability of bit error in additive white Gaussian noise

⎟⎟⎞

⎜⎜⎛

=2EQP b

Q S

• The BER of QPSK is identical to BPSK, but twice the bandwidth ffi i

⎟⎟⎠

⎜⎜⎝

=0

, NQP QPSKe


efficiency.


Spectrum and Bandwidth of QPSK Signalsp g

• The null-to-null RF b d idth i l t thbandwidth is equal to the bit rate Rb.

• The BW is half of a BPSK signal.



QPSK Signal Transmission Techniqueg q

• The bit stream m(t) is split into two bit streams mI(t) and mQ(t)(in-phase and quadrature stream).

• The two binary streams are separately modulated by two carriers, which are in quadrature.

1

0

1

2

0 0.5 1 1.5 2 2.5 3-1

0 1 0 0

Input binary 0 0.5 1 1.5 2 2.5 3

-1

0 0.5 1 1.5 2 2.5 3-2

0

1

sequence1 1 0 1 0 0

0 0.5 1 1.5 2 2.5 3-1

0

1

1 1 00

1


0 0.5 1 1.5 2 2.5 3-1


Coherent QPSK Signal Detection Techniqueg q

• The frontend bandpass filter remove the out-of-band noise and adjacent channel interference.

• The filtered output is split into two parts, and each part is coherently demodulated using in-phase and quadrature carriers.



Offset QPSK

• OQPSK signaling is similar to QPSK, except for the time alignment of the even and odd bit streams.

• Thus, OQPSK can eliminate 180° phase transition, and prevent the signal envelope to go to zero.



Offset QPSK

T iti f QPSK d l t d i l T iti f OQPSK d l t d i l

Variation of QPSK

Transitions for a QPSK modulated signal Transitions for a OQPSK modulated signal

Q channel is delayed by a ½ bit interval from I channelI and Q channel signals transition at different timesRange of phase transitions is from 0-90 degreesThi li i t th 180 d h hift OQPSK i lThis eliminates the 180 degree phase shift so an OQPSK signal never goes through a zeroIn non-linear amplification, a zero causes regeneration of sidelobes and spectral spreading in the signal


p p g gThus, OQPSK signals yield a more efficient amplification process


Differential Phase Shift Keying (DPSK)

• Differential PSK is a noncoherent form which avoids the need for a coherent reference signal at the receiver.

• Nocoherent receivers are easy and cheap to build, and hence are widely used in wireless communications.

• Transmitter: input sequence is first differentially encoded and then modulated.

e g (for BPSK) 1⊕= kkk dmde.g., (for BPSK)

dk: k-th transmitted symbol mk: k-th information symbol

1−⊕ kkk dmd

k y

• Receiver: the original sequence is recovered from the demodulated differentially encoded signal through a complementary process


differentially encoded signal through a complementary process.









⎞⎛

The BER of differential BPSK in an AWGN channel

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

0, exp

21

NEP b

DBPSKe

10-1

100

Coherent BPSKDifferential BPSK

The energy efficiency of

10-3

10-2

ER

gy ydifferential BPSK is inferior to coherent BPSK.

10-5

10-4B

E

At BER of 10-3 the difference in SNR is l th 3 dB

0 2 4 6 8 10 12 1410

-7

10-6

SNR (dB)

less than 3 dB.

At BER of 10-5, the difference in SNR is


SNR (dB)difference in SNR is less than 1 dB.



When the M-ary PSK modulations ( ), the 4≥M( ),degradation of the BER due to noncoherent detection is roughly 3 dB.



π/4 QPSK

• π/4 QPSK is a quadrature phase shift keying technique.

• It offers a compromises between OQPSK and QPSK.

• The maximum phase change of π/4 QPSK is limited to ±135°

• An extremely attractive feature of π/4 QPSK is that it can be

noncoherently detected.

• Further, it has been found that in the presence of multipath spread

and fading, π/4 QPSK performs better than OQPSK.



Constellation Diagram of π/4 QPSK Signal

Information bits Phase shift φk1 1 π/41 1 π/4 0 1 3π/4 0 0 - 3π/41 0 -π/41 0 π/4



Generic π/4 QPSK Transmitter



π/4 QPSK Baseband Differential Detector



π/4 QPSK IF Differential Detection



π/4 QPSK FM Discriminator



Constant Envelope Modulationp

• The constant envelope family of modulations has following advantage:advantage:– Power efficient amplifiers can be used without introducing

degradation in the spectrum occupancy of the transmitted signal.– Low out-of-band radiation of the order of -60 dB to -70 dB can be

achieved.– Limiter-discriminator detection can be used, which simplifiedLimiter discriminator detection can be used, which simplified

receiver design and provides high immunity against random FM noise and signal fluctuations due to Rayleigh fading



Binary Frequency Shift Keying (BFSK)

• The information of the transmitted signal is modulated into the frequency of the carrier signalfrequency of the carrier signal.

• In general, an FSK signal may be represented as

2E )tΔ22(cos2)()( ffTEtvtS cb

bHFSK ππ +==

)tΔ22(cos2)()( ffTEtvtS cb

bLFSK ππ −==



Phase Trajectory Examplej y p

0.5

1

-0.5

0

0 0.2 0.4 0.6 0.8 1-1

t/T

0.5

1

-0.5

0


0 0.2 0.4 0.6 0.8 1-1

t/T


Detection of Binary FSKy

• BPSK and BFSK)(tψ )(t

)(

2s1s“0” “1”

)(2 tψ )(1 tψ

1s bE bE221 =− ss“0”BPSK BFSK

)(1 tψbEbE−

bE221 =− ss2s

)(2 tψbE

“1”

2

0, ⎟

⎟⎠

⎞⎜⎜⎝

⎛=

NEQP b

BPSKe 0

, ⎟⎟⎠

⎞⎜⎜⎝

⎛=

NEQP b

BFSKecoherent detection0 ⎠⎝ N 0 ⎠⎝

exp21

0,, ⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

NEP b

NCBPSKe 2

exp21

0,, ⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

NEP b

NCBFSKenoncoherent detection


2 0 ⎠⎝ N 0 ⎠⎝ N


Detection of Binary FSKy

Coherent

NoncoherentNoncoherent



Minimum Shift Keying (MSK)y g ( )

• Minimum shift keying (MSK) is a special type of continuous phase-frequency shift keying (CPFSK)frequency shift keying (CPFSK).

• MSK is sometimes referred to as fast FSK, as the frequency spacing used is only half as much as that used in conventional noncoherent FSKnoncoherent FSK.

• An MSK signal also can be thought of as a special form of OQPSK where the baseband rectangular pulses are replaced with half-sinusoidal pulses.

( ) ( )tftttftttS 2)sin(sin)(2)cos(cos)()( πππ+( ) ( )tπf

Ttmtf

TtmtS c

bQ

bIMSK 2)sin

2(sin)(2)cos

2(cos)()( cπ +=



MSK Waveform


27


MSK Power Spectrump

• From this figure, the MSK spectrum has lower sidelobes than QPSK and OQPSK.QPSK and OQPSK.


27


Gaussian Minimum Shift Keying (GMSK)y g ( )

• GMSK is a simple binary modulation scheme which may be viewed as a derivative of MSK.

• In GMSK, the sidelobe levels of the spectrum are further reduced by passing the modulating NRZ data waveform throughreduced by passing the modulating NRZ data waveform through a premodulation Gaussian pulse-shaping filter.

• In practice, GMSK is most attractive for its excellent power efficiency (due to the constant envelope) and its excellent spectrum efficiency.

• GMSK is used in GSM, the world's most popular standard forGMSK is used in GSM, the world s most popular standard for mobile telephony systems.



GMSK Transmitter Using Direct FM Generationg

• The impulse response of the GMSK premodulation filter

BN=BTGMSK premodulation filter

2ln222

⎟⎞

⎜⎛ ππ

BtthG

2ln2 ,exp)( 22 =⎟

⎟⎠

⎞⎜⎜⎝

⎛−= ααπ

απ



Power Spectrum Density of a GMSK Signaly g



Combined Linear/Constant Envelope Modulation TechniquesTechniques

• Digital baseband data may be sent by varying both the envelope and phase (frequency) of an RF carrierand phase (frequency) of an RF carrier.

• This can offer two degrees of freedom, thus such modulation techniques are called M-ary modulation.

• In M-ary signaling scheme, two or more bits are grouped together to form symbols.

• Depending on whether the amplitude phase or frequency of the• Depending on whether the amplitude, phase, or frequency of the carrier is varied, the modulation scheme is called M-ary ASK, M-aryPSK, or M-ary FSK.

ff• M-ary modulation schemes achieve better bandwidth efficiency at the expense of power efficiency.



M-ary Phase Shift Keying (MPSK)y y g ( )

( ) ( )ssi tfini

TEtfi

TEtS 2s

M21)-(sin22cos

M21)-(cos2)( cc ⎥⎦

⎤⎢⎣⎡+⎥⎦

⎤⎢⎣⎡= ππππ ( ) ( )

bsbs

ssi

TMTEME

fT

fT

)(log and )(log whereM

)(M

)()(

22

cc

==

⎥⎦⎢⎣⎥⎦⎢⎣



M-ary PSK Power Spectral Densityy p y



M-ary Quadrature Amplitude Modulation (QAM)y p ( )

( ) ( )2sM21)-(sin22cos

M21)-(cos2)( c

minc

miniii tfinib

TEtfia

TEtS ππππ

⎥⎦⎤

⎢⎣⎡+⎥⎦

⎤⎢⎣⎡=

integers.t independen ofpair a are and and amolitude,lowest the withsignal theofenergy thes where

MM

min

ii

ss

baiE

TT ⎦⎣⎦⎣



M-ary Frequency Shift Keying (MFSK)

210)(cos2)( s MiTttinEtS ≤≤⎥⎤

⎢⎡

+π

y q y y g ( )

•

bdare sfrequencie signal theand ,integer fixed somefor 2/ where

,...,2,1 0 )(cos)(

cscc

scss

si

/nTnf

MiTttinTT

tS

=

=≤≤⎥⎦

⎢⎣

+=

Hertz.21by separated sT/

• MFSK is not used in traditional way because its spectral efficiency is poor.

• The orthogonality characteristic of MFSK has led researches to g yexplore Orthogonal Frequency Division Multiplexing (OFDM).



OutlinesOutlines

Concept of Modulation

Analog and Digital Modulations

Power and Spectral Efficiency

Pulse ShapingPulse Shaping

Digital Modulation Schemes

Linear – BPSK, QPSK, DPSK, OQPSK, π/4 QPSKea S , Q S , S , OQ S , π/ Q S

Nonlinear – FSK, MSK, GMSK

M-ary ASK, M-ary PSK, M-ary FSK

Coherent and Noncoherent Detection




R>C

R / W [bits/s/Hz]

R=C

M=256Unattainable region

Bandwidth limited M=8

M=16

M=64

M=256

R<CPractical regionM=2

M=4

M 8

M=2M=4M=8

M=16

Power limited

Shannon limit MPSKMQAMMFSK

510−=BP


[dB] / 0NEb


Homework Assignment 4Homework Assignment 4

1. Using Matlab, generate the QPSK waveform with the followingparameters: Symbol rate: 1000 baud; carrier frequency: 5000 Hz,bit sequence to be transmitted: 1 0 1 1 0 0 1 1 The in-phase andbit sequence to be transmitted: 1 0 1 1 0 0 1 1. The in phase andquadrature waveforms should be separated plotted. Usesufficiently high sampling rate to ensure smooth waveforms.Submit your waveforms with Matlab code.

2. Using Matlab, simulate the BER performance for QPSK signals.Geometric representations should be used. Plot the simulatedBER together with the theoretical result given in (6.79). Theevaluated value of Eb/N0 should be between 0 and 10 dBevaluated value of Eb/N0 should be between 0 and 10 dB.Sufficiently high number of random bits should be used to ensurehigh accuracy of the simulated BER. Submit your waveforms withMatlab code.

3. 6.12 (a) (b) (c) from the textbook.4. 6.13 from the textbook.5 6 15 from the textbook


5. 6.15 from the textbook.Deadline 2/15/11 Before next class begins

chapter 6 modulation techniques for mobile radio

Documents