Digital Communications I:Modulation and Coding Course

Term 3 - 2008Catharina Logothetis

Lecture 7

Lecture 7 2

Last time we talked about:

Another source of error due to filtering effect of the system: Inter-symbol interference (ISI)

The techniques to reduce ISI Pulse shaping to achieve zero ISI at the

sampling time Equalization to combat the filtering effect of

the channel

Lecture 7 3

Today, we are going to talk about:

Some bandpass modulation schemes used in DCS for transmitting information over channel M-PAM, M-PSK, M-FSK, M-QAM

How to detect the transmitted information at the receiver Coherent detection Non-coherent detection

Lecture 7 4

Block diagram of a DCS

FormatSourceencode

FormatSourcedecode

Channelencode

Pulsemodulate

Bandpassmodulate

Channeldecode

Demod. SampleDetect

Channel

Digital modulation

Digital demodulation

Lecture 7 5

Bandpass modulation

Bandpass modulation: The process of converting a data signal to a sinusoidal waveform where its amplitude, phase or frequency, or a combination of them, are varied in accordance with the transmitting data.

Bandpass signal:

where is the baseband pulse shape with energy . We assume here (otherwise will be stated):

is a rectangular pulse shape with unit energy. Gray coding is used for mapping bits to symbols. denotes average symbol energy given by

( ) TtttitTEtgts ici

Ti ≤≤+∆−+= 0 )()1(cos2)()( φωω

)(tgT

)(tgT gE

sE ∑ == M

i is EM

E1

1

Lecture 7 6

Demodulation and detection

Demodulation: The receiver signal is converted to baseband, filtered and sampled.

Detection: Sampled values are used for detection using a decision rule such as the ML detection rule.

Nz

z1

z=∫T

0

)(1 tψ

∫T

0

)(tNψ)(tr

1z

Nz

z Decision circuits

(ML detector)m̂

Lecture 7 7

Coherent detection

Coherent detection requires carrier phase recovery at the

receiver and hence, circuits to perform phase estimation.

Sources of carrier-phase mismatch at the receiver: Propagation delay causes carrier-phase offset in

the received signal. The oscillators at the receiver which generate

the carrier signal, are not usually phased locked to the transmitted carrier.

Lecture 7 8

Coherent detection ..

Circuits such as Phase-Locked-Loop (PLL) are implemented at the receiver for carrier phase estimation ( ).

PLL

Oscillator 90 deg.

( ) )()(cos2)()( tnttTEtgtr iii

T +++= αφω ( )αω ˆcos2 +tT c

( )αω ˆsin2 +tT c

Used by correlators

αα ˆ≈

I branch

Q branch

Lecture 7 9

Bandpass Modulation Schemes

One dimensional waveforms Amplitude Shift Keying (ASK) M-ary Pulse Amplitude Modulation (M-PAM)

Two dimensional waveforms M-ary Phase Shift Keying (M-PSK) M-ary Quadrature Amplitude Modulation

(M-QAM) Multidimensional waveforms

M-ary Frequency Shift Keying (M-FSK)

Lecture 7 10

One dimensional modulation, demodulation and detection

Amplitude Shift Keying (ASK) modulation:

( )φω += tTEts ci

i cos2)(

( )

cos2)(

,,1 )()(

1

1

ii

c

ii

Ea

tT

t

Mitats

=

+=

==

φωψ

ψ

)(1 tψ1s2s0 1E

“0” “1”On-off keying (M=2):

Lecture 7 11

One dimensional mod.,…

M-ary Pulse Amplitude modulation (M-PAM)

( )tT

ats cii ωcos2)( =

( )

( )

gs

gii

gi

c

ii

EME

MiEE

EMia

tT

t

Mitats

3)1(

12

)12(

cos2)(

,,1 )()(

2

22

1

1

−=

−−==

−−=

=

==

s

ωψ

ψ 4-PAM:

)(1 tψ2s1s0gE3−

“00” “01”4s3s

“11” “10”

gE− gE gE3

Lecture 7 12

Example of bandpass modulation:Binary PAM

Lecture 7 13

Coherent detection of M-PAM

∫T

0

)(1 tψ

ML detector(Compare with M-1 thresholds))(tr 1z m̂

One dimensional mod.,...–cont’d

Lecture 7 14

Two dimensional modulation, demodulation and detection (M-PSK)

M-ary Phase Shift Keying (M-PSK)

+=

Mit

TEts cs

iπω 2cos2)(

( ) ( )

2

21

21

2211

2sin 2cos

sin2)( cos2)(

,,1 )( )()(

iis

sisi

cc

iii

EE

MiEa

MiEa

tT

ttT

t

Mitatats

s==

=

=

−==

=+=

ππ

ωψωψ

ψψ

Lecture 7 15

Two dimensional mod.,… (MPSK)

)(1 tψ

2s1sbE

“0” “1”

bE−

)(2 tψ

3s

7s

“110”)(1 tψ

4s 2ssE

“000”

)(2 tψ

6s 8s

1s5s

“001”“011”

“010”

“101”

“111” “100”

)(1 tψ

2s 1s

sE

“00”

“11”

)(2 tψ

3s 4s“10”

“01”

QPSK (M=4)

BPSK (M=2)

8PSK (M=8)

Lecture 7 16

Two dimensional mod.,…(MPSK) Coherent detection of MPSK

Compute Choose smallest2

1arctanzz φˆ

|ˆ| φφ −i

∫T

0

)(1 tψ

∫T

0

)(2 tψ)(tr

1z

2z

m̂

Lecture 7 17

Two dimensional mod.,… (M-QAM)

M-ary Quadrature Amplitude Mod. (M-QAM)

( )ici

i tTEts ϕω += cos2)(

( ) ( )

3)1(2 and symbols PAM are and where

sin2)( cos2)(

,,1 )( )()(

21

21

2211

−=

==

=+=

MEaa

tT

ttT

t

Mitatats

sii

cc

iii

ωψωψ

ψψ

( )

+−−+−+−+−+−

−−−+−−+−−−−+−−+−

=

)1,1()1,3()1,1(

)3,1()3,3()3,1()1,1()1,3()1,1(

, 21

MMMMMM

MMMMMMMMMMMM

aa ii

Lecture 7 18

Two dimensional mod.,… (M-QAM)

)(1 tψ

)(2 tψ

2s1s 3s 4s“0000” “0001” “0011” “0010”

6s5s 7s 8s

10s9s 11s 12s

14s13s 15s 16s

1 3-1-3

“1000” “1001” “1011” “1010”

“1100” “1101” “1111” “1110”

“0100” “0101” “0111” “0110”

1

3

-1

-3

16-QAM

Lecture 7 19

Two dimensional mod.,… (M-QAM)

Coherent detection of M-QAM

∫T

0

)(1 tψ

ML detector1z

∫T

0

)(2 tψ

ML detector

)(tr

2z

m̂Parallel-to-serialconverter

s) threshold1 with (Compare −M

s) threshold1 with (Compare −M

Lecture 7 20

Multi-dimensional modulation, demodulation & detection

M-ary Frequency Shift keying (M-FSK)

( ) ( )

Tf

titTEt

TEts c

si

si

21

2

)1(cos2cos2)(

=∆=∆

∆−+==

πω

ωωω

( )2

1

0

cos2)(

,,1 )()(

iis

sijii

M

jjiji

EE

jijiEat

Tt

Mitats

s==

≠===

== ∑=

ωψ

ψ

)(1 tψ

2s

1s

3s

)(3 tψ

)(2 tψsE

sE

sE

Lecture 7 21

Multi-dimensional mod.,…(M-FSK)

Mz

z1

z=∫T

0

)(1 tψ

∫T

0

)(tMψ)(tr

1z

Mz

zML detector:

Choose the largest element

in the observed vector

m̂

Lecture 7 22

Non-coherent detection

Non-coherent detection: No need for a reference in phase with the

received carrier Less complexity compared to coherent

detection at the price of higher error rate.

Lecture 7 23

Non-coherent detection …

Differential coherent detection Differential encoding of the message

The symbol phase changes if the current bit is different from the previous bit.

( ) ,...,MiTtttTEts ii 1 ,0 ,)(cos2)( 0 =≤≤+= θω

)())1(()( nTTnnT ikk φθθ +−=

)(1 tψ

iφ

1s2s 0

0 1 2 3 4 5 6 7 1 1 0 1 0 1 11 1 1 0 0 1 1 1π π π π π π0 0

Symbol index: Data bits:Diff. encoded bitsSymbol phase: kθ

kmk

Lecture 7 24

Non-coherent detection … Coherent detection for diff encoded mod.

assumes slow variation in carrier-phase mismatch during two symbol intervals.

correlates the received signal with basis functions uses the phase difference between the current received

vector and previously estimated symbol

( ) TttnttTEtr i ≤≤+++= 0 ),()(cos2)( 0 αθω

)(1 tψ

)(2 tψ

),( 11 ba),( 22 ba

iφ

( ) ( ) )())1(()())1(()( nTTnnTTnnT ijiji φθθαθαθ =−−=+−−+

Lecture 7 25

Non-coherent detection … Optimum differentially coherent detector

Sub-optimum differentially coherent detector

Performance degradation about 3 dB by using sub-optimal detector

∫T

0

)(1 tψ

)(tr m̂Decision

DelayT

∫T

0)(tr m̂Decision

DelayT

Lecture 7 26

Non-coherent detection … Energy detection

Non-coherent detection for orthogonal signals (e.g. M-FSK)

Carrier-phase offset causes partial correlation between I and Q branches for each candidate signal.

The received energy corresponding to each candidate signal is used for detection.

Lecture 7 27

Non-coherent detection …

Non-coherent detection of BFSK

∫T

0

)cos(/2 1tT ω

∫T

0)(tr

11z

12z

∫T

0

∫T

0

21z

22z

Decision stage:

)cos(/2 2tT ω

)sin(/2 2tT ω

)sin(/2 1tT ω

( ) 2

( ) 2

( ) 2

( ) 2 +

-

)(Tz

0ˆ ,0)( if1ˆ ,0)( if

=<=>

mTzmTz

m̂

212

211 zz +

222

221 zz +