Slide 1

Digital CommunicationInter symbol interference, coherent and non-

coherent detectionLecture- 6 and 7

Ir. Muhamad Asvial, MSc., PhDCenter for Information and Communication Engineering Research (CICER)

Electrical Engineering Department - University of IndonesiaE-mail: asvial@ee.ui.ac.id

http://www.ee.ui.ac.id/cicer

Slide 2

Bandpass modulation Bandpass modulation: The process of converting

data signal to a sinusoidal waveform where its amplitude, phase or frequency, or a combination of them, is 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 ic

iTi 0 )()1(cos2)()(

)(tgT

)(tgT gE

sE

M

i is EM

E1

1

Slide 3

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 ML detection rule.

Nz

z1

z

T

0

)(1 t

T

0

)(tN)(tr

1z

Nz

z Decision circuits

(ML detector)m̂

Slide 4

Coherent detections

• Coherent detection– requires carrier phase recovery at the receiver and

hence, circuits to perform phase estimation.– Source 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.

Slide 5

Coherent detection ..

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

PLL

Oscillator 90 deg.

)()(cos2)()( tnttTEtgtr ii

iT ˆcos2

tT c

ˆsin2t

T c

Used by correlators

ˆ

I branch

Q branch

Slide 6

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)

Slide 7

One dimensional modulation, demodulation and detection

• Amplitude Shift Keying (ASK) modulation:

tTEts c

ii cos2)(

cos2)(

,,1 )()(

1

1

ii

c

ii

Ea

tT

t

Mitats

)(1 t1s2s0 1E

“0” “1”On-off keying:

Slide 8

Example of bandpass modulation:Binary PAM

Slide 9

• Coherent detection of M-PAM

T

0

)(1 t

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

m̂

One dimensional mod.,...–cont’d

Slide 10

Two dimensional mod.,…(MPSK)

• Coherent detection of MPSK

Compute Choose smallest

2

1arctanzz ̂

|ˆ| i

T

0

)(1 t

T

0

)(2 t)(tr

1z

2z

m̂

Slide 11

Two dimensional mod.,… (M-QAM)

• Coherent detection of M-QAM

T

0

)(1 t

ML detector1z

T

0

)(2 t

ML detector

)(tr

2z

m̂Parallel-to-serialconverter

s) threshold1 with (Compare M

s) threshold1 with (Compare M

Slide 12

Multi-dimensional mod.,…(M-FSK)

Mz

z1

z

T

0

)(1 t

T

0

)(tM)(tr

1z

Mz

zML detector:

Choose the largest element

in the observed vectorm̂

Slide 13

Non-coherent detection

• Non-coherent detection:– No need in a reference in phase with the received

carrier– Less complexity as compared to coherent detection at

the price of higher error rate.

Slide 14

Non-coherent detection …• Optimum differentially coherent detector

• Sub-optimum differentially coherent detector

» Performance degradation about 3 dB by using sub-optimum detector

T

0

)(1 t

)(tr m̂Decision

DelayT

T

0)(tr m̂Decision

DelayT

Slide 15

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 braches for each candidate signal.

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

Slide 16

Non-coherent detection …

• Non-coherent detection of BFSK

T

0

)cos(/2 1tT

T

0)(tr

11z

12z

T

0

T

0

21z

22z

Decision stage:

)cos(/2 2 tT

)sin(/2 2 tT

)sin(/2 1tT

2

2

2

2 +

-

)(Tz

0ˆ ,0)( if1ˆ ,0)( if

mTzmTz

m̂

212

211 zz

222

221 zz

Slide 17

Error probability of bandpass modulation

• Before evaluating the error probability, it is important to remember that: – Type of modulation and detection ( coherent or non-coherent),

determines the structure of the decision circuits and hence the decision variable, denoted by z.

– The decision variable, z, is compared with M-1 thresholds, corresponding to M decision regions for detection purposes.

Nr

r1

r

T

0

)(1 t

T

0

)(tN)(tr

1r

Nr

rDecision CircuitsCompare z

with threshold.

m̂

Slide 18

Error probability …

• Non-coherent detection of BFSK

T

0

)cos(/2 1tT

T

0)(tr

11r

12r

T

0

T

0

21r

22r

Decision rule:

)cos(/2 2 tT

)sin(/2 2 tT

)sin(/2 1tT

2

2

2

2 +

-

z

0ˆ ,0)( if1ˆ ,0)( if

mTzmTz

m̂

212

2111 rrz

222

2212 rrz

21 zzz

Decision variable:Difference of envelopes

Slide 19

Error probability …

• Coherent detection of M-QAM …• M-QAM can be viewed as the combination of two

modulations on I and Q branches, respectively. • No error occurs if no error is detected on either I and Q branches.

Hence:• Considering the symmetry of the signal space and orthogonality of I

and Q branches:

PAMM

branches) Q and Ion detectederror noPr(1)(1)( MPMP CE

22 1I)on error Pr(no

Q)on error I)Pr(noon error Pr(nobranches) Q and Ion detectederror noPr(

MPE

0

2

1log3114)(

NE

MMQ

MMP b

E Average probability of symbol error for PAMM

Slide 20

Error probability …

• Coherent detection of MPSK …• The detector compares the phase of observation vector to M-1

thresholds.• Due to the circular symmetry of the signal space, we have:

where

• It can be shown that

dpPP

MMPMP

M

Mc

M

mmcCE )(1)(1)(11)(1)(

/

/ ˆ11

ss

MNEQMP s

Esin22)(

0

MNEMQMP b

Esinlog22)(

0

2or

2|| ;sinexp)cos(2)( 2

00ˆ

NE

NEp ss

Slide 21

Error probability …

• Coherent detection of M-FSK …• The dimensionality of signal space is M. An upper bound for

average symbol error probability can be obtained by using union bound. Hence

or, equivalently

0

1)(NEQMMP s

E

0

2log1)(N

EMQMMP bE

Slide 22

Bit error probability versus symbol error probability

• Number of bits per symbol • For orthogonal M-ary signaling (M-FSK)

• For M-PSK, M-PAM and M-QAM

21lim

12/

122 1

E

Bk

k

k

E

B

PP

MM

PP

Mk 2log

1for EE

B PkPP

Slide 23

Probability of symbol error for binary modulation

EP

dB / 0NEb

Note!• “The same average symbol energy

for different sizes of signal space”

Slide 24

Probability of symbol error for M-PSK

EP

dB / 0NEb

Note!• “The same average symbol energy

for different sizes of signal space”

Slide 25

Probability of symbol error for M-FSK

EP

dB / 0NEb

Note!• “The same average symbol energy

for different sizes of signal space”

Slide 26

Probability of symbol error for M-PAM

EP

dB / 0NEb

Note!• “The same average symbol energy

for different sizes of signal space”

Slide 27

Probability of symbol error for M-QAM

EP

dB / 0NEb

Note!• “The same average symbol energy

for different sizes of signal space”