eee461lec16(performance of qam)

8/6/2019 EEE461Lec16(Performance of QAM)

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EEE 461 1

Chapter 7Performance of QAM

Huseyin Bilgekul

EEE 461 Communication Systems IIDepartment of Electrical and Electronic Engineering

Eastern Mediterranean University

Performance of QPSK Comparison of Digital Signaling Systems Symbol and Bit Error Rate for Multilevel

Signaling


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Performance of QPSK Modeled as two BPSK systems in parallel. One using a cosine carrier and the other a

sine carrier

Ts=2 Tb

Re

Im

x x

x

x

0 1 1 1 0 0 1 0

Serial to

Parallel

Converter

x

x

90

cos ct+

0 1 0 1

1 1 0 0

Rb

Rb/2

Rb/2

-BPF

Decision Regions


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Performance of QPSK


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Performance of QPSK Because the upper and lower channels are BPSK receivers the BER is the

same as BPSK.

=Q 2 (Matched Filter Detection)beo

EP

N

Twice as much data can be sent in the same bandwidth comparedto BPSK (QPSK has twice the spectral efficiency with identicalenergy efficiency).

Each symbol is two bits, Es=2Eb


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M-ary Communications Send multiple, M, waveforms

Choose between one of M symbols instead of 1 or 0.

Waveforms differ by phase, amplitude, and/or frequency

Advantage: Send more information at a time

Disadvantage: Harder to tell the signals apart or more bandwidth needed.

Different Mary types can be used.

Multiamplitude (MASK) +s(t), +3s(t), +5s(t),. . ., +(M-1)s(t).Multiple phase (MPSK, QPSK)

Multitone (MFSK)

Quadrature Amplitude Modulation (combines MASK and MPSK)

( )2 M


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As M increases, it is harder to make good

decisions, more power is used But, more information is packed into a symbol

so data rates can be increased

Generally, higher data rates require morepower (shorter distances, better SNR) to getgood results

Symbols have different meanings, so what

does the probability of error, PEmean?Bit error probability

Symbol error probability

M-ary Communications


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Multi-Amplitude Shift Keying (MASK) Send multiple amplitudes to denote different signals Typical signal configuration:

+/- s(t), +/- 3 s(t), .., +/- (M-1) s(t)

4-ary Amplitude Shift Keying

Each symbol sends 2 bits

Deciding which level is correct gets harder due to fading andnoise

Receiver needs better SNR to achieve accuracy

1011

01

00

Recived Signal


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Average Symbol and average Bit Energy

TransmitRm M-ary symbols/sec (Tm=1/ Rm)

Each pulse of form: ks(t)

Assume bit combination equally likely with probability 1/M

The average symbol energy is,

Each M-ary symbols has log2M bits of information so thebit energy Eb and the symbol enrgy EpM are related by

Same transmission bandwidth, yet more information

( )

( ) ( )2

2

2

2 22

0

29 ... 1

122 1 1

3 3

M

pM p p p

pp p

k

E E E M E M

M E E M E k M

M

=

= + + +

= + = ; ?

( )2

2 2

1

log 3log

ppM

b

M EEE

M M

= =


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MASK Error Probability

Same optimal receiver with matched filter to s(t)

Total probability ofSYMBOL ERRORfor Mequally likely signals:

s(T-t)

H(f)

s(t)+n(t) r(t) Threshold

Detector

t=Tp

r(Tp)

+kAp+n(Tp)

( ) ( ) ( )1 1

1M M

eM i i i

i i

P P m P m P m

M

= =

= =


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Decision Model

Two cases:

(M-1)p(t) just like

bipolar

Interior cases, can

have errors on bothsides

01 00 10 11

Ap-3Ap -Ap 3Ap

( ) pin

A P m Q

=

( ) 2 pin

A P m Q

=


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MASK Prob. Of Error

In a matched filter receiver, Ap/ n= 2Ep/N

( )

( )

( )

1

1

1

12 2

2 1

M

eM i

i

M p p p

i n n n

p

n

P P mM

A A AQ Q M Q

M

AM QM

=

=

=

= + +

=


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MASK Prob. Of Error

( )

( )

( )2

2

2 1

2 1 6log

1

p

eM

b

EMP Q

M

M EMQ

M M

=

=

N

N

( )2

2 2

1

log 3log

ppM

b

M EEE

M M

= =


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Bit Error Rate

Need to be able to compare like things

Symbol error has different cost than a bit error

For MASK

2log

eMb

PP

M=


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Error Probability Curves

Use codes so that asymbol error gives only

a single bit error.

Bandwidth stays sameas M increases, good if

you are not power-limited.

M=2

M=4

M=8

M=16


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M-ary PSK (MPSK)

Binary Phase Shift Keying (BPSK) 1: s1(t)= s(t) cos( ct)

0: s0(t)= s(t)cos( ct+ )

M-ary PSK

Re

Im

x x

( ) ( )2

cosk c s t s t t k M

= + Re

Im

x x

x x

x x

x

x


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MPSK

Must be coherent since envelope does not change Closest estimated phase is selected

MPSK P f


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MPSK Performance

Detection error if phase deviates by > /M

Strong signal approximation

( )1 MeMM

P p d

=

2 22 log log2 sin 2b beM E M E M P Q Q

M

2 ; ;

2N N

Re

Im

x x

x x

x x

x

x


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MPSK Waterfall Curve

QPSK gives equivalent performance to BPSK.

MPSK is used in modems to improve performance ifSNR is high enough.


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Quadrature Amplitude Modulation (QAM)

Amplitude-phase shift keying (APK or QAM)

The envelope and phases are,

( ) ( ) ( ) ( )( )

( ) ( )

cos sin

cos

k k c k c

k c k

s t s t a t b t

s t r t

= +

= +

2 2 tan kk k k k k

br a b

a

= + =

ri i

f


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QAM Performance

Analysis is complex and not treated here.

QAM-16

Upper Bound for general QAM depends onspectral efficiency relative to bipolar signals,

43

5

beM

EP Q

N

;

/M bR B =

QAM MPSK


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QAM vs. MPSK

M 2 4 8 16 32 64

M=Rb/B 0.5 1 1.5 2 2.5 3Eb/NO for

BER=10-6

10.5 10.5 14 18.5 23.4 28.5

M4 16 64 256 1024 4096

M=Rb/B 1 2 3 4 5 6

Eb/No for

BER=10-6

10.5 15 18.5 24 28 33.5

M

PS

K

Q

A

M

Very power efficient for high signal configurations, but requires a lot of power

Can give inconsistent results for different bit configurations


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Multitone Signaling (MFSK)

M symbols transmitted by M orthogonal pulses offrequencies:

Receiver:bank of mixers, one at each frequencyBank of matched filters to each pulse

HigherMmeans wider bandwidth needed or tones arecloser together

( )2 /k M N k T = +


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MFSK Receiver

x

Sqrt(2)cos 1t

H( )

C

omp

ara

tor

x

Sqrt(2)cos 2t

H( )

x

Sqrt(2)cos Mt

H( )


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MFSK Performance

When waveform 1 is sent, sampler outputs areAp+ n1, n2, n3, etc.

Error occurs when nj> Ap+ n1

Average Probability of error:

( ) ( )

( )( )

2

2

1 2 1 1

12 log / / 2

, , ,

11 1

2

b

M

M y E M

P m P r n r n r

e Q y dy

= = <

eee461lec16(performance of qam)

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