ECE4058 Digital Communication

Digital Communication

Electronics and Communication EngineeringHanyang University

Haewoon Nam

Lecture 12

(ECE4058)

1

ECE4058 Digital Communication

Digital Band Pass Modulation Technique

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• Digital band-pass modulation techniques– Amplitude-shift keying– Phase-shift keying– Frequency-shift keying

• Receivers– Coherent detection

• The receiver is synchronized to the transmitter with respect to carrier phases

– Noncoherent detection• The practical advantage of reduced complexity but at the cost of degraded

performance

ECE4058 Digital Communication

Digital Band Pass Modulation Technique

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• Given a binary source– The modulation process involves switching ore keying the amplitude,

phase, or frequency of a sinusoidal carrier wave

• All three of them are examples of a band-pass process– Binary amplitude shift-keying (BASK)

• The carrier amplitude is keyed between the two possible values used to represent symbols 0 and 1

– Binary phase-shift keying (BPSK)• The carrier phase is keyed between the two possible values used to

represent symbols 0 and 1.– Binary frequency-shift keying (BFSK)

• The carrier frequency is keyed between the two possible values used to represent symbols 0 and 1.

)1.7()2cos()( ccc tfAtc φπ +=

ECE4058 Digital Communication

Digital Band Pass Modulation Technique

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• Decreasing the bit duration Tb has the effect of increasing the transmission bandwidth requirement of a binary modulated wave.

• Differences that distinguish digital modulation from analog modulation.– The transmission bandwidth requirement of BFSK is greater than that of

BASK for a given binary source.– However, the same does not hold for BPSK.

)2.7(2b

c TA =

)3.7()2cos(2)( ccb

tfT

tc φπ +=

ECE4058 Digital Communication

Digital Band Pass Modulation Technique

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ECE4058 Digital Communication

Binary Amplitude Shift Keying

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• The ON-OFF signaling variety

• The average transmitted signal energy is ( the two binary symbols must by equiprobable)

)9.7(0 symbolbinary for ,01 symbolbinary for ,

)(

= bEtb

)10.7(0 symbolfor ,0

1 symbolfor ),2cos(2)(

= tfTE

ts cb

b π

)11.7(2av

bEE =

ECE4058 Digital Communication

Binary Phase Shift Keying

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• Binary Phase-Shift Keying (BPSK)– The special case of double-sideband suppressed-carried (DSB-SC)

modulation– The pair of signals used to represent symbols 1 and 0,

– An antipodal signals• A pair of sinusoidal wave, which differ only in a relative phase-shift of π

radians.– The transmitted energy per bit, Eb is constant, equivalently, the average

transmitted power is constant.– Demodulation of BPSK cannot be performed using envelope detection,

rather, we have to look to coherent detection.

)12.7( 2 toingcorrespond 0 symbolfor ),2cos(2)2cos(2

1 toingcorrespond 1 symbolfor ),2cos(2

)(

=−=+

==

itfTEtf

TE

itfTE

tsc

b

bc

b

b

cb

b

i

πππ

π

ECE4058 Digital Communication

Binary Phase Shift Keying

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Productmodulator

Non-return to zerolevel encoder

Binarydata

stream

BPSKsignal

2 cos 2(a) BPSK modulator

Productmodulator

2 cos 2BPSKsignal

Low-passfilter

Decision-makingdevice

Threshold

Sample attime

Say 1, if the thresholdis exceeded

Say 0, otherwise

(b) Coherent detector for BPSK, for the sampler, integer 0, 1, 2, ⋯

Antipodal signal

0

1

22 22

−=

),cos(

),cos()(

tfTE

tfTE

ts

cb

b

cb

b

i

π

π

Constellation plot

ECE4058 Digital Communication

Quadrature Phase Shift Keying

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• Quadrature Phase-Shift Keying (QPSK)– Efficient utilization of channel bandwidth– The phase of the sinusoidal carrier takes on one of the four equally

spaced values, such as π/4, 3π/4, 5π/4, and 7π/4

– Each one of the four equally spaced phase values corresponds to a unique pair of bits called dibit

)13.7(elsewhere ,0

0 ,4

)12(2cos2)(

≤≤

−+= Ttitf

TE

ts ci

ππ

)15.7()2sin(4

)12(sin2)2cos(4

)12(cos2)( tfiTEtfi

TEts cci ππππ

−−

−=

)14.7(2 bTT =

ECE4058 Digital Communication

Quadrature Phase Shift Keying

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• Quadrature Phase-Shift Keying (QPSK)– A QPSK signal consists of the sum of two BPSK signals– The first binary sinusoidal wave with an amplitude equal to ±√E/2

– The second binary wave also has an amplitude equal to ±√E/2

),2cos(4

)12(cos/2 tfiTE cππ

−

)16.7(3 2for 2/4 1for 2/

4)12(cos

=−=

=

−

,iE,iE

iE π

),2sin(4

)12(sin/2 tfiTE cππ

−−

)17.7(4 3for 2/2 1for 2/

4)12(sin

==−

=

−−

,iE,iE

iE π

cosine and sine carriersare orthogonal

ECE4058 Digital Communication

Quadrature Phase Shift Keying

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ECE4058 Digital Communication

Quadrature Phase Shift Keying

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• Constellation plot

BPSK

Bit 1Bit 0

2

2

QPSK

1000

01 11

ECE4058 Digital Communication

Quadrature Phase Shift Keying

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• QPSK transmitter

ECE4058 Digital Communication

Quadrature Phase Shift Keying

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• QPSK receiver

ECE4058 Digital Communication

M-ary Phase Shift Keying

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• Constellation plot

8-PSK

111001

110

000 101

011

010

100

16-PSK

01011001

1100

0001

0000

1010

1111

0010

1000

1011

0011

11101101

0100

0111

0110

ECE4058 Digital Communication

Frequency Shift Keying

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• Binary Frequency-Shift Keying (BFSK)– Each symbols are distinguished from each other by transmitting one of

two sinusoidal waves that differ in frequency by a fixed amount

– Sunde’s BFSK– When the frequencies f1 and f2 are chosen in such a way that they

differ from each other by an amount equal to the reciprocal of the bit duration Tb

)18.7( 2 toingcorrespond 0 symbolfor ),2cos(2

1 toingcorrespond 1 symbolfor ),2cos(2

)(2

1

=

==

itfTE

itfTE

ts

b

b

b

b

i

π

π

ECE4058 Digital Communication

Frequency Shift Keying

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ECE4058 Digital Communication

Frequency Shift Keying

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• Continuous-phase Frequency-Shift Keying– The modulated wave maintains phase continuity at all transition points,

even though at those points in time the incoming binary data stream switches back and forth

– Sunde’s BFSK, the overall excursion δf in the transmitted frequency from symbol 0 to symbol 1, is equal to the bit rate of the incoming data stream.

– MSK (Minimum Shift Keying)• The special form of CPFSK• Uses a different value for the frequency excursion δf , with the result that this

new modulated wave offers superior spectral properties to Sunde’s BFSK.

ECE4058 Digital Communication

Frequency Shift Keying

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• Noncoherent Detection of BFSK Signals– The receiver consists of two paths

• Path 1 : uses a band-pass filter of mid-band frequency f1. produce the output v1

• Path 2 : uses a band-pass filter of mid-band frequency f2. produce the output v2

– The output of the two paths are applied to a comparator

ECE4058 Digital Communication

Quadrature Amplitude Modulation

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• M-ary Quadrature Amplitude Modulation (QAM)– The mathematical description of the new modulated signal

– The level parameter for in-phase component and quadrature component are independent of each other for all I

– M-ary QAM is a hybrid form of M-ary modulation– M-ary amplitude-shift keying (M-ary ASK)

• If bi=0 for all i, the modulated signal si(t) of Eq. (7.40) reduces to

– M-ary PSK• If E0=E and the constraint is satisfied

)40.7( 0

1,...,1,0),2sin(2)2cos(2)( 00

TtMi

tfbTEtfa

TEts cicii ≤≤

−=−= ππ

1,...,1,0)2cos(2)( 0 −== MitfaTEts cii π

iEEbEa ii allfor ,)( 2/122 =+

ECE4058 Digital Communication

Quadrature Amplitude Modulation

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ECE4058 Digital Communication

Mapping of Modulated Symbols

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• Mapping of digitally modulated waveforms onto constellation of signal points for BPSK– The signal-space representation of BPSK is simple, involving a single

basis function

)44.7()2cos(2)(1 tfT

t cb

πφ =

ECE4058 Digital Communication

Mapping of Modulated Symbols

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• Mapping of digitally modulated waveforms onto constellation of signal points for BFSK– Two basis function each with different frequency

)52.7()2cos(2)( 11 tfT

tb

πφ = )53.7()2cos(2)( 22 tfT

tb

πφ =