Digital Communication - KOCWcontents.kocw.net/KOCW/document/2015/hanyang_erica/... ·...

ECE4058 Digital Communication

Digital Communication

Electronics and Communication EngineeringHanyang University

Haewoon Nam

Lecture 13

(ECE4058)

1


Binary Amplitude Shift Keying

2

• 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 =


Binary Phase Shift Keying

3

• 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


Binary Phase Shift Keying

4

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


Quadrature Phase Shift Keying

5

• 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 =



6

• 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



7



8

• Constellation plot

BPSK

Bit 1Bit 0

2

2

QPSK

1000

01 11



9

• QPSK transmitter



10

• QPSK receiver


M-ary Phase Shift Keying

11

• 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


M-ary Phase Shift Keying

12

• How to calculate bit error rate (BER) and symbol error rate (SER)?• For BPSK, QPSK, M-ary PSK?• How to draw a BER vs SNR curve?• For other modulations?


Frequency Shift Keying

13

• 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



14



15

• 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.



16

• 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


Quadrature Amplitude Modulation

17

• 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 =+


Quadrature Amplitude Modulation

18


Mapping of Modulated Symbols

19

• 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 =


Mapping of Modulated Symbols

20

• 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 =

Date post:	09-Apr-2020
Category:	Documents
Upload:	others
View:	10 times
Download:	0 times

Digital Communication - KOCWcontents.kocw.net/KOCW/document/2015/hanyang_erica/... ·...

Documents