1Dept. of EE, NDHU

Chapter Four

Bandpass Modulation and Demodulation

2Dept. of EE, NDHU

Bandpass Signaling

3Dept. of EE, NDHU

Why Modulate?

• The transmission of EM fields through space is accomplished with the antenna

• The size of the antenna depends on the wavelength l

– Telephone industry benchmark of l/4 as the antenna dimension

– Example : 3kHz baseband signal needs about 15 miles for the antenna diameter

– Example: 900MHz signal needs about 8cm for the antenna diameter

• Bandpass modulation is an essential step for all systems involving radio transmis

sion

• Modulation can separate the different signals (Ex. FDMA)

• Modulation can also be used to place a signal in a frequency band where design r

equirement can be easily met

4Dept. of EE, NDHU

Digital Bandpass Modulation Techniques

• Bandpass modulation is the process by which an information signal is converted

to a sinusoidal waveform (carrier waveform)

• Three features can be used to distinguish the sinusoidal waveform

– Amplitude, frequency, phase

• Coherent detection

– The receiver exploits knowledge of the carrier’s phase to detect the signa

– PSK, FSK, ASK, CPM, and Hybrid forms

• Non-coherent detection

– The receiver does not utilize the carrier’s phase reference information

– DPSK, FSK, ASK, CPM, and Hybrid forms

5Dept. of EE, NDHU

Digital Modulations

6Dept. of EE, NDHU

Detection of Signals in Gaussian Noise

• Bandpass model of the detection process is virtually identical to the baseband mo

del

• Decision regions

– Minimum error decision rule is to choose the signal class that the distance d(r,si) is mi

nimized, where r is the received signal

• Correlation receiver

– Transform the received waveform into a point in the decision space

– Determine in which decision region the point is located

Choose the si(t) whose index corresponds to max zi(T)

MidttstrTzT

ii ,,1 , )()()(

0

7Dept. of EE, NDHU

Decision Regions

8Dept. of EE, NDHU

Correlator Receiver with Reference Signals

9Dept. of EE, NDHU

Binary Correlator Receiver

10Dept. of EE, NDHU

Coherent Detection of PSK

• BPSK signal

• Decision stage chooses the signal with largest output value of matched

filter

)()( and )()(

0for cos2

)(function basis a and

0 )cos(2

)(

0 )cos(2

)(

1211

01

02

01

tEtstEts

TttT

t

TttT

Ets

TttT

Ets

11Dept. of EE, NDHU

Sampled Matched Filter

12Dept. of EE, NDHU

Coherent Detection of MPSK

• MPSK signal

• Signal space and decision regions for a QPSK (M=4) system

– As shown in Fig.4.11

– Make a decision by the phase information

)()2

sin( )()2

cos()(

0for sin2

)( and cos2

)( functions basis and

,,1 , 0 )2

cos(2

)(

21

0201

0

tM

iEt

M

iEts

TttT

ttT

t

MiTtM

it

T

Ets

i

i

13Dept. of EE, NDHU

Demodulator for MPSK Signals

14Dept. of EE, NDHU

Coherent Detection of FSK

• FSK signal

• The distance between any two signal vectors is

• Choose the largest output of matched filter

otherwise 0

for Therefore

cos2

cos2

,,1 cos2

)( functions basis and

,,1 , 0 )cos(2

)(

0

jiEa

tdtT

tT

Ea

NjtT

t

MiTttT

Ets

ij

j

T

iij

jj

ii

E2

15Dept. of EE, NDHU

Signal Space for a 3-ary FSK Signal

16Dept. of EE, NDHU

Signal Space for DPSK

17Dept. of EE, NDHU

Detection of Differential PSK

• Differential encoding for the PSK signal

• Signaling characteristics

• Non-coherent detection

• Compare with PSK and DPSK

– PSK detection is with only one noise signal

– DPSK detection is with two noise signal (differentially decoding)

MiTttnttT

Etr

MiTtttT

Ets

i

ii

,,1 , 0 , )(])(cos[2

)( : signal received

,,1 , 0 , )](cos[2

)( : waveformdtransmitte

0

0

)()()(])([])([ 21212 TTTTT ijkjk

18Dept. of EE, NDHU

Binary Differential PSK Example

Suboptimum detection

Optimum detection

)()1()( kmkckc

19Dept. of EE, NDHU

Non-coherent Detection of FSK

Quadrature Receiver

20Dept. of EE, NDHU

Non-coherent Detection of FSK

Non-coherent detection of FSK with envelop detector

21Dept. of EE, NDHU

Tone Spacing for Non-coherent Orthogonal FSK Signaling

• Two tones f1 and f2 are orthogonal

– For a transmitted tone f1, the sampled envelop of the receiver output

filter tuned to f2 is zero

• Minimum tone spacing for orthogonal FSK signaling

– Non-coherently detected FSK

– Coherent FSK signaling is 2/T

Tff

dttftfT

1 is spacing toneminimum

0 2cos)2cos(

21

021

Tff

dttftfT

2

1 is spacing toneminimum

0 2cos 2cos

21

021

22Dept. of EE, NDHU

Minimum Tone Spacing for Non-coherent Orthogonal FSK

• For binary FSK, bandwidth is two times the tone spacing

• For M-ary FSK, bandwidth is M/T

23Dept. of EE, NDHU

D8PSK Modulator

24Dept. of EE, NDHU

D8PSK Demodulator

25Dept. of EE, NDHU

Error Performance for Binary Systems

• Bit error probability for BPSK signaling

• Probability of bit error for coherent detected, differential encoded binary PSK

• Probability of bit error for coherently detected binary orthogonal FSK

• Probability of bit error for non-coherently detected binary orthogonal FSK

)2

(0N

EQP b

B

)]2

(1[)2

(2)]2

(1[)2

()]2

(1[)2

( 000000 N

EQ

N

EQ

N

EQ

N

EQ

N

EQ

N

EQ bbbbbb

)(0N

EQP b

B

)2

exp(2

1)

4exp(

2

1 /1let weIf

bandwidthfilter theis where, )4

exp(2

1

00

2

0

2

N

E

N

TAPTW

WWN

AP

bBf

ff

B

26Dept. of EE, NDHU

Binary DPSK

• DPSK signaling

• Pairs of DPSK signals, S1(t) and S2(t) are orthogonal

• DPSK detection can be implemented by matching signal envelopes

• Bit error probability is similar to the one for non-coherently detected binary FSK

Ttxxxxts

Ttxxxxts

TttT

Etx

TttT

Etx

20 ),(or ),()(

20 ),(or ),()(

0 )cos(2

)(

0 )cos(2

)(

12212

22111

02

01

)exp(2

1

0N

EP b

B

27Dept. of EE, NDHU

DPSK Detection

28Dept. of EE, NDHU

Bit Error Probability of Binary Systems

29Dept. of EE, NDHU

M-ary Signals and Performance

30Dept. of EE, NDHU

Ideal Probability of Bit Error Performance

31Dept. of EE, NDHU

Bit Error Performance for M-ary Orthogonal Signaling

32Dept. of EE, NDHU

Bit Error Performance for Multiple Phase Signaling

33Dept. of EE, NDHU

M-ary Signaling

• M-ary signaling instructs the modulator to produce one of M=2k waveforms

• M-ary multiple phase signaling

– The BER curve moves in the direction of degraded error performance as k increa

ses

– A larger bit rate can be transmitted within the same bandwidth as k increases

• M-ary orthogonal signaling

– The BER curve moves in the direction of improved error performance as k i

ncreases

– The required system bandwidth increases as k increases

34Dept. of EE, NDHU

Vectorial View of MPSK Signaling

35Dept. of EE, NDHU

Relation Between Eb/N0 and S/N

• General relationship between Eb/N0 and S/N

• For the QPSK signaling– QPSK bit stream is usually partitioned into an even and odd stream; each ne

w stream is at half the bit rate of the original stream

– Each of the quadrature BPSK signals has half of the average power of the ori

ginal QPSK signal (as shown in Fig. 4.31)

ratebit theis andpower signal average theis re whe)(0

RSR

W

N

S

N

Eb

)()2/

(2/

0 R

W

N

S

R

W

N

S

N

Eb

36Dept. of EE, NDHU

Vectorial View of MFSK Signaling

37Dept. of EE, NDHU

Symbol Error Performance for Coherent FSK Signaling

38Dept. of EE, NDHU

Eb/N0 and SNR in the MFSK

ratebit theis andpower signal average theis re whe)(0

RSR

W

N

S

N

Eb

)1

( Therefore,

;/1 rate symbol the toequal

typicallyis bandwidth detection thesignaling,FSK For

)()log

(

log Since

0

20

2

kN

S

N

E

T

W

k

WT

N

S

M

WT

N

S

N

ET

k

T

MR

b

b

39Dept. of EE, NDHU

Symbol Error Versus Bit Error for FSK Signaling

40Dept. of EE, NDHU

Symbol Error Performance for M-ary Systems

• Symbol error performance for coherently detected M-ary PSK

• Symbol error performance for differentially coherent detection of MPSK signal

• Probability of symbol error for coherently detected MFSK signal

• Probability of symbol error for non-coherently detected MFSK signal

points signal ed transmittany twobetween distance

Euclideansmallest theis where,)sin2

(2)2

(2)( min00

min dMN

EQ

N

dQMP s

E

)2

sin2

(2)(0 MN

EQMP s

E

)()1()(0N

EQMMP s

E

)exp()1()exp(1

)(020 jN

E

j

M

N

E

MMP s

M

j

jbE

41Dept. of EE, NDHU

Symbol Error Performance for Coherently Detected MPSK

42Dept. of EE, NDHU

Symbol Error Performance for Coherently Detected MFSK

43Dept. of EE, NDHU

Symbol Error Performance for Non-coherently Detected MFSK

44Dept. of EE, NDHU

Bit Error Versus Symbol Error Probability

• Orthogonal signal

2

1limget weincreases, as

1

2/

12

2

k

1

E

B

k

k

E

B

P

Pk

M

M

P

P

45Dept. of EE, NDHU

Bit Error Versus Symbol Error Probability

• Multiple Phase signals with Gray coded

• For BPSK and QPSK signaling

)1(for log2

EE

B PM

PP

BBBE

BE

PPPP

PP

2 :QPSK

:BPSK