Module III
Taub Ch.6
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PSK
QPSK
M-ary PSK
FSK
M-ary FSK
MSK
Examples of Modulation
• Amplitude Shift Keying (ASK) or On/Off
Keying (OOK):
• Frequency Shift Keying (FSK):
• Phase Shift Keying (PSK):
Description of binary ASK,PSK, and
FSK schemes
Bandpass binary data transmission system
Transmit
carrier
Clock pulses
Input
Binary
data
{bk}
Channel
Hc(f)
Modulator
Z(t)
Noise
n(t)
Local carrier
Clock pulses
ּ
+
Demodulator
+
(receiver)
+
V(t)
Binary data output
{bk}
Binary information over bandpass
channels
Digital modulation and channel
Digital Demodulator
Signal Regeneration
Bandwidth of signal
• Baseband versus bandpass:
Baseband
signal
Bandpass
signal
Local oscillator
BPSK-Transmitter
For each level data phase diff is 1800
1 2
Sinusoid of amplitude A, Ps  A ,  A  2 PS
2
Trnasmitted signal is either
vBPSK (t )  2 PS cos(0t )
or
vBPSK (t )  2 PS cos(0t   )   2 PS cos(0t )
If b(t )  1V for log ic level 1
b(t )  1V for log ic level 0
then vBPSK (t )  b(t ) 2 PS cos(0t )
In practice BPSK is generated by applying cos(0t ) as a
carrier to the balance mod ulator and b (t ) as mod ulating
waveform (~ AM )
Scheme to recover the baseband signal in
BPSK
BPSK-Receiver
Re cieved s / g
vBPSK (t )  b(t ) 2 PS cos(0t   )  b(t ) 2 PS cos 0 (t   / 0 )
 is a no min ally fixed phase shift corresponding to time delay  / 0
Synchronous de mod ulation  that w / f cos(0t   ) available at rxr
Squaring the rxd s / g (amplitudes not relevant or  unity )
1 1
cos (0t   )   cos 2(0t   )
2 2
The dc component is removed by BPF whose PB centered around 2 f 0 .
2
Frequency divider to generate w / f cos(0t   ).
The carrier having bieng re cov ered is multiplied with the rxd s / g
and applied to the int egrator.
b(t ) 2 PS cos(0t   ) cos(0t   )  b(t ) 2 PS cos 2 (0t   )
1 1

 b(t ) 2 PS   cos 2(0t   ) 
2 2

Cont..
The o / p is the int egrator o / p made available by s / w S S at the end of
a bit int erval but immediately before the clo sin g of s / w SC .
Assu min g n.T0  Tb  2 n.T0  2 Tb
2
 n.2 
Tb
T0
 n.2  2 f 0Tb
 n.2  0Tb
o / p voltage vo (kTb ) at the end of a bit int erval (k  1)Tb to kTb is
kTb
kT
b
1
1
vo (kTb )  b(kTb ) 2 PS 
dt  b(kTb ) 2 PS 
cos 2(0t   )dt
2
2
( k 1)Tb
( k 1)Tb
Tb
 b(kTb ) 2 PS
2
PS
 b(kTb )
Tb
2
Spectrum of BPSK
The w / f b(t ) NRZ which makes excursions b / w  PS with psd Gb ( f )
 sin  fTb 
Gb ( f )  PS Tb 


fT
b


2
The BPSK w / f {b(t ) 2 Ps cos 0t} is the NRZ w / f multiplied by
i.e.  PS . 2 cos 0t
U sin g if M ( j )  F  m(t )  then
1
 M ( j  j0 )  M ( j  j0 )
2
2
2

PS Tb   sin  ( f  f 0 )Tb   sin  ( f  f 0 )Tb  
 GBPSK ( f ) 

 
 
2    ( f  f 0 )Tb    ( f  f 0 )Tb  


F  m(t ) cos 0t  
2 cos 0t
PSD of NRZ data b(t) & binary PSK
Geometrical Representation of BPSK
Signals
BPSK s / g in terms of one orthonormal s / g u1 (t )  2 / Tb cos 0t as
2


vBPSK (t )   PS Tb b(t ) 
cos 0t   PS Tb b(t )  u1 (t )
Tb
The dis tan ce d between signals is
d  2 PS Tb  2 Eb , Eb energy contained in a bit duration
and d is inversely proportional to Pe .
Differential Phase-Shift Keying
• Merit – it eliminate the ambiguity about whether the
demodulated data is or is not inverted.
• Avoids the need to provide the synchronous carrier
required at the demodulator for detecting a BPSK signal.
• Arbitrarily assuming that in the first interval b(0)=0. In the
demodulator, the data will be correctly determined
regardless of our assumption concerning b(0) - Invariant
feature of the system.
• i.e no change in b(t) occur whenever d(t)=0, and a change
in b(t) occurs whenever d(t)=1.
• When d(t)=0 the phase of the carrier does not change at
the beginning of the bit interval, while when d(t)=1 there is
a phase change of magnitude .
Means of generating a DPSK
signal
Logic waveforms to illustrate the
response b(t) to an input d(t)
Method of recovering data from the
DPSK signal
b(t )b(t  Tb )(2 Ps ) cos(0t   ) cos[0 (t  Tb )   ]


 Tb
 b(t )b(t  Tb ) Ps cos 0Tb  cos  20  t 
2





  2  


Cont..
• The transmitted data d(t) can be readily
determined from the product b(t)b(t-Tb).
• If d(t)=0 then there was no phase change
and b(t)=b(t-Tb) both being +1V or both
being -1V. In this case b(t)b(t-Tb)=1.
• If however d(t)=1 then there was a phase
change and either b(t)=1V with b(t-Tb)=
-1V or vice versa.
• In either case b(t)b(t-Tb)= -1.
Type-D flip-flop
Quadrature Phase-Shift Keying
(QPSK)
• BW for BPSK must be nominally 2fb.
• QPSK allows bits to be transmitted at half
the BW.
• In a QPSK system the type D flip-flop is
used as a one bit storage device.
An offset QPSK Transmitter
Waveforms for the QPSK
Transmitter
OQPSK
vm (t )  so (t )  se (t )
vm (t )  Ps bo (t ) sin 0 (t )  Ps bs (t )co s 0 (t )
 In BPSK a bit stream with bit time Tb multiplies a carrier ,
the generated s / g has a no min al BW 2(1/ Tb ).
 In the w / f ' s bo (t ) and bs (t ) the bit times are each 1/ 2Tb ,
hence both so (t ) and se (t ) have half the no min al BW of BPSK .
The 4 possible o / p s / g ' s are in phase quadrature.
 At the end of each bit int erval bo or be can change, but both
cannot change at the same time  Offset or staggered QPSK
i.e. at each timeTb , the transmitted s / g , changes phase by 900.
Phasor diagram for sinusoids in
QPSK Transmitter
A QPSK Receiver
Carrier
Recovery
Circuit
Signal Space Representation


Four quadrature signals vm (t )  2 Ps cos 0t  (2m  1) 
4

U sin g two ort ho normal signals
u1 (t ) 
m  0,1, 2,3
2
2
cos 0t and u2 (t ) 
sin 0t
T
T
 2
 2


vm (t )   PT
cos(2
m

1)
cos

t

PT
sin(2
m

1)
sin 0t
s
0
s



4 T
4 T


If be  2 cos(2m  1)

and bo   2 sin(2m  1)
4
then vm (t )  Eb be (t )u1 (t )  Eb bo (t )u2 (t )

4
The four QPSK signal drawn in
signal space
T  2Tb  Ts
Es  PT
s s  Ps (2Tb )
2
d po int s differ in1 bit
d  2 PT
s b  2 Eb
2
M-ary PSK
In M  ary PSK the w / fs used to identify the symbols are
vm (t )  2 Ps cos(0t  m )
m  (2m  1)
(m  0,1,..., M  1)

M
The co  ordinate axis in the signal space are the orthonormal w / fs
2
2
u1 (t ) 
cos 0t and u2 (t ) 
sin 0t
Ts
Ts
The dis tan ce of each dot from the origin is
Es  PT
s s
vm (t )  ( 2 Ps cos m ) cos 0t  ( 2 Ps sin m ) sin 0t
pe  2 Ps cos m and po  2 Ps sin m
vm (t )  pe cos 0t  po sin 0t
Both pe and po can change every Ts  NTb and can assume any
of the possible M values. pe , po and m are random processes.
Geometrical representation of
M-ary PSK signals
Cont..
The psd ' s of pe and po are
 sin  fTs 
| Pe ( f ) |
2
Ge ( f ) 
 2 PT

s s cos m 
Ts

fT
s


2
 sin  fTs 
| Po ( f ) |
2
Go ( f ) 
 2 PT

s s sin m 
Ts

fT
s


2
Since m is uniformly distributed
2
2
2
1
cos m  sin m 
2
2
2
 sin  fTs 
Ge ( f )  Go ( f )  PT

s s

fT
s


When s / g ' s with spectral densities are multiplied by a carrier ,
the resul tan t spectrum is centered at the carrier frequency and
extends no min ally over a BW
fb
2
B   2 fs  2
T
N
Cont..
As we  N per symbol the BW becomes smaller , the dis tan ce
b / w symbol s / g po int s become smaller .
U sin g law of cos ines dis tan ce d is
d  4 Es sin 2 ( / M )  4 NEb sin 2 ( / 2 N )
Symbol energy Es  Ps ( NTb )  PT
s s  NEb and Bit energy Eb  PT
s b
As we  N , i.e. as we  the duration of the symbol , the BW , the
dis tan ce d  and Pe  .
Such is the case for all  ' s in N except for the  from N  1( BPSK )
to N  2(QPSK )
M-ary PSK Transmitter
M-ary PSK receiver
BFSK
vBFSK (t )  2 Ps cos[0t  d (t )t ]
Here d (t )  1 or  1 corresponding to log ic levels 1 or 0 of data.
The transmitted s / g is either vBFSK (t )  sH (t )  2 Ps cos(0  )t
or vBFSK (t )  sL (t )  2 Ps cos(0  )t
has an angular frequency 0   or 0   with  a cons tan t
offest from the no min al frequency 0 .
When d (t ) changes from  1 to  1 pH changes from 1 to 0 and
pL from 0 to 1. At any time either pH or pL is 1 but not both so
that the generated s / g is either at angular frequemcy H or L .
BFSK signal generator
Spectrum of BFSK
vBFSK (t )  2 Ps pH cos(H t   H )  2 Ps pL cos(Lt   L )
unipolar  bipolar
1 1
1 1
pH (t )   p 'H (t ) and pL (t )   p 'L (t )
2 2
2 2
When p 'H is  1, p 'L  1 and viceversa.
vBFSK (t ) 
Ps
Ps
cos(H t   H ) 
cos(Lt   L )
2
2
Ps
Ps

p 'H cos(H t   H ) 
p 'L cos(Lt   L )
2
2
In fig f H  f L  2( / 2 )  2 f b
and BW ( BFSK )  4 f b  2 BW ( BPSK )
The PSD of individual terms
A BFSK Receiver
Geometrical Representation of
Orthogonal BFSK
2
u1 (t ) 
cos 2 mf bt
Tb
u2 (t ) 
2
cos 2 nf bt
Tb
Different harmonics (m  n) are orthogonal over the int erval
of the fundamental period Tb  1/ f b .
If the frequencies f H and f L in a BFSK system are selected
to be (m  n) f H  mf b & f L  nf b , then the s / g vectors
sH (t )  Eb u1 (t )
sL (t )  Eb u2 (t )
d  2 Eb
Signal space representation
orthogonal / non-orthogonal
An M-ary Communication System
M-ary FSK
Select carrier frequency as successive even harmonics of
symbol frequency
f 0  kf s , f1  (k  2) f s , f 2  (k  4) f s , etc
To pass M  ary FSK the required spectral range is
B  2 Mf s
B  2 N 1 f b / N
M  ary FSK requires a considerably increased BW in
comparison to M  ary PSK , but Pe for M  ary FSK
decreases as M increases while it increases for M  ary PSK .
M  ary FSK d  2 Es  2 NEb is greater than that of
M  ary PSK except for M  2 and M  3.
Power Spectral Density of M-ary
FSK (four frequencies)
Geometrical Representation of orthogonal M-ary FSK
(M=3) when the frequencies are selected to generate
orthogonal signals
MSK