COMM702: Modulation II Lecture 10 - Minimum Shift Keying - Gaussian Minimum Shift Keying
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COMM702: Modulation II
Lecture 10
- Minimum Shift Keying
- Gaussian Minimum Shift Keying
Minimum Shift Keying (MSK)
• Minimum shift keying (MSK) is a special type of continuous phase-frequency shift keying (CPFSK) with modulation index=0.5.
• A modulation index of 0.5 corresponds to the minimum frequency spacing that allows two FSK signals to be coherently orthogonal, and the name minimum shift keying implies the minimum frequency separation that allows orthogonal detection.
Minimum Shift Keying
=
b
cT
ff4
11
b
cT
ff4
12
This is the minimum frequency spacing that allows the two FSK signals
representing 1 and zero to be coherently orthogonal in the sense that they do not interfere with each other in the process of detection. This is
the reason for that this type is called MSK.
Remember
Where: bR
ffMSKforThen 21,
2, 21
bRffMSKFor
Baseband signal
Minimum Shift Keying (MSK) • MSK is attractive because the phase continuity yields high
spectral efficiency, and the constant-envelope yields excellent power efficiency.
• The primary drawback is the high implementation complexity required for an optimal receiver.
• Discontinuous phase (for example QPSK) requires a relatively large percentage of the power to occur outside of the intended band (e.g., high fractional out-of-band power), leading to poor spectral efficiency.
Minimum Shift Keying (MSK) • Similar to OQPSK, MSK is encoded with bits alternating
between quadrature components, with the Q component delayed by one bit period.
• However, instead of square pulses as OQPSK uses, MSK encodes each bit as a half sinusoid (sin or cos). This results in a constant-modulus signal (constant envelope signal), which reduces problems caused by non-linear distortion.
• In addition to being viewed as related to OQPSK, MSK can also be viewed as a continuous phase frequency shift keyed (CPFSK) signal with a frequency separation of one-half the bit rate.
Minimum Shift Keying (MSK) • To guarantee phase continuity, we use the phase of the
previous bit. Therefore, MSK is called Modulation with memory. A continuous phase FSK (CPFSK) signal can be written as:
)1(
"0")0(2cos2
"1")0(2cos2
)(
2
1
fortfT
E
fortfT
E
ts
b
b
b
b
i
• Since
and
• By substituting these frequencies in (1) we have
b
cT
ff4
11 )2(
4
12
b
cT
ff
)3(
"0")0(2
2cos2
"1")0(2
2cos2
)(
forT
ttf
T
E
forT
ttf
T
E
ts
b
c
b
b
b
c
b
b
i
Phase of
cos for the
previous
bit interval
• Another useful way to represent CPFSK (It is seen as the usual FM):
• By comparing (3) and (4) we have:
Where the “+” sign corresponds to sending “1” and “-” sign
corresponds to sending “0”. At , equation (5) can be written as
bTt
)4()](2cos[2
)( ttfT
Ets c
b
b
)5(0,2
)0()( b
b
TttT
t
)6(
02/
12/
)0()(
bitfor
bitfor
Tb
.2/by it reduces "0" of sending and2/by signal
CPFSK a of phase theincreases "1" of sending is,That
Phase Trellis
Phase tree for the sequence: 1 1 0 1 0 0 0
02/
12/
)0()(
bitfor
bitfor
Tb
bT bT3 bT5 bT7
0)0( with
assametheisthatNote
T
TTTT
TTT
b
bbbb
bbb
2,
2)(
,0)0(:defineweThus
2,
2,...)5,3,(:ofmultiplesoddAt
,0,...)4,2,0(:ofmultipleevenAt-
:thatnotewe trellisprevious theFrom
Signal Space of MSK
)0(ononlydepends))(cos(
ofpolaritythe,
:intervaltheinthatfindWe
historypasttheondepending
,0)0(phasetheSince
t
TtT
oris
bb
)0(forsignand
0)0(forsignvewhere
ve
-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Signal Space of MSK
)( bT
)(ononlydepends))(sin(ofpolaritythe,20:intervaltheinthatfindWe bb TtTt
Signal Space of MSK
MSK has Continuous Phase How?
Continuous
phase MSK
signal
See page
393 of the
Text book
for more
details
Signal Space of MSK
Constellation of MSK
Prob of Error of MSK
o
bMSKe
N
EQP
2
o
bFSKCoherente
N
EQP:withCompare
Transmitter Block Diagram of MSK
s1
s2
b
cT
ff4
11
b
cT
ff4
12
tT
ftT
fT
T
ttf
T
b
c
b
c
b
b
c
b
)4
1(2cos()
4
1(2cos(
2
2
1
2cos)2cos(
2
b
c
bb
c
b
c
b T
ttf
Tt
Tft
Tf
T 2cos)2cos(
2)))
4
1(2cos())
4
1(2(cos(
2
2
1
b
c
bb
c
b
c
b T
ttf
Tt
Tft
Tf
T 2sin)2sin(
2)))
4
1(2cos())
4
1(2(cos(
2
2
1
))4
1(2cos(
2
2
1t
Tf
T b
c
b
))4
1(2cos(
2
2
1t
Tf
T b
c
b
Receiver Block Diagram of MSK
)(ts
2s
1s
Advantages of MSK
(1)Constant Envelope
(2)Small probability of error
(3)Smaller Bandwidth than discontinuous phase
FSK.
Gaussian Minimum Shift Keying (GMSK) • Gaussian Minimum Shift Keying (GMSK) is a modification of
MSK .
• A Gaussian pre-modulation filter is used to reduce the bandwidth of a baseband pulse train prior to modulation to make the signal has a much narrower bandwidth.
• This bandwidth reduction does not come for free since the pre-modulation filter smears the individual pulses in pulse train. As a consequence of this smearing in time, adjacent pulses interfere with each other generating inter-symbol interference.
• In the applications where GMSK is used, the trade-off between power efficiency and bandwidth efficiency is well worth the cost (the narrow filter increases the intersymbol interference and reduces the signal power).
Gaussian Minimum Shift Keying (GMSK)
As can be seen from above, GMSKs power spectrum drops much quicker
than MSK's. Furthermore, as is decreased, the roll-off is much quicker
Since lower time-bandwidth products produce a faster power-spectrum roll-off,
why not have a very small time-bandwidth product?. It happens that with lower
time-bandwidth products the pulse is spread over a longer time, which can
cause intersymbol interference
A Gaussian-shaped impulse response
filter generates a signal with low side
lobes and narrower main lobe than the
rectangular pulse.
Gaussian Shaping Filter:
Gaussian Shaping Filter:
Probability of Error of GMSK: Probability of error of GMSK over AWGN Channel is given by:
Probability of error of GMSK over Rayleigh Fading Channel is
given by:
rationoisetosignalaveragetheis
o
b
N
EQ
22)( yQyerfc
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