min shift keying
DESCRIPTION
Min Shift KeyingTRANSCRIPT
1
Minimum Shift Keying [MSK] Modulation---a special form of FSK
• MSK is generated as follows
g1(t)g1(t)ai
g2(t)g2(t)bi
sinωct
DD
cosωct
Delay=T2
1R
a1 a2 a3 a4 Input bits
1/R 1/R
T
•Similar to generation of OQPSK--- except for different I/Q baseband filters•Linear modulation ---> can equalize•Bandwidth determined by g1(t) and g2(t)
Si (t)
a1cosπt/T a2cosπt/T
b1sinπt/T b2sinπt/T
-T/2 0 T/2Time
In-phase terms
Quadrature offset
-T/2 0 TTime
g1(t)
g2(t)
Detect as SQAM signalb
a
Q
I
Not a strictly bandlimited signal---since time limited pulses are used for shaping
2
MSK is an FSK Signal
1 if
1 if 0 cos)(
1 ,1 cos
1 ,1 cos)(
−==
==
+−=
±=−=
+=
±==
=
i
iji
ci
iic
iici
a
aT
tbatts
baTt
t
baT
ttts
πθ
θθπ
ω
ππ
ω
πω
m
m
•The MSK signal can be written as
•The MSK signal has a constant envelope•As shown below, MSK may be interpreted as a form of FSK
( )( )
421
2or ,/ e wher
1 if 0 cos
1 if 0 cos )(
R
TfT
batt
battts
iic
iici
==∆
=∆=∆
==+∆−=
−==+∆+=
πω
πω
θθωωθθωω
3
Why Is It 'Minimum' Shift Keyed?• For the synchronous or coherent FSK detector shown below, using an integrator (over a symbol
period) as the linear filter, it can be shown that the closest that the two frequencies can be spaced(for the signals to be unambiguously resolved in the absence of noise) is R/4
• If the tranmitted signal is the lower frequency, then, to a first approximation, the output of thebottom integrator is
• For this integral to be zero, we have the condition
dt)tcos(1/2dtt(t)cos 2
1/R
0 12
1/R
0ω−ω=ω ∫∫ cf
Consider
∫∫ ∆∆ππ∆∆ππ
====ρρ
ππ==
ππ==
••==++
T21
T1nff
22
11
ft2ftsin2
dt(t)s(t)s
tfcos2T2
(t)S
tfcos2T2
(t)S
21
+
-
Low-passfilter
Low-passfilter
Low-passfilter
Low-passfilter
cosω1t
cosω2t
fc(t) Binaryoutput
ρρ
1/2MSK Optimal FSK
∆∆fT = .715~2 dB penalty antipodal(difficult to synchronize)
ρ ρ = inner product between s1(t) and s2(t); measuresthe degree of "orthogonality" between the 2 signals
∆∆fT
= 0sin 2∆ω∆ωR
⇒⇒ ∆ ∆f = R/4
∆∆f = f2 - f1
4
POWER SPECTRA FOR MSK AND QPSK
Spectrum
Frequency
MSK
QPSK
1.00
0.20
0.05
Tb = bit rate
0.5/Tb 1/Tb
fFraction of out-of-band power
QPSKMSK
MSK has lower side lobes than rectangularly filtered QPSK, as shown, and the out-of-band power is significantly lower. A measure ofthe compactness of a modulation spectrum is the bandwidth which contains 99% of the total power of the signal, 1.2/Tb for MSK.
5
GMSK Modulator: Gaussian Filter Precedes g1(t) and g2(t)and reduces the bandwidth [relative to MSK]
• Gaussian filter produces an even faster drop off in high frequency content than MSK
• No longer a linear modulation [like MSK]: since the baseband pulse is not a cos/sine timefunction
• Good approximation for MSK as a linear signal, so can equalize
Non Linearcos[ωωt+φφ(t,ααn)]
cosωωt
-sinωωt
GaussianFilter
GaussianFilter
CosCos
SinSin
φφ(t,ααn)
∫∫ dt∫∫ dt
Phase Pulse Shaping
Pulse Shaping
cos[φφ(t,ααn)]
sin[φφ(t,ααn)]
0.3RB
Gaussian
-3
dB
f
FrequencyPulse Shape
6
GMSK Coherent ReceiverLaurent, IEEE Trans. On Communications, February 1986
• LPF eliminates 2f0 terms
• Filtering is accomplished in BPF
cos 2ππf0t
- sin 2ππf0t
GaussianBPF
GaussianBPFxGMSK(t)
cos φ(t)
In-PhaseChannel
QuadratureChannel
sin φ(t)
Delay2T
Delay2T
Delay2T
Delay2T
DetectorDetector
DetectorDetector
LPFLPF
LPFLPF
SampleEvery 2T
SampleEvery 2T
0, 2T,…
T, 3T,…Bi
Can Detect GMSK as a Pair of Antipodal Quadrature Signals ----process as linear modulation: good approximation