cos w H t. output. + . Decision Circuit. . r(t). cos w L t. Probability of error in coherent FSK receiver given as:. P e,BFSK =. Coherent BFSK Detector. 2 correlators fed with local coherent reference signals difference in correlator outputs compared with threshold to
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cos wHt
output
+

Decision
Circuit
r(t)
cos wLt
Probability of error in coherent FSK receiver given as:
Pe,BFSK =
Coherent BFSK Detector
Matched Filter
fH
Envelope
Detector
+

r(t)
output
Tb
Decision
Circuit
Envelope
Detector
Matched Filter
fL
Pe,BFSK, NC =
Noncoherent Detection of BFSK
Average probability of error in noncoherent FSK receiver:
Ichannel
Z1(T)
(.)2
( 2/T) cos wHt
+
+
( 2/T) sin wHt
Z2(T)
(.)2
+

output
r(t)
Decision
Circuit
Qchannel
Z3(T)
Ichannel
(.)2
( 2/T) cos wLt
+
+
( 2/T) sin wLt
Z4(T)
(.)2
Qchannel
Noncoherent Quadrature BFSK Detector
(f2 – f1) for
(arbitrary phase )
Minimum Shift Keying ( fast FSK)
FSK modulation index
kFSK=
MSK modulation index is kMSK= 0.5
FMSK=
Minimum Shift Keying
Minimum Shift Keying
sMSK(t) =
½ sine pulse given by
p(t) =
m(t) = ±1 bipolar bit stream
p(t – 2iTbTb)sin(2πfct)
Transmitted MSK signal
(OQPSK variant)
p(t – 2iTb)cos(2πfct) +
d0 d1 d2 d3 d4 d5 d6 d7
d0 d2 d4 d6
d1 d3 d5 d7
d0 d1 d2 d3 d4 d5 d6 d7
d0 d2 d4 d6
d1 d3 d5 d7
sMSK(t) =
and
MSK waveform
 as a special case of CPFSK
MSK is FSK signal with binary signaling frequencies given by
Phase Continuity of MSK
h = ½
θ(t) = θ(0) ±
0 ≤ t ≤ T
θ(t) can take on only 2 values at odd or even multiples of T
t =even multiple of T θ(T)  θ(0)= πor 0
t = odd multiple of Tθ(T)  θ(0)= ± π/2
assuming θ(0) = 0
π
π/2
0
π/2
π
θ(t)  (0)
1 0 0 1 1 1 0
0 2T 4T 6T t
Phase Trellis: path depicts θ(t) corresponding to a binary sequence
Orthonormal basis for MSK as
1(t) =
2(t) =
0 ≤ t ≤ T
0 ≤ t ≤ T
bi
θ(0)
θ(T)
s1
s2
then
s(t) = s1(t)1(t) + s2(t)2(t)
with
‘0’
0
π/2
‘1’
π
π/2
s1=
T ≤ t ≤ T
‘0’
π
π/2
‘1’
0
π/2
s2=
=
0 ≤ t ≤ 2T
=
p(t) =
PMSK(f) =
MSK Power Spectrum
Normalized PSD for MSK is given as
PSD of MSK & QPSK signals
10
0
10
20
30
40
50
60
QPSK, OQPSK
MSK
normalized PSD (dB)
fc fc+0.5Rb fc+Rb fc+1.5Rb fc+2Rb
MSK spectrum
mI(t)
_
+
x(t)
SMSK(t)
+
+
y(t)
mQ(t)
+
+
cos(2fct)
cos(t/2T)
MSK Transmitter
(i) cos(2fct)cos(t/2T) 2 phase coherent signals atfc ¼R
(ii) Separate 2 signals with narrow bandpass filters
(iii) Combined to formI & Q carrier components x(t), y(t)
(iv) Mix and sum to yield SMSK(t) = x(t)mI(t) + y(t)mQ(t)
mI(t) & mQ(t) = even & odd bit streams
Coherent MSK Receiver
SMSK(t)
Coherent MSK Receiver
Threshold
Device
mI(t)
t = 2(k+1)T
x(t)
y(t)
Threshold
Device
mQ(t)
t = 2(k+1)T
Gaussian MSK
Gaussian MSK
Gaussian MSK
Impulse responseof premodulation Gaussian filter :
hG(t) =
transfer function of premodulation Gaussian Filter is given by
HG(f) =
is related toB3dB by
=
Gaussian MSK
Impact of B3dBTb
0
10
20
30
40
50
60
BTb = (MSK)
BTb = 1.0
BTb = 0.5
BTb = 0.2
0 0.5 1.0 1.5 2.0 (ffc)T
PSD of GMSK signals
RF bandwidth
containing % power as fraction of Rb
e.g. for BT = 0.2 99% of the power is in the bandwidth of 1.22Rb
Pe =
BER of GMSK for AWGN channel
Pe= bit error probability
is constant related to B3dBTb
Gaussian
LPF
FM
Transmitter
RF GMSK Output
NRZ bits
GMSK Transmitter Block Diagram
GMSK Transmitter
demodulated
signal
/2
modulated IF
input signal
loop
filter
Q
IF LO
I
/2
clock
recovery
(i) GMSK Receiver Block Diagramorthogonal coherent detectors
D Q
C
D Q
C
D Q
C
D Q
C
modulated IF
input signal
D Q
C
clock
recovery
demodulated
signal
D
C Q
loop
filter
VCO
Logic Circuit for GMSK demodulation
Detecting GMSK signal by sampling output of FM demodulator
is a nonoptimal, effective method