1. Coherent BFSK Detector
2 correlators fed with local coherent reference signals
difference in correlator outputs compared with threshold to
determine binary value
output + -
r(t)
Decision
Circuit
cos wLt
cos wHt 
Pe,BFSK =
Probability of error in coherent FSK receiver given as:

2. Non-coherent Detection of BFSK
operates in noisy channel without coherent carrier reference
pair of matched filters followed by envelope detector
- upper path filter matched to fH (binary 1)
- lower path filter matched to fL (binary 0)
envelope detector output sampled at kTb  compared to threshold
r(t)
output
Decision
Circuit + - 
Envelope
Detector
Matched Filter fL Tb fH
Average probability of error in non-coherent FSK receiver:
Pe,BFSK, NC =

3. Non-coherent Quadrature BFSK Detector
output
Decision
Circuit
r(t) +
( 2/T) cos wHt 
( 2/T) sin wHt
(.)2
Z1(T)
I-channel
Q-channel
Z2(T) -
Z3(T)
( 2/T) cos wLt
( 2/T) sin wLt
Z4(T)

4. Tutorial Derive minimum frequency spacing (f2 – f1) for 
Non-coherent detection
(arbitrary phase )
Coherent detection

5. Minimum Shift Keying ( fast FSK)
Type of continuous phase FSK (CPFSK)
Spectrally efficient
Constant envelope
Good BER performance
Self-synchronizing capability
Requires coherent detection

6. Minimum Shift Keying kFSK = FSK modulation index
minimum frequency spacing (bandwidth) for 2 FSK signals
to be coherently orthogonal
minimum bandwidth that allows orthogonal detection
FSK modulation index
kFSK =
MSK modulation index is kMSK = 0.5 
FMSK=

7. Minimum Shift Keying MSK can be thought of as special case of OQPSK
uses half-sinusoidal pulses instead of baseband rectangular pulses
arch shaped pulse of period = 2Tb
modify OQPSK equations using half-sine pulses for N-bit stream
several variations of MSK exist with different basic pulse shapes
e.g.
- use only positive ½ sinusoids
- use alternating negative & positive ½ sinusoids
all variations are CPFSK that use different techniques to achieve
spectral efficiency

8. Transmitted MSK signal
(OQPSK variant)
sMSK(t) =
p(t – 2iTb-Tb)sin(2πfct)
p(t – 2iTb)cos(2πfct) +
p(t) =
½ sine pulse given by
mIi(t) = ith bit of mI(t), the even bits of m(t)
mQi(t) = ith bit of mQ(t), the odd bits of m(t)
mI(t) & mQ(t)are bipolar bit streams (1) that feed I & Q
arms of the modulator - each arm fed at Rb/2
m(t) = ±1 bipolar bit stream

9. MSK example with ωcT=2.5π; ω1T=2π, ω2T=3π
d d d d d d d d7
d d d d6
d d d d7

10. MSK example with ωcT=4π; ω1T=3.5π, ω2T=4.5π
d d d d d d d d7
d d d d6
d d d d7

11. - as a special case of CPFSK
MSK waveform
- as a special case of CPFSK
sMSK(t) =
k = 0 or  depending on whether mI(t) = +1 to -1
sMSK(t) has constant amplitude
to ensure phase continuity at bit interval  select fc = ; n integer
MSK is FSK signal with binary signaling frequencies given by
fc +
fc -
and
phase of MSK varies linearly over Tb

12. Phase Continuity of MSK
0 ≤ t ≤ T
θ(t) = θ(0) ±
h = ½
Phase Continuity of MSK
θ(t) can take on only 2 values at odd or even multiples of T
t = even multiple of T  θ(T) - θ(0) = π or 0
t = odd multiple of T  θ(T) - θ(0) = ± π/2 bi t
θ(T) i T
-π/2
odd 1
π/2 2T
even π
assuming θ(0) = 0

13. Phase Trellis: path depicts θ(t) corresponding to a binary sequence
for h = ½  ΔF = Rb/4
minimum ΔF for two binary FSK signals
to be coherently orthogonal
e.g. if Rb = 100Mbps  = ΔF = 25MHz bi t
θ(T) i T
-π/2
odd 1
π/2 2T
even π
θ(t) - (0) π
π/2
-π/2 -π
T T T t i bi
θ(i-1)T
θ(iT) 1
π/2
odd 2
even 3
-π/2 4 π 5 6 7 8

14. Orthonormal basis for MSK as
0 ≤ t ≤ T
2(t) =
s1 = =
-T ≤ t ≤ T
s2 =
0 ≤ t ≤ 2T
with s1
π/2
‘1’ π
‘0’
-π/2 s2
θ(T)
θ(0) bi
s(t) = s1(t)1(t) + s2(t)2(t)
then

15. MSK Power Spectrum
RF power spectrum obtained by frequency shifting |F{p(t)}|2
F{} = fourier transform
p(t) = MSK baseband pulse shaping function (1/2 sin wave)
p(t) =
Normalized PSD for MSK is given as
PMSK(f) =

16. MSK spectrum PSD of MSK & QPSK signals QPSK, OQPSK MSK
(1) has lower side lobes than QPSK (amplitude)
(2) has wider side lobes than QPSK (frequency)
99% MSK power is within bandwidth B = 1.2/Tb
99% QPSK power is within bandwidth B = 8/Tb
normalized PSD (dB)
QPSK, OQPSK
MSK
PSD of MSK & QPSK signals
fc fc+0.5Rb fc+Rb fc+1.5Rb fc+2Rb 10
-10
-20
-30
-40
-50
-60

17. MSK
QPSK signaling is bandwidth efficient, achieving 2 bps per Hz of channel bandwidth. However, the abrupt changes results in large side lobes. Away from the main lobe of the signal band, the power spectral distribution falls off only as ω-2 .
MSK achieves the same bandwidth efficiency. With constant envelope (no discontinuity in phase), the power spectral distribution falls off as ω-4 away from the main signal band.

18. MSK spectrum MSK has faster roll-off due to smoother pulse function
Spectrum of MSK main lobe > QPSK main lobe
- using 1st null bandwidth  MSK is spectrally less efficient
MSK has no abrupt phase shifts at bit transitions
- bandlimiting MSK signal doesn’t cause envelop to cross zero
- envelope is  constant after bandlimiting
small variations in envelope removed using hardlimiting
- does not raise out of band radiation levels
constant amplitude  non-linear amplifiers can be used
continuous phase is desirable for highly reactive loads
simple modulation and demodulation circuits

19. MSK Transmitter mI(t)  cos(2fct) cos(t/2T) mQ(t)
(i) cos(2fct) cos(t/2T)  2 phase coherent signals at fc  ¼R
(ii) Separate 2 signals with narrow bandpass filters
(iii) Combined to form I & 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
x(t)
y(t)
SMSK(t)
mQ(t) _ + 
mI(t)
cos(2fct)
cos(t/2T)

20. Coherent MSK Receiver
(i) SMSK(t) split & multiplied by locally generated
x(t) & y(t) (I & Q carriers)
(ii) mixer outputs are integrated over 2T & dumped
(iii) integrate & dump output fed to decision circuit every 2T
input signal level compared to threshold  decide 1 or 0
output data streams correspond to mI(t) & mQ(t)
mI(t) & mQ(t) are offset & combined to obtain demodulated signal
*assumes ideal channel – no noise, interference

21. Coherent MSK Receiver Threshold Device mI(t) x(t) SMSK(t) y(t)
t = 2(k+1)T
x(t)
y(t)
Threshold
Device
mQ(t)
t = 2(k+1)T

22. Gaussian MSK Gaussian pulse shaping to MSK
smoothens phase trajectory of MSK signal 
over time, stabilizes instantaneous frequency variations
results in significant additional reduction of
sidelobe levels
GMSK detection can be coherent (like MSK)
or noncoherent (like FSK)

23. Gaussian MSK
premodulation pulse shaping filter used to filter NRZ data
- converts full response message signal into partial response scheme
full response  baseband symbols occupy Tb
partial response transmitted symbols span several Tb
- pulse shaping doesn’t cause pattern’s averaged phase trajectory to deviate from simple MSK trajectory

24. Gaussian MSK GMSKs main advantages are
power efficiency - from constant envelope (non-linear amplifiers)
excellent spectral efficiency
pre-modulation filtering introduces ISI into transmitted signal
if B3db Tb > 0.5  degradation is not severe
B3dB = 3dB bandwidth of Gaussian Pulse Shaping Filter
Tb = bit duration = baseband symbol duration
irreducible BER caused by partial response signaling is the
cost for spectral efficiency & constant envelope
GMSK filter can be completely defined from B3dB  Tb
- customary to define GMSK by B3dBTb

25. Gaussian MSK Impulse response of pre-modulation Gaussian filter :
hG(t) =
 is related to B3dB by
 =
transfer function of pre-modulation Gaussian Filter is given by
HG(f) =

26. Impact of B3dBTb
(i) Reducing B3dBTb : spectrum becomes more compact (spectral efficiency)
causes sidelobes of GMSK to fall off rapidly
B3dBTb = 0.5  2nd lobe peak is 30dB below main lobe
MSK  2nd peak lobe is 20dB below main lobe
MSK  GMSK with B3dBTb = 
(ii) increases irreducible error rate (IER) due to ISI
ISI degradation caused by pulse shaping increases
however - mobile channels induce IER due to mobile’s velocity
if GMSK IER < mobile channel IER  no penalty for using GMSK

27. PSD of GMSK signals BTb = 1.0 BTb = 0.5 BTb = 0.2 Increasing BTb
(f-fc)T
-10
-20
-30
-40
-50
-60
BTb =  (MSK)
BTb = 1.0
BTb = 0.5
BTb = 0.2
Increasing BTb
reduces signal spectrum
results in temporal spreading and distortion

28. containing % power as fraction of Rb
RF bandwidth
containing % power as fraction of Rb
BTb
90%
99%
99.9%
99.99%
0.2 GMSK
0.52
0.79
0.99
1.22
0.25 GMSK
0.57
0.86
1.09
1.37
0.5 GMSK
0.69
1.04
1.33
2.08
MSK
0.78
1.20
2.76
6.00
e.g. for BT = 0.2  99% of the power is in the bandwidth of 1.22Rb
[Ish81] BER degradation from ISI caused by GMSK filtering is
minimal at B3dBTb =
degradation in required Eb/N0 = 0.14dB compared to case of no ISI

29. BER of GMSK for AWGN channel
[Mur81] shown to perform within 1dB of optimal MSK with B3dBTb = 0.25
since pulse shaping causes ISI  Pe is function of B3dBTb
Pe =
Pe = bit error probability
 is constant related to B3dBTb
B3dBTb = 0.25   = 0.68
B3dBTb =    = 0.85 (MSK)

30. GMSK Transmitter GMSK Transmitter Block Diagram NRZ bits
(i) pass mNRZ(t) through Gaussian base band filter (see figure below)
- mNRZ(t) = NRZ bit stream
output of Gaussian filter passed to FM modulator
used in digital implementation for
- Global System for Mobile (GSM)
- US Cellular Digital Packet Data (CDPD)
(ii) alternate approach is to use standard I/Q modulator
GMSK Transmitter Block Diagram
NRZ bits
RF GMSK Output
Gaussian
LPF FM
Transmitter

31. RF GMSK signal can be detected using
GMSK Receiver
RF GMSK signal can be detected using
(i) orthogonal coherent detectors (block diagram)
(ii) simple non-coherent detectors (e.g. standard FM discriminators)
(i) GMSK Receiver Block Diagram-orthogonal coherent detectors
loop
filter
modulated IF
input signal
 /2
IF LO
clock
recovery 
demodulated
signal I Q

32. carrier recovery using De Budas method for (similar to Costas loop)
S’(t) = output of frequency doubler that contains 2 discrete frequency
components
- divide S’(t) by four: S’(t) /4
- equivalent to PLL with frequency doubler

33. De Budas method implemented using digital logic
2 D flip flops (DFF) act as quadrature product demodulator
XORs act as based band multipliers
mutually orthogonal reference carriers generated using 2 DFFs
VCO center frequency set to 4  fc ( fc = carrier center frequency)
demodulated
signal
clock
recovery
loop
filter
VCO
D Q C D
C Q
modulated IF
input signal
Logic Circuit for GMSK demodulation

34. Detecting GMSK signal by sampling output of FM demodulator
is a non-optimal, effective method
e.g.
Assume 0.25GMSK: B3dbTb = 0.25 & Rb = 270kbps
then
Tb = Rb-1 = 3.7us
B3dB = 0.25/Tb = kHz
Occupied Spectrum - 90% power  0.57Rb = 153.9kHz
- use table