lecture2.ppt

RFIC Design
Lecture 2:
newline
Modulation
and
demodulation

RFIC Design
2: Modulation and demodulation Slide 2
Outline
 Analog system
 Analog/Digital system
 AM,FM
 ASK, FSK, PSK

RFIC Design
Analog System

RFIC Design
Analog/Digital System

RFIC Design
Why modulation
 Antenna Issue
 Spectrum allocation (FCC)
 Bandwidth efficiency
 Against Noise
 Signal Quality

RFIC Design
Analog Modulation

RFIC Design
AM

RFIC Design
Amplitude Modulation
 Amplitude modulation

RFIC Design
Amplitude Modulation
 AM
– Sensitive to additive noise.
– Requires linear PA
( ) [1 ( )]cos
AM BB c
x t Ac mx t t

 

RFIC Design
AM Detector
 Coherent demodulation or Envelop detector
 The envelop of the modulated waveform does not
cross zero
( ) 1 ( )
AM BB
x t mx t
 

RFIC Design
DSC-SC

RFIC Design
DSC-suppress carrier
 Suppose ( ) cos
x x
x t A t



RFIC Design
DSC-SC Demodulation
 DSC-SC Demodulation
DSB-SC
demodulation :

RFIC Design
Angle Modulation
 FM & PM
( ) cos ( )
FM c c BB
x t A t m x t dt

 
 
 

 
( ) cos ( )
PM c c BB
x t A t mx t

 

RFIC Design
FM

RFIC Design
FM Modulator
 VCO can be a FM modulator
 phase is an integral form of frequency
 VCO frequency is determined by value of the
Inductor, which is modulated by XBB(t).
( ) cos ( )
FM c c BB
x t A t m x t dt

 
 
 


RFIC Design
Simple FM Demodulator
 Simple FM Demodulator :
– Differentiator
– High pass filter
 
   
1 1
( ) [ ( )]sin[ ( ) ]
out c c BB c BB
v t A R C mx t t m x t dt

RFIC Design
Quiz
 Why a high pass filter is a kind of differentiator?
 What will happen if driving a square wave to high
pass filter?
1 1
1 1
1/ 1
R R sC
Vout
Vin sC R R sC
 
 
•Electronics view :
•Mathematics view :

RFIC Design
FM Demodulation

RFIC Design
Narrow Bandwidth FM (1)
 If << 1 rad
( ) cos ( )
FM c c BB
x t A t m x t dt

 
 
 

, ( ) cos (sin ) ( )
FM NB c c c c BB
x t A t A m t x t dt
 
  
 ( )
BB
m x t dt

RFIC Design
Narrow Bandwidth FM (2)
 Single tone test , if 

( ) cos
BB m m
x t A t
( ) cos ( )
FM c c BB
x t A t m x t dt

 
 
 


RFIC Design
Narrow Bandwidth FM
 NBFM Spectrum

RFIC Design
FM spectrum
 Bessel Function
( ) cos
BB m m
x t A t


( ) cos[ ( / )sin ]
FM C C m m m
x t A t mA t
  
 
( ) ( )cos( )
FM C n C m
n
x t A J n t
  


 

m
m
mA



0 1
If << 1 rad
( ) 1
, ( ) Narrow Band FM
2
( ) 0 for 1
n
J J
J n


 





   



  

RFIC Design
FM spectrum
( ) ( )cos( )
FM C n C m
n
x t A J n t
  


 


RFIC Design
Carson’s rule
 Carson’s rule : If the bandwidth of FM ( ) is
defined as containing 98% signal power, the
following formula is derived
2( 1)
FM BB
BW BW

 
FM
BW

RFIC Design
Pre-emphasis of FM
 FM modulation is a low pass filter
 FM demodulation is a high pass filter
 In order to avoid amplifier the noise at high
frequency, a de-emphasis action will help to
suppress the high frequency noise.
mod

RFIC Design
Digital Modulation

RFIC Design
Digital Modulations
 ASK, PSK, FSK

RFIC Design
Digital Modulations
n
n
cos , if b 1
( )
0 ,if b 0
c
ASK
A t
x t
 

 


1 n
n
cos , if b 1
( )
cos 2 ,if b 0
FSK
A t
x t
A t




 


1 n
1 n
cos , if b 1
( )
cos ,if b 0
PSK
A t
x t
A t




 
 


RFIC Design
Constellation

RFIC Design
Digital demodulation
 Peak value sampling

RFIC Design
Digital demodulation
 Integration over one bit prior to sampling

RFIC Design
Optimal detection
 Implemented by Matched filter
 Input comes with an additive white noise n(t)
 To achieve a maximal input signal power or SNR for
input x(t) . The following formula is derived.
*
h(t)=p ( ) p( )
b b
T t T t
  

RFIC Design
Optimal detection
 Optimal detection using a correlator
  
  
  




  





b
0
( ) ( ) ( ) ,where h(t)=p(T ) for optimization
( ) ( )
( ) ( )
b
b b
T
y T x h T d t
x p d
x p d

RFIC Design
Optimal detection

RFIC Design
ASK modulation

RFIC Design
ASK
 The simplest form of bandpass data modulation is Amplitude Shift
Keying (ASK).
 In binary ASK, where only two symbol states are needed, the carrier is
simply turned on or off.
 ASK is sometimes referred to as ON-OFF Keying (OOK).

RFIC Design
Symmetry in ASK
 Consider a single frequency component, cos (wmt), from within the
baseband spectrum, and perform the mathematical multiplication with
the carrier, cos (w c t), the modulated signal becomes:
 cos (wmt) x cos( w c t) = 0.5 cos (w c – wm)t + 0.5 cos (w c + wm)t
 The modulated spectrum for this sample component becomes two
identical components symmetrically as AM.
Single tone test

RFIC Design
ASK data spectrum
 This ASK spectrum is a double sideband spectrum
 It has an upper and lower sideband with respect to the carrier.
 If we now include all the components in the baseband stream which will
mix with the carrier to generate a frequency sum(+) and difference(-)
component,
then 1. resulting spectrum is symmetrical about the carrier frequency
then 2. spectrum is with a positive and reversed image of the baseband
'sinc' spectrum for an unfiltered binary data stream.
Data stream in

RFIC Design
ASK Spectrum
 What would ASK spectrum look like ?
– Is it only a Sinc-shaped function?

RFIC Design
Spectrum of a data pulse
 The spectrum of a single pulse is a Sinc function

RFIC Design
Spectrum of pulse train
 Sampling in time domain will cause baseband
spectrum repeated periodically.
 Sampling in frequency domain will cause the pulse
waveform in time repeated periodically.

RFIC Design
Factors affecting signal bandwidth
 Reducing the width of the pulse but keeping the
period of the waveform constant results in
– the lower harmonic levels
– an increase in the level of the higher harmonics

RFIC Design
Impulse train
 What should the impulse train look like?

RFIC Design
Smooth transition
 Because the sharp changes in
waveform can only be constructed
from a large number of low-level
high frequency sinusoids in a
Fourier series expansion.
 So a waveform which has sharp
transitions in the time domain will
have a higher harmonic content
than smooth transitions.
 Hence, modulation that possess
smooth pulse shapes between
symbol states are to be favored
when bandwidth is limited.

RFIC Design
Nyquist filters
 A commonly used pulse-shaping method is to pass
the data stream through a low pass filter having a
raised cosine response.
 The raised cosine filter belongs to a family of filters
called Nyquist filters .
 It also reduces ISI problem.

RFIC Design
Spectrum of Data stream
 Fourier Series Expansion

RFIC Design
Generation of ASK modulated signals
 A simpler alternative, particularly for binary ASK, is
to use a switch to gate the carrier on and off, driven
by the data signal.

RFIC Design
Baseband filtering method
 Where can we put the filter to reduce spectrum?
– Before the Mixer or after the Mixer?
 Using a low pass (root raised cosine) filter.

RFIC Design
Bandpass filtering method
 In order to minimize the occupied bandwidth of the
transmitted ASK signal, filtering or pulse shaping is required
either prior to or after modulation onto a carrier.
 The switching method of ASK generation does not allow any
pre-filtering of the modulating baseband symbol stream, as
the switch is a non-linear process

RFIC Design
Non-coherent detection
 ∵With ASK, the information is conveyed in the amplitude or
envelope of the modulated carrier signal.
∴ the data can thus be recovered using an envelope detector.
 An simplest envelope detector comprises a diode rectifier and
smoothing filter
– non-coherent detector.

RFIC Design
Non-coherent detection
 If quadrature versions of the modulated carrier signal are available in
the receiver, that is,a(t) cos wct and a(t) sin wct (where a(t) represents
the data imposed amplitude modulation).
 Mathematically we get:
a(t)2 cos2wct + a(t)2 sin2wct
= a(t)2 (cos2wct + sin2wct) = a(t)2

RFIC Design
ASK Coherent detection
 Representing the modulated data signal as a(t) cos wct and the
reference carrier as cos(wct + q) , the mixer output becomes:
a(t) cos wct cos(wct + q)
= 0.5 a(t)cos(q) + 0.5 a(t)cos(2wct + q)
 If the carrier is phase coherent with the incoming modulated
carrier signal (that is, there is no frequency or phase difference
between them, q = 0o), then
the output is proportional to a(t) and perfect detection is
achieved.

RFIC Design
ASK Coherent detection
 If q = 90o, then cos(90o) = 0 and no output is obtained!
 It is thus essential to ensure that the carrier oscillator in the
receive modem unit is in some way phase-locked to the carrier
oscillator in the transmitter modem.
 Although coherent detection appears much more complicated
than non-coherent detection, it is able to recover the data
signal more accurately in the presence of noise.

RFIC Design
Carrier recovery for ASK
 It is beneficial to use coherent detection of ASK
 means of recovering the carrier frequency and
phase from the incoming data signal is needed.
 A technique that is well suited to this task is the
phase-locked loop (PLL)
 Issues:
– input referred noise
– Off state

RFIC Design
Coherent Matched filter
 Matched filtering of baseband data signals is for
optimizing the signal to noise ratio at the output of
a data receiver.
 Matched filtering is applicable to bandpass
modulation detection.
 A matched filter pair such as the root raised cosine
filters can thus be used to
– shape the source and
– received baseband data
symbols in ASK,

RFIC Design
Symbol timing recovery
 Pulse shaping for minimum inter symbol interference
highlighted the need for accurate
timing of the sampling point within each symbol.
 A common symbol timing circuit is
the early-late gate synchronizer.
 This circuit works on the basis that the optimum
point to sample the signal at the output of a matched
filter detector is when the signal is at its maximum.

RFIC Design
Symbol timing recovery
 early-late gate synchronizer

RFIC Design
vector diagram
 view the phasor or vector diagram representation of
ASK
 A vector diagram maps the amplitude of a signal by
the length of the line on the vector diagram, and
maps the instantaneous phase by the angle of the
line with respect to a horizontal reference frequency
and phase

RFIC Design
Coherent detection vs
non-coherent detection
 Let us now consider the case of detecting the ASK signal in the
presence of noise. For simplicity we will assume that the carrier
is in the 'off' state and that we have a specific noise component
of length N and phase 60 degree
 The non-coherent detector,
– which is performing amplitude detection, is simply
measuring the length of the composite (ASK + Noise)
vector regardless of the vector phase. It would thus produce
an output voltage proportional to N, the noise vector length.
 The coherent detector,
– acts by mixing the incoming signal with the reference carrier
cos wt. The result is that the voltage at the detector output
due to the noise is reduced by a factor cos(60o) = 0.5 and
is thus proportional to N/2.

RFIC Design
Coherent detection vs
non-coherent detection
 On average, the coherent detection method reduces
the noise voltage out of the detector by a factor of
root 2 and the noise power by 2.
 In other words, coherent detection of ASK can
tolerate 3 dB more noise than non-coherent ASK for
the same likelihood of detection error.

RFIC Design
BER performance of ASK
 The Eb/N0 value is for the average symbol power which is 3 dB less
than the peak symbol power for ASK (the carrier is off for
approximately half of the transmitted symbols).

RFIC Design
FSK

RFIC Design
FSK
 Simple both to generate and to detect
 An important property of FSK is that
the amplitude of the modulated wave is constant.

RFIC Design
FSK generation
 FSK can be generated by switching between distinct
frequency sources.
 Any phase discontinuity at the symbol boundary will
result in a much greater prominence of high
frequency terms in the spectrum

RFIC Design
FSK generation
 FSK can be realized by applying the data signal to a
voltage controlled oscillator (VCO) .
 The phase transition between consecutive symbol
states is guaranteed to be smooth (continuous).
 FSK with no phase discontinuity between symbols is
known as a Continuous Phase Frequency Shift
Keying (CPFSK) format.

RFIC Design
Vector modulator
 Vector modulator or quadrature
(正交) modulator
 To generate FSK requires the
generation of two symbols, one at
a frequency (c + 1) and one at
a frequency (c – 1).
 In order to generate a frequency
shift of + 1 at the output of the
vector modulator, the I and Q
inputs need to be fed with
+/-cos 1 and sin 1, respectively.
sin（α＋β）＝sinαcosβ＋cosαsinβ
sin（α－β）＝sinαcosβ－cosαsinβ

RFIC Design
Spectrum of FSK
 The spectrum of the FSK signal is not as easy to
derive as that for ASK because the FSK generation
process is non-linear.
 An approximation can be obtained by plotting the
spectra for two ASK streams centered on the
respective carrier frequencies

RFIC Design
Noncoherent FSK Detection
 More widely used in RF design owing to their lesser
complexity.

RFIC Design
PLL-based FSK detection
 VCO control voltage must change in order for the
PLL to track and lock onto a new input frequency.
 It provides a direct measure of the input signal
frequency for each symbol in the FSK stream.

RFIC Design
FSK Coherent Detection
 Coherent detection schemes require
phase synchronization
 Coherent detectors are usually based on the
matched filter concept
 Providing a lower BER than noncoherent

RFIC Design
BER

RFIC Design
Comparison
 Advantages of FSK
– FSK is a constant envelope modulation, and hence
insensitive to amplitude (gain) variations in the channel
– Compatible with non-linear transmitter and receiver
systems.
– The detection of FSK can be based on relative frequency
changes between symbol states and thus does not require
absolute frequency accuracy in the channel.
– (FSK is thus relatively tolerant to local oscillator drift and
Doppler shift.)
 Disadvantages of FSK
– FSK is slightly less bandwidth efficient than ASK or PSK
(excluding MSK implementation).
– The bit/symbol error rate performance of FSK is worse than
for PSK under the same SNR.

RFIC Design
PSK

RFIC Design
PSK
 PSK
 Differentially Coherent PSK (DPSK).

RFIC Design
PSK generation
 The simplest means of realizing unfiltered binary
PSK is to switch the sign of the carrier using the
data signal, causing a 0 or 180 degree phase shift.
 Just as for ASK, this method of generation is not
well suited to obtaining a Nyquist filtered waveform.
– Owing to the difficulty in implementing bandpass
high frequency, high Q filters.

RFIC Design
PSK generation
 If filtering is required, then linear multiplication must
be employed.
 The data stream to be pre-shaped at baseband prior
to the modulation process.

RFIC Design
PSK Detection
 There is no non-coherent equivalent detection process for PSK,
 We need zero phase error for optimum detection and must re-
visit the whole area of carrier recovery.
 Note that if the phase error reaches 90 the output falls to zero!

RFIC Design
Coherent BPSK

RFIC Design
Binary Modulation
 Binary Modulation
0
2 d
E
SNR
N

2
1 2
[ ( ) ( )]
d
E p t p t dt


 


RFIC Design
carrier recovery

RFIC Design
The Costas loop
   
1
sin cos sin sin
2
     
 
   
 
   
1
cos sin sin sin
2
     
 
   
 
   
1
cos cos cos cos
2
     
 
   
 
   
1
sin sin cos cos
2
     
 
    
 
9

RFIC Design
The Costas loop
 If qi-qo > 0 , then input of VCO will increase to trace
qi.
 Otherwise, it will operate inversely.
 Behave like a phase lock loop.
 LPF is used to enhance the stability of close loop.
Sin(qi-qo)
Vcoin
Enhance close loop
stability
9

RFIC Design
Differential data coding
 FSK is possible to determine the frequency
corresponding to each bit.
 However, the phase of PSK relates to the time origin
and has no “absolute” meaning.
 Both Costas loop and squaring circuit suffer from
phase ambiguity.
 Training sequence in the head of packet is a
possible solution.
 Differential data coding : If the information lies in the
phase change from one bit to the next , then a time
origin is not required.

RFIC Design
Excusive NOR
1
X
X
0
X
X
0
X X
1
X
X
 For XNOR
– If one of the input is 0, XNOR performs inverting
– If one of the input is 1, XNOR performs passing
 XOR Equation : Y = AB + AB

RFIC Design
Differential data encoding
 Differentially Encoded.
 If the present input bit is a ONE, then the output
state of encoder does not change

RFIC Design
Excusive NOR
1
0
1
0
1
1
1
1 1
0
1
0
 For XNOR
– If one of the input is the same, XNOR output 1.
– If one of the input is different , XNOR output 0.

RFIC Design
Differential data decoding
 If the now state is the same as the previous stat of
input, then decoder outputs ONE.
 What if the encoded Data are inverted?
 Or the first bit is ambiguous?

RFIC Design
Differential PSK (DPSK)
 Differential PSK (DPSK) is based on the same differential
encoding technique as used in DEPSK.
 Mixer or Multiplier behaves like a XNOR
 
 

 
1 1
1 1
if cos( ) cos( ),after filtering it output 1
if cos( ) cos( ),after filtering it output -1
t t
t t

RFIC Design
Differential PSK (DPSK)
 It improves upon it by incorporating the differential decoding
task as part of the data demodulation task.
 It does away with the need for a 'carrier recovery' mechanism .
 It rolls 'coherent detection' and 'differential decoding' into one
operation.
 Clearly, this detection process is much simpler than that
required for true coherent PSK.
 DPSK is widely used in wired and radio modems for medium-
rate signalling (up to 4800 bps).
 DPSK, however, has a slightly poorer noise immunity than PSK
since the phase reference for DPSK is now a noisy delayed
version of the input signal rather than potentially a well-filtered,
virtually noiseless reference from a carrier recovery process.

RFIC Design
BER & SNR

RFIC Design
Noise
Time average of mean
Statistical average
  ( )
n
n E n n P n dn


  


RFIC Design
Probability Density Function
 The PDF is defined as : Px(x)dx=probability that the
amplitude is between x and x+dx.
 Note that PDF does not tell us how fast the
waveform varies, that means no frequency relativity.

RFIC Design
Gaussian distribution
 Central Limit Theorem : If many independent
random process with arbitrary PDFs are added, the
PDF of the sum approaches a Gaussian distribution
 Gaussian PDF:
where and m are the standard deviation and the
mean,respectively.
 Remember that 68% for the sampled values fall
between m- and m+ and
99% between m-3 and m+3
2
2
1 ( )
( ) exp
2
2
x
x m
p x

 
 


 
 

RFIC Design
Power Spectral Density
 The PSD, Sn(f), of a random signal x(t) indicates
how much power the signal carries in a small
bandwidth around frequency f.

RFIC Design
PDF and PSD
 PDF is statistical indication of how often the
amplitude of a random process falls in a given range
of values.
 PSD shows how much power the signal is expected
to contain in a small frequency interval.
 In general, the PDF and PSD bear no relationship.
 Thermal noise has a Gaussian PDF and white PSD.
 Flicker noise the same type of PDF but a PSD
proportional to 1/f.

RFIC Design
PDF of Binary Modulation

RFIC Design
BER calculation
 
  1
( )/ n
set u A







   2 1
2
1 ( )/ 2
1
2 exp
2
2
n
e e A A
p p d


 2 1
( )
2 n
A A
Q
1 2
2
1
1 2
( )/ 2 2
( )
1 1
exp
2 2
2
e A A
n
u A
p du




 
 

 

2
1
Q(x)= exp
2
2 x
u
du



2
1
exp
2
x 2
x
Q function is also called erfc function, which is
equal to ( 1-erf(x) )

RFIC Design
BER calculation
 It demonstrates that BER is only concerned with SNR
 To gain a max SNR , E must be maximized too.
 
 
2
2 1
2 1
2
0
( ) ( )
2 2
2
e
n n
A A
A A E
p Q Q Q
N
 
 

  
  
 
 
2
2 1
2
0
( )
where,
/ 2
n
A A E
SNR
N


 

RFIC Design
BER of Match filter
 It has been proved that Match filter has a maximum
 For a differential signal, it has been proven that
2
[ ( )] , is called the energy of the signal.
P P
where E p t dt E


 
max
0 /2
P
E
SNR
N

max
0 /2
d
E
SNR
N

2
1 2
[ ( ) ( )]
d
where E p t p t dt


 

,min
0
( )
2
d
e
E
p Q
N

d,Max 1 2
E when p (t)=-p (t)

RFIC Design
Coherent BPSK

RFIC Design
Coherent BPSK


 

2
1 2
according to [ ( ) ( )]
Ed p t p t dt




2
0
2
(2 cos )
2
b
T
C c
c b
A t dt
A T
 
 

 
 
2
0
Hence c b
e
A T
P Q
N

 

2
2
b 0
E ( cos )
2
b
T
c b
C
A T
A t dt
 
  
 
 
0
2
Hence b
e
E
P Q
N
Large Ac&Tb cause low Pe

RFIC Design
Coherent FSK

RFIC Design
Coherent FSK
 For the orthogonal set, we must have
 
   
   
  

 
 
 
  
1 2
For 1+ 2 >> 1- 2
sin( 1- 2) /( 1- 2) 0
( 1- 2)
1
1- 2 or
2
b
b
b b
T
T n
f f
T T
1 2
0
cos cos 0
b
T
t tdt
 
 


RFIC Design
Coherent FSK


 

2
1 2
according to [ ( ) ( )]
Ed p t p t dt




  
 
  


2 2
1 1 1 2
1 1
2 2
1 2
2 2 2
[ ( ) 2 ( ) ( ) ( )]
& are orthogonal
= [ ( ) ( )]
1 1
2 2
C b C b C b
p t p t p t p t dt
p p
p t p t dt
A T A T A T
 
   
 
  
   
   
 
   
 
2
0 0 0
Finally,
2 2
d C b b
e
E A T E
P Q Q Q
N N N

RFIC Design
Coherent FSK
 For a given probability of error and noise density, the
bit energy in BFSK must be twice that in BPSK.
 The minimum distance between the points in the
constellation is greater in BPSK.
 Recall that SNRmax=2Ed/N0, the value of Ed reach
its maximum if p1(t)=-p2(t), which is the case for
BPSK.
 BPSK has a 3-dB advantage over BFSK
 However, BFSK is widely used in low data rate
application where Eb can be maximized by allowing
a long Tb.

RFIC Design
Quadrature Modulation
 It is often beneficial to subdivide a binary data
stream into pairs of two bits and perform the
Quadrature modulation:

RFIC Design
Quadrature Modulation
 Quadrature modulation encompasses two broad
categories:
– Quadrature Phase Shift Keying (QPSK),
– Minimum Shift Keying (MSK)
QPSK

RFIC Design
QPSK

RFIC Design
QPSK
 QPSK has more adjacent point with smaller minimum distance
 It can be proved that BPSK and QPSK have nearly equal
probabilities of error of

0
( 2 / )
e b
P Q E N

( ) cos( / 4), ( ) cos
QPSK c c BPSK c c
x t A t k x t A t
  
   
( ) ( / 2)cos( ) ( / 2)sin( )
QPSK c c c c
x t A t A t
 
  

RFIC Design
Phase transition
 Large phase (maximum 180 degrees) changes
occurs at the end of each symbol.
 Large phase transition causes large envelope
variation.(180 degree cross zero is worst).
 Such transition needs a linear power amplifier

RFIC Design
OQPSK
 Offset QPSK remedies the drawback of QPSK
 The bit error rate and spectrum of OQPSK are
identical to those of QPSK
 Offset QPSK (OQPSK) delays one of the bit streams
after serial parallel conversion:

RFIC Design
OQPSK
 Thus, A and B cannot simultaneously change state.
 a smoother transition here relaxes the linearity
requirement of the power amp.
 Maximum phase change is 90 degrees.

RFIC Design
/4 QPSK
 The signal set consists of two QPSK schemes, one
shifted by π/4 with respect to the other:
 The spectrum and BER of it are identical to those of
QPSK

RFIC Design
/4 QPSK

RFIC Design
/4 QPSK
 Maximum phase change is 135 degree

RFIC Design
Envelop variation of QPSK
 Quadrature Phase Shift Keying can be filtered using
raised cosine filters to achieve excellent out of band
suppression.
 Large envelope variations occur during phase
transitions, thus requiring linear amplification.

RFIC Design
Envelope of PSK
 Bandlimiting Effect on the Envelope of PSK

RFIC Design
Spectrum regrowth
Non-linear
Amplifier

RFIC Design
MSK
 QPSK-series all suffer from a large phase change
when bit stream are transferred.
 large phase change leads to a wide spectrum.
 QPSK-series also presenting difficulties in the
design of power amplifiers.
 MSK is designed to solve this problem.It is a kind of
continuous phase modulation schemes.

RFIC Design
Spectrum Comparison
 MSK (or GMSK) has wider but sharper baseband
spectrum

RFIC Design
MSK Generation
 From the view of frequency. MSK is a subset of FSK,
which satisfies the following condition:
 
Hence, phase change is within one b
f T T
   0.5
b
f T

RFIC Design
MSK Generation
 From the view of phase
 Within 1 Tb , C or D has 90 phase change and x(t)
experiences 180 phase change.

RFIC Design
MSK Generation
 MSK modulation by Quadrature modulation:
 Note that am changes only at (2k+1)Tb and am+1
changes at (2k * Tb )
 For examples, am+1 goes from +1 to –1 and am are 1.
Please recall trigonometric function

    

  
1 1 1 1
( ) cos cos sin sin ,where
2
MSK m c m c
b
y t a t t a t t
T
 
1 1
(2 1) 1 1 1
(from Tb to 2Tb) 1
( ) goes from cos( ) to cos ( )
set (2 1)
( ) ( ) 2 2 0
2
(2Tb-Tb) = - 90
2
c c
b
t k Tb c c b
b
o
y t t t
t K T
t t t T
T
    

          

 
 
  
 
                 
    

RFIC Design
MSK
 MSK exhibiting the same error rate as QPSK with
sharper decay in its spectrum than the retangular-
pulse QPSK family.
 The smooth phase transitions in MSK lower the
signal power in the sidelobes of the spectrum
 But widens the main lobe.
 MSK spectrum has a decay proportional to
4
f

RFIC Design
Phase change
 Phase change of MSK and GMSK
– All continuous in phase domain
– MSK is discontinuous in frequency domain

RFIC Design
GMSK
 Generation of GMSK signal

RFIC Design
Gaussian filter
 In MSK , the BT is infinity and this allows the square
bit transients to directly modulate the VCO.
 BT is 3dB bandwidth symbol time product
 If BT is less than 0.3, some form of combating the
ISI is required.

RFIC Design
GMSK
 Lowe BT
– Narrow BW
– Sever ISI Problem

RFIC Design
Reference
 B. Razavi, “RF Microelectronics,” Upper Saddle
River: Prentice-Hall,1998.
 Andy Bateman, “Digital Communications: Design for
the Real World,” Addison-Wesley.

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