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Modulation Techniques for Mobile Radio
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Modulation is the process of encoding the
baseband or source information (voice, video,
text) in a manner suitable for transmission.
It generally involves translating a base band
signal (or source) to a band pass signal,
centered at a high carrier frequency.
Demodulation is the process of extracting the
base band message from the carrier.
Modulation Techniques
Modulation
Analog Modulation
(First Generation (1G)
Mobile Radio)
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Digital Modulation
(2G, 3G and 4G
systems)
Review of Analog Modulation Techniques
Amplitude Modulation (AM)
• Message Signal -• Carrier Signal -• AM Signal
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m(t)
Ac cos(2πfc t)
-- SAM (t) = Ac [1+m(t)]cos(2fc t)
AM Spectrum
S AM (f) = 0.5A [ (f - f ) + M(f - f ) + (f + f ) + M(f + f )]
c
Carrier
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c
Sidebands
c
c
c
AM Parameters
• Modulation Index
-- k= A / A  1
m
c
• Bandwidth
--
BAM = 2 fm
• Total Power in AM Signal
PAM = 0.5A 2 [ 1 + 2 <m(t)> + <m2 (t)> ]
c
• Power in the carrier
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--
Pc = Ac 2 / 2
Single Singleband AM Signal
Lower Sideband
S SSB
 A c [m(t)cos(2fc t)  m(t)sin(2fc t)]
Upper Sideband
Where the Hilbert transform is defined as:
m(t)  m(t)  h(t)
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;
h(t)  1/ t
SSB Generation
Filter Method

Baseband Filter
m(t) A cos(2f t)
c
c
SSSB (t)
Baseband filter passes upper or lower sidebands
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Balanced Modulator

Carrier fc
m(t)
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-90o phase shift
∑
90o

SSSB (t)
Properties of SSB
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Bandwidth of SSB is very efficient = fm
.However, Doppler spreading and Rayleigh
fading can shift the signal spectrum, causing
distortion.
Frequency of the receiver oscillator must be
exactly the same as that of the transmitted
carrier fc. If not, this results in a frequency
shift fc f, causing distortion.
Pilot Tone SSB
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Transmit a low level pilot tone along with
the SSB signal.
The pilot tone has information on the frequency
and amplitude of the carrier.
The pilot tone can be tracked using signal
processing FFSR - Feed Forward Signal
Regeneration.
TTIB (Transparent Tone In-Band) System
a

~
b


m(t)
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a

~
c
f1
~
d
e

~
f2

f
a
b
c
f1
d
e
f
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f2
BW  f 2  f 1
frequency
Properties of TTIB system
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Base band signal is split into two equal width
segments.
Small portion of audio spectrum is removed and
a low-level pilot tone is inserted in its place.
This procedure maintains the low bandwidth of
the SSB signal.
Provides good adjacent channel protection.
Demodulation of AM signals
• Coherent Modulation
• Non-coherent demodulation
• Envelope Detectors
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Demodulation of AM signals
Coherent Modulation
SAM  R(t)cos(2fc t  r )

A o cos(2fc t  o )
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LPF
VOUT (t)  0.5A oR(t)cos(r  o )
Frequency Modulation
• Message Signal
– m(t)
• FM Signal – S (t)  A cos[2f t  2k
FM
C
c
• Power in FM Signal – PFM  A c / 2
2
t
f
 m(t)dt]

• Frequency modulation
index
–   k A / W  f / W
f
f
M
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W = Highest frequency component in message signal
AM = Peak value of modulating signal
Phase Modulation
• PM Signal
SPM (t) = Ac cos[2 fc t +k m(t)]
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• Phase Modulation Index
  k  A M
• Power in PM signal
PPM  A c 2 / 2
• Bandwidth
BT  2f
FM methods
FM Modulation
 Direct Method – VCO
 Indirect Method – Armstrong
FM Detection
 Slope Detection
 Zero Crossing Detection
 PLL Detection
 Quadrature Detection
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Comparison between AM and FM
FM
AM
•FM signals are less noisy, •AM signals are more noisy,
because amplitude of signal amplitude cannot be limited
is constant
•The modulation index can
be varied to obtain greater
SNR(6dB for each doubling
in bandwidth)
•FM signals occupy more
bandwidth (good for audio)
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•Modulation index cannot
be changed automatically.
•AM signals occupy lesser
bandwidth (good for video)
Digital Modulation
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VLSI and DSP promoted the advent of Digital
Modulation
Low noise
Easier multiplexing of information (voice, data,
video)
Can accommodate digital transmission errors,
source coding, encryption and equalization.
DSP can implement digital modulators,
demodulators completely in software.
Basics of digital communications
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In digital communication systems, the
message) is represented as a time sequence of
symbols or pulses.
Each symbol has m finite states
Number of bits required for m states:
n = log2m bits/symbol
Shannon’s bandwidth theorem
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Bandwidth efficiency B = R / B bps/Hz
R=Data rate in bits/second
B=Bandwidth of modulated RF signal
Shannon's formula:
Bmax = C/B = channel capacity (bits/s)
RF bandwidth
= log2(1 + S/N)
S/N = Signal to Noise ratio
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Practical digital systems
For US digital cellular standard, R = 48.6 kbps
RF bandwidth = 30 KHz
For SNR 20 dB => 100
C = 30000 * log2(1 + S/N)
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= 30000 * log2(1 + 100) = 199.75 kbps
For GSM standard, R = 270.833 kbps
C = 1.99 Mbps for S/N = 30 dB
Line Coding
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Line codes are used to provide particular spectral
characteristics of a pulse train.
Line codes provide the pulses to represent 0s
and 1s.
Line codes can be:
o Return-to-zero (RZ)
o Non-return-to-zero (NRZ)
Line codes are Unipolar (0,V) or Bipolar (-V, V )
1
0
Unipolar NRZ
1
V
0
Unipolar RZ
V
Bipolar NRZ
-V
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1
0
Pulse Shaping Techniques
Bandlimited
Channel
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ISI – Inter Symbol Interference  errors in
transmission of symbols
Pulse shaping techniques reduce the intersymbol effects
Pulse shaping filters
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Raised cosine filter
hRC (t)
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sin(t/Ts ) cos(at/Ts)

[
]
2
(t/Ts ) (1 4at/2Ts)
As the value of a (roll-off factor) increases, the
bandwidth of the filter also increases
As the value of a (roll-off factor) increases, the
time sidelobe levels decrease.
Implementation of raised-cosine filter
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Use identical [HRC (f)]1/2 filters at transmitter and
receiver
Symbol rate possible through raised cosine filter
Rs  1/ Ts  2B/(1  a)
where B is the filter bandwidth
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Types of Digital Modulation
Linear
Non-Linear
Amplitude of
Amplitude of
transmitted signal
carrier is constant
varies linearly with
message signal m(t)
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Spread
Spectrum
Transmission
bandwidth >>
signal
bandwidth
Low bandwidthallows more users
High bandwidth – More usersLow noise
high bandwidth
Example systems:
BPSK, QPSK
FSK, GMSK
W-CDMA,
cdma 2000
Linear digital modulation
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PSK or Phase Shift Keying of carrier:
SPSK = A cos(wt + fk)
fk = 0,  (BPSK)
fk = 0, /2, , 3/2 (QPSK)
fk = 0,/4,/2,3/4,,5/4,3/2,7/4 (0PSK)
Constellation Diagram
Q(Quadrature)
I (In Phase)
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Properties of BPSK and QPSK
BPSK
BW = 2 RB = 2 / TB
Pe,QPSK = Q[√(2 EB / N0)]
RB – Bit rate, TB – Bit period
EB – Energy/bit, N0 – Noise spectral density
 QPSK
BW = RB = 1 / TB
Pe,QPSK = Q[√(2 EB / N0)]
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Nonlinear or envelope modulation
Frequency shift keying
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The frequency of a constant amplitude carrier
signal is switched between 2 values ( 1 and 0)
SFSK  Vh (t)  (2Eb / Tb ) cos[2fc  2f]t,0  T  Tb
1/ 2
SFSK  Vi (t)  (2Eb / Tb ) cos[2fc  2f]t,0  T  Tb
1/ 2
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Properties of FSK
Transmission Bandwidth
BT = 2f + 2B
B = Bandwidth of digital base-band signal
 If a raised cosine pulse-shaping filter is used
BT = 2f + (1 + a)R
 Probability of error
1/2
Pe,FSK = Q[(EB / N0) ]
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Spread Spectrum Modulation techniques
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Spread spectrum techniques employ a
transmission bandwidth >> signal bandwidth
The system is inefficient for a single user, but
is efficient for many users
Many users use the same bandwidth without
significantly interfering with one another
Principle of spread spectrum
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Spread spectrum signals are pseudo random,
and spreading waveform is controlled by a PN
(pseudo – noise) sequence or code.
Spread spectrum signals are demodulated at
the receiver by cross correlation (matching)
with the correct PN sequence.
Advantages of spread spectrum techniques
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PN codes are approximately orthogonal, and
the receiver can separate each user based on
their codes.
Resistance to multi-path fading, because of
large bandwidths and narrow time widths.
PN Sequences
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Pseudo Noise or Pseudo random sequence is
a binary sequence of 1s and -1s
PN sequences are generated by using
sequential logic circuits
Very low cross correlation exists between any
two PN sequences
High cross correlation exists between
identical PN sequences
Frequency Hopped Spread spectrum (FHSS)
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A frequency hopping signal periodically
changes the carrier frequency in a pseudorandom fashion. The set of possible carrier
frequencies is called a hopset.
Bandwidth of channel used in hopset 
Instantaneous bandwidth B
Bandwidth of spectrum over which the hopping
occurs  total hopping bandwidth Wss
Methodology of FHSS
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Time duration between hops  hopping period
Ts
Data is sent by hopping the transmitter carrier
to seemingly random channels
Small bursts of data are sent using
conventional narrow band modulation before
T/R hops again
Hit -> Two users using the same frequency
band at the same time
Frequency Hopping Modulator
Modulator
DATA
Oscillator
Code Block
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
Frequency
Hopping
Signal
Frequency
Synchronizer
PN Code
Generator
Frequency hopping demodulator
Wideband
Filter
Frequency
Hopping
Signal
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
BP Filter
Demodulation
DATA
Frequency
Synthesizer
PN Code
Generator
Synchronization
System
Properties of FHSS
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Fast frequency hopping
More than one frequency hop during each
transmitted symbol
-> Hopping rate ≥ symbol rate
Slow frequency hopping
Hopping rate < symbol rate
Parameters of FH-SS
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Probability of error for BPSK Spread Spectrum
Pe = 0.5 x e -Eb/ 2N0 x (1 – ph ) + 0.5 ph
ph = probability of hit = 1 – (1 – 1/M)K-1
M = number of hopping channels
K = Total number of users
Processing gain = Wss / B
Direct Sequence Spread Spectrum (DSSS)
code
C1
C2
CN
time
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frequency
Properties of Message Signal
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m(t) is a time sequence of non-overlapping
pulses of duration T, each of which has an
amplitude (+/-) 1.
The PN waveform consists of N pulses or chips
for message symbol period T.
NTC = T
where TC is the chip period.
Example:
N=4
1
-1
1
-1
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PN Wave for N =4
DSSS Transmitter
S1(t)
m1 (t)
PN1(t)
cos(2fc t  1 )
k
mk(t)
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1
PNK (t)
cos(2fc t  k )

r(t)
Principles of transmitter operation
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The narrowband message signal mi(t) is
multiplied by a pseudo noise code
sequence that has a chip rate >> data rate
of message.
All users use the same carrier frequency
and may transmit simultaneously. The kth
transmitted signal is given by:
Sk (t)  (2Es / Ts )1/ 2mk (t)pk (t)cos(2fc t  k )
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CDMA Receiver
k
Zi (t)
(.)dt
r(t)
PNK (t)
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cos(2fc t  k )


mk (t)
Principles of receiver operation

At the receiver, the received signal is
correlated with the appropriate PN sequence
to produce desired variable.
Z i1 (t) 
iT 1

(i 1)T 1
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r(t)p1 (t  1 )cos[2fc (t  1 )  1 ]dt
Correlator output for ith user
Z i1 (t) 
iT 1

r(t)p1 (t  1 )cos[2fc (t  1 )  1 ]dt
(i 1)T 1
•The multiplied signal will be p2(t) = 1 for the
correct signal and will yield the dispersed signal
and can be demodulated to yield the message
signal mi(t).
S1(t)  (2Es / Ts ) m1(t)p1(t)cos(2fc t  1)
1/ 2
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Parameters of DSSS
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Probability of bit error
Pe = Q {1/ [(K –1)/3N + (N0/2Eb)]1/2}
K = Number of users
N = Number of chips/ symbol
When Eb/No  
Pe = Q{[3N/(K-1)]1/2 }
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Important Advantages of CDMA
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Many users of CDMA use the same frequency.
Either TDD or FDD may be used.
Multipath fading may be substantially reduced
because of large signal bandwidth.
There is no absolute limit on the number of
users in CDMA. Rather the system
performance gradually degrades for all users as
the number of users is increased.
Drawbacks of CDMA
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Self-jamming is a problem in a CDMA system.
Self-jamming occurs because the PN
sequences are not exactly orthogonal.
The near- far problem occurs at a CDMA
receiver if an undesired user has high detected
power as compared to the desired user.
Modulation performance in fading channels
Fading Channel
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s(t)
r(t)
r(t) = a(t) e-j(t) s(t) + n(t)
a(t) = gain of the channel
(t) = phase shift of the channel
n(t) = additive gaussian noise
Average signal to noise ratio at receiver
 = (EB / N0) a2
Probability of error in fading channels

Probability of error

Pe   Pe (X)p(X)dX
0
Pe (X)= Probability of error for parent
modulation, such as BPSK, FSK
p(X) = pdf of x due to fading channel
= (1/ )exp( x / ),x  0
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Pe (X) and Pe for different systems
Coherent binary PSK
Pe (X)  Q[(2EB /N0 ) ]
1/ 2
Pe  0.5[1  /(1 )]
Coherent binary FSK
Pe (X)  Q[(EB /N0 ) ]
1/ 2
Pe  0.5[1  /(2  )]
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Differential Binary PSK
Pe (X)  0.5exp[(EB /N0 )]
Pe  [0.5/(1  )]
Non-coherent orthogonal binary FSK
Pe (X)  0.5exp[(EB / 2N0 )]
Pe  [0.5/(2  )]
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Coherent GMSK
Pe (X)  Q[(2EB )]
Pe  0.5{1  [  /(  1)]
1/ 2
 1/ 4
=0.68, BT = 0.25,  = 0.68
=0.85, BT = ,  = 0.85
BT = Bandwidth – bit duration product for GMSK
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