EE5713 : Advanced Digital Communications
Week 6:
Bandpass Modulation
MPSK
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MPSK
MASK, OOK
MFSK
� In-phase and Quadrature (I&Q) Representation
– Any bandpass signal can also be represented as
• x(t) is a real-valued signal called In-phase (I)
• y(t) is a real-valued signal called Quadrature (Q)
)sin()()cos()()( 00 ttyttxts ωω −=
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– This is often a convenient form which
• Emphasizes the fact that two signals may be transmitted within the same bandwidth
• Closely parallels the physical implementation of the Tx/Rx
Concept of a constellation diagram
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Digital Modulation Schemes
� Basic Digital Modulation Schemes:
– Amplitude Shift Keying (ASK)
– Frequency Shift Keying (FSK)
– Phase Shift Keying (PSK)
– Amplitude Phase Keying (APK)
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� For Binary signals (M = 2), we have
– Binary Amplitude Shift Keying (BASK)
– Binary Phase Shift Keying (BPSK)
– Binary Frequency Shift Keying (BFSK)
� For M > 2, many variations of the above techniques exit usually classified as M-ary Modulation/detection
Bandpass MOdulation and DEModulation
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Overview of Modulation Schemes
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digital modulations, (a) PSK (b) FSK (c) ASK (d) ASK/PSK (APK)
Amplitude Shift Keying
� Modulation Process
– In Amplitude Shift Keying (ASK), the amplitude of the carrier is switched between two (or more) levels according to the digital data
– For BASK (also called ON-OFF Keying (OOK)), one and zero are
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Keying (OOK)), one and zero are represented by two amplitude levels A1 and A0
� Analytical Expression:
where Ai = peak amplitude
TttAts ci ≤≤= 0),cos()( ω
)cos(2)cos(2)cos()( 02
00 tAtAtAtsrmsrms ωωω ===
2E
Amplitude Shift Keying
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Hence,
where
)cos(2
)cos(2 00 tT
EtP ωω ==
MiTttT
tEts i
i ,......2,1,0),cos()(2
)( 0 =≤≤= ω
1,......2,0,)(0
2 −=∫= MidttsET
i
� Where for binary ASK (also known as ON OFF Keying (OOK))
� Mathematical ASK Signal Representation
– The complex envelope of an ASK signal is:
10),cos()()(1 binaryTtttmAts cc ≤≤+= φω00,0)(0 binaryTtts ≤≤=
)()( tmAtg =
Amplitude Shift Keying
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– The magnitude and phase of an ASK signal are:
– The in-phase and quadrature components are:
the quadrature component is wasted.
)()( tmAtg c=
0)(),()( == ttmAtA c φ
)()( tmAtx c=
,0)( =ty
ASK, OOK, MASK� The amplitude (or height) of the sine wave varies to
transmit the ones and zeros
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� One amplitude encodes a 0 while another amplitude encodes a 1 (a form of amplitude modulation)
Implementation of binary ASK
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OOK and MASK� OOK (On-OFF Key)
– 0 silence.
– Sensor networks: battery life, simple implementation
� MASK: multiple amplitude levels
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Pro, Con and Applications� Pro
– Simple implementation
� Con
– Major disadvantage is that telephone lines are very susceptible to variations in transmission quality that can affect amplitude
– Susceptible to sudden gain changes
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– Susceptible to sudden gain changes
– Inefficient modulation technique for data
� Applications
– On voice-grade lines, used up to 1200 bps
– Used to transmit digital data over optical fiber
– Morse code
– Laser transmitters
Detectors for ASK: Coherent Receiver
Coherent detection requires the phase information
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� Coherent detection requires the phase information� A coherent detector mixes the incoming signal with a locally generated
carrier reference� Multiplying the received signal r(t) by the receiver local oscillator (say
Accos(wct)) yields a signal with a baseband component plus a component at 2fc
� Passing this signal through a low pass filter eliminates the high frequency component� In practice an integrator is used as the LPF
� The output of the LPF is sampled once per bit period
� This sample z(T) is applied to a decision rule
– z(T) is called the decision statistic� Matched filter receiver of OOK signal
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� A MF pair such as the root raised cosine filter can thus be used to shape the source and received baseband symbols
� In fact this is a very common approach in signal detection in most bandpass data modems
Noncoherent Receiver– Does not require a phase reference at the receiver
– If we do not know the phase and frequency of the carrier, we can use a noncoherent receiver to recover ASK signal
� Envelope Detector:
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– The simplest implementation of an envelope detector comprises a diode rectifier and smoothing filter
Frequency Shift Keying (FSK)� In FSK, the instantaneous carrier frequency is switched between 2 or more levels
according to the baseband digital data
– data bits select a carrier at one of two frequencies
– the data is encoded in the frequency
� In the past, FSK has been the most widely used form of digital modulation;Why?
– Simple both to generate and detect
– Insensitive to amplitude fluctuations in the channel
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– Insensitive to amplitude fluctuations in the channel
� FSK conveys the data using distinct carrier frequencies to represent symbol states
� An important property of FSK is that the amplitude of the modulated wave is constant
� Waveform
� Analytical Expression
1,....1,0),cos(2
)( −=+= MitT
Ets i
s
si 321
φω
formAnalog)()(
])([)(
0
0
+==
+= ∫ ∞−
tmfftdt
df
dmtt
dii
t
di
θ
ττωωθ
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� General expression is
Where
)()( 0
+== tmfftdt
f dii θ
bsbsi kTTkEEandfiff ==∆+= ,0
1−−=∆ ii fff
1,....1,0),22cos(2
)( 0 −=∆+= MiftitfT
Ets
s
si ππ
Frequency Shift Keying
� One frequency encodes a 0 while another frequency encodes a 1 (a form of frequency modulation)
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� Represent each logical value with another frequency (like FM)
( )
=ts( )tfA 12cos π( )tfA 22cos π
1binary 0binary
Multiple Frequency-Shift Keying (MFSK)
� More than two frequencies are used
� More bandwidth efficient but more susceptible to error
• f i = f c + (2i – 1 – M)f d
( ) tfAts ii π2cos= Mi ≤≤1
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i c d
• f c = the carrier frequency
• f d = the difference frequency
• M = number of different signal elements = 2 L
• L = number of bits per signal element
Phase Shift Keying
� One phase change encodes a 0 while another phase change encodes a 1 (a form of phase modulation)
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( )
=ts( )tfA cπ2cos( )ππ +tfA c2cos
1binary 0binary
DBPSK, QPSK� Differential BPSK
– 0 = same phase as last signal element
– 1 = 180º shift from last signal element
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� Four Level: QPSK
( )
=ts
+4
2cosππ tfA c 11
+4
32cos
ππ tfA c
−4
32cos
ππ tfA c
−4
2cosππ tfA c
01
00
10
QPSK Example
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FSK Vs PSK
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PSK
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BPSK
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BPSK Detector
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M=4 QPSK
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QPSK
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QPSK Detection
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QPSK Detection: Matched Filter
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MPSK
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MPSK
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MPSK Detection
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Matched filter detection
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Properties of MPSK Constellation
� In time domain, all M signals have the same amplitudes.
� All M signals have the same energy.
� All M constellation points are the same distance from the origin -- they are equally spaced on a circle
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� They differ in phase only (i.e. the data is encoded in the phase of the transmitted carrier).
� Each phase differs by 2p/M radians.
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