part3-digital modulation small
TRANSCRIPT
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Part 3. Digital Modulation
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Whats Modulation & Demodulation?
Digital modulation and demodulation:
Modulation (demodulation) maps (retrieves) the digital
information into (from) an analog waveform appropriatefor transmission over the channel.
Generally involve translating (recovering) the baseband
digital information to (from) a bandpass analog signal at
a carrier frequency that is very high compared to the
baseband frequency.
Examples: ASK, FSK, QPSK, 16QAM
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Modulation & Demodulation
Baseband
Modulation
CarrierCommunication
Channel
Synchronization/Detection/
Decision
Carrier
Data in Data out
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Why Carrier?
Effective radiation of electromagnetic waves
requires antenna dimensions comparable with the
signals wavelength: Antenna for 3 kHz carrier would be ~100 km long
Antenna for 3 GHz carrier is 10 cm long
Frequency division multiplexing
Shifting the baseband signals to different carrier
frequencies
Sharing the communication channel resources
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Digital modulation involves choosing a particular
analog signal waveform si(t) from a finite set S of
possible signal waveforms based on the information
bits applied to the modulator.
Forbinary modulation schemes, a binary information
bit is mapped directly to a signal and S contains only 2signals, representing 0 and 1.
ForM-ary modulations, S contains more than 2 signals
and each represents more than a single bit ofinformation. With a signal set of size M, it is possible
to transmit up to log2Mbits per signal.
Geometric Representation (1)
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Any element of set S, S={s1(t), s2(t),, sM(t)}, can
be represented as a point in a vector space whose
coordinates are basis signals j(t), j=1,2,,N, suchthat
Geometric Representation (2)
( ) ( )
( )2
0, ; ( orthogonal)
1; ( normalization)
i j
i
t t dt i j
E t dt
=
= =
( ) can be represented as a linear combination of the basis signals.is t
( ) ( )1
, 1,2, ,N
i ij j
j
s t s t i M =
= =
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( ) ( )
( ) ( )
( ) ( )
1
1
2
2cos 2 ,
; 0
2 cos 2 ;
energy per bit; bit period
For this signal set, there is a single basis s
2cos
ignal
2 ; 0c cb
bc c
b
BPSK b
bc c
b
b b
Es t f t
TS t T
Es t f t T
E T
t f t t T T
= +
=
= +
=
=
=
+
( ) ( ){ }1 1
,BPSK
b
b bS E t E t = -Eb Eb
Q
I
Constellation diagram
Example: BPSK Geometric Representation
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Constellation Diagram
A graphical representation of the complex envelope of
each possible signal
The x-axis represents the in-phase component and they-axis represents the quadrature component of the
complex envelope
The distance between signals on a constellation
diagram relates to how different the modulation
waveforms are and how well a receiver can
differentiate between them when random noise ispresent.
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Performance Measures (1)
Two key performance measures of a modulation
scheme are power efficiency and bandwidth efficiency
Power efficiency is a measure of how favorably thetradeoff between fidelity and signal power is made, and
is expressed as the ratio of the signal energy per bit
(Eb) to the noise PSD (N0) required to achieve a givenprobability of error (say 105):
0Small is preferred
bp p
E
N =
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Performance Measures (2)
Bandwidth efficiency describes the ability of a
modulation scheme to accommodate data within a
limited bandwidth, In general, it is defined as the ratio
of the data bit rate R to the required RF bandwidth B:
Channel capacity gives an upper bound of achievable
bandwidth efficiency:
(bps/Hz) Large is preferredB B
R
B =
max 2log (1 )BC S
B N = = +
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Modulation Schemes Classification
Linear modulation: the amplitude of the transmitted
signal,s(t), varies linearly with the modulating digital
signal, m(t).
Bandwidth efficient but power inefficient
Example: ASK, QPSK
Nonlinear modulation: the amplitude of the
transmitted signal,s(t), does not vary linearly with the
modulating digital signal
Power efficient but bandwidth inefficient
Example: FSK, constant envelope modulation
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Demodulation (1)
Coherent demodulation: requires a replica carrier
wave of the same frequency and phase at the receiver
The received signal and replica carrier are cross-correlated
Also known assynchronous demodulation
Carrier recovery methods
Using PLL to recover the carrier phase and frequency from the
transmitted pilot carrier signal,
Recovering the carrier from the received signals using costas
loop
Applicable to: PSK, FSK, ASK, etc.
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Demodulation (2)
Example of BPSK coherent demodulator:Carrier
recovery
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Demodulation (3)
Non-coherent demodulation: does not require a
reference carrier wave
It is less complex than coherent demodulation (easier toimplement), but has worse performance
Applicable to: DPSK, FSK, etc.
Example: FSK non-coherent demodulator
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Part 3.1 Basic Modulation
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Modulation Process
Modulation implies varying one or more characteristics
(modulation parameters a1, a2, an) of a carrierfinaccordance with the information-bearing (modulating)
baseband signal.
Sinusoidal waves, pulse train, square wave, etc. can be
used as carriers
( )1 2 3
1 2 3
, , ,... , ( carrier)
, , ,... ( modulation parameters)
( time)
n
n
f f a a a a t
a a a a
t
=
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Continuous Carrier
Carrier:A cos[t +]
A = const
= const = const
Amplitude modulation (AM)
A = A(t) carries information
= const
= const
Frequency modulation (FM)
A = const
= (t) carries information = const
Phase modulation (PM)
A = const
= const
= (t) carries information
Modulation methods: usingamplitude, phase or frequency of the carrier.
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Basic Modulation
Modulation involves operations on one or more of the
three characteristics of a carrier signal:amplitude,
frequency and phase.
The three basic modulation methods are:
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying (FSK)
These could be applied to binary or M-ary signals.
There are other variants as well.
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Amplitude Shift Keying (ASK) (1)
The modulation signal set is
Ts is the symbol period
fc is the carrier frequency, is the carrier initial phase g(t) is a real-value signal pulse whose shape influences the spectrum
of the transmitted signal;Pulse shaping
Used to simultaneously reduce the intersymbol effects and the spectralwidth of a modulated digital signal
Example: rectangular pulse, Nyquist pulse shaping, raised cosine pulseshaping, Gaussian pulse shaping, etc.
Ai=(2i-1-M)d, each symbol represents log2Mbits
[ ]
1,2, ,
( ) ( )cos 2 , 0i i c c s
i M
s t A g t f t t T
=
= +
c
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Amplitude Shift Keying (ASK) (2)
The single basis signal is
The modulated signal:
[ ]12
( ) ( )cos 2 c cg
t g t f t
= +
1
( ) ( ), 2i i i i g
s t s t s A = =
ASK demonstrates poor performance, as it is heavily affected by noise,
fading, and interference. It is rarely used on its own.
Rectangular pulse
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Phase Shift Keying (PSK)
The modulation signal set is
Ac is the carrier amplitude,
carries information, each symbol represents log2Mbits
[ ]( ) ( )cos 2 , 1,2, ,2
0( 1)
i c c c i
si
s t A g t f t i M
t TiM
= + + = =
i
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Binary Phase Shift Keying (BPSK)
M=2: minimum phase separation: 180 o
s1(t) ands2(t) represent bit 0 and bit 1,respectively
The single basis:
The set :
[ ]( ) ( )cos 2 ( 1) , 1,2, 0i c c c bs t A g t f t i i t T = + + =
[ ]12
( ) ( )cos 2 c cg
t g t f t
= +
1 1( ), ( )2 2
g g
c cS A t A t
=
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Quadrature Amplitude Modulation (QAM) (1)
Combined amplitude/phase shift keying
As both amplitude and phase are used to carry symbol
information, it is very bandwidth efficient
Signal set size M=M1M2: 21 21 = 4, 22 22 = 16, 23
23 = 64, etc 4QAM, 16QAM, 64QAM
The larger M is, the better bandwidth efficiencybut
lower robustness against noise and fading
1 2
( ) ( )cos 2 ,
1,2, , , 1,2, , ,0
i i c c j
s
s t A g t f t
i M j M t T
= + + = =
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Performance in AWGN Channel (1)
The channel is assumed to corrupt the signal by the
additive white Gaussian noise.
Distortion
Channels(t)
n(t)
r(t)=s(t)+n(t)
Perfect channel White noise
2 0noise power:
2n
N =
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Performance in AWGN Channel (3)
ASK: symbol error probability
( )
( )
2 ,
2
0
,
6log2( 1)
1is the average bit energy
b av
M
b av
MMP Q
MM N
=
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Overview of TCM (2)
Solution: Trellis coded modulation (TCM)
The combination of coding and modulation
Coding gain without expanding bandwidth
Using a constellation with more points than that
required without coding
Typically, the number of points is doubled
The symbol rate is unchanged and the bandwidth
remains unchanged.
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History of TCM
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Basic Principles of TCM (1)
TCM is to devise an effective method for mapping the
coded bits into signal points such that the minimum
Euclidean distance is maximized.
Ungerboek idea: mapping by set partitioning
The signal constellation is partitioned in a systematic manner
to form a series of smaller subsets.
The resulting subsets have a larger minimum distance than
their parent.
The goal of partitioning: each partition should produce
subsets with increased minimum distance.
E l f S P i i i
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Example of Set Partitioning
B i P i i l f TCM (2)
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Basic Principles of TCM (2)
In general, the encoding is performed as follows:
A block ofm information bits is separated into two groups oflength k1 and k2, respectively.
The k1bits are encoded into nbits, while the k2bits are leftuncoded.
The nbits from the encoder are used to select one of thepossible subsets in the partitioned signal set, while the k2bitsare used to select one of 2k2 signal points in each subset.
The coder need not code all the incoming bits. Whenk2=0, all m information bits are encoded.
There are many ways to map the coded bits into
symbols. The choice of mapping will drastically affectthe performance of the code.
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B i P i i l f TCM (4)
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Basic Principles of TCM (4)
The basic rules for the assignment of signal subsets to
state transitions in the trellis
Use all subsets with equal frequency in the trellis
Transitions originating from the same state or merging into
the same state in the trellis are assigned subsets that are
separated by the largest Euclidean distance
Parallel state transitions (when they occur) are assignedsignal points separated by the largest Euclidean distance.
Parallel transitions in the trellis are characteristic of TCM that
contains one or more uncoded information bits.
Examples of TCM (1)
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Examples of TCM (1)
8-PSK constellation partition
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Examples of TCM (3)
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Examples of TCM (3)
Uncoded
QPSK
Trellis coded
8PSK
modulation
min,
Minimum Euclidean distance:
2uncodedd =
2 2 2
000 212 0 1
Distance : (0, 0, 0) (2, 1, 2)
2
(2 2) 4 4.585
d d d
= +
= + =
2 2
000 400 2
Distance : (0, 0, 0) (4, 0, 0)
Parallel transition
4
:
d d
= =
Examples of TCM (4)
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Examples of TCM (4)
2/3 TCM encoder
with 8 states
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Coding Gain (1)
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The minimum Euclidean distance between paths that
diverge from any state and remerge at the same state in
the trellis code is calledfree Euclidean distance Dfed
Asymptotic coding gain:
Coding Gain (1)
min,In the 4-state example, 2 , 2
=2 3dB coding gain
fed uncoded D d
= =
2 2
min, ,
2
,
2min,
where E is the normalized average received en
when
gerg
,
y
fed coded
uncoded code
uncode
du
d coded
uncoded fed co
nc
ed
d
d
ode
D
E E
d
E E
D
d
=
= =
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Viterbi Decoding (1)
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Two steps:
Step 1: At each branch in the trellis,
Compare the received signal to each of the siganls allowed forthat branch.
Save the signal closest to the received signal
Label the branch with a metric proportional to the Euclidean
distance between the two signals.
Branch metric calculation
g ( )
Determining the best signal within each subset, i.e.,the signal with the smallest distance to the received
signalsubset decoding
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