Part3-Digital Modulation Small

8/3/2019 Part3-Digital Modulation Small

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ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 1

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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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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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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Part3-Digital Modulation Small