CSNCTU Lecture 2 Modulation and Demodulation Reference Chap 5 in Goldsmiths book Instructor Kate Ching Ju Lin 林靖茹 1 Modulation 2 From Wikipedia The process of varying ID: 631017
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Wireless Communication Systems@CS.NCTU
Lecture 2: Modulation and DemodulationReference: Chap. 5 in Goldsmith’s book Instructor: Kate Ching-Ju Lin (林靖茹)
1Slide2
Modulation2
From Wikipedia: The process of varying
one or more properties of a periodic
waveform
with a modulating signal that typically contains information to be transmitted.
modulateSlide3
Example 13
= bit-stream?(a) 10110011
(b) 00101010
(c) 10010101Slide4
Example 24
= bit-stream?(a) 01001011(b) 00101011
(c) 11110100Slide5
Example 3 5
= bit-stream?(a) 11010100(b) 00101011
(c) 01010011
(d) 11010100 or
00101011 Slide6
Types of Modulation
Amplitude
ASK
Frequency
FSK
Phase
PSKSlide7
ModulationMap bits to signals
wirelesschannel
TX
transmitted
Signal s(t)
1
0
1
1
0
bit stream
modulationSlide8
DemodulationMap signals to bits
RX
1
0
1
1
0
demodulation
received
signal x(t)
wireless
channel
TX
transmitted
Signal s(t)
1
0
1
1
0
bit stream
modulationSlide9
Analog and Digital Modulation
Analog modulationModulation is applied continuouslyAmplitude modulation (AM)Frequency modulation (FM)Digital modulationAn analog carrier signal is modulated by a discrete signal Amplitude-Shift Keying (ASK)Frequency-Shift Keying
(FSK
)
Phase-Shift Keying (PSK)
Quadrature Amplitude Modulation (QAM)9Slide10
Advantages of Digital Modulation
Higher data rate (given a fixed bandwidth)More robust to channel impairmentAdvanced coding/decoding can be applied to make signals less susceptible to noise and fadingSpread spectrum techniques can be applied to deal with multipath and resist interferenceSuitable to multiple accessBecome possible to detect multiple users simultaneously
Better security and privacy
Easier to encrypt
10Slide11
Modulation and DemodulationModulation
Encode a bit stream of finite length to one of several possible signalsDelivery over the airSignals experience fading and are combined with AWGN (additive white Gaussian noise)DemodulationDecode the received signal by mapping it to the closest one in the set of possible transmitted signals
11
modulate
demodulateSlide12
Band-pass Signal RepresentationGeneral form
Amplitude is always non-negativeOr we can switch the phase by 180 degreesCalled the canonical representation of a band-pass signal12
amplitude
frequency
phaseSlide13
In-phase
and Quadrature Components
:
In-phase component of s(t) :
Quadrature component of s
(t)
13
Amplitude:
Phase:Slide14
We can also represent s(t) as
s’(t) is called the complex envelope of the band-pass signalThis is to remove the annoying in the analysis
Band-Pass
Signal Representation
exp
(
iθ
)
= cos
(
θ
)
+
jsin
(
θ
)
I
QSlide15
Types of ModulationAmplitude
M-ASK: Amplitude Shift KeyingFrequencyM-FSK: Frequency Shift KeyingPhaseM-PSK: Phase Shift KeyingAmplitude +
Phase
M-QAM: Quadrature Amplitude Modulation
s
(t) = Acos(
2πfct
+𝜙)Slide16
Amplitude Shift Keying (ASK)A bit stream is encoded in the amplitude
of the transmitted signalSimplest form: On-Off Keying (OOK)‘1’A=1, ‘0’A=016
TX
RX
signal
s(t)
1
0
1
1
0
1
0
1
1
0
bit stream
b
(t)
modulation
demodulationSlide17
M-ASKM-ary
amplitude-shift keying (M-ASK)17Slide18
Example: 4-ASK
Map ‘00’, ‘01’, ‘10’, ’11’ to four different amplitudes18Slide19
Pros and Cons of ASKPros
Easy to implementEnergy efficientLow bandwidth requirementConsLow data ratebit-rate = baud rateHigh error probabilityHard to pick a right threshold
1 baud
1 second
Bandwidth is the difference between the upper and lower frequencies in a continuous set of frequencies.Slide20
Types of ModulationAmplitude
M-ASK: Amplitude Shift KeyingFrequencyM-FSK: Frequency Shift KeyingPhaseM-PSK: Phase Shift KeyingAmplitude +
Phase
M-QAM: Quadrature Amplitude Modulation
s
(t) = Acos(2π
fct+𝜙
)Slide21
Frequency Shift Keying (FSK)A bit stream is encoded in the
frequency of the transmitted signalSimplest form: Binary FSK (BFSK)‘1’f=f1, ‘0’f=f2
21
TX
signal
s(t)
1
0
1
1
0
bit stream
modulation
RX
1
0
1
1
0
demodulationSlide22
M-FSKM-
ary frequency-shift keying (M-FSK)Example:
Quaternary
Frequency Shift
Keying (QFSK)
Map ‘00’, ‘01’, ‘10’, ’11’ to four different frequencies
22Slide23
Pros and Cons of FSKProsEasy to implement
Better noise immunity than ASKConsLow data rateBit-rate = baud rateRequire higher bandwidthBW(min) = N
b
+
N
bSlide24
Types of ModulationAmplitude
M-ASK: Amplitude Shift KeyingFrequencyM-FSK: Frequency Shift KeyingPhaseM-PSK: Phase Shift KeyingAmplitude +
Phase
M-QAM: Quadrature Amplitude Modulation
s
(t) = Acos(2π
fct+
𝜙)Slide25
Phase Shift Keying (PSK)A bit stream is
encoded in the phase of the transmitted signalSimplest form: Binary PSK (BPSK)‘1’𝜙
=
0
, ‘0’
𝜙=π25
TX
RX
signal
s(t)
1
0
1
1
0
bit stream
s(t)
modulation
1
0
1
1
0
demodulationSlide26
Constellation Points for BPSK‘1’
𝜙=0cos(2πfct+0)= cos(0)cos(2π
f
c
t
)-sin(0)sin(2πfct)
= sI
cos(2πf
ct) – s
Qsin(
2πfct)
‘0’
𝜙
=
π
cos
(
2π
f
c
t
+
π
)
=
cos
(
π
)
cos(
2π
f
c
t
)-
sin
(
π
)
sin
(
2π
f
c
t
)
=
s
I
cos
(
2π
f
c
t
) –
s
Q
sin
(
2π
f
c
t
)
I
Q
𝜙=0
I
Q
𝜙=π
(
s
I
,
s
Q
)
=
(
1
,
0
)
‘1’
1+0i
(
s
I
,
s
Q
)
=
(-
1
,
0
)
‘0’
-
1+0iSlide27
‘1’
‘0’
Demodulate BPSK
Map to the closest constellation point
Quantitative measure of the distance
between the received signal
s’ and any possible signal s
Find |s’-s|
in the I-Q plane
I
Q
s
1
=1+0i
n
1
n
0
n
1
=|s’-s
1
|=|s’-(1+0i)|
n
0
=|
s’-
s
0
|=|
|s’
-(-1+0i)|
since
n
1
< n
0,
map
s’
to (1+0i)
‘1’
s’=
a+bi
s
0
=-1+0iSlide28
I
Q
s
1
=1+0i
‘1’
‘0’
s
0
=-1+0i
Demodulate BPSK
Decoding error
When the received signal is mapped to an incorrect symbol (constellation point) due to a large error
Symbol error rate
P(mapping to a symbol
s
j
,
j
≠
i
|
s
i
is sent )
Given the transmitted symbol s
1
s’=
a+bi
incorrectly map s’
to
s
0
=(-1+0)
‘
0’, when
the error is too largeSlide29
SNR of BPSKSNR: Signal-to-Noise Ratio
Example:Say Tx sends (1+0i) and Rx receives (1.1 – 0.01i)SNR?
I
Q
n
s’ =
a+biSlide30
SER/BER of BPSKBER (Bit Error
Rate) = SER (Symbol Error Rate)30
From Wikipedia
:
Q(x) is the probability that a normal (Gaussian) random variable will obtain a value larger than x standard deviations above the mean
.
Minimum distance of any
two cancellation pointsSlide31
Constellation point for BPSKSay we send the signal with phase delay π
31
Illustrate this by the
constellation point
(-1 + 0i) in an I-Q plane
I
Q
𝜙=π
-1+0i
Band-pass representationSlide32
Quadrature PSK (QPSK)Use four phase rotations 1/4π, 3/4π
, 5/4π, 7/4π to represent ‘00’, ‘01’, ‘11’, 10’ 32
I
Q
‘00’
‘10’
‘01’
‘11’Slide33
Quadrature PSK (QPSK)Use 2 degrees of freedom in I-Q plane
Represent two bits as a constellation pointRotate the constellations by π/2Demodulation by mapping the received signal to the closest constellation pointDouble the bit-rateNo free lunch: Higher error probability (Why?)
I
Q
‘00’
‘10’
‘01’
‘11’Slide34
Quadrature PSK (QPSK)
Maximum power is boundedAmplitude of each constellation point should still be 1
I
Q
‘00’ = 1/√2(1+1i)
‘10’
‘01’
‘11’
Bits
Symbols
‘00’
1/√2+1/√2i
’
01’
-1/√2+1/√2i
‘10’
1/√2-1/√2i
‘11’
-1/√2-1/√2iSlide35
Higher Error Probability in QPSKFor a particular error
n, the symbol could be decoded correctly in BPSK, but not in QPSKWhy? Each sample only gets half power
I
Q
n
1
✔
in BPSK
I
Q
✗
In QPSK
n
1/√2
‘0’
‘1’
‘x1’
‘x0’Slide36
Trade-off between Rate and SER
Trade-off between the data rate and the symbol error rateDenser constellation points More bits encoded in each symbol Higher data rate
Denser constellation points
Smaller distance between any two points
Higher decoding error probability
36Slide37
SEN and BER of QPSKSNR
s: SNR per symbol; SNRb: SNR per bit SER: The probability that each branch has a bit error
BER
37
QPSK: M=4
E
s
is the bounded maximum powerSlide38
M-PSK
38
I
Q
‘10’
‘01’
‘11’
I
Q
‘1’
‘0’
I
Q
‘111’
‘100’
‘010’
‘011’
‘001’
‘000’
‘100’
‘101’
I
Q
‘1111’
‘0000’
BPSK
QPSK
8-PSK
16-PSKSlide39
M-PSK BER versus SNR
Denser constellation points
higher BER
Acceptable reliabilitySlide40
Types of ModulationAmplitude
M-ASK: Amplitude Shift KeyingFrequencyM-FSK: Frequency Shift KeyingPhaseM-PSK: Phase Shift KeyingAmplitude +
Phase
M-QAM: Quadrature Amplitude Modulation
s
(t) = Acos(2π
fct+
𝜙)Slide41
Quadrature Amplitude ModulationChange both amplitude and phase
s(t)=Acos(2πfct+𝜙)
64-QAM: 64 constellation points, each with 8 bits
I
Q
‘1000’
‘1100’
‘0100’
‘0000’
‘1001’
‘1101’
‘0101’
‘0001’
‘1011’
‘1111’
‘0111’
‘0011’
‘1010’
‘1110’
‘0110’
‘0010’
Bits
Symbols
‘1000’
s
1
=3a+3ai
’
1001’
s
2
=3a+ai
‘1100’
s
3
=a+3ai
‘1101’
s
4
=
a+ai
a
3a
16-QAMSlide42
M-QAM BER versus SNRSlide43
Modulation in 802.11802.11a
6 mb/s: BPSK + ½ code rate 9 mb/s: BPSK + ¾ code rate12 mb/s: QPSK + ½ code rate18 mb/s: QPSK + ¾ code rate24 mb
/s: 16-QAM + ½ code rate
36
mb
/s: 16-QAM + ¾ code rate48 mb/s: 64-QAM + ⅔ code rate54 mb
/s: 64-QAM + ¾ code rateFEC (forward error correction)k/n: k-bits useful information among n-bits of data
Decodable if any k bits among n transmitted bits are correctSlide44
Signal Encoder
90 degree shift
Message Source
Band-pass
Signal
s
(
t
)
Map each bit into
s
I
(
t
) and
s
Q
(
t
)
Band-Pass
Signal Transmitter
s
I
(
t
)
s
Q
(
t
)
m
ixer
cos(2
π
f
c
t
)
sin(2
π
f
c
t
)Slide45
Band-Pass Signal Receiver
Band-pass Filter90 degree shift
Message Sink
Received Signal
plus noise
Filters out out-of-band signals and noises
x
(t) =
s
(
t
) +
n(t)
Low-pass Filter
Signal Detector
Low-pass Filter
0.5[
A
c
s
I
(
t
) +
n
I
(t)]
0.5[
A
c
s
Q
(
t
) +
n
Q
(t)]
cos(2
π
f
c
t
)
sin(2
π
f
c
t
)Slide46
DetectionMap the received signal to one of the possible transmitted signal with the minimum distance
Find the corresponding bit streams46
received signal
possible transmitted signals
c
orresponding bit streams
…
…
closestSlide47
AnnouncementInstall Matlab
Teaming Elevator pitch: 2 per group (Each group talks about 3-5 minutes. Each member needs to talk)Lab and project: 3-4 members per groupSend your team members to the TA (張威竣)Sign up for the talk topicPick the paper (topic) according to your preference or scheduleSign up from 18:00@Thu (will announce the
url
in the
announcement
tab of the course website)Pick your top five choices (from Lectures 4-18)FIFS
47Slide48
QuizWhat are the four types of modulation introduced in the class?
Say Tx sends (-1 + 0i) and Rx receives -(0.95+0.01i). Calculate the SNR.48