Week8_ECE9308_2020_Modulation_Part_II_OFDM.pptx

Introduction to Orthogonal Frequency
Division Multiplexing (OFDM)
Prof. Xianbin (Warren) Wang
March 2023

Outline
• What’s OFDM?
 OFDM stands for Orthogonal Frequency Division Multiplexing
 Multicarrier modulation technique
• Principles of OFDM
 Transmitter
 Receiver
• Advantages / Disadvantages
 Peak-to-Average Power Ratio
 Sensitivity to carrier frequency offset
• OFDM System Design
 Channel Estimation
 Time and Frequency Domain Synchronization

f
OFDM is a multicarrier modulation technique that divides high-speed serial
information signal into multiple lower-speed sub-signals. Transmission is
simultaneously at different frequencies in parallel.
Different subcarriers are overlapped in the frequency domain to improve the
spectrum efficiency.
What is OFDM? (I)
y(n)
f0
f1
fn-1
+
S/P
Data
X0
X1
XN-1

Single Carrier System
Sequential Transmission of
Waveforms
Waveforms are Short Duration
T
Waveforms Occupy
Full System Bandwidth 1/T
What is OFDM? (II)

Multi-Carrier System
Parallel Transmission of
Waveforms
Waveforms are Long Duration
MT
Waveforms Occupy 1/M th
Of System Bandwidth 1/T
What is OFDM? (III)

OFDM: Dense Multichannel System
Conventional multichannel system
Uses Non-Overlapping Adjacent Channels.
Channels separated by some guard band in
frequency domain
OFDM Multichannel System
50% Overlap of Adjacent Channels
Channels separated by Half
Their Two Sided bandwidth
What is OFDM? (IV)

Why do we need OFDM? (I)
• hc(t) = åk ak d(t - tk)
where k = 0, …, K-1
ak : path gain (complex)
t0 = 0 normalize relative delay of first path
Dk = tk - t0 difference in time-of-flight
| a0 | | a1 | | a2 |
D1
D2
a0
a1
a2

Why do we need OFDM? (II)
-6 -4 -2 0 2 4 6
-0.2
0
0.2
0.4
0.6
0.8
1
t/Ts
2Ts 4Ts
Ts
-6 -4 -2 0 2 4 6 8
-0.5
0
0.5
1
t/T
s
-6 -4 -2 0 2 4 6 8
-0.2
0
0.2
0.4
0.6
0.8
t/T
s
Single carrier modulated communication system requires
complex adaptive equalization to remove resulting ISI.
Multipath can cause destructive interference and time dispersion (inter symbol
interference)
With OFDM, the ISI can be effectively mitigated as the symbol duration in OFDM
system is significantly longer.

r(t) = a0 s(t-t0) + a1 s(t-t1) + a2 s(t-t2) + a3 s(t-t3)
channel
Input
(Tx signal)
Output
(Rx signal)
Impulse
Response h(t)
t3 - t0
time
a3
a0
freq.
Frequency
Response H(f)
Why do we need OFDM? (III)

subchannel
frequency
magnitude
carrier
channel
-6 -4 -2 0 2 4 6
-0.2
0
0.2
0.4
0.6
0.8
1
t/T
s
2Ts 4Ts
Ts
-6 -4 -2 0 2 4 6 8
-0.5
0
0.5
1
t/T
s
-6 -4 -2 0 2 4 6 8
-0.2
0
0.2
0.4
0.6
0.8
t/Ts
Why do we need OFDM? (IV)

Outline
• What’s OFDM?
 OFDM stands for Orthogonal Frequency Division Multiplexing
 It’s multicarrier modulation technique
• Principles of OFDM
 Transmitter
 Receiver
• Advantages / Disadvantages
 Peak-to-Average Power Ratio
 Sensitivity to carrier frequency offset
• OFDM System Design
 Channel Estimation
 Time and Frequency Domain Synchronization

P/S
QAM
decoder
FEQ
frequency
domain
equalizer
S/P
QAM
encoder
N-IFFT
cyclic
prefix
P/S
D/A +
transmit
filter
N-FFT S/P
remove
cyclic
prefix
TRANSMITTER
RECEIVER
N subchannels N complex samples
N complex samples
N subchannels
Receive
filter
+
A/D
multipath channel
OFDM Transceiver
Bits
00110

Continuous Time: Orthogonal Time Signal Set
k
0
0 ,1, 2, , 1
( ):
0
0 ,1, 2, , 1
2
( ) exp( ):
0
0
( ) ( )
k
T
n m
k N
t
t T
k N
t j k t
t T
T
if n m
t t dt
T if n m



  
 
 
 
  
 






OFDM Principle (I)

Discrete Time: Orthogonal Time Signal Set




 
   



  
 
  
 
  
 
 
  
 



 

k
1
0
0 ,1, 2,...., 1
( ) :
0 1
0 ,1, 2,...., 1
2
( ) exp( ) :
/ ,
0 ,1, 2,...., 1
2
exp( ) :
0
0
( ) ( )
: ( ) ( ) ( ) ( )
k
N
n m
n
k N k k N k
k N
n
n N
k N
n j k nT
NT t T N
k N
j k n
N n N
if n m
n n
N if n m
NOTE n n n n
OFDM Principle (II)

1
,..,
1
,
0
,
)
(
)
(
1
0
)
2
(





N
n
e
k
X
n
y
N
k
n
N
k
j

Easy Modulation of Orthogonal Carriers Using IDFT
OFDM Transmitter

x(t) h(t) y(t)
t t t
t
t
Adjacent Symbols
Symbol Channel Distorted Symbol
OFDM ISI Removal: Cyclic Prefix (I)

 Cyclic Prefix
 Add the last part of the packet to the beginning of the signal
 Duration of the CP larger than multipath delay spread
 Orthogonality of the subcarriers not affected.
 Simple frequency domain equalizer can be used.
OFDM ISI Removal: Cyclic Prefix (II)

• OFDM is a block transform method.
• A “block” consists of a single OFDM symbol and its cyclic
prefix.
• A new block follows each previous block, and so on.
OFDM ISI Removal: Cyclic Prefix (III)

OFDM ISI Removal: Cyclic Prefix (IV)

Cyclic Prefix and OFDM Equalization (I)
Received Analog Signal:
Received Digital Signal:
Question: At the output of the FFT, does for OFDM
signal without cyclic prefix?

Cyclic Prefix and OFDM Equalization (II)
• Answer: NO!!!
• FFT-domain multiplication results in time-domain circular
convolution.
• Solution: Force cyclic convolution by making x(n) appear
periodic to the channel.
• The Result: adding a cyclic prefix of equal or greater
length than the channel impulse response .

Cyclic Prefix and OFDM Equalization (III)
• DFT properties
• Prefix and postfix extension convert linear convolution to cyclic convolution
• Equalization: multiply FFT output vectors Y with .
• Downside: data rate reduced by factor .
}
{
}
{
}
{ n
n
n
n h
DFT
d
DFT
h
d
DFT 


Transmitted time-domain data block
Cyclic prefix N-point data block

OFDM In-band Pilots
• In-band pilots are subcarriers which always available for
reference.
• Receiver needs to reliably estimate the channel and detect
signal presence, synchronization.
Time
Frequency

y(n)
y(n)
y(n)
X(0)
X(1)
X(N-1)
P
/S
D
F
T
...
y(n)
n = 0,1,..,N-1
.
.
.
Demodulation of the the Orthogonal Carriers
1
,..,
1
,
0
,
)
(
)
(
1
0
)
2
(






N
n
e
n
y
k
X
N
n
k
N
n
j

Easy Demodulation of Orthogonal Carriers Using DFT
OFDM Receiver

Channel Estimation & Interpolation
1
,...,
1
,
0
),
(
)
(
).
(
)
( 


 N
k
where
k
N
k
H
k
X
k
Y
)
(
)
(
)
(
)
(
)
(
ˆ k
N
k
H
k
X
k
Y
k
H 



N
M
M
k
M
k
N
k
H
k
H ,...,
2
,
,
1
,
)
(
)
(
)
(
ˆ 


Frequency Domain Channel
Estimation
Interpolation between in-band
Pilots Tones
• Boosted Pilots for Better Estimate
• Interpolation Method

Transmitting Procedure Summary
• Encode the incoming data
• Insert In-band pilots
• Multiplex data and pilots
• IFFT modulation
• Cyclic prefix insertion

Receiver Procedure
• Timing Synchronization
• Removal of Cyclic prefix
• FFT demodulation
• Channel estimation
• Equalization
• Data recovery

Symbol Duration and Subcarrier Spacing
 To maintain orthogonality, let where
 = sub-carrier spacing
 = symbol duration
 If N-point IDFT (or FFT) is used
 Total bandwidth (in Hz) =
 , symbol duration after CP addition
1
f
T

f

T
f
N
W 

CP s
T T T
 

OFDM Advantages & Disadvantages
• Negligible ISI
• High Spectral Efficiency
• Robust to Multipath
• Simple receiver design
 High peak-to-average
power ratio
 Sensitive to frequency
offsets and phase noise
Advantages Disadvantages

OFDM Advantages
• Lower equalization complexity compared to single-carrier modulation
due to efficiency of FFT algorithm
• Immune to intersymbol interference caused by multipath channel with
cyclic prefix ( or guard time)
• Higher bandwidth efficiency compared to conventional FDM and single
carrier modulation system
• Spectrum is very flat ( hard for a single-carrier system which requires
very sharp pulse shaping filters)

OFDM Challenges
• Subject to frequency offset and random phase shift among each
subcarrier
• Very high peak to average power ratio (PAPR)
• Subject to narrow band interference ( OFDM with FEC can
efficiently mitigate this problem)
• Sensitive to nonlinear distortion because the spectrum of each
carrier overlapped tightly

PAPR (1/4)
• Large peak-to-average ratio (PAPR) problem
2
2
( )
( )
Peak Power Peak Amplitude
PAPR
Average Power RMS Amplitude
 

PAPR(2/4)
• OFDM signal at any time instant is the summation of N subcarrier signals.
• Each carrier is multiplied by a independent modulated constellation
generated from the input data.
f
S(f)
f1
f2
fn
Foutput
+
S/P
0
Data
d1.m
d2.m
dN.m

PAPR (3/4)
• High peak-to-average power ratio
– It increased complexity of the analog-to-digital and digital-
to-analog converters
– It reduced efficiency of the RF power amplifier
• The PAPR puts a stringent requirement on
the power amplifier and reduces the
efficiency in the sense that a higher input
backoff factor is needed before the peaks
in the signal experience significant
distortion due to power amplifier
nonlinearity.

Power Amplifier Non-Linearity
0 1 2 3 4
0
0.5
1
1.5
2
2.5
3
3.5
4
Nonlinear Transfer Function of Amplifier
1-dB Compression Point
0 2 4 6 8 10
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Input and Output of Non-Linear Amplifier
-0.5 0 0.5
-60
-50
-40
-30
-20
-10
0
10
Spectrum of Two Input Sinusoids
Normalized Frequency
-0.5 0 0.5
-60
-50
-40
-30
-20
-10
0
10
Spectrum of Two Output Sinusoids
Normalized Frequency

PAPR in Clipped OFDM
0 500 1000 1500 2000 2500 3000 3500
0
0.5
1
1.5
2
2.5
Mag Square of CC Rate 1/2 OFDM
0 500 1000 1500 2000 2500 3000 3500
0
2
4
6
8
Mag Square of Coded Rate 1/2 OFDM
Mean = 1
Mean = 1
Peak = 2
Peak = 6.26

Clipping Effect on OFDM Spectra
-4 -3 -2 -1 0 1 2 3 4
-60
-50
-40
-30
-20
-10
0
10
Spectrum at Input to Amplifier
Normalized Frequency (f/fsym
)
Log
Magnitude
(dB)
-4 -3 -2 -1 0 1 2 3 4
-60
-50
-40
-30
-20
-10
0
10
Spectrum at Output of Amplifier
Normalized Frequency (f/fsym
)
Log
Magnitude
(dB)
SPECTRAL REGROWTH

Timing Offset Impact
• The cyclic prefix and the channel estimator provide some
immunity to small time offsets
• Larage time offset leads to intersymbol interference
time
no offset
time offset

Frequency Offset Impact
• Due to base carrier frequency difference between the transmitter and the
receiver
• Leading to serious inter-channel-interference (ICI)
• Must be estimated and compensated by using specific preambles or pilots
No CFO CFO in presence

Constellation with Frequency Offset
-1.5 -1 -0.5 0 0.5 1 1.5
-1.5
-1
-0.5
0
0.5
1
1.5
5000 Constellations, Zero Carrier Frequency Offset
-1.5 -1 -0.5 0 0.5 1 1.5
-1.5
-1
-0.5
0
0.5
1
1.5
400 pilot, Zero Carrier Frequency Offset
-1.5 -1 -0.5 0 0.5 1 1.5
-1.5
-1
-0.5
0
0.5
1
1.5
5000 Constellations, 5 ppm Carrier Frequency Offset
-1.5 -1 -0.5 0 0.5 1 1.5
-1.5
-1
-0.5
0
0.5
1
1.5
400 pilot, 5 ppm Carrier Frequency Offset

STA
STA
STA STA
AP
AP
ESS
BSS
BSS
Existing
Wired LAN
Infrastructure
Network
Overview, 802.11 Architecture

Wireless Networking (Wi-Fi)
• Data Link Layer over radio
frequencies
• Many standards
• Notably IEEE 802.11
Application Layer
(e.g. HTTP, DNS)
Transport Layer
(e.g. TCP, UDP)
Network Layer
(e.g. IP, IPv6)
Data Link Layer (e.g.
Ethernet, 802.11)

OFDM Systems
System Transform
Size
Number
Carriers
Channel
Spacing
kHz
Bandwidth
MHz
Sample
Rate
MHz
Symbol
Duration
sec
Data
Rate
Mbits/s
HyperLAN/2 64 52
4
312.5 16.25 20 3.2
0.8
6-54
802.11a 64 52
4
312.5 16.56 20 3.2
0.8
6-54
DAB 2048
1024
1712
842
4.464 7.643 9.174 224 0.68-14.92
DVB-T 2048
8192
1536 1.00 1.536 2.048 24/48/96
msec
3.072
ADSL 256 (down)
64 (up)
36-127
7-28
4.3125 1.104 1.104 231.9 0.64-8.192

OFDM Pilot in DVB-T
DVB-T
Data
Continuous Pilot
Scattered Pilot
TPS Carriers
Frequency Spectrum
•Continual Pilots
•Scattered Pilots.
•Transmission Protocol Signals TPS.

Week8_ECE9308_2020_Modulation_Part_II_OFDM.pptx

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