2. Textbooks and References
“Wireless OFDM Systems: How to Make Them Work”
Marc Engels, Editor
“OFDM Wireless LANs: A Theoretical and Practical Guide”
Juha Heiskala and John Terry
“OFDM for Wireless Multimedia Communications”
Richard Van Nee and Ramjee Prasad
“Single and Multi-Carrier Quadrature Amplitude Modulation”
Lajos Hanzo, William Webb, and Thomas Keller
“ADSL, VDSL, and Multicarrier Modulation”
John Bingham
“Implementing ADSL”
David Ginsburg
“DSL Advances
Massimo Sorbara, John Cioffi, and Peter Silverman
3. OFDM
OFDM also known as
Multi-Carrier or Multi-Tone Modulation
DAB-OFDM
Digital Audio Broadcasting
DVD-OFDM
Digital Video Broadcasting
ADSL-OFDM
Asynchronous Digital Subscriber Line
Wireless Local Area Network
IEEE-802.11a, IEEE-802.11g
ETSI BRAN (Hyperlan/2)
5. OFDM Advantages
Efficiently Deals With Multi-path Fading
Efficiently Deals With Channel Delay Spread
Enhanced Channel Capacity
Adaptively Modifies Modulation Density
Robustness to Narrowband Interference
6. OFDM Disadvantages
OFDM Sensitive to
Small Carrier Frequency Offsets
OFDM Exhibits
High Peak to Average Power Ratio
OFDM Sensitive to
High Frequency Phase Noise
OFDM Sensitive to
Sampling Clock Offsets
7. Single Carrier System
Sequential Transmission
of Waveforms
Waveforms are
Short Duration T
Waveforms Occupy
Full System Bandwidth 1/T
9. OFDM: Dense Multichannel System
Conventional Multichannel System
Non Overlapping Adjacent Channels.
Channels separated by More
Than Their Two Sided bandwidth
OFDM Multichannel System
50% Overlap of Adjacent Channels
Available bandwidth is Used Twice
Channels separated by Half
Their Two Sided bandwidth
16. Rectangle Pulse: DC Centered Spectrum
with Equally Spaced Zeros
0
sin(2 )
2
( )
(2 )
2
P
P
P
T
f
H f AT
T
f
17. Shift Spectrum with Linear Phase on DC
Pulse: Move Spectrum to First Spectral Zero
)
2
)
1
(
2
(
)
2
)
1
(
2
sin(
)
(
P
p
P
p
P
k
T
T
k
f
T
T
k
f
AT
f
H
21. Continuous Time: Orthogonal Time Signal Set
T
m
n
k
m
n
if
T
m
n
if
dt
t
t
T
t
k
t
k
T
j
t
T
t
k
t
0
k
0
)
(
)
(
0
,
,
2
,
1
,
0
,
1
,
2
,
:
)
2
exp(
)
(
0
,
,
2
,
1
,
0
,
1
,
2
,
:
)
(
22. Discrete Time: Orthogonal Time Signal Set
k
1
0
..., 2, 1, 0 ,1, 2,....,
( ) :
0 1
0 ,1, 2,...., 1
2
( ) exp( ) :
0
0 ,1, 2,...., 1
2
exp( ) :
0
0
( ) ( )
: ( ) ( ) ( ) ( )
k
N
n m
n
k N k k N k
k
n
n N
k N
n j k nT
NT nT NT
k N
j k n
N n N
if n m
n n
N if n m
NOTE n n n n
45. Time and Spectra of Sparse OFDM Symbol
0 10 20 30 40 50 60 70 80 90 100
-1
-0.5
0
0.5
1
Real Part OFDM Time Series
Normalized Time
Amplitude
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-60
-50
-40
-30
-20
-10
0
10
Spectrum
Normalized Frequency
Log
Magnitude
(dB)
46. Time and Spectra With Frequency Offset = 0.1 Bin
0 10 20 30 40 50 60 70 80 90 100
-1
-0.5
0
0.5
1
Real Part OFDM Time Series with Offset Frequency = 0.1 Bin Width
Normalized Time
Amplitude
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-60
-50
-40
-30
-20
-10
0
10
Spectrum With Frequency Offset = 0.1 Bin Width
Normalized Frequency
Log
Magnitude
(dB)
47. Time and Spectra With Sample Clock Offset = 1.02 fs
0 10 20 30 40 50 60 70 80 90 100
-1
-0.5
0
0.5
1
Real Part OFDM Time Series with Sampling Clock = 1.02 fs
Normalized Time
Amplitude
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-60
-50
-40
-30
-20
-10
0
10
Spectrum With Sampling Clock = 1.02 fs
Normalized Frequency
Log
Magnitude
(dB)
48. Time and Spectra With Sample Clock Offset = 0.98 fs
0 10 20 30 40 50 60 70 80 90 100
-1
-0.5
0
0.5
1
Real Part OFDM Time Series with Sampling Clock = 0.98 fs
Normalized Time
Amplitude
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-60
-50
-40
-30
-20
-10
0
10
Spectrum With Sampling Clock = 0.98 fs
Normalized Frequency
Log
Magnitude
(dB)
49. Ideal I-Q Up and Down Conversion
S
hape
S
hape
Match
Match
CHANNEL
cos( t)
cos( t)
-sin( t)
-sin( t)
n(t)
I(t) I(t)
Q(t)
Q(t)
^
^
83. Selecting Reserve Frequency Bins
-60 -40 -20 0 20 40 60
0
0.2
0.4
0.6
0.8
1
Spectrum 11-Adjacent Frequencies
-0.5 0 0.5
0
0.2
0.4
0.6
0.8
1
Time Series for 11-Adjacent Frequencies
-60 -40 -20 0 20 40 60
0
0.2
0.4
0.6
0.8
1
Spectrum 11-Equally Spaced Frequencies
-0.5 0 0.5
0
0.2
0.4
0.6
0.8
1
Time Series for 11-Equally Spaced Frequencies
-60 -40 -20 0 20 40 60
0
0.2
0.4
0.6
0.8
1
Spectrum 11-Randomly Spaced Frequencies
-0.5 0 0.5
0
0.2
0.4
0.6
0.8
1
Time Series for 11-Randomly Spaced Frequencies
84. Reserve Bin Canceller Clipping at 2.5 (8 dB)
0 50 100 150 200 250
0
1
2
3
4
5
Peak envelope, input to PAR control
0 50 100 150 200 250
0
1
2
3
4
5
Peak envelope, output of first pass PAR control
data
clip level
data std dev
average peak
0 50 100 150 200 250
0
1
2
3
4
5
Peak envelope, output of second pass PAR control
data
clip level
data std dev
average peak
0 50 100 150 200 250
0
1
2
3
4
5
Peak envelope, output of third pass PAR control
data
clip level
data std dev
average peak
85. Statistics for Clip at 2.5 (8 dB)
0 1 2 3 4
0
0.005
0.01
0.015
0.02
0.025
input histogram
0 1 2 3 4
0
0.005
0.01
0.015
0.02
0.025
std dev =0.928
clip level
output histogram
-5 0 5 10
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
average =-0.648 dB
prob of level crossing
PAR (dB)
input
pass-1
pass-2
pass-3
86. Reserve Bin Canceller Clipping at 2.2 (6.9 dB)
0 50 100 150 200 250
0
1
2
3
4
5
Peak envelope, input to PAR control
0 50 100 150 200 250
0
1
2
3
4
5
Peak envelope, output of first pass PAR control
data
clip level
data std dev
average peak
0 50 100 150 200 250
0
1
2
3
4
5
Peak envelope, output of second pass PAR control
data
clip level
data std dev
average peak
0 50 100 150 200 250
0
1
2
3
4
5
Peak envelope, output of third pass PAR control
data
clip level
data std dev
average peak
87. Statistics for Clip at 2.2 (6.9 dB)
0 1 2 3 4
0
0.005
0.01
0.015
0.02
0.025
input histogram
0 1 2 3 4
0
0.005
0.01
0.015
0.02
0.025
std dev =0.928
clip level
output histogram
-5 0 5 10
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
average =-0.653 dB
prob of level crossing
PAR (dB)
input
pass-1
pass-2
pass-3
88. Reserve Bin Canceller Clipping at 2.0 (6 dB)
0 50 100 150 200 250
0
1
2
3
4
5
Peak envelope, input to PAR control
0 50 100 150 200 250
0
1
2
3
4
5
Peak envelope, output of first pass PAR control
data
clip level
data std dev
average peak
0 50 100 150 200 250
0
1
2
3
4
5
Peak envelope, output of second pass PAR control
data
clip level
data std dev
average peak
0 50 100 150 200 250
0
1
2
3
4
5
Peak envelope, output of third pass PAR control
data
clip level
data std dev
average peak
89. Statistics for Clip at 2.0 (6 dB)
0 1 2 3 4
0
0.005
0.01
0.015
0.02
0.025
input histogram
0 1 2 3 4
0
0.005
0.01
0.015
0.02
0.025
std dev =0.927
clip level
output histogram
-5 0 5 10
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
average =-0.659 dB
prob of level crossing
PAR (dB)
input
pass-1
pass-2
pass-3
92. Preamble and Pilot Structure
Short Symbols
Start of Frame Detection
Signal Strength Indication
Frequency Offset Resolution
Long Symbols
Channel Estimate
Fine Time Resolution
Distributed Pilots
Carrier Tracking
Sample Clock Tracking
98. Frequency and Signal Strength Estimates
0 0.5 1 1.5 2 2.5 3 3.5 4
-10
-5
0
5
10
Estimate of Frequency Offset
Sample Time
Frequency
Offset
in
FFT
Bins
0 0.5 1 1.5 2 2.5 3 3.5 4
0
0.02
0.04
0.06
0.08
0.1
Estimate of Signal Strength
Sample Time
Mag
Square
Known Offset
3.3 FFT Bins
99. Cross Correlation of Long Preamble
0 1 2 3 4 5 6 7
0
2
4
6
8
10
12
14
Cross Correlation of Input Signal With Long Preamble Section
Time Samples
Amplitude
4.3 4.4 4.5 4.6 4.7 4.8
0
5
10
15
Zoom to First Correlation Peak
Time Samples
Amplitude
5.3 5.4 5.5 5.6 5.7 5.8
0
5
10
15
Zoom to Second Correlation Peak
Time Samples
Amplitude
Expected Peak Position Expected Peak Position
100. Clipped Cross Correlation of Long Preamble
0 100 200 300 400 500 600 700 800 900
0
10
20
30
40
50
Clipped Cross Correlation of Input Signal With Long Preamble Section
Time Samples
Amplitude
4.3 4.4 4.5 4.6 4.7 4.8
0
10
20
30
40
50
Zoom to First Correlation Peak
Time Samples
Amplitude
5.3 5.4 5.5 5.6 5.7 5.8
0
10
20
30
40
50
Zoom to Second Correlation Peak
Time Samples
Amplitude
Clipped Correlator
Replica Signal Clipped Version of Template Signal
Sign[Real(Template)]+j*sign[Imag(Template)]
101. Channel Probe With Long Preamble
-0.5 0 0.5
0
1
2
3
4
5
6
7
Channel Probe, Long Segment of Preamble
Normalized Frequency
Amplitude
-0.5 0 0.5
0
1
2
3
4
5
6
7
Response of Channel Probe, One Look
Normalized Frequency
Amplitude
-0.5 0 0.5
0
1
2
3
4
5
6
7
Response of Channel Probe, No Noise
Normalized Frequency
Amplitude
-0.5 0 0.5
0
1
2
3
4
5
6
7
Response of Channel Probe, Average of Two Looks
Normalized Frequency
Amplitude
103. Frequency Domain Residual Carrier Offset
-30 -20 -10 0 10 20 30
-1.5
-1
-0.5
0
0.5
1
1.5
60 Frames Real Part FFT: Zero Carrier Frequency Offset
Frequency Index
Amplitude
-30 -20 -10 0 10 20 30
-1.5
-1
-0.5
0
0.5
1
1.5
60 Frames Real Part FFT: 5 ppm Carrier Frequency Offset
Frequency Index
Amplitude
105. Frequency Domain With Sample Clock Offset
-30 -20 -10 0 10 20 30
-1.5
-1
-0.5
0
0.5
1
1.5
80 Frames Real Part FFT: Zero Clock Frequency Offset
Frequency Index
Amplitude
-30 -20 -10 0 10 20 30
-1.5
-1
-0.5
0
0.5
1
1.5
80 Frames Real Part FFT: 300 ppm Clock Frequency Offset
Frequency Index
Amplitude
106. Other Variants of OFDM
Amplitude and Phase Overlays
Shaped OFDM
OQAM OFDM
Coded OFDM
CI OFDM
121. Inserting CC in OFDM
2 2
2
( ) ( ) ( ) ( ) 2 ( )
( ) ( ) 2 (A Constant Power Level)
Since Sample Values ( ) are equal to 1
Average Power in ( ) = N
2N
Thus Peak to Average Power Ratio 2
N
N N N N
N N
N
N
A n A n A n A n N n
A B N
A n
A
Now Reverse Domains
Use Complementary Code Sequence
as amplitude of Carriers in Frequency Domain
Then time series has
Peak Squared Magnitude = 2N
Average Magnitude = N
for Peak to Average Power Ratio = 2
126. C-I OFDM
Carrier Interferometry
OFDM with Phase Overlay
In Conventional OFDM
Rectangle Envelope in Time
Dirichlet Kernel in Frequency
In CI-OFDM
Rectangle Envelope in Frequency
Dirichlet Kernel in Time
Sin(x)/x in Time Domain Without Excess Bandwidth,
No Square-Root Nyquist Shaping Filter
133. 1-to-2 Interpolated Time Domain Data Points
-20 -15 -10 -5 0 5 10 15 20
-0.2
0
0.2
0.4
0.6
0.8
1
CI-OFDM Real Time Series and 1-Modulation Sample
Time
Amplitude
-20 -15 -10 -5 0 5 10 15 20
-0.2
0
0.2
0.4
0.6
0.8
1
CI-OFDM Real Time Series and 4-Modulation Samples
Time
Amplitude
134. CI-OFDM Data Frame
-25 -20 -15 -10 -5 0 5 10 15 20
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
CI-OFDM Real Time Series and 32-Modulation Samples
Time
Amplitude
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-60
-50
-40
-30
-20
-10
0
10
Spectrum
Normalized Frequency
Log
Magnitude
(dB)
Cyclic Prefix