E225C – Lecture 16
OFDM Introduction
EE225C
Introduction to OFDM
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Basic idea
» Using a large number of parallel narrow-band subcarriers instead of a single wide-band carrier to
transport information
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Advantages
» Very easy and efficient in dealing with multi-path
» Robust again narrow-band interference
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Disadvantages
» Sensitive to frequency offset and phase noise
» Peak-to-average problem reduces the power
efficiency of RF amplifier at the transmitter
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Adopted for various standards
– DSL, 802.11a, DAB, DVB
1
Multipath can be described in two domains:
time and frequency
Time domain: Impulse response
time
time
time
Impulse response
Frequency domain: Frequency response
time
time
time
Sinusoidal signal as input
f
time
Frequency response
Sinusoidal signal as output
Modulation techniques:
monocarrier vs. multicarrier
Channel
N carriers
Channelization
Similar to
FDM technique
Guard bands
B
Pulse length ~1/B
– Data are transmited over only one carrier
Drawbacks
B
Pulse length ~ N/B
– Data are shared among several carriers
and simultaneously transmitted
Advantages
– Selective Fading
Furthermore
– Flat Fading per carrier
– Very short pulses
– N long pulses
– ISI is compartively long
– ISI is comparatively short
– EQs are then very long
– N short EQs needed
– Poor spectral efficiency
because of band guards
– Poor spectral efficiency
because of band guards
– It is easy to exploit
Frequency diversity
– It allows to deploy
2D coding techniques
– Dynamic signalling
To improve the spectral efficiency:
Eliminate band guards between carriers
To use orthogonal carriers (allowing overlapping)
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Orthogonal Frequency Division Modulation
N carriers
Symbol: 2 periods of f0
Transmit
+
f
Symbol: 4 periods of f0
f
B
Symbol: 8 periods of f0
Channel frequency
response
Data coded in frequency domain Transformation to time domain:
each frequency is a sine wave
in time, all added up.
Decode each frequency
bin separately
Receive
time
f
B
Time-domain signal
Frequency-domain signal
OFDM uses multiple carriers
to modulate the data
N carriers
Frequency
Time-frequency grid
B
Data
Carrier
f0
B
Features
– No intercarrier guard bands
– Controlled overlapping of bands
– Maximum spectral efficiency (Nyquist rate)
– Easy implementation using IFFTs
– Very sensitive to freq. synchronization
T=1/f0
One OFDM symbol
Time
Intercarrier Separation =
1/(symbol duration)
Modulation technique
A user utilizes all carriers to transmit its data as coded quantity at each
frequency carrier, which can be quadrature-amplitude modulated (QAM).
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OFDM Modulation and Demodulation
using FFTs
d0
b0
d1
P/S
IFFT
b1
d2
d0, d1, d2, …., dN-1
b2
Inverse fast
d3
Parallel
to
.
Fourier transform
.
serial converter
.
Transmit time-domain
.
f .
samples of one symbol
.
.
.
time
bN-1
dN-1
Data coded in
Data in time domain:
frequency domain:
one symbol at a time
one symbol at a time
d0’
d1’
d2’
.
.
.
.
dN-1’
S/P
d0’, d1’, …., dN-1’
Receive time-domain
samples of one symbol
Serial to
parallel converter
time
Decode each
b0’
frequency bin
b1’
independently
b2’
.
.
f .
.
bN-1’
FFT
Fast Fourier
transform
Loss of orthogonality (by frequency offset)
ψ k (t) = exp( jk 2π t / T ) y ψ k +m ( t) = exp ( j2π (k + m )t / T )
Transmission pulses
ψ k+ m (t) = exp ( j2π (k + m + δ ) / T ) con δ ≤ 1 / 2
δ
Reception pulse with offset δ
Interference between
channels k and k+m
I m (δ) =
Summing up
∀m
π m+δ
∑I
m
N −1
2
m
(δ ) ≈ (Tδ)2 ∑
m =1
1
23
≈ (Tδ )2
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m2
-10
m=1
-20
m=3
m=5
m=7
-50
Asymetric
-70
-0.4
-0.3
-0.2
0
-0.1
0.1
Frequency offset: ∂
j 2π(m + δ )
N >> 1 (N > 5
Is enough )
Total ICI due to loss of orthogonality
-40
-60
for
T (1 − exp(− j2πδ ))
-10
-15
δ =0.05
-20
-25
δ =0.02
-30
δ =0.01
-35
δ =0.005
-40
Practical
-45
δ =0.002
δ assumed
r.v.
-50
δ =0.001
Gaussian
σ=δ
-55
-60
2
4
6
8
10
12
14
16
Carrier position within the band (N=16)
ICI in dB
Interference: Im(? )/T en dB
T
0
Loss for 8 carriers
0
-30
T sin πδ
I m (δ ) = ∫ exp( jk2πt / T ) exp(− j(k + m + δ )2πt / T )dt =
0.2
0.3
0.4
limit
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Loss of orthogonality (time)
Let us assume
a misadjustment τ
Then
if m=k-l
Xi = c 0 ∫
− T /2+ τ
−T /2
ψ k (t )ψ l (t − τ )dt + c 1 ∫
*
τ

senmπ
2 T
T , c ≠c
0
1
Xi = 
mπ

0,
c0 = c1

In average, the interfering
power in any carrier is
X 2
E i2
 T
T/ 2
independent
on m
τ

2  , τ << T

T
Per carrier
ICI ≈ 20log
2
2

1
τ 1
τ
 = 4 T  2 + 0 2 = 2 T 

ICI due to loss of orthogonaliy
45
Doubling N means 3 dB more ICI
40
m=1
35
ICI in dB
Interference en dB
τ
Xi 2mπ T
τ
≈
=2
T
T
mπ
Or approximately,
when τ<<T
Loss for 16 carriers
0
-5
-10
-15
-20
-25
-30
-35
-40
-45
-50
0
2 consecutive
symbols
ψ k (t )ψ l (t − τ )dt
*
−T / 2+τ
m=5
m=10
τ assumed an Uniform r.v.
30
25
Max. practical limit
N=8
20
15
0.1
0.2
Zone of interest
0.3 0.4 0.5 0.6 0.7
Relative misadjustment τ
0.8
0.9
1
10
0
N=64
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Typical deviation for the relative misadjustment
Including a “cyclic prefix”
To combat the time dispersion: including ‘special’ time guards in the symbol transitions
co p y
Furthemore it converts Linear conv. = Cyclic conv.
CP
τ
(Method: overlap-save)
T
Tc
Without the Cyclic Prefix
Including the Cyclic Prefix
Symbol: 8 periods of fi
Initial transient
Channel:h(n )=(1 ) – n / n
n =0 , …,2 3
≠Ψ i(t)
Loss of orthogonality
Decaying transient
Symbol: 8 periods of fi
Passing the channel h(n)
Passing the channel h(n)
CP
Ψi(t)
Ψi(t)
Initial transient
remains within
the CP
The inclusion of a CP
maintains the orthogonality
Ψj (t)
Ψ j(t)
Symbol: 4 periods of fi
Final transient
remains within
the CP
Symbol: 4 periods of fi
CP functions:
– It acomodates the decaying transient of the previous symbol
– It avoids the initial transient reachs the current symbol
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Cyclic Prefix
Tg
T
Multi-path components
τmax
Tx
T
Sampling start
802.11a System Specification
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10
GI2
Short training sequence:
AGC and frequency offset
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l
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l
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T1
T2
GI
OFDM Symbol
GI
OFDM Symbol
Long training sequence:
Channel estimation
Sampling (chip) rate: 20MHz
Chip duration: 50ns
Number of FFT points: 64
FFT symbol period: 3.2µs
Cyclic prefix period: 16 chips or 0.8µs
» Typical maximum indoor delay spread < 400ns
» OFDM frame length: 80 chips or 4µs
» FFT symbol length / OFDM frame length = 4/5
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Modulation scheme
» QPSK: 2bits/sample
» 16QAM: 4bits/sample
» 64QAM: 6bits/sample
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Coding: rate ½ convolutional code with constraint length 7
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Frequency diversity using coding
Random errors: primarily introduced by thermal and circuit noise.
Channel-selected errors: introduced by magnitude distortion in
channel frequency response.
Data bits
Frequency
Time-frequency grid
B
Bad carriers
f0
f
Frequency response
T=1/f0
Time
Errors are no longer random. Interleaving is often used to scramble
the data bits so that standard error correcting codes can be applied.
Spectrum Mask
Power Spectral Density
-20 dB
-28 dB
-40 dB
-30
-20
-11 -9
f carrier
9 11
20
30
Frequency (MHz)
• Requires extremely linear power amplifier design.
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Adjacent Channel and
Alternate Channel Rejection
Date
rate
6 Mbps
M inimum
Sensibility
-82 d B m
Adjacent Channel
Rejection
16 dB
Alternate
Channel rejection
32 dB
12Mbps
-79 d B m
13 dB
29 dB
24Mbps
-74 d B m
8 dB
24 dB
36Mbps
-70 d B m
4 dB
20 dB
54Mbps
-65 d B m
0 dB
15 dB
32 dB blocker
16 dB blocker
Signal
Frequency
• Requires joint design of the anti-aliasing filter and ADC.
OFDM Receiver Design
Yun Chiu, Dejan Markovic, Haiyun Tang,
Ning Zhang
EE225C Final Project Report, 12 December
2000
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OFDM System Block Diagram
Synchronization
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Frame detection
Frame start
Tg
T
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Frequency offset compensation
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Sampling error
» Usually less 100ppm and can be ignored
– 100ppm = off 1% of a sample every 100 samples
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System Pilot Structure
IEEE 802.11a OFDM Txer
Short Preamble Gen.
Long Preamble Gen.
OFDM Data Path
10 x 0.8 = 8 uS
1 2
3
4
5 6
7
2 x 0.8 + 2 x 3.2 = 8 uS
8
9 10
GI2
T1
T2
Signal Detection, AGC,
Channel & Fine Freq.
Diversity Selection
Offset Estimation
Coarse Freq. Offset
Est.,Timing Sync.
0.8 + 3.2 = 8 uS 0.8 + 3.2 = 8 uS 0.8 + 3.2 = 8 uS
GI
Signal
Rate, Length
GI
Data
Data
GI
Data
Data
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Short & Long Preambles
1+j
-24
-20
-12
-16
-1-j
f
Short Preamble
Period = 16 Chips
+1
-26
-24
-16
-12
f
-1
Long Preamble
Period = 64 Chips
Correlation of Short Preamble
Correlation
Fine Timing
AutoCorrelation
Coarse Timing
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Synchronization
From AGC
16Td
Td
Td
*
Td
Td
*
Td
Td
... T
... *
*
d
...
Σ
Moving AutoCorr. Unit
Td
From AGC
Td
Moving SP
Corr. Unit
Td
*
Td
*
... T
... *
*
d
Σ
...
Short Preamble (LUT)
Impairments: Multi-Path Channel
Tc
0
0
2T
T
T
0
2T
t
0
T
T
2T
3T
4T
0
0
T
t
c
Ch. Impulse
Response
2T
t
T
3T
3T
t
4T
4T
T
t
t
5T
0
2T
3T
4T
t
c
t
T
2T
3T
5T
4T
t
5T
Auto-Correlation w/
Multi-Path Channel
Response.
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Impairments: Frequency Offset
0
0
T
T
2T
2T
3T
3T
4T
4T
t
t
t
0
T
2T
3T
4T
t
Fine Frequency Offset Est.
Accumulator
Complex
Multiplier
Sync. Signal
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0
Coarse-Fine Joint Estimation &
Decision Alignment Error Correction
π
π
3
4
1
5
8
6
0
π
Average over
64 chips
π
B A
C D
−π
7
0
π
π
Average over
16 chips
2
0
0
Coarse
Fine
Folding Signal
π
0
Vin
Folding ADC
±100ppm ∆fc
@ 5.8GHz
0
π
0
π
Frequency Offset Compensation
Decision
Alignment
Channel
Joint CoarseFine Est.
Offset Corr.
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Performance Summary
Parameters
Metrics
Number of sub-carriers
48 data +4 pilot
OFDM symbol freq.
4 µs
Modulation Scheme
BPSK up to 64-QAM
Sampling clock freq.
20 MHz
Sync. Frame Start Accuracy
Freq. Offset Est. Range
≤ 8 chips (CP = 16
chips)
± 5π = ± 100ppm @ 5.8 GHz
Freq. Offset Est. Accuracy
1% (@ 15dB SNR)
Critical path delay
12.7 ns
Silicon area
397,080 µm2
Total power consumption
3.4 mW @ 20 MHz
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