E225C – Lecture 16
OFDM Introduction
EE225C
Introduction to OFDM
l
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)
2
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).
3
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
14
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
4
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<- Xem thêm -