Lecture 16
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E225C – Lecture 16
OFDM Introduction
EE225C
Introduction to OFDM
l Basic idea
» Using a large number of parallel narrow-band sub-
carriers instead of a single wide-band carrier to
transport information
l Advantages
» Very easy and efficient in dealing with multi-path
» Robust again narrow-band interference
l Disadvantages
» Sensitive to frequency offset and phase noise
» Peak-to-average problem reduces the power
efficiency of RF amplifier at the transmitter
l 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 f time
Sinusoidal signal as input Frequency response Sinusoidal signal as output
Modulation techniques:
monocarrier vs. multicarrier
Channel
Channelization N carriers
Similar to
Guard bands
FDM technique
B B
Pulse length ~1/B Pulse length ~ N/B
– Data are transmited over only one carrier – Data are shared among several carriers
and simultaneously transmitted
Drawbacks Advantages
Furthermore
– Selective Fading – Flat Fading per carrier
– It is easy to exploit
– Very short pulses – N long pulses Frequency diversity
– ISI is compartively long – ISI is comparatively short – It allows to deploy
2D coding techniques
– EQs are then very long – N short EQs needed
– Dynamic signalling
– Poor spectral efficiency – Poor spectral efficiency
because of band guards because of band guards
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
Data coded in frequency domain Transformation to time domain: response
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
Time-frequency grid Data
N carriers
Frequency
B Carrier
f0
B
One OFDM symbol
T=1/f0
Features Time
– No intercarrier guard bands
Intercarrier Separation =
– Controlled overlapping of bands
– Maximum spectral efficiency (Nyquist rate) 1/(symbol duration)
– Easy implementation using IFFTs
– Very sensitive to freq. synchronization
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
b1 IFFT
d2 d0, d1, d2, …., dN-1
b2 Inverse fast d3 Parallel to
. Fourier transform . serial converter
.
f . . Transmit time-domain
. samples of one symbol
.
.
bN-1 time
dN-1
Data coded in
frequency domain: Data in time domain:
one symbol at a time one symbol at a time
d0’ Decode each
b0’
d0’, d1’, …., dN-1’ S/P d1’ FFT b1’
frequency bin
d2’ Fast Fourier independently
b2’
Serial to . transform .
Receive time-domain parallel converter . .
samples of one symbol . f .
. .
dN-1’ bN-1’
time
Loss of orthogonality (by frequency offset)
Transmission pulses ψ k (t) = exp( jk 2π t / T ) y ψ k +m ( t) = exp ( j2π (k + m )t / T )
ψ k+ m (t) = exp ( j2π (k + m + δ ) / T ) con δ ≤ 1 / 2
δ
Reception pulse with offset δ
T (1 − exp(− j2πδ ))
I m (δ ) = ∫ exp( jk2πt / T ) exp(− j(k + m + δ )2πt / T )dt =
T
Interference between
channels k and k+m 0
j 2π(m + δ )
N −1
T sin πδ 1 23
I m (δ) =
π m+δ
Summing up
∀m ∑ I (δ ) ≈ (Tδ) ∑ m ≈ (Tδ ) 14
2
m
2
2
2
for N >> 1 (N > 5 Is enough )
m m =1
Loss for 8 carriers Total ICI due to loss of orthogonality
0
-10
-10 m=1
Interference: Im(? )/T en dB
-15 δ =0.05
-20 -20
δ =0.02
m=3
m=5 -25
-30 m=7 -30 δ =0.01
ICI in dB
-40 -35 δ =0.005
-40
Practical limit
-50 -45 δ =0.002
Asymetric δ assumed
-50 r.v. δ =0.001
-60
Gaussian
-55 σ=δ
-70 -60
0
-0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 2 4 6 8 10 12 14 16
Frequency offset: ∂ Carrier position within the band (N=16)
4
Loss of orthogonality (time)
− T /2+ τ T/ 2 2 consecutive
Let us assume Xi = c 0 ∫ ψ k (t )ψ l (t − τ )dt + c 1 ∫ ψ k (t )ψ l (t − τ )dt
* *
a misadjustment τ −T /2 −T / 2+τ symbols
τ
senmπ
2 T T , c ≠c τ
Then Xi = mπ
0 1
Or approximately, Xi 2mπ T τ independent
≈ =2
when τ< if m=k-l 0, c0 = c1
τ
X 2 ICI ≈ 20log 2 , τ << T
τ 1 τ
2 2
In average, the interfering T
E i2 = 4 + 0 = 2
1
power in any carrier is T 2 T
T 2 Per carrier
Loss for 16 carriers ICI due to loss of orthogonaliy
0 45
-5
m=1 40 Doubling N means 3 dB more ICI
-10
Interference en dB
-15 35
τ assumed an Uniform r.v.
-20
ICI in dB
m=5 30
-25
-30 m=10 25 N=8 Max. practical limit
-35 20
-40 N=64
15
-45
-50 10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Relative misadjustment τ Typical deviation for the relative misadjustment
Zone of interest
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 T (Method: overlap-save)
Tc
Without the Cyclic Prefix Including the Cyclic Prefix
Symbol: 8 periods of fi
CP
Symbol: 8 periods of fi
Passing the channel h(n)
Passing the channel h(n)
Ψi(t)
Ψi(t)
Channel:h(n )=(1 ) – n / n n =0 , …,2 3
≠Ψ i(t)
Initial transient The inclusion of a CP Final transient
remains within maintains the orthogonality remains within
Initial transient Loss of orthogonality Decaying transient
the CP the CP
Ψ j(t) Ψj (t)
Symbol: 4 periods of fi
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
5
Cyclic Prefix
Tg T
Multi-path components
τmax
Tx Sampling start T
802.11a System Specification
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 GI2 T1 T2 GI OFDM Symbol GI OFDM Symbol
Short training sequence: Long training sequence:
AGC and frequency offset Channel estimation
l Sampling (chip) rate: 20MHz
l Chip duration: 50ns
l Number of FFT points: 64
l FFT symbol period: 3.2µs
l 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
l Modulation scheme
» QPSK: 2bits/sample
» 16QAM: 4bits/sample
» 64QAM: 6bits/sample
l Coding: rate ½ convolutional code with constraint length 7
6
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
Time-frequency grid
Frequency
B
Bad carriers
f0
f Time
Frequency response T=1/f0
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 9 11 20 30
f carrier
Frequency (MHz)
• Requires extremely linear power amplifier design.
7
Adjacent Channel and
Alternate Channel Rejection
Date M inimum Adjacent Channel Alternate
rate Sensibility Rejection Channel rejection
6 Mbps -82 d B m 16 dB 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
8
OFDM System Block Diagram
Synchronization
l Frame detection
Tg T
Frame start
l Frequency offset compensation
l Sampling error
» Usually less 100ppm and can be ignored
– 100ppm = off 1% of a sample every 100 samples
9
System Pilot Structure
IEEE 802.11a OFDM Txer
Short Preamble Gen.
Long Preamble Gen.
OFDM Data Path
10 x 0.8 = 8 uS 2 x 0.8 + 2 x 3.2 = 8 uS 0.8 + 3.2 = 8 uS 0.8 + 3.2 = 8 uS 0.8 + 3.2 = 8 uS
1 2 3 4 5 6 7 8 9 10 GI2 T1 T2 GI Signal GI Data GI Data
Signal Detection, AGC, Channel & Fine Freq. Rate, Length Data Data
Diversity Selection Offset Estimation
Coarse Freq. Offset
Est.,Timing Sync.
10
Short & Long Preambles
1+j
-20
-24 -12
-16 f
-1-j
Short Preamble
+1 Period = 16 Chips
-24
-26
-16 -12
f
-1
Long Preamble
Period = 64 Chips
Correlation of Short Preamble
Correlation
Fine Timing
Auto-
Correlation
Coarse Timing
11
Synchronization
From AGC
16Td Td Td Td ... T d
* * *
... * Σ
Moving Auto-
Corr. Unit
Td Td Td ... Td
From AGC
Td Td Td ... T d
* * *
... * Σ
Moving SP
Corr. Unit ...
Short Preamble (LUT)
Impairments: Multi-Path Channel
Tc
2T 0 0
0 T
T 2T
3T t T t
t 4T c
0 T
T 2T
2T 3T t t
3T t 4T
4T 5T
0 0 0
T T
2T 2T
T t 3T t 3T t
c 4T 4T
5T 5T
Auto-Correlation w/
Ch. Impulse
Multi-Path Channel
Response
Response.
12
OFDM Introduction
EE225C
Introduction to OFDM
l Basic idea
» Using a large number of parallel narrow-band sub-
carriers instead of a single wide-band carrier to
transport information
l Advantages
» Very easy and efficient in dealing with multi-path
» Robust again narrow-band interference
l Disadvantages
» Sensitive to frequency offset and phase noise
» Peak-to-average problem reduces the power
efficiency of RF amplifier at the transmitter
l 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 f time
Sinusoidal signal as input Frequency response Sinusoidal signal as output
Modulation techniques:
monocarrier vs. multicarrier
Channel
Channelization N carriers
Similar to
Guard bands
FDM technique
B B
Pulse length ~1/B Pulse length ~ N/B
– Data are transmited over only one carrier – Data are shared among several carriers
and simultaneously transmitted
Drawbacks Advantages
Furthermore
– Selective Fading – Flat Fading per carrier
– It is easy to exploit
– Very short pulses – N long pulses Frequency diversity
– ISI is compartively long – ISI is comparatively short – It allows to deploy
2D coding techniques
– EQs are then very long – N short EQs needed
– Dynamic signalling
– Poor spectral efficiency – Poor spectral efficiency
because of band guards because of band guards
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
Data coded in frequency domain Transformation to time domain: response
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
Time-frequency grid Data
N carriers
Frequency
B Carrier
f0
B
One OFDM symbol
T=1/f0
Features Time
– No intercarrier guard bands
Intercarrier Separation =
– Controlled overlapping of bands
– Maximum spectral efficiency (Nyquist rate) 1/(symbol duration)
– Easy implementation using IFFTs
– Very sensitive to freq. synchronization
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
b1 IFFT
d2 d0, d1, d2, …., dN-1
b2 Inverse fast d3 Parallel to
. Fourier transform . serial converter
.
f . . Transmit time-domain
. samples of one symbol
.
.
bN-1 time
dN-1
Data coded in
frequency domain: Data in time domain:
one symbol at a time one symbol at a time
d0’ Decode each
b0’
d0’, d1’, …., dN-1’ S/P d1’ FFT b1’
frequency bin
d2’ Fast Fourier independently
b2’
Serial to . transform .
Receive time-domain parallel converter . .
samples of one symbol . f .
. .
dN-1’ bN-1’
time
Loss of orthogonality (by frequency offset)
Transmission pulses ψ k (t) = exp( jk 2π t / T ) y ψ k +m ( t) = exp ( j2π (k + m )t / T )
ψ k+ m (t) = exp ( j2π (k + m + δ ) / T ) con δ ≤ 1 / 2
δ
Reception pulse with offset δ
T (1 − exp(− j2πδ ))
I m (δ ) = ∫ exp( jk2πt / T ) exp(− j(k + m + δ )2πt / T )dt =
T
Interference between
channels k and k+m 0
j 2π(m + δ )
N −1
T sin πδ 1 23
I m (δ) =
π m+δ
Summing up
∀m ∑ I (δ ) ≈ (Tδ) ∑ m ≈ (Tδ ) 14
2
m
2
2
2
for N >> 1 (N > 5 Is enough )
m m =1
Loss for 8 carriers Total ICI due to loss of orthogonality
0
-10
-10 m=1
Interference: Im(? )/T en dB
-15 δ =0.05
-20 -20
δ =0.02
m=3
m=5 -25
-30 m=7 -30 δ =0.01
ICI in dB
-40 -35 δ =0.005
-40
Practical limit
-50 -45 δ =0.002
Asymetric δ assumed
-50 r.v. δ =0.001
-60
Gaussian
-55 σ=δ
-70 -60
0
-0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 2 4 6 8 10 12 14 16
Frequency offset: ∂ Carrier position within the band (N=16)
4
Loss of orthogonality (time)
− T /2+ τ T/ 2 2 consecutive
Let us assume Xi = c 0 ∫ ψ k (t )ψ l (t − τ )dt + c 1 ∫ ψ k (t )ψ l (t − τ )dt
* *
a misadjustment τ −T /2 −T / 2+τ symbols
τ
senmπ
2 T T , c ≠c τ
Then Xi = mπ
0 1
Or approximately, Xi 2mπ T τ independent
≈ =2
when τ<
τ
X 2 ICI ≈ 20log 2 , τ << T
τ 1 τ
2 2
In average, the interfering T
E i2 = 4 + 0 = 2
1
power in any carrier is T 2 T
T 2 Per carrier
Loss for 16 carriers ICI due to loss of orthogonaliy
0 45
-5
m=1 40 Doubling N means 3 dB more ICI
-10
Interference en dB
-15 35
τ assumed an Uniform r.v.
-20
ICI in dB
m=5 30
-25
-30 m=10 25 N=8 Max. practical limit
-35 20
-40 N=64
15
-45
-50 10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Relative misadjustment τ Typical deviation for the relative misadjustment
Zone of interest
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 T (Method: overlap-save)
Tc
Without the Cyclic Prefix Including the Cyclic Prefix
Symbol: 8 periods of fi
CP
Symbol: 8 periods of fi
Passing the channel h(n)
Passing the channel h(n)
Ψi(t)
Ψi(t)
Channel:h(n )=(1 ) – n / n n =0 , …,2 3
≠Ψ i(t)
Initial transient The inclusion of a CP Final transient
remains within maintains the orthogonality remains within
Initial transient Loss of orthogonality Decaying transient
the CP the CP
Ψ j(t) Ψj (t)
Symbol: 4 periods of fi
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
5
Cyclic Prefix
Tg T
Multi-path components
τmax
Tx Sampling start T
802.11a System Specification
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 GI2 T1 T2 GI OFDM Symbol GI OFDM Symbol
Short training sequence: Long training sequence:
AGC and frequency offset Channel estimation
l Sampling (chip) rate: 20MHz
l Chip duration: 50ns
l Number of FFT points: 64
l FFT symbol period: 3.2µs
l 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
l Modulation scheme
» QPSK: 2bits/sample
» 16QAM: 4bits/sample
» 64QAM: 6bits/sample
l Coding: rate ½ convolutional code with constraint length 7
6
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
Time-frequency grid
Frequency
B
Bad carriers
f0
f Time
Frequency response T=1/f0
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 9 11 20 30
f carrier
Frequency (MHz)
• Requires extremely linear power amplifier design.
7
Adjacent Channel and
Alternate Channel Rejection
Date M inimum Adjacent Channel Alternate
rate Sensibility Rejection Channel rejection
6 Mbps -82 d B m 16 dB 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
8
OFDM System Block Diagram
Synchronization
l Frame detection
Tg T
Frame start
l Frequency offset compensation
l Sampling error
» Usually less 100ppm and can be ignored
– 100ppm = off 1% of a sample every 100 samples
9
System Pilot Structure
IEEE 802.11a OFDM Txer
Short Preamble Gen.
Long Preamble Gen.
OFDM Data Path
10 x 0.8 = 8 uS 2 x 0.8 + 2 x 3.2 = 8 uS 0.8 + 3.2 = 8 uS 0.8 + 3.2 = 8 uS 0.8 + 3.2 = 8 uS
1 2 3 4 5 6 7 8 9 10 GI2 T1 T2 GI Signal GI Data GI Data
Signal Detection, AGC, Channel & Fine Freq. Rate, Length Data Data
Diversity Selection Offset Estimation
Coarse Freq. Offset
Est.,Timing Sync.
10
Short & Long Preambles
1+j
-20
-24 -12
-16 f
-1-j
Short Preamble
+1 Period = 16 Chips
-24
-26
-16 -12
f
-1
Long Preamble
Period = 64 Chips
Correlation of Short Preamble
Correlation
Fine Timing
Auto-
Correlation
Coarse Timing
11
Synchronization
From AGC
16Td Td Td Td ... T d
* * *
... * Σ
Moving Auto-
Corr. Unit
Td Td Td ... Td
From AGC
Td Td Td ... T d
* * *
... * Σ
Moving SP
Corr. Unit ...
Short Preamble (LUT)
Impairments: Multi-Path Channel
Tc
2T 0 0
0 T
T 2T
3T t T t
t 4T c
0 T
T 2T
2T 3T t t
3T t 4T
4T 5T
0 0 0
T T
2T 2T
T t 3T t 3T t
c 4T 4T
5T 5T
Auto-Correlation w/
Ch. Impulse
Multi-Path Channel
Response
Response.
12