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
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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 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
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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<
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 l l l l l
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 l
Frame detection
Frame start
Tg
T
l
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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