E225C – Lecture 16 OFDM Introduction EE225C. Multipath can be described in two domains: time and...
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Transcript of E225C – Lecture 16 OFDM Introduction EE225C. Multipath can be described in two domains: time and...
E225C – Lecture 16OFDM Introduction
EE225CEE225C
Multipath can be described in two domains: time and frequency
time
time
Sinusoidal signal as input
time
time
Sinusoidal signal as output
f
Frequency response
Time domain: Impulse response
Frequency domain: Frequency response
time
Impulse response
timetime
Modulation techniques: monocarrier vs. multicarrier
To improve the spectral efficiency:
To use orthogonal carriers (allowing overlapping)Eliminate band guards between carriers
– Selective Fading
– Very short pulses
– ISI is compartively long
– EQs are then very long
– Poor spectral efficiency because of band guards
Drawbacks
– It is easy to exploitFrequency diversity
– Flat Fading per carrier
– N long pulses
– ISI is comparatively short
– N short EQs needed
– Poor spectral efficiency because of band guards
Advantages
Furthermore
– It allows to deploy2D coding techniques
– Dynamic signalling
N carriers
B
Pulse length ~ N/B
Similar toFDM technique
– Data are shared among several carriers and simultaneously transmitted
B
Pulse length ~1/B
– Data are transmited over only one carrier
Channel
Guard bands
Channelization
Orthogonal Frequency Division Modulation
Data coded in frequency domain
N carriers
B
Transformation to time domain:each frequency is a sine wavein time, all added up.
f
Transmit
Symbol: 8 periods of f0
Symbol: 4 periods of f0
Symbol: 2 periods of f0
+
Receivetime
B
Decode each frequencybin separately
Channel frequencyresponse
f
f
Time-domain signal Frequency-domain signal
OFDM uses multiple carriersto modulate the data
N carriers
B
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).
Intercarrier Separation = 1/(symbol duration)
– No intercarrier guard bands– Controlled overlapping of bands– Maximum spectral efficiency (Nyquist rate)
– Very sensitive to freq. synchronization– Easy implementation using IFFTs
Features
Data
Carrier
T=1/f0Time
f0B
Fre
quen
cy
One OFDM symbol
Time-frequency grid
OFDM Modulation and Demodulation using FFTs
b0b1b2....bN-1
Data coded infrequency domain:one symbol at a time
IFFT
Inverse fastFourier transform
Data in time domain:one symbol at a time
d0d1d2d3....dN-1
time
f
P/S
Parallel toserial converter
Transmit time-domainsamples of one symbol
d0, d1, d2, …., dN-1
Receive time-domainsamples of one symbol
d0’, d1’, …., dN-1’ S/P
Serial toparallel converter
d0’d1’d2’....dN-1’
time
FFTFast Fouriertransform
b0’b1’b2’....bN-1’
f
Decode eachfrequency binindependently
Loss of orthogonality (by frequency offset)
k (t) exp( jk2t /T ) y km( t)exp j2 (k m)t /T
km (t) exp j2 (k m ) / T con 1/ 2
Transmission pulses
Reception pulse with offset
2 4 6 8 10 12 14 16-60
-55
-50
-45
-40
-35
-30
-25
-20
-15
-10
Total ICI due to loss of orthogonality
Carrier position within the band (N=16)
ICI
in d
B =0.05
=0.02
=0.01
=0.005
=0.002
=0.001
Practical limit assumed r.v.Gaussian =
0-0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4
Frequency offset:
Inte
rfe
renc
e:
Im(Ž
)/T
en
dB
Loss for 8 carriers
m=1
m=3m=5m=7
-70
-60
-50
-40
-30
-20
-10
0
Im( ) exp jk2t /T exp j(k m )2t / T dt0
T
T 1 exp( j2 )
j2(m )
Im () T sin m
Im2 ()
m T 2 1
m 2m1
N 1
T 2 2314
for N 1 (N 5 Is enough)
Interference betweenchannels k and k+m
Summing upm
Asymetric
Loss of orthogonality (time)
X i c0 k (t) l* ( t )dt
T / 2
T / 2
c1 k (t) l* (t )dt
T / 2
T / 2
Let us assumea misadjustment
2 consecutivesymbols
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.0810
15
20
25
30
35
40
45
Typical deviation for the relative misadjustment
ICI
in d
B
N=8
N=64
ICI due to loss of orthogonaliy
assumed an Uniform r.v.
Max. practical limit
Doubling N means 3 dB more ICI
EXi
2
T 2
4
T
2 1
2 0
1
22
T
2 ICI 20log 2T
, T
Per carrier
In average, the interferingpower in any carrier is
XiT
2m
Tm
2T
Or approximately,when <<T
independenton m
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
Relative misadjustment
Inte
rfe
ren
ce
en
dB
Loss for 16 carriers
m=1
m=5
m=10
Then Xi 2T
senmT
m, c0 c1
0, c0 c1
Zone of interest
if m=k-l
Including a “cyclic prefix”
CP
Pas
sin
g t
he
chan
nel
h(n
)
i(t)
j(t)
h(n)=(1)–n/n n=0,…,23
j(t)
i(t)
i(t)
To combat the time dispersion: including ‘special’ time guards in the symbol transitions
CP
TTc
copyFurthemore it converts Linear conv. = Cyclic conv.
(Method: overlap-save)
CP functions: – It acomodates the decaying transient of the previous symbol – It avoids the initial transient reachs the current symbol
Including the Cyclic Prefix
Symbol: 8 periods of fi
Symbol: 4 periods of fi
Initial transientremains within
the CP
Final transientremains within
the CP
The inclusion of a CPmaintains the orthogonality
Pas
sin
g t
he
chan
nel
h(n
)
Initial transient Decaying transient
Channel:
Symbol: 8 periods of fi
Symbol: 4 periods of fi
Without the Cyclic Prefix
Loss of orthogonality
802.11a System Specification
Sampling (chip) rate: 20MHz Chip duration: 50ns Number of FFT points: 64 FFT symbol period: 3.2s Cyclic prefix period: 16 chips or 0.8s
» Typical maximum indoor delay spread < 400ns» OFDM frame length: 80 chips or 4s» FFT symbol length / OFDM frame length = 4/5
Modulation scheme» QPSK: 2bits/sample» 16QAM: 4bits/sample» 64QAM: 6bits/sample
Coding: rate ½ convolutional code with constraint length 7
GI2 T1 GI OFDM Symbol GI OFDM SymbolT2t1 t2 t3 t4 t5 t6 t7 t8 t9 t10
Short training sequence:AGC and frequency offset
Long training sequence:Channel estimation
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
Bad carriers
T=1/f0Time
f0
B
Fre
qu
en
cy
Time-frequency grid
Frequency response
Errors are no longer random. Interleaving is often used to scramblethe data bits so that standard error correcting codes can be applied.
f
Spectrum Mask
Frequency (MHz)f carrier
Power Spectral Density
9 11 20 30-9-11-20-30
-20 dB
-28 dB
-40 dB
• Requires extremely linear power amplifier design.
Adjacent Channel and Alternate Channel Rejection
• Requires joint design of the anti-aliasing filter and ADC.
Daterate
MinimumSensibility
Adjacent ChannelRejection
AlternateChannel rejection
6 Mbps -82 dBm 16 dB 32 dB
12Mbps -79 dBm 13 dB 29 dB
24Mbps -74 dBm 8 dB 24 dB
36Mbps -70 dBm 4 dB 20 dB
54Mbps -65 dBm 0 dB 15 dB
16 dB blocker
32 dB blocker
Signal Frequency
OFDM Receiver Design
Yun Chiu, Dejan Marković, Haiyun Tang, Ning Zhang
EE225C Final Project Report, 12 December
2000
Introduction to OFDM Basic idea
» Using a large number of parallel narrow-band sub-carriers instead of a single wide-band carrier to transport information
Advantages» Very easy and efficient in dealing with multi-path» Robust again narrow-band interference
Disadvantages» Sensitive to frequency offset and phase noise» Peak-to-average problem reduces the power efficiency of RF
amplifier at the transmitter Adopted for various standards
– DSL, 802.11a, DAB, DVB
Data set to be encoded on sub-carriers
IFFT at transmitter
FFT at receiver
OFDM Signal Representation
Cyclic Prefix
Tg T
max
Tx
Multi-path components
TSampling start
OFDM System Block Diagram
Synchronization
Frame detection
Frequency offset compensation
Sampling error » Usually less 100ppm and can be ignored
– 100ppm = off 1% of a sample every 100 samples
Tg TFrame start
Channel Estimation
0 20 40 60 80 100 1200
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Multipath propagation distance
A
Simulated multipath components on 3rd floor of Soda Hallfrom transmitter (26, 18) to receiver (9, 22.5)
Channel Estimation
0 20 40 60 80 100 1200
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Multipath propagation distance
A
Simulated multipath components on 3rd floor of Soda Hallfrom transmitter (26, 18) to receiver (9, 22.5)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
x 107
0
0.005
0.01
0.015
0.02
0.025
0.03
Hz
Simulated channel frequency response from (26, 18) to (9, 22.5)
System Pilot Structure
Synchronization, Frequency
Offset Compensation
Outline
• IEEE 802.11a OFDM Transmitter Model
• Receiver Synchronization Module A Robust Double Correlation (Correlation & Auto-
Correlation) Based Algorithm
• Receiver Frequency Offset Estimation Module A Coarse-Fine Joint Estimation Algorithm with Decision-
Alignment Error Correction
• Receiver Frequency Offset Compensation Module
• Performance Summary
IEEE 802.11a OFDM Txer
Short Preamble Gen.Long Preamble Gen.
OFDM Data Path
Signal Data Data21 4 73 5 986 T1GI2 GIGI GI10
Signal Detection, AGC,Diversity Selection
10 x 0.8 = 8 uS
T2
2 x 0.8 + 2 x 3.2 = 8 uS
Channel & Fine Freq.Offset Estimation
Coarse Freq. OffsetEst.,Timing Sync.
0.8 + 3.2 = 8 uS 0.8 + 3.2 = 8 uS 0.8 + 3.2 = 8 uS
Rate, Length Data Data
Short & Long Preambles
f-24
1+j
-20
-16-12
-1-j
f-1
-16
-26
+1
-24
-12
Short Preamble
Long Preamble
Period = 16 Chips
Period = 64 Chips
Correlation of Short Preamble
Correlation
Coarse Timing
Fine Timing
Auto-Correlation
Synchronization
16Td
* S
Td Td Td...
* * *...
Td Td Td Td...
Td
From AGC
* S
Td Td Td...
* * *...
Short Preamble (LUT)
...
Td
From AGC
Moving Auto-Corr. Unit
Moving SP Corr. Unit
Impairments: Multi-Path Channel
tT
0 2T
t
0
t
0T
2T3T
4T
Tc
Tc
Ch. Impulse Response
t
0
t
0T
2T3T
4T Tc
t5T
T2T
3T4T
t
0T
2T3T
4T5T
t
t
0T
2T3T
4T5T
Auto-Correlation w/ Multi-Path Channel Response.
Impairments: Frequency Offset
t
0T
2T3T
4T
t
0T 2T
3T4T
t
t
0T
2T3T
4T
Fine Frequency Offset Est.
Complex Multiplier
Sync. Signal
Accumulator
Coarse-Fine Joint Estimation & Decision Alignment Error Correction
00
0
0
1
23
76
4
85
0
AD
BC
Vin
Folding Signal
0
0 0 Folding ADC
Coarse Fine ±100ppm fc @ 5.8GHz
Average over 16 chips
Average over 64 chips
Frequency Offset Compensation
Joint Coarse-Fine Est.
Offset Corr.
Decision Alignment
Channel
Performance Summary
Parameters MetricsNumber of sub-carriers 48 data +4 pilot
OFDM symbol freq. 4 s
Modulation Scheme BPSK up to 64-QAM
Sampling clock freq. 20 MHz
Sync. Frame Start Accuracy 8 chips (CP = 16 chips)
Freq. Offset Est. Range ± 5 = ± 100ppm @ 5.8 GHz
Freq. Offset Est. Accuracy 1% (@ 15dB SNR)
Critical path delay 12.7 ns
Silicon area 397,080 m2
Total power consumption 3.4 mW @ 20 MHz