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Signal Processing for
OFDM
Communication
Systems
Eric Jacobsen
Minister of Algorithms, Intel Labs
Communication Technology Laboratory/
Radio Communications Laboratory
July 29, 2004
With a lot of material from Rich Nicholls, CTL/RCL
and Kurt Sundstrom, of unknown whereabouts
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Outline
OFDM
–
What and Why
Subcarrier Orthogonality and Spectral Effects
Time Domain Comparison
Equalization
Signal Flow
PAPR management
Cool Tricks
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Digital Modulation Schemes
Single Carrier
PSK, QAM, PAM, MSK, etc.
Demodulate with matched filter, PLLs
Common Standards: DVB

S, Intelsat, GSM, Ethernet,
DOCSIS
Multi

Carrier
OFDM, DMT
Demodulate with FFT, DSP
Common Standards: DVB

T, 802.11a, DAB, DSL

DMT
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What is OFDM?
Orthogonal Frequency Division Multiplexing
Split a high symbol rate data stream into N lower rate streams
Transmit the N low rate data streams using N subcarriers
Frequency Division Multiplexing (FDM)
& Multi

Carrier Modulation (MCM)
N
subcarriers
must be mutually orthogonal
. . .
High Rate
Complex
Symbol Stream
Complex
Baseband
OFDM Signal
s(t)
OFDM Conceptual Block Diagram
Stream

N/2
Stream N/2

1
Stream 1
Serial to Parallel
Hold (T
hold
= 1/
f sec)
. . .
t
f
N
j
2
2
exp
. . .
t
f
j
2
exp
t
f
N
j
1
2
2
exp
Subcarrier spacing =
f
f
Partition available bandwidth
into N orthogonal subchannels
0

N(
f)/2
(N

1)(
f)/2
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Why OFDM?
Reduces symbol rate by more than N, the number of subcarriers
Fading per subcarrier is flat, so single coefficient equalization
Reduces equalizer complexity
–
O(N) instead of O(N
2
)
Fully Captures Multipath Energy
For Large Channel Coherence Time, OFDM/DMT can Approach “Water
Pouring” Channel Capacity
Narrowband interference will corrupt small number of subcarriers
Effect mitigated by coding/interleaving across subcarriers
Increases Diversity Opportunity
Frequency Diversity
Increases Adaptation Opportunities, Flexibility
Adaptive Bit Loading
OFDMA
PAPR largely independent of modulation order
Helpful for systems with adaptive modulation
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Downsides of OFDM
Complexity
FFT for modulation, demodulation
Must be compared to complexity of equalizer
Synchronization
Overhead
Cyclic Extension
Increases the length of the symbol for no increase in capacity
Pilot Tones
Simplify equalization and tracking for no increase in capacity
PAPR
Depending on the configuration, the PAPR can be ~3dB

6dB worse than a single

carrier system
Phase noise sensitivity
The subcarriers are N

times narrower than a comparable single

carrier system
Doppler Spread sensitivity
Synchronization and EQ tracking can be problematic in high doppler environments
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Subcarrier Orthogonality
Orthogonality simplifies recovery of the N data streams
Orthogonal subcarriers = No inter

carrier

interference (ICI)
Time Domain Orthogonality:
Every subcarrier has an integer number of cycles within T
OFDM
Satisfies precise mathematical definition of orthogonality for complex
exponential (and sinusoidal) functions over the interval [0, T
OFDM
]
Frequency Domain Orthogonality:
f
ICI = 0 at f = nf
0
f
Some FDM systems achieve
orthogonality through zero
spectral overlap
BW inefficient!
OFDM systems have overlapped
spectra with each subcarrier spectrum
having a Nyquist “zero ISI pulse shape”
(really zero ICI in this case).
BW efficient!
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OFDM Signal (Time & Frequency)
0
2
4
6
8
10
12
0.4
0.2
0
0.2
0.4
0.6
0.8
1
FREQUENCY DOMAIN: OFDM Subcarriers 2 through 10
Frequency (Normalized by 1/Tofdm)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1.5
1
0.5
0
0.5
1
1.5
TIME DOMAIN: 2 OFDM subcarriers (BPSK)
Time (Normalized by Tofdm)
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Practical Signal Spectra
0
500
1000
1500
2000
30
20
10
0
Frequency
Magnitude
Single carrier signals require
filtering for spectral containment.
This signal has narrow rolloff
regions which requires long filters.
OFDM spectra have naturally steep
sides, especially with large N.
The PAPR is often higher, which may
result in more spectral regrowth.
The blue trace is an unfiltered OFDM signal with
216 subcarriers. The red trace includes the effects
of a non

linear Power Amplifier.
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Time

Domain Comparisons
...
Cyclic Prefix
Previous
Symbol
FFT Window
Last t
g
portion of symbol
t
g
...
...
…
t
g
Multipath Delay Profile
OFDM Symbol Period
Single Carrier
Symbol Period
Equivalent EQ Length
Residual energy from previous symbol due to
multipath is inconsequential up to this point in time
By greatly increasing the symbol period the fading per subcarrier
becomes flat, so that it can be equalized with a single coefficient
per subcarrier. The addition of the cyclic prefix eliminates Inter

Symbol Interference (ISI) due to multipath.
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Frequency Domain Equalization
Frequency
Channel Frequency Response (at time t)
Subcarrier n
Design System Such That T
Delay Spread
< T
Guard
and B
Coherence
> B
Subcarrier
–
Subcarriers are perfectly orthogonal (no ISI or ICI)
–
Each Subcarrier experiences an AWGN channel
Equalizer Complexity : Serial Data Rate = 1/T, OFDM Symbol Rate = 1/(NT)
–
FEQ performs N complex multiplies in time NT (or 1 complex mult per time T)
–
Time domain EQ must perform MT complex multiplies in time T where M is the
number of equalizer coefficients
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802.11a PHY Block Diagram
IFFT (TX)
FFT(RX)
FEC
Encoder
Interleaver
QAM
Mapping
Pilot
Insertion
Data
Scrambler
S/P
P/S
Guard
Interval
Insertion
Window
DAC
FEC
Decoder
Deinterleaver
QAM
Demap
Data
Descrambler
P/S
S/P
Guard
Interval
Removal
ADC
Frequency
Offset
Estimation
Frequency
Correction
Channel
Estimation &
Correction
BPF
LPF
LPF
ADC
/2
BPF
Duplexer
DAC
LNA
I
Q
HPA
I & Q
I
Q
AGC
/2
Digital
LPF
Symbol
Timing
Signal
Detect
RSSI
To MAC
Sublayer
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802.11a Processing
802.11a is a TDD contention

based, bursty protocol
Full acquisition, synchronization, and EQ training can be
performed for each burst or “frame”
The “short training symbols” provide timing, AGC,
diversity selection, and initial carrier offset
The “long training symbols” provide fine
synchronization and channel estimation
Two FFT periods allow 3dB increase in channel estimation
SNR by combining (averaging) the estimates
Tracking is facilitated by the four pilot tones
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802.11a Time/Frequency Signal Structure
800 ns
4
s
0

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53 Subcarriers (48 data, 4 pilot, 0 @ DC)
DATA FRAME
Indicates Pilot Tone Location
…
…
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DVB

T Time/Frequency Signal Structure
Since DVB

T is a continuous transmit signal, channel estimation is
facilitated easily by rotating pilots across the subcarrier indices. Interpolation
provides channel estimation for every subcarrier.
This figure is from reference [4]
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Peak to Average Power Ratio
Single Carrier Systems
PAPR affected by modulation scheme, order, and filtering
Constant

envelope schemes have inherently low PAPR
–
For example: MSK, OQPSK
PAPR increases with modulation order
–
e.g., 64

QAM PAPR is higher than QPSK
As Raised Cosine excess bandwidth decreases, PAPR increases
–
Squeezing the occupied spectrum increases PAPR
Multi

Carrier Systems
PAPR affected by subcarrier quantity and filtering
PAPR is only very weakly connected to modulation order
PAPR increases with the number of subcarriers
–
Rate of increase slows after ~64 subcarriers
–
The Central Limit Theorem is still your friend
Whitening is very effective at reducing PAPR
Symbol shaping decreases PAPR
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PAPR with 240 subcarriers
3
4
5
6
7
8
9
10
11
12
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
PAPR Cumulative Distribution Function
64

QAM
20% RRC
64

QAM
OFDM

48
802.11a
64

QAM
OFDM

240
P(PAPR < Abscissa)
PAPR (dB)
N = 240 requires
no more than 1dB
additional backoff
compared to
802.11a, and about
3.5dB more than
a single

carrier
system.
The results shown
use only data
whitening for
PAPR reduction.
Additional
improvements may
be possible with
other techniques.
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PAPR Mitigation in OFDM
Scrambling (whitening) decreases the probability of
subcarrier alignment
Subcarriers with common phase increase PAPR
Symbol weighting reduces the effects of phase
discontinuities at the symbol boundaries
Raised Cosine Pulse weighting
–
Works well, requires buffering
Signal filtering
–
Easier to implement
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Time

Domain Weighting
The phase
discontinuities
between symbols
increase the size
of the spectral
sidelobes.
Weighting the
symbol transitions
smooths them
out and reduces
the sidelobe
amplitudes.
Typically Raised

Cosine weighting
Is applied.
This figure is informative content from the IEEE 802.11a specification. The two

fft period case applies only to preambles for synchronization and channel
estimation.
Tapered
Regions
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Effect of Symbol Weighting
With 1% RC weighting
With no RC weighting
Applying a tiny bit of symbol weighting in the time domain has a
significant effect on PAPR. In this case only 1% of the symbol time
is used for tapering. The blue trace is prior to the PA, the red trace after.
Application of the 1% RC window meets the green transmit mask.
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Cool and Interesting Tricks
OFDMA
Different users on different subcarriers
Adaptive Bit Loading
Seeking water filling capacity
Adaptation to Channel Fading
Adaptation to Interference
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...
Pilot Tones
Data Subcarriers
User #1
User #2
User #3
User #N1
User #N
Control
Redundant
Control
OFDMA Subcarrier Division
The 802.16 standard describes multiple means to implement OFDMA. In one
mode each user’s signal occupies contiguous subcarriers which can be
independently modulated. Another mode permutes each user’s subcarriers
across the band in a spreading scheme so that all user’s subcarriers are
interlaced with other user’s subcarriers. The first method allows for adaptive
modulation and the second method increases frequency diversity.
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Each color is for a distinct terminal
.
Redundant Control Subcarriers
Control Subcarriers
OFDM Symbols
Subcarriers
Subcarrier Division with TDM
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Channel Frequency Response
Multipath
Frequency Selective Fading
30
25
20
15
10
5
0
5
5
4
3
2
1
0
1
2
3
4
5
Frequency (MHz)
Response (dB)
30
25
20
15
10
5
0
5
5
4
3
2
1
0
1
2
3
4
5
Frequency (MHz)
Response (dB)
30
25
20
15
10
5
0
5
5
4
3
2
1
0
1
2
3
4
5
Frequency (MHz)
Response (dB)
30
25
20
15
10
5
0
5
5
4
3
2
1
0
1
2
3
4
5
Frequency (MHz)
Response (dB)
30
25
20
15
10
5
0
5
5
4
3
2
1
0
1
2
3
4
5
Frequency (MHz)
Response (dB)
30
25
20
15
10
5
0
5
5
4
3
2
1
0
1
2
3
4
5
Frequency (MHz)
Response (dB)
30
25
20
15
10
5
0
5
5
4
3
2
1
0
1
2
3
4
5
Frequency (MHz)
Response (dB)
30
25
20
15
10
5
0
5
5
4
3
2
1
0
1
2
3
4
5
Frequency (MHz)
Response (dB)
30
25
20
15
10
5
0
5
5
4
3
2
1
0
1
2
3
4
5
Frequency (MHz)
Response (dB)
30
25
20
15
10
5
0
5
5
4
3
2
1
0
1
2
3
4
5
Frequency (MHz)
Response (dB)
30
25
20
15
10
5
0
5
5
4
3
2
1
0
1
2
3
4
5
Frequency (MHz)
Response (dB)
v
= 100 km/hr
f
= 2 GHz
t
= 0.5 m sec
Shannon’s Law applies in each “flat” subinterval
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Adaptive Bit Loading
Deep Fade
(Bad)

30

25

20

15

10

5
0
5

5

4

3

2

1
0
1
2
3
4
5
Frequency (MHz)
Response (dB)
6 bps/Hz
4 bps/Hz
2 bps/Hz
0 bps/Hz
High SNR At Receiver
Low SNR At Receiver
Channel Bandwidth
64 QAM
16 QAM
QPSK
Sub Carriers
OFDM “Symbol”
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Per

Subcarrier Adaptive Modulation
Frequency
Signal level
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References
[1] IEEE Std 802.11a

1999
[2] Robert Heath, UT at A,
http://www.ece.utexas.edu/~bevans/courses/realtime/lectures/20_OFDM/346,22,OFDM and MIMO Systems
[3] Hutter, et al,
http://www.lis.ei.tum.de/research/lm/papers/vtc99b.pdf
[4] Zabalegui, et al, http://www.scit.wlv.ac.uk/~in8189/CSNDSP2002/Papers/G1/G1.2.PDF
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Backup
No!
–
Go forward!
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Cyclic Prefix (Guard Interval)
Delay Spread Causes Inter

Symbol

Interference (ISI) and Inter

Carrier

Interference (ICI)
Non

linear phase implies different subcarriers experience different delay
(virtually all real channels are non

linear phase)
Adding a guard interval between OFDM symbols mitigates this problem
Zero valued guard interval will eliminate ISI but causes ICI
Better to use cyclic extension of the symbol
T
OFDM
T
G
T
FFT
3.5 cycles of subcarrier #1
inside the FFT integration
period
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Gu慲d湴敲v慬a敬e浩m慴敳
䥓䤠晲潭 浢o氠⌱ to
獹浢o氠⌲
Symbol #2
Symbol #1
Subcarrier #2
Subcarrier #1
(delayed relative
to #2 )
ICI
T
OFDM
Cyclic extension
removes ISI and ICI !
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DVB

T Time/Frequency Signal Structure
Since DVB

T is a continuous transmit signal, channel estimation is
facilitated easily by rotating pilots across the subcarrier indices.
Interpolation provides channel estimation for every subcarrier.
This figure is from reference [3]
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Advantages
SCM
Sensitivity (margin)
Complexity
Memory
Phase noise sensitivity
Frequency registration
Reduced PA Backoff
Less Overhead (no
cyclic prefix)
OFDM
Single Frequency Networks
Simple EQ
Flexibility
Statistical Mux
OFDMA
–
BW, TDMA
LOW SNR, avoid DFE
PAPR not affected by
modulation order.
Automatically integrates
multipath.
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