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
N


exp  j 2 f t 
2


Subcarrier spacing = f
Partition available bandwidth
into N orthogonal subchannels
exp j 2 f t
Stream 1

...
...
Hold (Thold = 1/f sec)
...
High Rate
Complex
Symbol Stream
Serial to Parallel
Stream -N/2
Complex
Baseband
OFDM Signal
s(t)
f
-N(f)/2
0
(N-1)(f)/2


N 
exp  j 2   1f t 
2



Stream N/2-1
OFDM Conceptual Block Diagram
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Why OFDM?
Communication and Interconnect Technology Lab
 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(N2)
 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 TOFDM
 Satisfies precise mathematical definition of orthogonality for complex
exponential (and sinusoidal) functions over the interval [0, TOFDM ]
 Frequency Domain Orthogonality:
ICI = 0 at f = nf0
f
Some FDM systems achieve
orthogonality through zero
spectral overlap
 BW inefficient!
f
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)
TIME DOMAIN: 2 OFDM subcarriers (BPSK)
1.5
1
0.5
0
-0.5
-1
-1.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Time (Normalized by Tofdm)
1.6
1.8
2
FREQUENCY DOMAIN: OFDM Subcarriers 2 through 10
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
0
2
4
6
8
Frequency (Normalized by 1/Tofdm)
10
12
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Practical Signal Spectra
Single carrier signals require
filtering for spectral containment.
This signal has narrow rolloff
regions which requires long filters.
Magnitude
0
10
20
30
0
500
1000
Frequency
1500
2000
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
...
...
...
Equivalent EQ Length
Multipath Delay Profile
Previous
Symbol
Cyclic Prefix
Single Carrier
Symbol Period
…
FFT Window
tg
tg
Last tg portion of symbol
OFDM Symbol Period
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 InterSymbol Interference (ISI) due to multipath.
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Frequency Domain Equalization

Design System Such That TDelay Spread < TGuard and BCoherence > BSubcarrier
– 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
Channel Frequency Response (at time t)
Subcarrier n

Frequency
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802.11a PHY Block Diagram
I
Guard
Interval
Insertion
DAC
HPA
I&Q
/2
Window
Q
Duplexer
DAC
Data
Scrambler
FEC
Encoder
Interleaver
QAM
Mapping
Pilot
Insertion
S/P
Data
Descrambler
FEC
Decoder
Deinterleaver
QAM
Demap
Channel
Estimation &
Correction
P/S
To MAC
Sublayer
BPF
IFFT (TX)
FFT(RX)
P/S
S/P
Guard
Interval
Removal
I
RSSI
ADC
LPF
LNA
Digital
LPF
Symbol
Timing
Frequency
Correction
Frequency
Offset
Estimation
Signal
Detect
AGC
Q
/2
ADC
BPF
LPF
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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
DATA FRAME
53 Subcarriers (48 data, 4 pilot, 0 @ DC)
FREQUENCY
8.125 MHz
Short
Training
Symbols
Long
Training
Symbols
Data
Symbols
…
0
…
-8.125 MHz
Indicates Pilot Tone Location
800 ns
4 s
TIME
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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
PAPR Cumulative Distribution Function
1
N = 240 requires
no more than 1dB
additional backoff
compared to
802.11a, and about
3.5dB more than
a single-carrier
system.
64-QAM
20% RRC
0.9
P(PAPR < Abscissa)
0.8
64-QAM
OFDM-48
802.11a
0.7
0.6
64-QAM
OFDM-240
0.5
The results shown
use only data
whitening for
PAPR reduction.
Additional
improvements may
be possible with
other techniques.
0.4
0.3
0.2
0.1
0
3
4
5
6
7
8
9
10
11
12
PAPR (dB)
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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.
Tapered
Regions
Weighting the
symbol transitions
smooths them
out and reduces
the sidelobe
amplitudes.
Typically RaisedCosine weighting
Is applied.
This figure is informative content from the IEEE 802.11a specification. The twofft period case applies only to preambles for synchronization and channel
estimation.
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Effect of Symbol Weighting
With no RC weighting
With 1% 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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OFDMA Subcarrier Division
Pilot Tones
Data Subcarriers
...
Control User #1
User #2
User #3
User #N-1
User #N
Redundant
Control
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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Subcarrier Division with TDM
Each color is for a distinct terminal.
Subcarriers
Control Subcarriers
Redundant Control Subcarriers
OFDM Symbols
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Channel Frequency Response
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Multipath  Frequency Selective Fading
Frequency (MHz)
-5
-4
-3
-2
-1
0
1
2
3
4
5
5
Response (dB)
0
-5
-10
-15
-20
-25
-30
Shannon’s Law applies in each “flat” subinterval
v = 100 km/hr f = 2 GHz
t = 0.5 m sec
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Adaptive Bit Loading
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Frequency (MHz)
-5
-4
-3
-2
-1
0
1
2
3
4
5
5
Response (dB)
High SNR At Receiver
0
6 bps/Hz
-5
4 bps/Hz
-10
-15
-20
2 bps/Hz
Deep Fade
(Bad)
0 bps/Hz
-25
-30
Low SNR At Receiver
Channel Bandwidth
64 QAM
16 QAM
QPSK
Sub Carriers
OFDM “Symbol”
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Signal level
Per-Subcarrier Adaptive Modulation
Frequency
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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-CarrierInterference (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
Symbol #1
Symbol #2
TOFDM
TOFDM
TG
TFFT
ICI
Subcarrier #2
Subcarrier #1
(delayed relative
to #2 )
Guard interval eliminates
ISI from symbol #1 to
symbol #2
Cyclic extension
removes ISI and ICI !
3.5 cycles of subcarrier #1
inside the FFT integration
period  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
 OFDM
 Sensitivity (margin)
 Single Frequency Networks
 Simple EQ
 Complexity
 Flexibility
 Memory
 Statistical Mux
 Phase noise sensitivity
 OFDMA – BW, TDMA
 Frequency registration
 LOW SNR, avoid DFE
 Reduced PA Backoff
 PAPR not affected by
modulation order.
 Less Overhead (no
cyclic prefix)
 Automatically integrates
multipath.
 IEEE Politics
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