Signal Processing for

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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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12

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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19

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 #N-1
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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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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31

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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