# Signal Processing for

AI and Robotics

Nov 24, 2013 (4 years and 7 months ago)

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Signal Processing for
OFDM
Communication
Systems

Eric Jacobsen

Minister of Algorithms, Intel Labs

Communication Technology Laboratory/

July 29, 2004

With a lot of material from Rich Nicholls, CTL/RCL

and Kurt Sundstrom, of unknown whereabouts

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2

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

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

OFDMA

PAPR largely independent of modulation order

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Downsides of OFDM

Complexity

FFT for modulation, demodulation

Must be compared to complexity of equalizer

Synchronization

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

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

< 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
Frequency
Offset
Estimation
Frequency
Correction
Channel
Estimation &
Correction
BPF
LPF
LPF

/2
BPF
Duplexer
DAC
LNA
I
Q
HPA
I & Q
I
Q
AGC

/2
Digital
LPF
Symbol
Timing
Signal
Detect
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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16

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

compared to

3.5dB more than

a single
-
carrier

system.

The results shown

use only data

whitening for

PAPR reduction.

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

Seeking water filling capacity

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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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24

Channel Frequency Response

Multipath

-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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25

-
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

Channel Bandwidth

64 QAM

16 QAM

QPSK

Sub Carriers

OFDM “Symbol”

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Per
-

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)

-
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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䥓䤠晲潭⁳ 浢o氠⌱ to

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

SCM

Sensitivity (margin)

Complexity

Memory

Phase noise sensitivity

Frequency registration

Reduced PA Backoff

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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