® signal processing for ofdm communication systems eric jacobsen minister of algorithms, intel...

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Signal Processing for OFDM Communication Systems

Signal Processing for OFDM Communication Systems

Eric JacobsenEric Jacobsen

Minister of Algorithms, Intel LabsMinister of Algorithms, Intel Labs

Communication Technology Laboratory/Communication Technology Laboratory/

Radio Communications LaboratoryRadio Communications Laboratory

July 29, 2004July 29, 2004

With a lot of material from Rich Nicholls, CTL/RCLWith a lot of material from Rich Nicholls, CTL/RCLand Kurt Sundstrom, of unknown whereaboutsand Kurt Sundstrom, of unknown whereabouts

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Communication and Interconnect Technology Lab

OutlineOutline OFDM – What and WhyOFDM – What and Why

Subcarrier Orthogonality and Spectral EffectsSubcarrier Orthogonality and Spectral Effects

Time Domain ComparisonTime Domain Comparison

EqualizationEqualization

Signal FlowSignal Flow

PAPR managementPAPR management

Cool TricksCool Tricks

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Digital Modulation SchemesDigital Modulation Schemes Single CarrierSingle Carrier

PSK, QAM, PAM, MSK, etc.PSK, QAM, PAM, MSK, etc.

Demodulate with matched filter, PLLsDemodulate with matched filter, PLLs

Common Standards: DVB-S, Intelsat, GSM, Ethernet, Common Standards: DVB-S, Intelsat, GSM, Ethernet, DOCSISDOCSIS

Multi-CarrierMulti-Carrier

OFDM, DMTOFDM, DMT

Demodulate with FFT, DSPDemodulate with FFT, DSP

Common Standards: DVB-T, 802.11a, DAB, DSL-DMTCommon Standards: DVB-T, 802.11a, DAB, DSL-DMT

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What is OFDM?What is OFDM? Orthogonal Frequency Division MultiplexingOrthogonal Frequency Division Multiplexing

Split a high symbol rate data stream into N lower rate streamsSplit a high symbol rate data stream into N lower rate streams

Transmit the N low rate data streams using N subcarriersTransmit the N low rate data streams using N subcarriers

Frequency Division Multiplexing (FDM) & Multi-Carrier Modulation (MCM)Frequency Division Multiplexing (FDM) & Multi-Carrier Modulation (MCM)

N N subcarrierssubcarriers must be mutually orthogonal must be mutually orthogonal

. . .

High RateComplex

Symbol Stream

ComplexBaseband

OFDM Signals(t)

OFDM Conceptual Block Diagram

Stream -N/2

Stream N/2-1

Stream 1

Se

rial t

o P

ara

llel

Ho

ld (

Tho

ld =

1/

f se

c)

. . .

tf

Nj

2 2exp

. . . tfj 2exp

tfN

j 12

2exp

Subcarrier spacing = f

f

Partition available bandwidthinto N orthogonal subchannels

0-N(f)/2 (N-1)(f)/2

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Why OFDM?Why OFDM? Reduces symbol rate by more than N, the number of subcarriersReduces symbol rate by more than N, the number of subcarriers

Fading per subcarrier is flat, so single coefficient equalizationFading per subcarrier is flat, so single coefficient equalization Reduces equalizer complexity – O(N) instead of O(NReduces equalizer complexity – O(N) instead of O(N22))

Fully Captures Multipath EnergyFully Captures Multipath Energy

For Large Channel Coherence Time, OFDM/DMT can Approach “Water For Large Channel Coherence Time, OFDM/DMT can Approach “Water Pouring” Channel CapacityPouring” Channel Capacity

Narrowband interference will corrupt small number of subcarriersNarrowband interference will corrupt small number of subcarriers Effect mitigated by coding/interleaving across subcarriersEffect mitigated by coding/interleaving across subcarriers

Increases Diversity OpportunityIncreases Diversity Opportunity Frequency DiversityFrequency Diversity

Increases Adaptation Opportunities, FlexibilityIncreases Adaptation Opportunities, Flexibility Adaptive Bit LoadingAdaptive Bit Loading OFDMAOFDMA

PAPR largely independent of modulation orderPAPR largely independent of modulation order Helpful for systems with adaptive modulationHelpful for systems with adaptive modulation

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Downsides of OFDMDownsides of OFDM ComplexityComplexity

FFT for modulation, demodulationFFT for modulation, demodulation Must be compared to complexity of equalizerMust be compared to complexity of equalizer

SynchronizationSynchronization

OverheadOverhead Cyclic ExtensionCyclic Extension

Increases the length of the symbol for no increase in capacityIncreases the length of the symbol for no increase in capacity

Pilot TonesPilot Tones Simplify equalization and tracking for no increase in capacitySimplify equalization and tracking for no increase in capacity

PAPRPAPR Depending on the configuration, the PAPR can be ~3dB-6dB worse than a single-Depending on the configuration, the PAPR can be ~3dB-6dB worse than a single-

carrier systemcarrier system

Phase noise sensitivityPhase noise sensitivity The subcarriers are N-times narrower than a comparable single-carrier systemThe subcarriers are N-times narrower than a comparable single-carrier system

Doppler Spread sensitivityDoppler Spread sensitivity Synchronization and EQ tracking can be problematic in high doppler environmentsSynchronization and EQ tracking can be problematic in high doppler environments

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Subcarrier OrthogonalitySubcarrier Orthogonality Orthogonality simplifies recovery of the N data streamsOrthogonality simplifies recovery of the N data streams

Orthogonal subcarriers = No inter-carrier-interference (ICI)Orthogonal subcarriers = No inter-carrier-interference (ICI)

Time Domain Orthogonality:Time Domain Orthogonality:

Every subcarrier has an integer number of cycles within TEvery subcarrier has an integer number of cycles within TOFDMOFDM

Satisfies precise mathematical definition of orthogonality for complex Satisfies precise mathematical definition of orthogonality for complex exponential (and sinusoidal) functions over the interval [0, Texponential (and sinusoidal) functions over the interval [0, TOFDM OFDM ]]

Frequency Domain Orthogonality:Frequency Domain Orthogonality:

f

ICI = 0 at f = nf0

f

Some FDM systems achieveorthogonality through zero spectral overlap BW inefficient!

OFDM systems have overlappedspectra with each subcarrier spectrumhaving a Nyquist “zero ISI pulse shape” (really zero ICI in this case). BW efficient!

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OFDM Signal (Time & Frequency)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

1.5TIME DOMAIN: 2 OFDM subcarriers (BPSK)

Time (Normalized by Tofdm)

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Practical Signal SpectraPractical Signal Spectra

0 500 1000 1500 200030

20

10

0

Frequency

Mag

nitu

de

Single carrier signals requireSingle carrier signals requirefiltering for spectral containment.filtering for spectral containment.This signal has narrow rolloffThis signal has narrow rolloffregions which requires long filters.regions which requires long filters.

OFDM spectra have naturally steepOFDM spectra have naturally steepsides, especially with large N.sides, especially with large N.The PAPR is often higher, which mayThe PAPR is often higher, which mayresult in more spectral regrowth.result in more spectral regrowth.The blue trace is an unfiltered OFDM signal withThe blue trace is an unfiltered OFDM signal with216 subcarriers. The red trace includes the effects216 subcarriers. The red trace includes the effectsof a non-linear Power Amplifier.of a non-linear Power Amplifier.

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Time-Domain ComparisonsTime-Domain Comparisons...

Cyclic PrefixPreviousSymbol FFT Window

Last tg portion of symbol

tg

... ...

…tg

Multipath Delay Profile

OFDM Symbol Period

Single Carrier Symbol Period

Equivalent EQ Length

Residual energy from previous symbol due tomultipath is inconsequential up to this point in time

By greatly increasing the symbol period the fading per subcarrierBy greatly increasing the symbol period the fading per subcarrierbecomes flat, so that it can be equalized with a single coefficientbecomes flat, so that it can be equalized with a single coefficientper subcarrier. The addition of the cyclic prefix eliminates Inter-per subcarrier. The addition of the cyclic prefix eliminates Inter-Symbol Interference (ISI) due to multipath. Symbol Interference (ISI) due to multipath.

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Frequency Domain EqualizationFrequency Domain Equalization

Frequency

Channel Frequency Response (at time t)

Su

bca

rrie

r n

Design System Such That TDesign System Such That TDelay SpreadDelay Spread < T < TGuardGuard and B and BCoherenceCoherence > B > BSubcarrierSubcarrier

– Subcarriers are perfectly orthogonal (no ISI or ICI)Subcarriers are perfectly orthogonal (no ISI or ICI)– Each Subcarrier experiences an AWGN channel Each Subcarrier experiences an AWGN channel

Equalizer Complexity : Serial Data Rate = 1/T, OFDM Symbol Rate = 1/(NT)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)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 Time domain EQ must perform MT complex multiplies in time T where M is the

number of equalizer coefficientsnumber of equalizer coefficients

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802.11a PHY Block Diagram802.11a PHY Block Diagram

IFFT (TX)

FFT(RX)

FEC Encoder

InterleaverQAM

MappingPilot

InsertionData

ScramblerS/P P/S

GuardInterval

InsertionWindow

DAC

FECDecoder

DeinterleaverQAM

DemapData

DescramblerP/S S/P

GuardInterval

Removal

ADC

FrequencyOffset

Estimation

FrequencyCorrection

ChannelEstimation &Correction

BPF

LPF

LPFADC

/2 BPF Duplexer

DAC

LNA

I

Q

HPAI & Q

I

Q

AGC/2

DigitalLPF

SymbolTiming

SignalDetect

RSSITo MACSublayer

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802.11a Processing802.11a Processing 802.11a is a TDD contention-based, bursty protocol802.11a is a TDD contention-based, bursty protocol

Full acquisition, synchronization, and EQ training can be Full acquisition, synchronization, and EQ training can be performed for each burst or “frame”performed for each burst or “frame”

The “short training symbols” provide timing, AGC, The “short training symbols” provide timing, AGC, diversity selection, and initial carrier offsetdiversity selection, and initial carrier offset

The “long training symbols” provide fine The “long training symbols” provide fine synchronization and channel estimationsynchronization and channel estimation

Two FFT periods allow 3dB increase in channel estimation Two FFT periods allow 3dB increase in channel estimation SNR by combining (averaging) the estimatesSNR by combining (averaging) the estimates

Tracking is facilitated by the four pilot tonesTracking is facilitated by the four pilot tones

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802.11a Time/Frequency Signal Structure802.11a Time/Frequency Signal Structure

800 ns 4 s

0

-8.125 MHz

8.125 MHz

FR

EQ

UE

NC

Y

TIME

ShortTrainingSymbols

LongTrainingSymbols

DataSymbols

53 S

ubca

rrie

rs (

48 d

ata,

4 p

ilot,

0 @

DC

)

DATA FRAME

Indicates Pilot Tone Location

……

……

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DVB-T Time/Frequency Signal StructureDVB-T Time/Frequency Signal StructureSince DVB-T is a continuous transmit signal, channel estimation isSince DVB-T is a continuous transmit signal, channel estimation isfacilitated easily by rotating pilots across the subcarrier indices. Interpolation facilitated easily by rotating pilots across the subcarrier indices. Interpolation provides channel estimation for every subcarrier.provides channel estimation for every subcarrier.

This figure is from reference [4]This figure is from reference [4]

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Peak to Average Power RatioPeak to Average Power Ratio Single Carrier SystemsSingle Carrier Systems

PAPR affected by modulation scheme, order, and filteringPAPR affected by modulation scheme, order, and filtering Constant-envelope schemes have inherently low PAPRConstant-envelope schemes have inherently low PAPR

– For example: MSK, OQPSK PAPR increases with modulation orderPAPR increases with modulation order

– e.g., 64-QAM PAPR is higher than QPSK As Raised Cosine excess bandwidth decreases, PAPR increasesAs Raised Cosine excess bandwidth decreases, PAPR increases

– Squeezing the occupied spectrum increases PAPR Multi-Carrier SystemsMulti-Carrier Systems

PAPR affected by subcarrier quantity and filteringPAPR affected by subcarrier quantity and filtering PAPR is only very weakly connected to modulation orderPAPR is only very weakly connected to modulation order PAPR increases with the number of subcarriersPAPR 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 PAPRWhitening is very effective at reducing PAPR Symbol shaping decreases PAPRSymbol shaping decreases PAPR

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PAPR with 240 subcarriersPAPR with 240 subcarriers

3 4 5 6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1PAPR Cumulative Distribution Function

64-QAM64-QAM20% RRC20% RRC

64-QAM64-QAMOFDM-48OFDM-48802.11a802.11a

64-QAM64-QAMOFDM-240OFDM-240

P(P

AP

R <

Ab

scis

sa

)P

(PA

PR

< A

bsc

iss

a)

PAPR (dB)PAPR (dB)

N = 240 requiresN = 240 requiresno more than 1dBno more than 1dBadditional backoffadditional backoffcompared tocompared to802.11a, and about802.11a, and about3.5dB more than3.5dB more thana single-carriera single-carriersystem.system.

The results shownThe results shownuse only datause only datawhitening forwhitening forPAPR reduction.PAPR reduction.AdditionalAdditionalimprovements mayimprovements maybe possible withbe possible withother techniques.other techniques.

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PAPR Mitigation in OFDMPAPR Mitigation in OFDM Scrambling (whitening) decreases the probability of Scrambling (whitening) decreases the probability of

subcarrier alignmentsubcarrier alignment

Subcarriers with common phase increase PAPRSubcarriers with common phase increase PAPR

Symbol weighting reduces the effects of phase Symbol weighting reduces the effects of phase discontinuities at the symbol boundariesdiscontinuities at the symbol boundaries

Raised Cosine Pulse weightingRaised Cosine Pulse weighting

– Works well, requires buffering Signal filteringSignal filtering

– Easier to implement

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Time-Domain WeightingTime-Domain WeightingThe phaseThe phasediscontinuitiesdiscontinuitiesbetween symbolsbetween symbolsincrease the sizeincrease the sizeof the spectralof the spectralsidelobes.sidelobes.

Weighting theWeighting thesymbol transitionssymbol transitionssmooths themsmooths themout and reducesout and reducesthe sidelobethe sidelobeamplitudes.amplitudes.

Typically Raised-Typically Raised-Cosine weightingCosine weightingIs applied.Is applied. This figure is informative content from the IEEE 802.11a specification. The This figure is informative content from the IEEE 802.11a specification. The

two-fft period case applies only to preambles for synchronization and channel two-fft period case applies only to preambles for synchronization and channel estimation.estimation.

TaperedTaperedRegionsRegions

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Effect of Symbol WeightingEffect of Symbol Weighting

With 1% RC weightingWith 1% RC weightingWith no RC weightingWith no RC weighting

Applying a tiny bit of symbol weighting in the time domain has aApplying a tiny bit of symbol weighting in the time domain has asignificant effect on PAPR. In this case only 1% of the symbol timesignificant effect on PAPR. In this case only 1% of the symbol timeis used for tapering. The blue trace is prior to the PA, the red trace after.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.Application of the 1% RC window meets the green transmit mask.

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Cool and Interesting TricksCool and Interesting Tricks OFDMAOFDMA

Different users on different subcarriersDifferent users on different subcarriers

Adaptive Bit LoadingAdaptive Bit Loading

Seeking water filling capacitySeeking water filling capacity

Adaptation to Channel FadingAdaptation to Channel Fading

Adaptation to InterferenceAdaptation to Interference

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...

Pilot Tones Data Subcarriers

User #1 User #2 User #3 User #N-1 User #NControl RedundantControl

OFDMA Subcarrier DivisionOFDMA Subcarrier Division

The 802.16 standard describes multiple means to implement OFDMA. In one The 802.16 standard describes multiple means to implement OFDMA. In one mode each user’s signal occupies contiguous subcarriers which can be mode each user’s signal occupies contiguous subcarriers which can be independently modulated. Another mode permutes each user’s subcarriers independently modulated. Another mode permutes each user’s subcarriers across the band in a spreading scheme so that all user’s subcarriers are 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 interlaced with other user’s subcarriers. The first method allows for adaptive modulation and the second method increases frequency diversity.modulation and the second method increases frequency diversity.

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Each color is for a distinct terminalEach color is for a distinct terminal..

Redundant Control Subcarriers

Control Subcarriers

OFDM Symbols

Su

bca

rrie

rsSubcarrier Division with TDMSubcarrier Division with TDM

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Channel Frequency ResponseChannel 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)

Re

sp

on

se

(d

B)

-30

-25

-20

-15

-10

-5

0

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

Frequency (MHz)

Re

sp

on

se

(d

B)

-30

-25

-20

-15

-10

-5

0

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

Frequency (MHz)

Re

sp

on

se

(d

B)

-30

-25

-20

-15

-10

-5

0

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

Frequency (MHz)

Re

sp

on

se

(d

B)

-30

-25

-20

-15

-10

-5

0

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

Frequency (MHz)

Re

sp

on

se

(d

B)

-30

-25

-20

-15

-10

-5

0

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

Frequency (MHz)

Re

sp

on

se

(d

B)

-30

-25

-20

-15

-10

-5

0

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

Frequency (MHz)

Re

sp

on

se

(d

B)

-30

-25

-20

-15

-10

-5

0

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

Frequency (MHz)

Re

sp

on

se

(d

B)

-30

-25

-20

-15

-10

-5

0

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

Frequency (MHz)

Re

sp

on

se

(d

B)

-30

-25

-20

-15

-10

-5

0

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

Frequency (MHz)

Re

sp

on

se

(d

B)

-30

-25

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-10

-5

0

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

Frequency (MHz)

Re

sp

on

se

(d

B)

v = 100 km/hr f = 2 GHzt = 0.5 m secShannon’s Law applies in each “flat” subinterval

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Adaptive Bit LoadingAdaptive Bit Loading

Deep Fade(Bad)

-30

-25

-20

-15

-10

-5

0

5

-5 -4 -3 -2 -1 0 1 2 3 4 5Frequency (MHz)

Res

po

nse

(d

B)

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 ModulationPer-Subcarrier Adaptive Modulation

Frequency

Sig

nal l

evel

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ReferencesReferences[1] IEEE Std 802.11a-1999[1] IEEE Std 802.11a-1999[2] Robert Heath, UT at A, [2] Robert Heath, UT at A,

http://www.ece.utexas.edu/~bevans/courses/realtime/lectures/20_OFDM/346,22,OFDM and MIMO Systemshttp://www.ece.utexas.edu/~bevans/courses/realtime/lectures/20_OFDM/346,22,OFDM and MIMO Systems[3] Hutter, et al, [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[4] Zabalegui, et al, http://www.scit.wlv.ac.uk/~in8189/CSNDSP2002/Papers/G1/G1.2.PDF

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BackupBackup

No! – Go forward!No! – Go forward!

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Cyclic Prefix (Guard Interval)Cyclic Prefix (Guard Interval) Delay Spread Causes Inter-Symbol-Interference (ISI) and Inter-Carrier-Interference (ICI)Delay Spread Causes Inter-Symbol-Interference (ISI) and Inter-Carrier-Interference (ICI)

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

Adding a guard interval between OFDM symbols mitigates this problemAdding a guard interval between OFDM symbols mitigates this problem

Zero valued guard interval will eliminate ISI but causes ICIZero valued guard interval will eliminate ISI but causes ICI

Better to use cyclic extension of the symbolBetter to use cyclic extension of the symbol

TOFDM

TG TFFT

3.5 cycles of subcarrier #1inside the FFT integration period ICI !

Guard interval eliminatesISI from symbol #1 to symbol #2

Symbol #2Symbol #1

Subcarrier #2

Subcarrier #1(delayed relativeto #2 )

ICI

TOFDM

Cyclic extension removes ISI and ICI !

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DVB-T Time/Frequency Signal StructureDVB-T Time/Frequency Signal StructureSince DVB-T is a continuous transmit signal, channel estimation isSince DVB-T is a continuous transmit signal, channel estimation isfacilitated easily by rotating pilots across the subcarrier indices.facilitated easily by rotating pilots across the subcarrier indices.Interpolation provides channel estimation for every subcarrier.Interpolation provides channel estimation for every subcarrier.

This figure is from reference [3]This figure is from reference [3]

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AdvantagesAdvantages SCMSCM

Sensitivity (margin)Sensitivity (margin)

ComplexityComplexity

MemoryMemory

Phase noise sensitivityPhase noise sensitivity

Frequency registrationFrequency registration

Reduced PA BackoffReduced PA Backoff

Less Overhead (no Less Overhead (no cyclic prefix)cyclic prefix)

OFDMOFDM

Single Frequency NetworksSingle Frequency Networks

Simple EQSimple EQ

FlexibilityFlexibility

Statistical MuxStatistical Mux

OFDMA – BW, TDMAOFDMA – BW, TDMA

LOW SNR, avoid DFELOW SNR, avoid DFE

PAPR not affected by PAPR not affected by modulation order.modulation order.

Automatically integrates Automatically integrates multipath.multipath.

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® signal processing for ofdm communication systems eric jacobsen minister of algorithms, intel...

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n f2 n

interconnect technology

t ofdm

n orthogonal subchannels

outline ofdm

n lower rate streams

adaptive modulation

docsis multicarrier