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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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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
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-5
0
5
-5 -4 -3 -2 -1 0 1 2 3 4 5
Frequency (MHz)
Re
sp
on
se
(d
B)
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0
5
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Frequency (MHz)
Re
sp
on
se
(d
B)
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0
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Frequency (MHz)
Re
sp
on
se
(d
B)
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-5 -4 -3 -2 -1 0 1 2 3 4 5
Frequency (MHz)
Re
sp
on
se
(d
B)
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sp
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(d
B)
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sp
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(d
B)
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sp
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(d
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B)
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B)
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Frequency (MHz)
Re
sp
on
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(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
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-15
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-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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