1. 1
OFDM Tutorial – Part IIOFDM Tutorial – Part II
Design Issues in OFDM systemsDesign Issues in OFDM systems
ByBy
Arpan PalArpan Pal
Center of Excellence for Embedded SystemsCenter of Excellence for Embedded Systems
Tata Consultancy ServicesTata Consultancy Services
KolkataKolkata
IndiaIndia
A tutorial presentation at NCC2004A tutorial presentation at NCC2004
2. 2
AgendaAgenda
• OFDM Modem Block DiagramOFDM Modem Block Diagram
• OFDM Signal DescriptionOFDM Signal Description
• Receiver Design IssuesReceiver Design Issues
• Time & Frequency SynchronizationTime & Frequency Synchronization
• Channel EqualizationChannel Equalization
• Signal Dynamic Range IssuesSignal Dynamic Range Issues
•IEEE 802.11a / g OFDM SystemIEEE 802.11a / g OFDM System
3. 3
An OFDM ModemAn OFDM Modem
P/S
Demodulat
or /
Demapper
Channel
equalizer
S/P
Modulator /
Mapper
N-IFFT
add
cyclic
prefix
P/S
D/A +
transmit
filter
N-
FFT
S/P
remove
cyclic
prefix
TRANSMITTER
RECEIVER
Nsubchannels 2N real samples
2N real samplesNsubchannels
Recei
ve
filter
+
A/D
multipath channel
Bits
00110
Freq
Offset
Corre
ction
Phase
Track
er
4. 4
OFDM Signal Description - TransmitterOFDM Signal Description - Transmitter
The transmitted baseband signal forThe transmitted baseband signal for llthth
OFDM symbol,OFDM symbol, ssll((tt) can be) can be
expressed asexpressed as
XXl,kl,k = Constellation points to IDFT input at= Constellation points to IDFT input at kkthth
subcarrier ofsubcarrier of llthth
OFDM symbolOFDM symbol
TTsymsym = Symbol duration,= Symbol duration, NNsymsym = Number of samples in= Number of samples in TTsymsym
TTCPCP = Duration of Cyclic Prefix(CP),= Duration of Cyclic Prefix(CP), NNCPCP = Number of samples in= Number of samples in TTCPCP
TTss = Duration of a sampling instant= Duration of a sampling instant
TTdd = Duration of data portion, N= Duration of data portion, Ndd = Number of data samples (equal to FFT length) = N= Number of data samples (equal to FFT length) = N
TTsymsym == TTdd ++ TTCPCP andand NNsymsym == NNdd ++ NNCPCP
6. 6
OFDM Signal Description - ReceiverOFDM Signal Description - Receiver
The received baseband signal r(t) can be expressed asThe received baseband signal r(t) can be expressed as
HHkk = Channel TF for k= Channel TF for kthth
subcarrier, h(subcarrier, h(ττ) = Channel Impulse Response) = Channel Impulse Response
(upto(upto ττmaxmax))
In presence of carrier frequency offsetIn presence of carrier frequency offset ξ =ξ = Frx-Ftx,
7. 7
OFDM Signal Description - ReceiverOFDM Signal Description - Receiver
In presence of sampling frequency offsetIn presence of sampling frequency offset ζ,ζ, receiver sampling timereceiver sampling time
TTss’’ == TTss(1 +(1 + ζζ), t = n), t = n TTss’’
ForFor nn == mm ++ NNCPCP ++ lNlNsymsym andand mm εε [0[0,N,Ndd ],],
8. 8
OFDM Signal Description – ReceiverOFDM Signal Description – Receiver
After DFT at Receiver, received signalAfter DFT at Receiver, received signal
Simplifying,Simplifying,
Where,Where,
9. 9
OFDM Signal Description – ReceiverOFDM Signal Description – Receiver
Where,Where,
Further Simplifying, the received kFurther Simplifying, the received kthth
data point of the ldata point of the lthth
symbol can besymbol can be
expressed asexpressed as
10. 10
Receiver Design IssuesReceiver Design Issues
Effects of Carrier Frequency OffsetEffects of Carrier Frequency Offset Original Observed
SNR = 50 dB
11. 11
Receiver Design IssuesReceiver Design Issues
Effects of Sampling Clock OffsetEffects of Sampling Clock Offset Original Observed
SNR = 50 dB
12. 12
Receiver Design IssuesReceiver Design Issues
Effects of Multipath ChannelEffects of Multipath Channel Original Observed
SNR = 50 dB
13. 13
Receiver Design IssuesReceiver Design Issues
Combined Effects of Sampling Clock Offset and Multipath ChannelCombined Effects of Sampling Clock Offset and Multipath Channel
Original ObservedSNR = 50 dB
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Receiver Design Issues - SummaryReceiver Design Issues - Summary
• Phase of Received signalPhase of Received signal
• Carrier Frequency Offset results in constant PhaseCarrier Frequency Offset results in constant Phase
Rotation at DFT outputRotation at DFT output
• Sampling Clock Offset results in linearly increasingSampling Clock Offset results in linearly increasing
Phase Rotation with sub-carrier index at DFT outputPhase Rotation with sub-carrier index at DFT output
• Affected by Channel Transfer FunctionAffected by Channel Transfer Function
• Also affects orthogonality of the sub-carriersAlso affects orthogonality of the sub-carriers
• Amplitude of Received SignalAmplitude of Received Signal
• Multiplied by the Channel Transfer FunctionMultiplied by the Channel Transfer Function
• Carrier Frequency Phase Offset contributes to aCarrier Frequency Phase Offset contributes to a
constant term in Amplitudeconstant term in Amplitude
15. 15
Receiver Design Issues - SolutionsReceiver Design Issues - Solutions
• There is need forThere is need for
• Frequency Synchronization (Frequency Offset & Phase)Frequency Synchronization (Frequency Offset & Phase)
• Time Synchronization (Phase)Time Synchronization (Phase)
• Channel EqualizationChannel Equalization
• Achieved byAchieved by
• Frequency Offset Correction through dedicated pilotFrequency Offset Correction through dedicated pilot
preamblespreambles
• Carrier Phase Tracking though pilots inserted inside DataCarrier Phase Tracking though pilots inserted inside Data
StreamStream
• Takes care of Sampling Clock Offset and Residual FrequencyTakes care of Sampling Clock Offset and Residual Frequency
OffsetOffset
16. 16
Receiver Design -Receiver Design - Frequency Offset CorrectionFrequency Offset Correction
• Received Signal due to Frequency offset only (AssumingReceived Signal due to Frequency offset only (Assuming ζζ
= 0 and channel compensation done),= 0 and channel compensation done),
RRll = X= Xll exp(j.2exp(j.2ππ..ξξ.l.T.l.Tss))
If there are two repeated symbols sent at delay D and the receivedIf there are two repeated symbols sent at delay D and the received
symbols are correlated,symbols are correlated,
Z =Z = ΣΣ (R(Rll . R. R**
l+Dl+D) which on simplification gives) which on simplification gives
Estimated Frequency OffsetEstimated Frequency Offset
ξestest= angle (Z) / (2= angle (Z) / (2ππ.D.T.D.Tss))
• resolution guided by Dresolution guided by D
• residual error remainsresidual error remains
• need to send at least two sets of known repeated symbols asneed to send at least two sets of known repeated symbols as
pilotpilot
• Correction is achieved by multiplying the received signalCorrection is achieved by multiplying the received signal
before DFT by exp(-j.2before DFT by exp(-j.2ππ..ξξestest))
17. 17
Receiver Design -Receiver Design - Frequency Offset CorrectionFrequency Offset Correction
Original
ObservedSNR = 50 dB
18. 18
Receiver Design -Receiver Design - Channel EqualizationChannel Equalization
• Pilot-aided Channel equalizationPilot-aided Channel equalization
Received Signal due to Channel only (AssumingReceived Signal due to Channel only (Assuming ζζ = 0 and= 0 and
ξ = 0ξ = 0),),
RRl,kl,k = X= Xl.kl.k HHkk
If there are known symbol sent as pilot,If there are known symbol sent as pilot,
Channel TF can easily estimated byChannel TF can easily estimated by
HHkk
estest
= R= Rl,kl,k / X/ Xl.kl.k
Correction is achieved by multiplying the received signalCorrection is achieved by multiplying the received signal
after DFT by Hafter DFT by Hkk
estest
• Blind Channel Equalization also possibleBlind Channel Equalization also possible
20. 20
Receiver Design -Receiver Design - Carrier Phase TrackingCarrier Phase Tracking
• Phase Rotation at DFT output due toPhase Rotation at DFT output due to
• Sampling Clock OffsetSampling Clock Offset ζζ
• Residual Frequency Offset after correctionResidual Frequency Offset after correction ξξresres== ξξ –– ξξestest
Sub-carrier no. kSub-carrier no. k
PhasePhase
OffsetOffsetφφ
Due to
Due to ζ +ζ + ξξresres
Due toDue to ξξresres
PP11 PP22 PP33 PP44
• EstimateEstimate φφ at Pat P1,1, PP2,2, PP3,3, PP44
• Calculate Slope and averageCalculate Slope and average
• Interpolate and find outInterpolate and find out φφ for all other sub-carriersfor all other sub-carriers
• Correct by multiplying each data with exp(-j.Correct by multiplying each data with exp(-j. φφkk.C.l).C.l)
-N/2-N/2 N/2N/2
Due toDue to ζζ
22. 22
Signal Dynamic Range IssuesSignal Dynamic Range Issues
Peak-to-average ratio (PAR)Peak-to-average ratio (PAR)
• A measure of how the signal is distributed over the amplitude rangeA measure of how the signal is distributed over the amplitude range
• For a sinusoidal signalFor a sinusoidal signal
• Dynamic range is directly related to PARDynamic range is directly related to PAR
• For 64 Point IFFT (Multi-carrier), PAR will be 8 = 18 dBFor 64 Point IFFT (Multi-carrier), PAR will be 8 = 18 dB
• Large PAR means Large Amplifier back-off which in turn meansLarge PAR means Large Amplifier back-off which in turn means
small power efficiencysmall power efficiency
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Signal Dynamic Range IssuesSignal Dynamic Range Issues
Typical PAR for OFDM WaveformTypical PAR for OFDM Waveform
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Signal Dynamic Range SolutionsSignal Dynamic Range Solutions
• Methods on Minimization of PARMethods on Minimization of PAR
• Scrambling to reduce long runs of 1s and 0sScrambling to reduce long runs of 1s and 0s
• Introduction of apriori-known phase shiftsIntroduction of apriori-known phase shifts
• Use of Peak WindowingUse of Peak Windowing
• Reduce out-of-band Interference by multiplying peaks with aReduce out-of-band Interference by multiplying peaks with a
window of good spectral propertieswindow of good spectral properties
• Use of Coding Schemes – Complementary codesUse of Coding Schemes – Complementary codes
• No good codes known for large no. of sub-carriersNo good codes known for large no. of sub-carriers
• Clipping – In-band and Out-of-band InterferenceClipping – In-band and Out-of-band Interference
• In-band Interference can be handled by codingIn-band Interference can be handled by coding
• Out-of-band Interference poses major problemOut-of-band Interference poses major problem
26. 26
802.11a/g OFDM PHY Timing Diagram802.11a/g OFDM PHY Timing Diagram
0 160 192 256 320 336 400 416 480 496 560 576 x50 ns
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 GI2 LT1 LT2 GI SIGNAL GI DATA GI DATA GI DATA
time…
• Packet
Detection
• Symbol
Sync
• Energy
Estimation
Coarse
Freq.
Estimation
AGC
Control
Coarse Frequency Correction
Fine Freq.
Estimation &
Channel
Estimation
FFT
Phase
Tracker
FFT
Phase
Tracker
FFT
Phase
Tracker
Fine Frequency Correction
Channel Correction
Phase Correction
27. 27
802.11a/g OFDM PHY Pilot Structure802.11a/g OFDM PHY Pilot Structure
#7, #21, #-21, #-7 are the pilots.#7, #21, #-21, #-7 are the pilots.
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802.11a/g OFDM PHY Design Parameters802.11a/g OFDM PHY Design Parameters
• Data Rate from 6 Mbps to 54 MbpsData Rate from 6 Mbps to 54 Mbps
• BPSK, QPSK, QAM-16, QAM-64 Modulation (Data RateBPSK, QPSK, QAM-16, QAM-64 Modulation (Data Rate
Dependant)Dependant)
• Low SNR Operation (11 dB for BPSK to 27 dB for QAM-64)Low SNR Operation (11 dB for BPSK to 27 dB for QAM-64)
• Indoor Channel Models with Delay spreads up to 250 nsecIndoor Channel Models with Delay spreads up to 250 nsec
• Carrier Frequency 5 GHz for 802.11a and 2.4 GHz for 802.11gCarrier Frequency 5 GHz for 802.11a and 2.4 GHz for 802.11g
• 20 MHz Sampling Frequency20 MHz Sampling Frequency
• +/- 25 ppm Carrier Frequency Offset+/- 25 ppm Carrier Frequency Offset
• +/- 20 ppm Sampling Clock Offset+/- 20 ppm Sampling Clock Offset
29. 29
802.11a/g OFDM PHY Design Challenges802.11a/g OFDM PHY Design Challenges
• Time Critical OperationsTime Critical Operations
• 64 point FFT : 3.2 usec64 point FFT : 3.2 usec
• Frequency Offset Estimation : 0.8 usecFrequency Offset Estimation : 0.8 usec
• Channel Estimation : 0.8 usecChannel Estimation : 0.8 usec
• Frequency Offset Correction, Channel Equalization, PhaseFrequency Offset Correction, Channel Equalization, Phase
Tracking and Phase Correction : 50 nsec per sampleTracking and Phase Correction : 50 nsec per sample
30. 30
802.11a/g OFDM PHY Design Challenges802.11a/g OFDM PHY Design Challenges
• Phase Shift due to Frequency OffsetPhase Shift due to Frequency Offset
• 0.80.8ππl (l: OFDM symbol index) – need for correction before DFTl (l: OFDM symbol index) – need for correction before DFT
• Phase Shift due to Sampling Clock OffsetPhase Shift due to Sampling Clock Offset
• 0.0050.005ππl (max. value for the last sub-carrier)l (max. value for the last sub-carrier)
• Robust Operational Requirement under low SNR conditionsRobust Operational Requirement under low SNR conditions
• Channel Correction and Phase Tracking prone to high errorChannel Correction and Phase Tracking prone to high error
under low SNRunder low SNR
•Averaging Needed to improve SNRAveraging Needed to improve SNR
• High PAR handling – PAR reduced to 10 dB using ScramblingHigh PAR handling – PAR reduced to 10 dB using Scrambling
32. 32
ReferencesReferences
1.1. Juha Heiskala and John Terry, “OFDM Wireless LANs: A Theoretical andJuha Heiskala and John Terry, “OFDM Wireless LANs: A Theoretical and
Practical Guide”, SAMS, 2002Practical Guide”, SAMS, 2002
2.2. Mikael Karlsson Rudberg, Ericsson Microelectronics AB, “Introduction toMikael Karlsson Rudberg, Ericsson Microelectronics AB, “Introduction to
Telecommunication”, System Design TSTE91, lecture 3Telecommunication”, System Design TSTE91, lecture 3
3.3. Robert W. Heath Jr., “Wireless OFDM Systems”, Telecommunications andRobert W. Heath Jr., “Wireless OFDM Systems”, Telecommunications and
Signal Processing Research Center, The University of Texas at Austin,Signal Processing Research Center, The University of Texas at Austin,
http://wireless.ece.utexas.edu/http://wireless.ece.utexas.edu/
4.4. Richard Van Nee, “Basics and History of OFDM”, Woodside Networks,Richard Van Nee, “Basics and History of OFDM”, Woodside Networks,
Breukelen, NetherlandsBreukelen, Netherlands
5.5. Michael Speth et. al., “Optimum Receiver Design for Wireless Broad-BandMichael Speth et. al., “Optimum Receiver Design for Wireless Broad-Band
Systems Using OFDM—Part I”, IEEE Trans. On Comm., Vol. 47, No. 11, NovSystems Using OFDM—Part I”, IEEE Trans. On Comm., Vol. 47, No. 11, Nov
19991999
6.6. Michael Speth et. al., “Optimum Receiver Design for OFDM-Based BroadbandMichael Speth et. al., “Optimum Receiver Design for OFDM-Based Broadband
Transmission—Part II: A Case Study”, IEEE Trans. On Comm., Vol. 49, No. 4,Transmission—Part II: A Case Study”, IEEE Trans. On Comm., Vol. 49, No. 4,
April 2001April 2001
