ncc2004 ofdm tutorial part ii-apal
TRANSCRIPT
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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
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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
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An OFDM ModemAn OFDM Modem
P/SDemodulat
or / Demapper
Channelequalizer
S/PModulator / Mapper
N-IFFTadd
cyclic prefix
P/SD/A +
transmit filter
N-FFT
S/Premove cyclic prefix
TRANSMITTER
RECEIVER
Nsubchannels 2N real samples
2N real samplesNsubchannels
Receive filter
+A/D
multipath channel
Bits
00110
Freq Offset Correction
Phase Track
er
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OFDM Signal Description - TransmitterOFDM Signal Description - TransmitterThe transmitted baseband signal for The transmitted baseband signal for llthth OFDM symbol, OFDM symbol, ssll((tt) can ) can
be expressed asbe expressed as
XXl,kl,k = Constellation points to IDFT input at = Constellation points to IDFT input at kkthth subcarrier of subcarrier 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
TTd d = Duration of data portion, N= Duration of data portion, Ndd = Number of data samples (equal to FFT length) = Number of data samples (equal to FFT length)
= N= N
TTsymsym = = TTdd + + TTCPCP and and NNsymsym = = NNdd + + NNCPCP
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OFDM Signal Description – Transmitter OFDM Signal Description – Transmitter waveformwaveform
TCP Td
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OFDM Signal Description - ReceiverOFDM Signal Description - ReceiverThe 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() = Channel Impulse Response ) = Channel Impulse Response
(upto (upto maxmax))
In presence of carrier frequency offset In presence of carrier frequency offset Frx-Ftx,
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OFDM Signal Description - ReceiverOFDM Signal Description - Receiver
In presence of sampling frequency offset In presence of sampling frequency offset receiver sampling timereceiver sampling time
TTss’’ = = TTss(1 + (1 + ), t = n ), t = n TTss’’
For For n n = = m m + + NNCPCP + + lNlNsymsym and and m m [0[0,N,Ndd ],],
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OFDM Signal Description – Receiver OFDM Signal Description – Receiver After DFT at Receiver, received signalAfter DFT at Receiver, received signal
Simplifying,Simplifying,
Where,Where,
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OFDM Signal Description – Receiver OFDM Signal Description – Receiver
Where,Where,
Further Simplifying, the received kFurther Simplifying, the received kthth data point of the l data point of the lthth symbol can be symbol can be
expressed asexpressed as
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Receiver Design IssuesReceiver Design IssuesEffects of Carrier Frequency OffsetEffects of Carrier Frequency Offset Original Observed SNR = 50 dB
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Receiver Design IssuesReceiver Design IssuesEffects of Sampling Clock OffsetEffects of Sampling Clock Offset Original Observed SNR = 50 dB
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Receiver Design IssuesReceiver Design IssuesEffects of Multipath ChannelEffects of Multipath Channel Original Observed SNR = 50 dB
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Receiver Design IssuesReceiver Design IssuesCombined 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 signal Phase of Received signal • Carrier Frequency Offset results in constant Carrier Frequency Offset results in constant
Phase Rotation at DFT outputPhase Rotation at DFT output
• Sampling Clock Offset results in linearly Sampling Clock Offset results in linearly
increasing Phase Rotation with sub-carrier index increasing Phase Rotation with sub-carrier index
at DFT outputat 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 a Carrier Frequency Phase Offset contributes to a
constant term in Amplitudeconstant term in Amplitude
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Receiver Design Issues - SolutionsReceiver Design Issues - Solutions
• There is need forThere is need for• Frequency Synchronization (Frequency Offset & Frequency Synchronization (Frequency Offset &
Phase)Phase)
• Time Synchronization (Phase)Time Synchronization (Phase)
• Channel EqualizationChannel Equalization
• Achieved byAchieved by• Frequency Offset Correction through dedicated Frequency Offset Correction through dedicated
pilot preamblespilot preambles
• Carrier Phase Tracking though pilots inserted Carrier Phase Tracking though pilots inserted
inside Datainside Data
StreamStream• Takes care of Sampling Clock Offset and Residual Takes care of Sampling Clock Offset and Residual
Frequency OffsetFrequency Offset
• Channel Equalization through dedicated pilot Channel Equalization through dedicated pilot
preamblespreambles
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Receiver Design - Receiver Design - Frequency Offset CorrectionFrequency Offset Correction• Received Signal due to Frequency offset only Received Signal due to Frequency offset only
(Assuming (Assuming = 0 and channel compensation done), = 0 and channel compensation done),RRll = X = Xll exp(j.2 exp(j.2...l.T.l.Tss))
If there are two repeated symbols sent at delay D and the If there are two repeated symbols sent at delay D and the
received symbols are correlated,received symbols are correlated,
Z = Z = (R (Rll . R . R**l+Dl+D) which on simplification gives) which on simplification gives
Estimated Frequency OffsetEstimated Frequency Offset
estest= angle (Z) / (2= angle (Z) / (2.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 need to send at least two sets of known repeated
symbols as pilotsymbols as pilot
• Correction is achieved by multiplying the received Correction is achieved by multiplying the received
signal before DFT by exp(-j.2signal before DFT by exp(-j.2..estest))
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Receiver Design - Receiver Design - Frequency Offset CorrectionFrequency Offset CorrectionOriginal
ObservedSNR = 50 dB
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Receiver Design - Receiver Design - Channel EqualizationChannel Equalization
• Pilot-aided Channel equalization Pilot-aided Channel equalization
Received Signal due to Channel only (Assuming Received Signal due to Channel only (Assuming = =
0 and 0 and ),),
RRl,kl,k = X = Xl.kl.k H Hkk
If there are known symbol sent as pilot,If there are known symbol sent as pilot,
Channel TF can easily estimated by Channel TF can easily estimated by
HHkkestest = R = Rl,kl,k / X / Xl.kl.k
Correction is achieved by multiplying the Correction is achieved by multiplying the
received signal after DFT by Hreceived signal after DFT by Hkkestest
• Blind Channel Equalization also possibleBlind Channel Equalization also possible
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Original
Observed
Receiver Design - Receiver Design - Channel EqualizationChannel EqualizationSNR = 50 dB
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Receiver Design - Receiver Design - Carrier Phase TrackingCarrier Phase Tracking
• Phase Rotation at DFT output due toPhase Rotation at DFT output due to
• Sampling Clock Offset Sampling Clock Offset
• Residual Frequency Offset after correction Residual Frequency Offset after correction resres= = ––estest
Sub-carrier no. kSub-carrier no. k
Phase
Phase
O
ffse
t O
ffse
t
Due to Due to resres
Due to Due to resres
PP11 PP22 PP33 PP44
• Estimate Estimate at P at P1, 1, PP2, 2, PP3, 3, PP44
• Calculate Slope and averageCalculate Slope and average
• Interpolate and find out Interpolate and find out for all other sub-carriers for all other sub-carriers
• Correct by multiplying each data with exp(-j. Correct by multiplying each data with exp(-j. kk.C.l).C.l)
-N/2-N/2 N/2N/2
Due to Due to
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Original
Observed
Receiver Design - Receiver Design - Carrier Phase TrackingCarrier Phase Tracking
SNR = 50 dB
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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 means Large 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 a Reduce 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
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802.11a/g OFDM PHY Block Diagram802.11a/g OFDM PHY Block DiagramAssemble
frameScrambler
Convolution Encoder
Block Interleaver
Bit Mapper IFFT Add Guard Interval
Window
MAC Layer
DA
C RF Transmitter
Transmit
Remove Guard
Interval
FFT Channel / PhaseCorrection
De-mapper
De-interleaver Viterbi Decoder Descrambler Disassemble
Frame
Channel Estimator
Phase Estimation
MAC Layer
AD
C
RF Receiver
AGC
Receive
FrameSync &Freq.
Correction
Receiver Sync
Preamble & Pilot Insertion
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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
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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 Mbps Data Rate from 6 Mbps to 54 Mbps
• BPSK, QPSK, QAM-16, QAM-64 Modulation (Data Rate BPSK, QPSK, QAM-16, QAM-64 Modulation (Data Rate
Dependant)Dependant)
• Low SNR Operation (11 dB for BPSK to 27 dB for QAM-Low SNR Operation (11 dB for BPSK to 27 dB for QAM-
64)64)
• Indoor Channel Models with Delay spreads up to 250 Indoor Channel Models with Delay spreads up to 250
nsecnsec
• Carrier Frequency 5 GHz for 802.11a and 2.4 GHz for Carrier Frequency 5 GHz for 802.11a and 2.4 GHz for
802.11g802.11g
• 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
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802.11a/g OFDM PHY Design Challenges802.11a/g OFDM PHY Design Challenges
• Time Critical Operations Time 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, Frequency Offset Correction, Channel Equalization,
Phase Phase Tracking and Phase Correction : 50 nsec Tracking and Phase Correction : 50 nsec
per sampleper sample
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802.11a/g OFDM PHY Design Challenges802.11a/g OFDM PHY Design Challenges
• Phase Shift due to Frequency OffsetPhase Shift due to Frequency Offset• 0.80.8l (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• 0.0050.005l (max. value for the last sub-carrier)l (max. value for the last sub-carrier)
• Robust Operational Requirement under low SNR Robust Operational Requirement under low SNR
conditionsconditions
• Channel Correction and Phase Tracking prone to Channel Correction and Phase Tracking prone to
high error under low SNR high error under low SNR
•Averaging Needed to improve SNRAveraging Needed to improve SNR
• High PAR handling – PAR reduced to 10 dB using High PAR handling – PAR reduced to 10 dB using
ScramblingScrambling
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802.11a/g OFDM PHY Simulation Results802.11a/g OFDM PHY Simulation Results
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ReferencesReferences1.1. Juha Heiskala and John Terry, “OFDM Wireless LANs: A Theoretical and Juha 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 Mikael Karlsson Rudberg, Ericsson Microelectronics AB, “Introduction
to Telecommunication”, System Design TSTE91, lecture 3to Telecommunication”, System Design TSTE91, lecture 3
3.3. Robert W. Heath Jr., “Wireless OFDM Systems”, Telecommunications Robert W. Heath Jr., “Wireless OFDM Systems”, Telecommunications
and Signal Processing Research Center, The University of Texas at and Signal Processing Research Center, The University of Texas at
Austin, http://wireless.ece.utexas.edu/Austin, 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-Michael Speth et. al., “Optimum Receiver Design for Wireless Broad-
Band Systems Using OFDM—Part I”, IEEE Trans. On Comm., Vol. 47, Band Systems Using OFDM—Part I”, IEEE Trans. On Comm., Vol. 47,
No. 11, Nov 1999No. 11, Nov 1999
6.6. Michael Speth et. al., “Optimum Receiver Design for OFDM-Based Michael Speth et. al., “Optimum Receiver Design for OFDM-Based
Broadband Transmission—Part II: A Case Study”, IEEE Trans. On Broadband Transmission—Part II: A Case Study”, IEEE Trans. On
Comm., Vol. 49, No. 4, April 2001Comm., Vol. 49, No. 4, April 2001
