Recent Advances in Frequency Domain Equalization · 2010-09-08 · cochannel interference estimates...

Recent Advances in Frequency Domain Equalization

David Falconer

Broadband Communications and Wireless Systems (BCWS) Centre

Dept. of Systems and Computer EngineeringCarleton University

[email protected]/bcws

2

Outline

• Motivation for the frequency domain approach – OFDM, single carrier and generalizations

• Linear, decision feedback, and turbo frequency domain equalization

• Channel estimation

• Equalization and channel estimation for MIMO systems

• Power amplifier nonlinearity considerations

• Dealing with phase noise and frequency offset

• Applications and summary

3

Motivation for the Frequency Domain Approach: Delay Spread Spans Many Data Symbols

• Maximum aggregate bit rate up to 100 Mb/s, or even 1 Gb/s in non-line of sight frequency-selective radio propagation environments.– Calls for fast Fourier transform (FFT)-based block frequency

domain transmission and/or reception.

S/PFFT orInverseFFT

P/S

Complexity ~ log(delay spread)

4

SC-FDE transmitter: Linear SC receiver:

IFFT CPI FFT Invertchannel

Detect

CPI DetectIFFT

Channel

Channel

OFDM transmitter: OFDM receiver:

OFDM and Single Carrier with Linear Frequency Domain Equalization (SC-FDE)

(I)FFT=(inverse) fast Fourier transform

CPI=cyclic prefix insertion:

FFT Invertchannel

Last Lsymbolsrepeated

Lsymbols

Block of M data symbolsCyclicprefix

5

OFDM: SC-FDE:

• Parallel transmission on multiple subcarriers →high peak-to average power ratio (PAPR)

• Very flexible, adaptive, efficient spectrum usage with OFDMA

• Powerful decoding for frequency selective channels through knowledge of each data symbol’s SINR

• Frequency offset and phase noise cause intersymbol interference in frequency domain

• Serial transmission on one carrier →low PAPR

• Less flexible spectrum usage than with OFDMA

• Powerful turbo equalization

• Frequency offset and phase noise cause easily-correctable slow-varying phase rotations on data symbols

Pr(amp.>x)

x

SCOFDM

User #1 User #2Frequency

FrequencyRef: M. Sabbaghian and D. Falconer, “Joint Turbo Frequency Domain Equalization and Carrier Synchronization”, IEEE Trans. Wireless Comm., Vol. 7, No. 1, January 2008, pp. 204-212.

6

M data symbols

Time

S/P

M-point FFT

Frequency

Frequency

Map to M out of N selected frequencies

N-point inverse FFT

P/S convert and transmit

A Generalized Multicarrier Transmission Scheme: DFT-Precoded OFDM

7

Different forms of DFT-Precoded OFDM

• Contiguous mapping → equivalent to SC-FDE with 0% rolloff sinc pulses

• Equally-spaced subcarriers, with different users frequency-interleaved →equivalent to spread-spectrum SC-FDE, with low PAPR

• Equally-spaced blocks, with different users’ blocks interleaved → not equivalent to pure SC-FDE, but with lower PAPR than equivalent OFDMA

• Frequency-multiplexed pilots → not equivalent to pure SC-FDE, but with lower PAPR than equivalent OFDMA

Freq.

Freq.

Freq.

User #1

User #2

Pilot

Freq.

8

Typical Roles of OFDM(A) and SC or DFT-Precoded OFDM

• OFDMA is most suitable for downlink (base to wireless terminal) and for non SNR-limited scenarios such as wireless LANs.– It benefits from its link adaptation flexibility and good performance

with coding.– In these scenarios, power efficiency and PAPR is of less

importance.

• SC-FDE or DFT-precoded OFDM is most suitable for uplink(wireless terminal to base) in SNR-limited scenarios such as wide-area cellular systems.– It benefits from its decreased PAPR, thus reducing required

transmit power backoff and enhancing power efficiency

9

Outline








10

FFTMultiplyby coeff.{Wl}

IFFT Detect

B Feedback taps {fk}

{rm} {Rl} {zm}+

-{am}

)2exp( where

)2exp(1 output DFE

1

0

*1

0

mN

jrR

afmN

jRWN

z

cu

N

mm

kmFk

kN

cuMm

cu

B

cu

l

l

l

lll

π

π

−∑=

∑−∑==

−

=

−∈

−

=

).)(E MSE (Minimize .Error 2mmmm eaze =−=

FB is a set of B feedback tap delays corresponding to the B largest channelImpulse response postcursors.

Linear and Decision Feedback Frequency Domain Equalization

Linear FDETime domain decision feedback

11

FFT

H(f)

∑ W(i)(f) ∑ IFFTIterativesoft detect/decode

FFT+ +

-

+

Iterative Block Decision Feedback Equalization (IBDFE) and Turbo Equalization (TE)

NR receive antennas NT simultaneous user data streams

a(i)(n) A(i)(f)

Subtractself- and cochannelinterferenceestimates

Restore currentsoft data estimates

Data symboloutputs

At each iteration, outputs conditional means of all users’ data symbols. For turbo equalization, includes de-interleaving, decoder extrinsic info output and re-interleaving.

12

Analysis tools for Iterative Systems

• Extrinsic Information chart (EXIT chart)• Disadvantages:

– Histogram based analysis• Problematic for turbo frequency domain equalization (TFDE) with time-

varying channels– Asymptotic based analysis

• Non-accurate results for small block length

• Bit Error Rate Transfer chart (BERT chart)• Advantages of the BERT chart versus the EXIT chart:

– Analytical approach for the equalizer• No need for histogram generation

– Using the empirically generated decoder BER curve• Accurate results for small block length

Ref.: M. Sabbaghian and D. Falconer, “BERT Chart Analysis of Adaptive and Non-adaptive Turbo Frequency Domain Equalization”, Proc. VTC fall 2007

13

BERT Chart Analysis of Turbo Frequency Domain Equalizer

Wk+IFFT

FFTChannel {H}

Soft Sym. Gen.

_FFT DecoderR

R

)1( −ix

λ

Gaussian R.V.

Consistent Gaussian R.V.

||22ii m=υ

Distribution of the soft estimated symbols

),,( )1(22 −=∑ ii xHf σ

Pi

( )[ ]212|| ii PQm −=


)1( −ix

14

Equations for Iterative Block Equalization

For FFT block size=M, noise variance=σ2 and data symbol variance=1, and for the non-adaptive case:

1,..1,0for ,22

*−=

+= Mk

H

HW

k

kk

σ

For the adaptive case:

1,..1,0for ,22

*−=

+= Mk

H

HKW

k

kk

νσ

where

∑+

=

=∑=

−

=

−

=

1

0 22

2

1

0

1

1 and

on,distributioutput decoder from computed

symbol, datath of covariance lconditiona and 1

M

m m

m

mM

mm

H

HM

K

mM

σν

ννν

15

0.10.2 0.05

10-4

10-3

10-2

10-1

100

BERdec,in BEReq,out

BE

Rde

c,ou

t B

ER

eq,in

Equalizer curve in the first iterationEqualizer curve in the second iterationEqualizer curve in the third iterationDecoder curve

0.10.2 0.05

10-4

10-3

10-2

10-1

100

BERdec,in BEReq,out

BE

Rde

c,ou

t B

ER

eq,in

Equalizer curve Decoder curve

Equalizer curve

Equalizer curve in first iteration

Equalizer curve in second iteration


Illustration of BERT Chart Analysis

16

BERT Chart Result for 16-QAM

• Rate ½ regular (3,6) LDPC code with block length=1008.

• 6 LDPC (inner iterations per outer iteration

• 4 equalizer/decoder (outer) iterations

• 20 MHz bandwidth; 6-tap 3GPP type A channel.

Refs.: M. Sabbaghian and D. Falconer, “BERT Chart Analysis of Adaptive and Non-adaptive Turbo Frequency Domain Equalization”, Proc. VTC fall 2007.“An Analytical Approach for Finite Block Length Performance Analysis of Turbo FrequencyDomain Equalization”, to appear in IEEE Trans. Vehic. Technol.

5 6 7 8 9 10 1110-6

10-5

10-4

10-3

10-2

10-1

100

Eb/No (dB)

BE

R

non-adaptive, simulation resultnon adaptive, BERT chart resultadaptive, simulation resultadaptive, BERT chart result

17

Outline








18

Channel Estimation

• For both time and frequency-multiplexed pilots, interpolation in frequency and time is necessary, to keep pilot overhead low.

• Pilot overhead increases for spatial multiplexing/SDMA and adaptive transmission.

• Challenges: estimation of channels with rapid time variation andwith large delay spread.

19

Time Division Multiplexed (TDM) Pilots

Data Pilot TDM pilots DataCP CP

CP Data

Time →

User #1 pilotUser #2 pilot.User #U pilot

Freq.

Block without pilots:

Length of pilot block proportional to number of users

Each user’s frequency domainpilot symbols are the DFT of aChu sequence – to maintain constant amplitude property.

i.e. Each TDM pilot signal is an IFDMA signal.

Block with pilots:

Extra overhead

20

Frequency Division Multiplexed (FDM) Pilots

CP Data and frequency-multiplexed pilots

Time →

Each user’s frequency domainpilot symbols are the DFT of aChu sequence (pilots are shownwith a power boost)

User #1 pilotUser #2 pilot

User #1 data.

Freq.

21

Multiplexing of Frequency Domain Pilots: Two Variants

FET (frequency expanding FDSPT (frequency domaintechnique): superimposed pilot technique):(Data subcarriers shown in red, pilots in blue)

Frequency

22

• Issue of noise enhancement due to Gaussian like frequency response of data decisions:

• Frequency replacement algorithm: replace the noise enhanced raw estimates with previouse estimates, using threshold

Iterative Channel Estimator for Serial Modulation Systems

2x1D WienerChannel

Estimator #1

FD-IBSDFE

2x1D WienerChannel

Estimator #2

FrequencyReplacement FFT

S

lH~

lY

)0(~lH

lP

lY

kb~

malA

)0(~lH De-

Interleaver

Interleaver

Decoder

Encoder

ma~

kb

FRλ

llll AVHH ˆ/ˆ +=

FRλ

23

2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 31 0 - 3

1 0 - 2

1 0 - 1

1 0 0

S N R [ d B ]

FER

S M - F D E P , W 2 x 1 DT D M , W 2 x 1 DF D S P , W 2 x 1 DS M , K n o w n C S IO F D M - F D E P , W 2 x 1 DO F D M , K n o w n C S I

S c e n a r i o B :m a t c h e d t oτ m a x = 1 . 4 7 μ s , 5 0 k m / h

Non-Iterative Channel Estimation for Single-User OFDM and DFT-Precoded OFDM

From C-T Lam, G. Auer, F. Danilo-Lemoine, D. Falconer, “Design of Time and FrequencyDomain Pilots for Generalized Multicarrier Systems”, Proc. ICC 2007, Glasgow, June 2007

C2 channel, 16.25 MHz used bandwidth, 50 kph. Rate ½ convolutional code. 4.2% pilot overhead for FET, 0% overhead for FDSPT. Soft DFE equalizer used for serial modulation.

1. For known channel, SM with soft DFE is about 0.7 dB better than OFDM.2. Non-iterative channel estimation with FET incurs about 1.5 dB loss.

3. Non-iterative channel estimation with FDSPT incurs about 2.5 dB loss.

1. 1. 2. 3.

24

Iterative Decision Directed Channel Estimation for DFT-Precoded OFDM

a) Iterative CE (FET) b) Iterative CE (FDSPT)

5 6 7 8 9 10 11 1210-3

10-2

10-1

100

SNR [dB]

FER

Non-iterativeH-ICE1, λFR=0.3

H-ICE1-C, λFR=0.3

K-ICE1, λFR=0.3

Known CSI

3 4 5 6 7 8 9 10 11 12 1310-3

10-2

10-1

100

SNR [dB]

FER

FET, H-ICE1-C, λFR=0.3

FDSPT, Non-IterativeFDSPT, H-ICE1, λFR=0.3

FDSPT, H-ICE1-C, λFR=0.3

Known CSI

From C-T Lam, D. Falconer and F. Danilo-Lemoine, “A Low Complexity Frequency Domain Iterative Decision-Directed Channel estimation Technique for Single Carrier Systems”, Proc. VTC 2007 spring,

1. Iterative channel estimation, including decoder, incurs only about 0.5 dB loss for FET.

2. Iterative channel estimation, including decoder, incurs only about 1.2 dB loss for FDSPT.

1. 1. 2. 2.

25

Outline








26

MIMO Iterative Block DFE(SD-IBDFE)

⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

−−− )

)((2tanh()

)((2tanh(

21)(ˆ

)1()1()1(

estest

imagrealJ

tj

Jt

tii

i vvs

[ ] [ ])()(12)()( ][ˆ~][ˆ][][ˆ][ˆ iiMn

ii nσnnnn μΩHIHΩHW d

r−+=−H

The update for the frequency domain feed forward equalizer’s coefficients are;

Frequency domain feed back equalizer’s coefficients are:

][ˆ][ˆ][ˆ )()( nnn iK

i WHIF H−=

][ˆ][ˆ][][ˆ][ )1()()()( nnnnn iiii −+= SFYWV HH

Lagrange multiplier vector)(iμr

∑=

−−=2

2

N

n

ii tsN

tΩ1

2)1()( )(ˆ11)(

The corresponding soft decisions are

Frequency Domain Equalizer output samples:

Ref.: F. Siddiqui, F. Danilo-Lemoine and D. Falconer, “PIC-Assisted IBDFE Based Iterative Spatial Channel Estimation with Intra- and Inter-Cell Interference in SC-FDE System”, Proc. VTC fall 2007.

27

Channel Estimation: Pilot-assisted and Parallel Interference Cancellation (PIC)

• 1- Initial Pilot-based Short Estimates• Received signal:

m=1,2,…M (Antenna Element Index)n=1,2,…N2 (sub-carrier index)w=1,2,…F (Symbol index)

• Initial CE (Chu Sequences are used for Initial training) :

• 2- Full Length Channel estimates via 2x1D Interpolation

• 3- Hard Decisions after Decoding

• 4- Parallel Interference Cancellation (PIC)

i=1,2,…Ie (SD-IBDFE iteration index)j=1,2,…Iice (DFICE iteration index)The Received Array Input is:

• In-Cell Interference-free Array Input w.r.t. the Desired User k:

∑≠=

−−=K

k

ijjij lnDlnnknll ,1

),()1(),( ],[ˆ],[ˆ][],[ HYX

∑+

=

+=P

g

ggmm nNnDnHnY

1

][][][][1

wmww

((((

][][)(

nnn

D

YH (

((

=

][ˆ nH

][ˆ , nijD

][nY

∑≠=

−K

k

ijj lnDlnll ,1

),()1( ],[ˆ],[H


28

Channel Estimation (cont’d)DFICE and LS Adaptation

• 5- Decision Feedback Iterative Channel Estimation

• 6- Threshold-based Noise Enhancement avoidance

• 7- Least Squares (LS) Forward Filter Processing to Suppress Interference

Where F is the Time averaging interval (in OFDM symbols or FFT blocks)

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡= ∑∑

=

−

=

F

t

ijk

ijk

F

t

ijk

ijk

ijk tnDtntntnn

1

*),(),(1

1

*),(),(),( ],[ˆ],[],[],[][ XXXW

][ˆ

][][ˆ

),(

),()(

n

nn ij

ijj

D

XH =

⎪⎪⎩

⎪⎪⎨

⎧

=

<

=

−

.Otherwise..........][ˆ][][ˆ

|][ˆ| .....if.................... ][ˆ

][ˆ

,

),(,

,),1(

,

nDnn

nDn

nij

k

ijij

k

ijk

ijk

ijk XH

H

H

μt


29

Simulation Signal and Channel ParameterNotations and Simulation Parameters

•PCSI: Perfect channel state information.•LE: Linear Equalization.•SD: Soft Decision.•PIC: Parallel Interference Cancellation.•ICU: In-Cell User.•OCI: Out of Cell Interferer.•DFICE: Decision Feedback IterativeChannel Estimation.

• Modulation Scheme = QPSK.• Carrier frequency = 3.7GHz.• Signal BW = 40MHz.• Sub-Carrier spacing = 39.0625kHz.• Short training blocks for time averaging (NT) = 1 or 2.• Reliability Threshold in DFICE (μ) = 13.• Independent C2-Urban Macro 20-path channel model.• BS Antenna elements = M = 2 or 4.• In- Cell Users = K = 2.• Out of Cell Interferers = P = 4.• LE and SD-IBDFE Equalization (iterations=4).• DFICE Iterations = 1 or 2.• Used sub-carriers N2 = 1024. • Mobility = 50 km./hr.• Symbols/Frame = F = 12.• First and last symbol of each 12-symbol frame contain training. • Pilots per training block = 256.• 2x1D Wiener interpolation based on max. delay spread and Doppler.

Power in dB

-0.50 0 -3.40 -2.80 -4.60 -0.90 -6.70 -4.50 -9.00 -7.80 -7.40 -8.40 -11.00 -9.00 -5.10 -6.70 -12.10 -13.20 -13.70 -19.80

Delays in microsecond

0 .005 .135 .160 .215 .260 .385 .400 .530 .540 .650 .670 .720 .750 .800 .945 1.035 1.185 1.390 1.470

C2- Channel Model, Avg. PDP:

Notations:

Simulation Parameters:


30

2. SD-IBDFE (non-iterative CE) gives an improvement of 0.4dB over the LE, with –15dB OCIs.

4. The SNR penalty relative to PCSI is about 3 dB at 10-2 FER, for the 2 OCIs per ICU at -15 dB.

Simulation Results (cont’d) Non-iterative CE and PIC-assisted DFICE

1. With OCIs at –15dB knowing only the ICUs’ channels causes about a 0.4 dB SNR penalty relative to the case where all channels are known.

3. SD-IBDFE with iterative CE gives SNR improvement of about 1.8dB @ FER of 10e-2 over non-iterative CE.


• LS Adaptation (not shown here) gives a further SNR improvement of 0.5 to 1 dB.

2. 1. 1. 3. 3.4. 4.

31

Use of Soft-decisions in ICE (SD-DFICE) with Turbo Equalization

Turbo-SD-based DFICE in LS-IS

SoISoO-IBDFE

Turbo iterationsMIMO

Channel

][nYy1

yM

1

K)]([ qsk

eΩr

LDPCDec/Enc

Decisions)]([1 qskΔ&&

+

)]([2 qskΔ&&

+)]([ qsk

dΩr

-

-

Soft symbol mapping &

CFR Estimation

][ˆ nH

Extrinsic information

Utilizing Soft Decisions in DFICE:

1. SD-DFICE algorithm exceeds the HD-DFICE performance by ~ 1.5dB.

2. SD-DFICE comes within about 0.5dB of turbo equalization with PCSI.

Ref.: F. Siddiqui, “Channel Estimation in Single Carrier Frequency DomainEqualization Space Division Multiple Access Systems”, PhD thesis, Carleton Univ., April, 2008

2. 1. 1.

32

Outline








33

Power Amplifier Linearity Requirements and Cost

• The greater the modulation scheme’s peak to average ratio PAPR), the greater the required backoff, and the greater the required maximum rated power to achieve the link budget.

• HPA cost rises sharply with maximum power rating.

Input power

Outputpower

High PAPR signal

Low PAPRsignal

HPA required for high power backoff($$$)

HPA required for lower power backoff($)

At a certain max. power level(e.g. ~ 30 dBm), cost isdetermined by thermodynamics

340 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.2

0.4

0.6

0.8

1

1.2

p=2p=10

p=50

Input amplitude

Out

put a

mpl

itude

Rapp model AM/AM nonlinearity

Typical Nonlinear PA Characteristics

)2/(12

1

1pp

sat

inin

out

VV

VV

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡+

=

35

Comparison of Backoff Required for OFDM and Serial Modulation with QPSK Modulation and 0% Excess Bandwidth

Backoff difference between OFDM and serial mod. About 2 dB with p=2 and about2.5 with p=10.

Rapp model parameter p=2 (HPA exhibits significant nonlinearity below saturation)

0 0.5 1 1.5 2 2.5 3 3.5-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

frequency normalized to symbol rate

Upp

er h

alf o

f pow

er s

pect

rum

(dB

)

SERMOD, dB backoff=7OFDMA, dB backoff=9

0 0.5 1 1.5 2 2.5 3 3.5-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10


Upp

er h

alf o

f pow

er s

pect

rum

(dB

)

SERMOD, dB backoff=4.8OFDMA, dB backoff=7.3

Rapp model parameter p=10 (HPA approximates an ideal linear clipper)

36

A PAPR Reduction Method: Selective Mapping

• Generate Ns different transformations on each block of data, transmit the one with least peak value, as well as the identity of the transform. (Muller and Huber Proc. PIMRC 1997).

• Modification for serial modulation (Sabbaghian and Falconer, Proc. VTC 2006 spring) - Pick least-squares waveform, and use block permutations:

∑ ≤≤=−

=

1

0

2 1|)(|N

nskk Nknem

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧ ≥−

=otherwise0

9.|)(|9.|)(|)( ,, satkinsatkin

kVnVVnV

newhere

37

0 0.5 1 1.5 2 2.5 3 3.5-80

-70

-60

-50

-40

-30

-20

-10

0

10


Upp

er h

alf o

f pow

er s

pect

rum

(dB

)

SerMod. without SLMSerMod. with SLM

IBO=5 dB, p=2

IBO=5 dB, p=10

IBO=7 dB, p=10

0 0.5 1 1.5 2 2.5 3 3.5-80

-70

-60

-50

-40

-30

-20

-10

0

10


Upp

er h

alf o

f pow

er s

pect

rum

(dB

)

OFDM, without SLMOFDM with SLM

IBO=5 dB, p=2

IBO=5 dB, p=10

IBO=7 dB, p=10

DFT-precoded OFDM (SM) OFDM

Effect of SLM for 16 QAM with Ns=4

Again, the backoff reduction is more effective for p=10

38

Another PAPR Reduction Method for GMC Signals with Pilots

• Try pilot sequences from a set of Ns possible orthogonal sequences, and select the resulting composite waveform with minimum peak value (Garcia et al, IEEE Trans. Wireless Comm., Jan. 2006).

• Modification for DFT-precoded OFDM (Lam, Falconer and Danilo-Lemoine, Proc. WCNC, 2007):

– Use orthogonal cyclically-shifted Chu sequences to generate possible pilot sequences– Use least-squares selection rule.

39

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-80

-70

-60

-50

-40

-30

-20

-10

0

10

Frequency normalized to symbol rate

Upp

er h

alf o

f pow

er s

pect

rum

(dB

)

SERMOD, Ns=1SERMOD, Ns=32SERMOD, no pilotsOFDMA, Ns=1OFDMA, Ns=32OFDMA, no pilots

PAPR Reduction By Pilot sequence Selection for QPSK OFDM and DFT-Precoded OFDM (Serial Modulation)

Rapp parameter p=10 Backoff=7 dB

Again, backoff reduction is more significant for p=10.

40

Outline








41

Dealing with Phase Noise and Frequency Offset

OFDM: Single Carrier:

Frequency

Phase noise and frequency offsetcause inter-subcarrier (and thereforeintersymbol) interference. Remedy: complex linear processingin the frequency domain. Phase noise and frequency offset

cause time domain rotation of serial data symbols.Remedy: decision-directed phase locked loop processing at equalizer output.

42

Phase Noise and Frequency Offset Compensation for QPSK Using Turbo-Equalized Decision-Directed ProcessingRef: M. Sabbaghian and D. Falconer, “Joint Turbo Frequency Domain Equalization and Carrier Synchronization”, IEEE Trans. Wireless Comm., Vol. 7, No. 1, January 2008, pp. 204-212.

43

Outline








44

Applications of DFT-Precoded OFDM

• Single carrier is one of the three physical layer modes specified in the IEEE 802.16a and e standards, but it has not been implemented.

• 3GPP-LTE standard specifies DFT-precoded OFDM (which it calls SC-FDMA) as the uplink transmission mode.

• The recently completed EU WINNER Project recommends DFT-precoded OFDM as the uplink transmission mode for wide area FDD non-frequency adaptive uplinks in future generation wireless systems– Non-adaptive frequency diversity achieved with block-interleaved

frequency division multiple access (B-IFDMA) for uplink transmitter power efficiency.

45

Summary

• DFT-precoded OFDM, with frequency domain equalization, has an important role in the “OFDM era”.

• Iterative block and turbo equalization are powerful equalizationtechniques for DFT-recoded OFDM.– Adaptive turbo equalization, can be analyzed by the refined BERT

chart technique, even for small block lengths.• Channel estimation is aided by time- or frequency-multiplexed

pilots, and is enhanced by iterative methods.• DFT-precoded OFDM has lower PAPR and lower required

power backoff than comparable OFDM– PAPR reduction methods used for OFDM can be modified and

used effectively for DFT-precoded OFDM.• DFT-precoded OFDM (SC-FDMA) has been specified for the

uplink in emerging broadband wireless standards.

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