Fraunhofer InstitutNachrichtentechnikHeinrich-Hertz-Institut

Optimal transmitter

and receiver

design

for

SC-FDMA

V. Jungnickel, S. Jaeckel, T. Haustein, H. Wu

SC-FDMA Workshop, March

13, 2009, New York

Outline

•

Introduction

•

Advanced waveform

–

Raised cosine filtering for localized SC-FDMA–

Impact on peak-to-average power ratio

•

Receiver design

–

Two approaches: Advanced Rake vs. FDE+IDFT–

Proof that both are equivalent–

Impact of MMSE

•

Real-time multiuser detection experiments

•

Conclusions

Introduction

•

SC-FDMA is used as a multiple access scheme in LTE uplink

–

localized form is considered here

•

Several questions concerning SC-FDMA physical layer

•

Transmitter side

–

Why is the PAPR of SC-FDMA not comparable to classical single-carrier?

–

Can we improve this by advanced filtering?

•

Receiver side

–

How the optimal linear receiver for SC-FDMA looks like?

–

Is there a low-complexity implementation?

•

Multiuser detection experiments (virtual MIMO)

Advanced waveform design

•

to improve PAPR, digital filtering can be used

•

so we need up-sampling

•

let us emulate up-sampling in the frequency domain

•

up-sampling in t-domain is equivalent to repetition in f-domain

•

repeat the waveform in the frequency domain

•

apply raised cosine filtering

N*FDFTN-DFT

AA AAA

F-times upsampling

F repetions of N-DFT output

DFT-based SC transmitter (similar to LTE)

•

formal changes make waveform comparable to classical SC

data burst

source

length = N

2048IFFT

inner OFDM transmitter

CPcyclic

shift byround(F/2)

F=round(2048/N)

DFTlength

N

map DCto

centre

cyclic shift

Direct mapping

= DFT output at Tx

= IDFT input at Rx

DC

1 N/2 N

1 Nc

(a)

(b)

(c)

(d)

A

A

A

A

B

B

B

B

•

map the DC component (index = 1) on the center of a resource block

Advanced transmitter

•

emulate up-sampling by repetition in the frequency domain

•

then apply a raised cosine filter

data burst

source

length = N

2048IFFT

inner OFDM transmitter

CPcyclic

shift byround(F/2)

F=round(2048/N)

DFTlength

Nrepeater

map DCto

centre

RRC filter in

F-Domain

cyclic shift

Advanced mapping

virtual antenna signals

= DFT output at Tx

= IDFT input at Rx

DC

1

1 N/2 N

Nc

(a)

(b)

(c)

(d)

(e)

A

A

A A

A A

A

B

B

B B

B B

B

MRC or joint MIMO signal processing

•

at the receiver exploit redundant signals by maximum ratio combining

Spectra

•

classical SC spectra

realized in f-domain

•

Little more bandwidth

is needed

200 300 400 500 600 700

-50

-40

-30

-20

-10

0

10

subcarrier index

pow

er [d

B]

classical

TDfilter

FDfilter

DFT-based OFDMA

withspectral expansionwith without

with

w/oadvanced

filter

Filtered waveform

1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600

-0.03

-0.02

-0.01

0

0.01

0.02

0.03 classical Tx, TD filteringDFT-based Tx with spectral expansionRRC filtered data sequence, N= 25, F = 82

sample index

real

par

t

•

full: classical SC Tx

•

dotted: DFT-based Tx

•

same waveform as

classical SC

•

envelope = RRC-filtered

single-carrier signal

•

inner oscillation = centre

subcarrier

Origin of PAPR degradation in LTE

•

direct mapping corresponds to roll-off factor α=0•

rectangular window in f-domain creates sinx/x

pulse shape

•

“ringing”

of the rectangular filter causes overshooting in LTE PAPR degradation

•

with raised cosine filtering and α>0 regular SC envelope, reduced PAPR

0 500 1000 1500 2000-0.2

0

0.2

0 500 1000 1500 2000-0.2

0

0.2

•

rectangular window

(like LTE)

•

Advanced raised

cosine filter (α=0.7)

Optimal roll-off

0,0 0,2 0,4 0,6 0,8 1,0

3

4

5

6

mea

n P

AP

R [d

B]

roll-off factor α•

direct mapping corresponds to α=0, i.e. there is no roll-off in LTE

•

for reducing the PAPR, roll-off with α=0.6…0.7 may be applied

direct

mapping

(LTE)

advancedfiltering

PAPR

2 4 6 8 100

0.5

1

PAPR [dB]

cdf

SC DFT+SESC DFTOFDMA

N = 25, BPSK

2 4 6 8 100

0.5

1

PAPR [dB]

cdf

SC DFT+SESC DFTOFDMA

N = 25, QPSK

2 4 6 8 100

0.5

1

PAPR [dB]

cdf

SC DFT+SESC DFTOFDMA

N = 25, 16-QAM

•

BPSK:–

DFT precoding

has almost no effect on PAPR

–

3 dB gain with advanced filtering

•

QPSK–

2 dB gain due to DFT pre-coding–

further enhanced by advanced filtering

•

16-QAM–

still some gain due to DFT, but no significant gain by adv. filtering

•

advanced filtering is effective for constant amplitude modulation

adv. filtering is useful at low SNR

Excess

bandwidth

•

already with 25% more bandwidth, the PAPR is substantially reduced

•

reasonable mapping may be data/resource block size=4/5

•

With fixed resource block size and fixed data rate: increase the code rate

•

+2.6 dB back-off gain-

1.4 dB less coding gain+1.2 dB net gain20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54

2,0

2,5

3,0

3,5

4,0

4,5

5,0

5,5

6,0

6,5OFDMA

BPSKRRC filterα=0.7

optim

al fo

r RR

C fi

lter

reas

onab

le fo

r up-

link

dow

n-lin

k

mea

n PA

PR [d

B]

chunk width [subcarriers]

V. Jungnickel, T. Hindelang, T. Haustein, W. Zirwas, „SC-FDMA waveform

design, performance, power dynamics

and evolution

to MIMO“, IEEE Portable 2007, Orlando

Receiver performance

•

two basic receiver designs

–

RAKE: collects all multipath components and combines them–

Frequency-domain equalizer (FDE) with subsequent IDFT

•

both receivers do have the same performance, but why?

Rake

for

SC-FDMA

•

the Rake can be derived from maximum likelihood sequence detection

•

MLSE minimizes the MSE over all possible received waveforms yα

•

the Rake for MC-CDMA is derived in [Chen et al., Asilomar

2004]

–

sufficient statistics

–

new transmission eqn.

–

where G is effective channel

–

SC-FDMA applies DFT spreading

•

thus, G becomes circulant

∑ −==

cN

nnn

1

2minarg yyα α

α

Circulant

matrices

•

circulant

matrices have nice properties

–

eigenvalues

can be computed by DFT of first row Go

as

–

eigenvectors are colums

(or rows) of DFT matrix W

–

inverses, products and sums of circulant

matrices are also circulant

•

inverse of G is given as

•

circulant

properties are directly related to the DFT spreading in SC-FDMA

•

Other spreading codes may not have these nice properties

Main result

•

the optimal Rake for SC-FDMA is equivalent to frequency-domain equalization

(FDE) with subsequent IDFT

•

this has been verified for zero forcing (ZF) and minimum mean square error (MMSE) receivers

S. Jaeckel

and V. Jungnickel „On the

optimality

of frequency-domain

equalization

in DFT-

spread

MIMO-OFDM systems“, IEEE WCNC 2008, Las Vegas

Impact of MMSE

•

varying the number of taps in the channel indicates that

–

SC-FDMA + ZF has worse performance compared to OFDM, but–

by using MMSE we can realize the multipath diversity before FEC

Complexity

reduction

•

FDE+IDFT is not just a straight-forward receiver implementation

•

In fact it is the optimal linear multiuser receiver for SC-FDMA

•

Substantially reduced complexity

•

DFT spreading greatly simplifies optimal linear multiuser detection.

Instead

of one

hugematrix

G for

all codes

and all antennas…

… we

have

to handleN

smaller

matrices

on each

sucarrier, and perform

IDFT

afterwards.

Real-time

multiuser

detection

using

SC-FDMA

•

2 users, single

base

station

with

2 antennas

•

synchronization

+ all physical

layer

functions

in real time (DL+UL)

•

fixed

modulation, MUD demo

over

20 MHz, indoors, 2.6 GHz FDD

One of two

test terminals

Pre-commercial

LTE base

station

V. Jungnickel et al.„

Demonstration of virtual

MIMO in the

uplink“, IET Seminar on Cooperative

Communications, (invited

talk), London, 2007

Frequency

advance

•

downlink

and uplink

RF oscillators

are

coupled

to the

same

reference

clock

•

Based

on downlink

synchronization, we

canpre-compensate

the

uplink

CFO at the

terminal

•

Using

coarse

and fine frequency

and timing

correction

at the

terminal

and in addition

frequency

and

timing

advance, multiple user

signals

arrive

with

almost

no frequency

and

almost

no timing

offset

at the

base

station.

•

In this

way, high fidelity

MUD becomes

practical.

RF

Corr FIR

FFT

DDS

exp(j2 f t)π DLCFO

exp(-j2 f t)π ULCFO

+

symbol start

CPEestim.

downlink baseband

uplink baseband

DDS

downupCFOCFO f

NMf −=

Conclusions

•

SC-FDMA is favorable for future wireless systems since

–

it is easily realized using DFT-spread OFDM + cyclic shift

–

with advanced filtering, it allows very low PAPR at low SNR

–

the optimal Rake receiver can be realized using FDE+IDFT

•

Owing to these unique properties, SC-FDMA allows

–

the practical use of advanced multi-antenna techniques, such as multiuser detection in the uplink (virtual MIMO)

–

superior performance with limited complexity

Receiver with advanced fitering

•

Slightly more complex processing at receiver side

IDFTlength

N

optional:MRC- or joint MIMO

procesing for spectral compression

spectralmaskuser k

cyclic shift by

-round(F/2) CP

inner OFDM receiver

2048FFT

Extension to MIMO and SDMA

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•

Stack redundant signals per antenna in sub-vectors

•

Form extended space-frequency vectors

•

virtual MIMO system with 3 NTx

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•

Solve for DFT output signal vector using standard MIMO techniques

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