SC-FDMA and LTE Uplink Physical Layer Design · SC-FDMA and LTE Uplink Physical Layer Design Seminar LTE: ... in the subsequent part. 9/339/33 Burcu Hanta – SC-FDMA and LTE Uplink

SC-FDMA and LTE Uplink Physical Layer DesignSC-FDMA and LTE Uplink Physical Layer Design

Seminar LTE: Der Mobilfunk der ZukunftSeminar LTE: Der Mobilfunk der Zukunft

Burcu Hanta

University Erlangen-Nürnberg

Chair of Mobile Communications

November 18, 2009

OutlineOutline

1 Introduction

Structure of SC-FDMA vs. OFDMA

Why SC-FDMA?

2 Uplink Time and Frequency Structure

3 Uplink Physical Channel

4 SC-FDMA Transmission

Localized and Distributed Mode

Comparison Criteria for Different Carrier Modes

Transmitter Structure

Receiver Structure

5 Conclusion

Burcu HantaBurcu Hanta – SC-FDMA and LTE Uplink Physical Layer Design– SC-FDMA and LTE Uplink Physical Layer Design1 /331 /33

IntroductionIntroduction


Remark on Orthogonal Frequency Division Multiple Access

(OFDMA):

A multiple access scheme which provides multiple

channels for different users

Used in many applications including the downlink of LTE.

Robust to time delays especially in multiple fading

channels

If orthogonality of subcarriers cannot be ensured, high

performance degradation is observed.

Important problem: Peak-to-average power ratio (PAPR)



Peak-to-Average Power Ratio Problem in OFDMAPeak-to-Average Power Ratio Problem in OFDMA

PAPR =Ppeak

Pavg(1)

The OFDM transmitter performs a linear transform over a

large number of i.i.d. QAM-modulated complex symbols.

The time domain OFDM symbol can be approximated as a

Gaussian waveform from the central limit theorem [1].

⇒High PAPR in the OFDM signal.

High PAPR causes:

Either non-linear operation or high power consumption in

power amplifiers due to clipping.

A brand new system is introduced for the uplink: Single

Carrier FDMA.


IntroductionIntroduction Structure of SC-FDMA vs. OFDMAStructure of SC-FDMA vs. OFDMA

Structure of SC-FDMA vs. OFDMAStructure of SC-FDMA vs. OFDMA

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��&��

��

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{ }nx��

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Figure: Transmitter and receiver structure of OFDMA [2].


IntroductionIntroduction Structure of SC-FDMA vs. OFDMAStructure of SC-FDMA vs. OFDMA

Structure of SC-FDMA vs. OFDMAStructure of SC-FDMA vs. OFDMA

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Figure: Transmitter and receiver structure of SC-FDMA [2].


IntroductionIntroduction Why SC-FDMA?Why SC-FDMA?

Why SC-FDMA?Why SC-FDMA?

The subcarriers are transmitted sequentially instead of in

parallel as in OFDM.

⇒ The transmitted waveform is no longer a Gaussian

waveform which is probable to have high peak variations.

This helps to reduce the PAPR.


Uplink Time and Frequency StructureUplink Time and Frequency Structure

SC-FDMA Frame StructureSC-FDMA Frame Structure

<��#�� 3�!

=7 =0 =' =� =0> =0?

<��!��7��

<��" ��07��

Figure: Type 1 Frame structure [3].


Uplink Time and Frequency StructureUplink Time and Frequency Structure

Resource GridResource Grid

�!��=7 =0?

<��" ��

��#��

��

��

.��

�&

<A;):��8A;)��&�#�!��

RB

RB scN N×

12

RB

scN

=

symbN

��#!��

��!��

RB

symb scN N= × ��!��

Figure: Uplink resource grid for one slot [3].


Uplink Physical ChannelUplink Physical Channel

Physical Channel IPhysical Channel I

ScramblingModulation

mapper

Transform

precoder

Resource

element mapper

SC-FDMA

signal gen.

Figure: Uplink physical channel [4].


Uplink Physical ChannelUplink Physical Channel

Physical Channel IIPhysical Channel II

Scrambler: scrambles the coded bits in order to

randomize the interference and thus ensure that the

processing gain provided by the channel code can be fully

used.

Modulation mapper: performs the 4QAM or 16QAM

modulation on data blocks.

Transform precoder: supports multi-layer transmission in

MIMO systems.

Resource element mapper: assignment of the data blocks

to the suitable physical resource blocks.

SC-FDMA signal generation: will be detailed investigated

in the subsequent part.


SC-FDMA TransmissionSC-FDMA Transmission


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Figure: SC-FDMA transmission chain [2].



Subcarrier Allocation Methods ISubcarrier Allocation Methods I

f0

f1

fM- 1

f0

f1

fM- 1

Subcarrier

Mapping

N-point

IFFTAdd cyclic

prefix

Parallel to

Serial

converter

M-point

DFT

Spreading

f0

f1

fM- 1

f0

f1

fM- 2

Localized

Subcarrier

Mapping

0

0

0

0

0

0

0

0

0

0

f2

f3

fM- 4f

fM-1f

fM- 3f

Localized

0 1 2 3 4Frequency Frequency

f0

f1

fM-

f0

f1

fM-

Distributed

Subcarrier

Mapping

f2f

f3f

fM-f

fM-f

fM-f

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Distributed

1

2

3

4

Serial toParallelConverter

Incoming BitStream

m bitsBit to

ConstellationMapping

Bit toConstellationMapping


m bits

m bits

x(0,n)

x(1,n)

x(M - 1,n)

Serial toParallelConverter



-

Transmission

circuitry

Figure: SC-FDMA transmitter for localized and distributed subcarrier

mappings [1].



Subcarrier Allocation Methods IISubcarrier Allocation Methods II

Terminal 1

Terminal 2

Terminal 3SubcarrierSubcarrier

Distributed Mode Localized Mode

Figure: Subcarrier allocation methods for multiple users (3 users, 12

subcarriers, and 4 subcarriers per user) [5].


SC-FDMA TransmissionSC-FDMA Transmission Localized and Distributed ModeLocalized and Distributed Mode

Localized and Distributed ModeLocalized and Distributed Mode

Localized Mode

Each terminal uses a set of adjacent subcarriers to

transmit its symbols.

Along with channel dependent scheduling (CDS), it offers

high multi-user diversity.

Distributed Mode

The subcarriers used by a single terminal are distributed

over the whole frequency band.

Since the subcarriers are spread over the different parts

of the frequency band, the subcarrier data transmitted

over different channels are subject to different fading.

This provides high frequency diversity.


SC-FDMA TransmissionSC-FDMA Transmission Comparison Criteria for Different Carrier ModesComparison Criteria for Different Carrier Modes

Comparison Criteria for Different Carrier ModesComparison Criteria for Different Carrier Modes

Comparison criteria:

System throughput

PAPR

Problem: trade-off between these criteria.

Solution: find the optimum mode for the system by

testing.

The localized carrier transmission mode is used in LTE uplink

since it offers much better performance with the arrangement

of pulse-shaping filter.



Effect of CDS on System PerformanceEffect of CDS on System Performance

Key question:

“How to allocate time and frequency resources among

users while achieving multi-user diversity and frequency

diversity?” [6].

Aim:

Maximize the user utility in each transmission time

interval.

All in all, CDS improves the throughput of the system for

localized mode much more than the distributed mode where

the throughput measure is the Shannon’s channel capacity

formula, C = BW log (1 + SNR).



Effect of Pulse Shaping IEffect of Pulse Shaping I

Aim:

Mitigate the out-of-band signal energy.

Problem:

Pulse shaping increases the PAPR, especially too much for

localized FDMA.

However, the PAPR of SC-FDMA signals is still lower than

OFDMA signals and in terms of system throughput, localized

FDMA with CDS is much better than distributed FDMA.



Effect of Pulse Shaping IIEffect of Pulse Shaping II

0 2 4 6 8 1010

-4

10-3

10-2

10-1

100

Pr(

PA

PR

>P

AP

R0)

PAPR0 [dB]

CCDF of PAPR: QPSK, Nfft

= 256, Noccupied

= 64

Solid lines: without pulse shaping

Dotted lines: with pulse shaping

IFDMA LFDMA

α=0.4α=0.6

α=0.2

α=0

α=0.8

α=1

�

0 2 4 6 8 1010

-4

10-3

10-2

10-1

100

Pr(

PA

PR

>P

AP

R0)

PAPR0 [dB]

CCDF of PAPR: 16-QAM, Nfft

= 256, Noccupied

= 64

Solid lines: without pulse shaping

Dotted lines: with pulse shaping

IFDMALFDMA

α=0.4α=0.6α=0.2

α=0

α=0.8

α=1

� '(� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � '�(�

�

Figure: Comparison of complementary cumulative distribution

function (CCDF) of PAPR for distributed FDMA and localized FDMA

with 256 system subcarriers, 64 subcarriers per user and rolloff

factor of α ∈ {0,0.2,0.4,0.6,0.8,1} [6].


SC-FDMA TransmissionSC-FDMA Transmission Transmitter StructureTransmitter Structure

Transmitter Structure ITransmitter Structure I

a1[k ]

a2[k ]M–DFT

M–DFT

W

W

A1[µ]

A2[µ] Subcarrier

Subcarrier

Mapping

Mapping

K

K

B1[ν]

B2[ν]N–IDFT

N–IDFT

VH

VH

b1[κ]

b2[κ] CP

CP

extension

extension

bc1[κ]

bc2[κ]

P in

P in

Figure: Transmitter structure of LTE uplink [5].

MIMO ISI channel.

Single user MIMO transmission with 2 transmit antennas.

Data streams are divided into blocks of length M.

ai [k ]: 4QAM or 16QAM coded complex data symbols.



Transmitter Structure IITransmitter Structure II

First block: M-point DFT applied to the data sequences.

This can be represented as follows:

A i = Wa i

where,

A i = [Ai [0] Ai [1] ... Ai [M − 1]]T ,

a i = [ai [0] ai [1] ... ai [M − 1]]T , and

W is unitary M-point DFT matrix with entries

wmn = 1√Mexp (− j2πmn

M), m,n ∈ {0,1,2, ...,M − 1}.



Transmitter Structure IIITransmitter Structure III

Second block: Subcarrier assignment.

.............

...

...

...

.............

...

..........

Zeros

Zeros

Zerosν0 Zeros

(N − M − ν0) Zeros

Ai [0]

Ai [0]

Ai [1]Ai [1]

Ai [2]

Ai [M − 1]

Ai [M − 1]

Bi [0]Bi [0]

Bi [N − 1]Bi [N − 1]

Distributed Mode Localized Mode

Figure: Subcarrier Mapping in Distributed and Localized Mode [5].



Transmitter Structure IVTransmitter Structure IV

B i = [0 ... 0︸︷︷︸

ν0

Ai [0] Ai [1] ... Ai [M − 1] 0 ... 0︸︷︷︸

N−M−ν0

]T = KA i

with frequency shift ν0.

The assignment matrix K is:

K =

0ν0×M

IM

0(N−M−ν0)×M



Transmitter Structure VTransmitter Structure V

Third block: N-point inverse DFT. In the output of this

block, there are the time-domain transmit sequences,

b i = VHB i where V is a unitary N-point DFT matrix.

Fourth block: Cyclic prefix extension of length Lc > qh ,

where qh is the channel order. The transmission blocks

are:

b ci = [bi [N − Lc ] ... bi [N − 1] bi [0] bi [1] ... bi [N − 1]]T .



Cyclic Prefix Extension ICyclic Prefix Extension I

Cyclic prefix (CP) is a copy of the last N symbols of the block

in interest which is pasted at the start of the block.

CP

copy

b i

b ci

Figure: Addition of cyclic prefix [5].



Cyclic Prefix Extension IICyclic Prefix Extension II

There are a couple of reasons for CP extension.

CP works as a guard interval between subsequent blocks.

⇒ prevents the inter-block interference (IBI) due to

multipath fading.

It is a copy of the last part of the block.

⇒ converts a linear convolution to a circular convolution.

⇒ provides a very simple frequency domain equalization

technique for this system.


SC-FDMA TransmissionSC-FDMA Transmission Receiver StructureReceiver Structure

Receiver Structure IReceiver Structure I

. . .

. . .

r1[κ]

rNR[κ]

M–IDFT

M–IDFT

WH

WH

Y1[µ]

YNR[µ]Subcarrier

Subcarrier

Demapping

Demapping

KH

KH

R1[ν]

RNR[ν]

N–DFT

N–DFT

V

V

y1[k ]

yNR[k ]CP

CP

deletion

deletionrc1[κ]

rcNR[κ]

Pout

Pout

Figure: System model of the LTE Base Station [5].



Receiver Structure IIReceiver Structure II

NR -fold receive antenna diversity.

Received signal at l th antenna is:

rl [κ] =∑2

i=1

∑L−1λ=0 hl ,i [λ]bci [κ − λ] + nl [κ]

where,

hl ,i [λ]: discrete time channel impulse response of length L

(channel order qh = L − 1) from ith transmit antenna to

the lth receive antenna,

nl [κ] is the discrete time AWGN of lth receive antenna.

First block: Cyclic prefix is removed. In other words, the

first Lc values in rl [κ] are removed.



Receiver Structure IIIReceiver Structure III

CP

deletion

r l

rcl

Figure: Deletion of cyclic prefix [5].



Receiver Structure IVReceiver Structure IV

⇒ The following matrix model is obtained:

r l = H l ,1b1 + H l ,2b2 + n l

with the circulant channel matrices:

H l ,i =

hl ,i [0] 0 · · · 0 · · · 0.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

hl ,i [qh ] · · · hl ,i [0] 0 · · · 0

0 hl ,i [qh ] · · · hl ,i [0] 0.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

. 0

0 · · · 0 hl ,i [qh ] · · · hl ,i [0]



Receiver Structure VReceiver Structure V

Second block: N-point DFT is applied to r l .

R l = Vr l =∑2

i=1 VH l ,iVHB i + N l

H l ,i is a circulant matrix,

⇒ H l ,iVH = VH

Λl ,i , where

Λl ,i = diag{Hl ,i [0],Hl ,i [1],Hl ,i [N − 1]}.

Since the columns of VH are the eigenvectors of H l ,i

(VH l ,iVH = Λl ,i ), the following equation is obtained.

R l =∑2

i=1 Λl ,iB i + N l



Receiver Structure VIReceiver Structure VI

Third block: Subcarrier demapping in the frequency

domain.

Y l = KHR l

Fourth block: M-point inverse DFT applied on demapped

symbols.

y l = WHY l


ConclusionConclusion

Conclusion IConclusion I

Structure: DFT-spread OFDMA.

Localized FDMA → high PAPR, high throughput.

Distributed FDMA → low PAPR, low throughput.

Lower PAPR and higher system throughput compared to

OFDMA.

Pulse shaping operation might cause performance

degradation if not carefully designed.

High power consumption at the mobile station is avoided

by applying simple equalization at the base station.



Conclusion IIConclusion II

All of these phenomena reveal that single-carrier FDMA is a

better solution than OFDMA for the uplink of the LTE radio

system.



ReferencesReferences

[1] S. Sesia, I. Toufik, M. Baker: LTE-The UMTS Long Term

Evolution: From Theory to Practice, John Wiley, 2009.

[2] H. G. Myung, J. Lim, D. J. Goodman: Single Carrier

FDMA for Uplink Wireless Transmission, IEEE Vehicular

Technology Magazine, Sep. 2006.

[3] H. G. Myung: Technical Overview of 3GPP LTE,

Internet, May 2008.

[4] 3GPP TS 36.211 V8.3.0, 2008.

[5] M. Ruder: Multiuser MIMO Receiver for the Uplink of

Long Term Evolution (LTE), Nov. 2008.

[6] H. G. Myung: Single Carrier Orthogonal Multiple

Access Technique for Broadband Wireless

Communications, Dissertation, Jan. 2007.


Documents

SC-FDMA and LTE Uplink Physical Layer Design · SC-FDMA and LTE Uplink Physical Layer Design Seminar LTE: ... in the subsequent part. 9/339/33 Burcu Hanta – SC-FDMA and LTE Uplink