Forschungszentrum T elekommunikation Wien - …read.pudn.com/downloads161/doc/comm/732822/OFDMA_SCFDMA.pdf · Forschungszentrum T elekommunikation Wien ... Outline Part I - OFDMA

Forschungszentrum Telekommunikation Wien

OFDMA/SC-FDMA Basics for 3GPP LTE(E-UTRA)

T. Zemen

April 24, 2008

Outline

Part I - OFDMA and SC/FDMA basics

Multipath propagationOrthogonal frequency division multiplexing (OFDM)Soft frequency reusePeak-to-average power ratio (PAPR)Single carrier/frequency division multiple access(SC/FDMA)

Part II - Time-variant channel estimation for OFDM

Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 2/37

References

Motorola, ”Long Term Evolution (LTE): Overview of LTE Air-Interface,”Technical White Paper, 2007

Rohde&Schwarz, ”UMTS Long Term Evolution (LTE) TechnologyIntroduction,” 2007.

Freescale, ”Overview of the 3GPP Long Term Evolution Physical Layer,”2007.

3GPP TS 36.2111, ”Physical Channels and Modulation (Rel. 8),” March,2008.

H. G. Myung, J. Lim, and D. J. Goodman, ”Single Carrier FDMA forUplink Wireless Transmission,” IEEE Vehicular Technology Magazin, pp.30-38, September, 2006.

U. Sorger, I. De Broeck, and M. Schnell, ”Interleaved FDMA - A NewSpread Spectrum Multiple-Access Scheme,” Proc. IEEE ICC ’98,Atlanta, GA, pp-1013-1017, June, 1998.

T. Zemen and C. F. Mecklenbrauker, ”Time-Variant Channel Estimationusing Discrete Prolate Spheroidal Sequences,” IEEE Transactions onSignal Processing, vol. 53, no. 9, September 2005, pp. 3597-3607.


Time-Variant Multipath Propagation

η0ej2πf0tδ(t − τ0)

scatterer

user

scatterer


v

receiver


v velocity

` path

η` attenuation

τ` time delay

f` Doppler shift

L′ number ofpaths

Time-variant channel impulse response

h(t , τ) =L′−1∑`=0

η`ej2πf`tδ(t − τ`)


OFDM Fundamentals (I)

Single carrier versus multi carrier

t

f

t

f

0 0 N

d[0

]

d[0]

d[1]

d[2]

d[3]

d[4]

d[5]

d[6]

d[7]

d[1

]

d[2

]

d[3

]

d[4

]

d[5

]

d[6

]

d[7

]

single carrier multi carrier

TC

TC

1/TC Chip rate

N Number of subcarriers

d [0] . . . d [7] Data symbols


OFDM Fundamentals (II)

Orthogonal subcarriers

f

fq

fq+1

0

Df

1

magnitude

. . . . . .

fq = q/(NTC)

q ∈ {0, . . . ,N − 1} Subcarrier indexThomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 6/37

OFDM Fundamentals (III)

Processing steps

t t

t t t

t t

f

2*f

3*f

1

1

1

subcarriers modulatedsubcarriers

symbols(BPSK)

*(+1)

*(+1)

*(-1) +

Efficiently implementable by means of an inverse discreteFourier transform.


OFDM Fundamentals (IV)

Cyclic prefix insertion

t

TS

TS OFDM symbol duration.

A copy of the signal tail (length TG) is inserted at thebeginning of each OFDM symbol.Absorbs multipath components.


OFDM Fundamentals (V)

OFDM time frequency representation

…

Sub-carriersFFT

Time

Symbols

5 MHz Bandwidth

Guard Intervals

…

Frequency


OFDM System Design

No inter-symbol interference: Guard interval larger thanthe delay spread TD

GTC = TG > TD

Spectral efficiency: Symbol duration much larger thandelay spread

NTC = TS � TD

Inter-carrier interference: Symbol rate much higher thanDoppler shift fD

1/TS � fD

G cyclic prefix length in number of chipsN number of subcarriers


Receiver Side Processing

Drop cyclic prefix and perform DFTChannel partitioned in N parallel frequency flat channelsSimple equalization - complexity grows with N log(N)

d q[ ] y q[ ]

y[0]

y N[ -1]

g q[ ] n q[ ]

d[0]

d N[ -1]

...

...

...

...

... ...

g[0] n[0]

q subcarrier index

d data symbol

g subcarrier channelcoefficient

n additive noise

y received symbol


OFDMA (I)

Orthogonal time-frequency grid

time

frequency

an OFDM symbol

a subcarrier


OFDMA (II)

Time division multiple access (TDMA)

time

frequency

user 1

user 2

user 3

user 4

user 5

user 6

fre

qu

en

cy

div

ers

ity


OFDMA (II)

Frequency division multiple access (FDMA)

time

frequency

user 1

user 2

user 3

user 4

user 5

user 6

time diversity


LTE Parameters (Downlink)


LTE Resource Grid (Downlink)


LTE Resource Blocks (Downlink)


OFDMA (III)

Time-variant frequency-selective channel

time

time diversity

fre

qu

en

cy

div

ers

ity

frequency


OFDMA (III)

Time-frequency pattern

time

time diversity

fre

qu

en

cy

div

ers

ity

frequency

user 1

user 2

user 3

user 4


Soft Frequency Reuse (I)

At cell boundaries the signal to interference ratio (SIR) isapprox. 0 dB due to frequency reuse 1DS-CDMA uses soft handover at the cell boundaryOFDM based air interface allows soft frequency reuse forusers at the cell boundary


Soft Frequency Reuse (II)

MS 21

MS 11

BS 1

BS 3

BS 2

Power density

sub-

carr

ier

powerdensity

Power

dens

ity

Sub-carriers

sub-

carri

er

MS 31

MS 12

MS 22

MS 32


LTE Uplink

Power consumption in user equipment (UE) terminals islimited by batteryOFDM requires large dynamic range due to high peak toaverage power ratio (PAPR)Linear power amplifiers with wide dynamic range have badefficiencySingle carrier/Frequecy division multiple access(SC/FDMA) used for the uplink in LTE


Comparison OFDMA vs. SC/FDMA


SC/FDMA Distributed vs. Localized


SC/FDMA


Processing Steps


PAPR comparison


Conclusions - Part I

OFDM enables wireless communication in frequencyselective channelsChannel equalization in the frequency domainLow complexity implementation - fast Fourier transform(FFT) algorithmsTime and frequency diversity can be exploitedSC/FDMA is OFDM with precodingPAPR of SC/FDMA is 2dB smaller compared to OFDMA


Outline

Part I - OFDMA and SC/FDMA Basics

Part II - Time-variant channel estimation for OFDM

Signal modelDiscrete prolate spheroidal sequencesReduced-rank channel estimationMean square error (MSE) sensitivity to velocity of userequipment


Time-Variant Channel Estimation forOFDM

Signal model for a single flat-fading subcarrierq ∈ {0, . . . , N − 1}

ym,q = gm,qdm,q + zm,q

ym,q ∈ C , received symbol on subcarrier q at discrete timem ∈ {0, . . . ,M − 1}

zm,q ∈ C , additive noise

dm,q ∈ C data symbol


LTE Pilot Pattern


Reduced-Rank Channel Description

Second order statistic is unknownDoppler bandwidth upper bounded by νDmax

Estimation per frequency-flat subcarrier q ∈ {0, . . . ,N − 1}

Basis Expansion

gm,q ≈D−1∑i=0

γi,qui,m for m ∈ {0, . . . ,M − 1} , D ≤ M

gm,q channel coefficient for subcarrier q at time m

ui,m basis function

γi,q expansion coefficient


Slepian Basis Expansion

D. Slepian et al. (1961,1978) asked, which sequences have

1 maximum time concentration λ =

M−1∑m=0|um|2

∞∑m=−∞

|um|2

2 while being bandlimited in [−νDmax, νDmax]

M−1∑`=0

sin(2πνDmax(`−m))

π(`−m)ui,` = λiui,m

Discrete prolate spheroidal (DPS) sequences ui [m]

Doubly orthogonal on {−∞, . . . ,∞} and {0, . . . ,M − 1}Subspace has dimension D′ = d2νDmaxMe+ 1


Slepian Sequences

0 50 100 150 200 250

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

m

u0[m]

u1[m]

u2[m]

u3[m]

u4[m]

M = 256 block length

1/TS = 49 ks−1 symbol rate

vmax = 100 km/h velocity

fC = 2 GHz carrier

D = 5 dimensions


Time-Variant Channel Estimation

Signal model for a single subcarrier q

ym,q = gm,qdm,q + zm,q

ym,q ∈ C , received symbol on subcarrier q at discrete time m


γi,q ∈ C , basis expansion coefficient


Time-Variant Channel Estimation

Signal model for a single subcarrier q

ym,q =D−1∑i=0

ui,mγi,qdm,q + zm,q

ym,q ∈ C , received symbol on subcarrier q at discrete time m


γi,q ∈ C , basis expansion coefficient


Pilot Based Channel Estimation (I)

ym,q =D−1∑i=0

ui,mγi,qdm,q + zm,q

Time multiplexed pilot and data symbols, dm = bm + pm(pilots are known at the receiver side).bm ∈ {±1± j}/

√2 for m /∈ P and bm = 0 for m ∈ P

pm = {±1± j}/√

2 for m ∈ P and pm = 0 for m /∈ P

P =

{⌊iMJ

+M2J

⌋| i ∈ {0, . . . , J − 1}

}J pilot symbols


Pilot Based Channel Estimation (II)

... omitting q

Basis function vector f m =

u0,m...

uD−1,m

∈ R D ,

Coefficient estimates γ = G−1 ∑m∈P

ymp∗mf ∗m

where γ = [γ0, . . . , γ(D−1)]T and the correlation matrix

G =∑l∈P

f l f Hl .


MSE Sensitivity to User Velocity

MSEM =1M

M−1∑m=0

E{|gm − gm|2

}Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 36/37

Conclusions - Part II

Detailed channel information at receiver side difficult toacquireDiscrete prolate spheroidal sequences describe thesubspace of band-limited sequencesReduced-rank channel description using DPS sequencesallows for simple UE algorithmMean-square error (MSE) is practically independent ofuser velocity


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Forschungszentrum T elekommunikation Wien - …read.pudn.com/downloads161/doc/comm/732822/OFDMA_SCFDMA.pdf · Forschungszentrum T elekommunikation Wien ... Outline Part I - OFDMA