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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.
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 3/37
Time-Variant Multipath Propagation
η0ej2πf0tδ(t − τ0)
scatterer
user
scatterer
η1ej2πf1tδ(t − τ1)
v
receiver
η2ej2πf2tδ(t − τ2)
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`)
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 4/37
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
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 5/37
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.
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 7/37
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.
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 8/37
OFDM Fundamentals (V)
OFDM time frequency representation
…
Sub-carriersFFT
Time
Symbols
5 MHz Bandwidth
Guard Intervals
…
Frequency
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 9/37
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
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 10/37
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
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 11/37
OFDMA (I)
Orthogonal time-frequency grid
time
frequency
an OFDM symbol
a subcarrier
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 12/37
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
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 13/37
OFDMA (II)
Frequency division multiple access (FDMA)
time
frequency
user 1
user 2
user 3
user 4
user 5
user 6
time diversity
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LTE Parameters (Downlink)
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 14/37
LTE Resource Grid (Downlink)
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LTE Resource Blocks (Downlink)
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 16/37
OFDMA (III)
Time-variant frequency-selective channel
time
time diversity
fre
qu
en
cy
div
ers
ity
frequency
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 17/37
OFDMA (III)
Time-frequency pattern
time
time diversity
fre
qu
en
cy
div
ers
ity
frequency
user 1
user 2
user 3
user 4
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 17/37
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
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 18/37
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
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 19/37
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
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Comparison OFDMA vs. SC/FDMA
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SC/FDMA Distributed vs. Localized
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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
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 26/37
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
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 27/37
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
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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
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 30/37
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
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 31/37
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
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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
zm,q ∈ C , additive noise
γi,q ∈ C , basis expansion coefficient
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 33/37
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
zm,q ∈ C , additive noise
γi,q ∈ C , basis expansion coefficient
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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
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 34/37
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 .
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 35/37
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
Thomas Zemen OFDMA/SC-FDMA Basics for 3GPP LTE (E-UTRA) April 24, 2008 37/37