Post on 08-Sep-2019
Analyse theorique du compromis entre lerendement et la linearite de l’amplificateur de
puissance dans un contexte OFDM
O. Abel GOUBA
Signal Communications & Embedded ElectronicsIETR/SUPELEC, Rennes campus,
France
Seminaire SCEE03 Mai 2012
Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Outline
1 Background and motivation
2 Linearity considering PAPR reduction and PredistortionPredistortion error ε definitionExpressions of 1st and 2nd order moment of εLinearity performance measured by EVM
3 PA efficiency considering PAPR reduction and PredistortionDefinition of PA efficiencyExpression of the power efficiency
4 Joint combination of PAPR reduction and PredistortionDiscussion and analysisSimulations and results
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Background and motivation
1 Background and motivation
2 Linearity considering PAPR reduction and Predistortion
3 PA efficiency considering PAPR reduction and Predistortion
4 Joint combination of PAPR reduction and Predistortion
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Background
High power fluctuations cause OFDM problems
PA P
R
O
B
L
E
M
S OFDM signal with high peaks Non-linear device
0inV
outV
High power fluctuations of multi-carrier signals like OFDM,represented by Peak-to-Average Power Ratio (PAPR).
In-bound and out-of-bound distortions caused by transmitter’sPower Amplifier (PA) for a signal with high peaks.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Background
PA’s behavior to high peaks signals
IBO*
Signal to be amplified
A perfect linearity isobserved when thepower efficiency islow and vice versa.
Two solutions proposed separately:1 Linearization that compensates the PA non-linearities.
(eg: Predistortion, Feedback, etc.)2 PAPR reduction that reduces signal fluctuations and thus
increases PA efficiency. (eg: Clipping, Tone Reservation, etc.)
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Background
Combination of PAPR reduction and Linearization
S
O
L
U
T
I
O
N
S OFDM signal with
high peaks
Power amplifier
0inV
outV
PAPR Reduction Linearization
Since PAPR reduction and Linearization are complementarysolutions, two approaches of combination:
1 Simple combination of a PAPR reduction technique followedby Linearization.
2 Joint combination that takes into consideration the mutualeffects of PAPR reduction and Linearization.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Background
Combination of PAPR reduction and Linearization
S
O
L
U
T
I
O
N
S OFDM signal with
high peaks
Power amplifier
0inV
outV
PAPR Reduction Linearization
PAPR reduction and Linearization are designed and optimizedseparately:
A joint analysis of linearity and PA efficiency.A trade-off is needed for optimal combination.
Our approach: Theoretical analysis.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Background
Combination of PAPR reduction and Linearization
S
O
L
U
T
I
O
N
S OFDM signal with
high peaks
Power amplifier
0inV
outV
PAPR Reduction Linearization
PA model: Memory-less Solid State Power Amplifier (SSPA).
Linearization method selected: Predistortion.
PAPR reduction methods selected: Probabilistic methods andClipping technique.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Motivation
Study objectives
Theoretical expressions of the linearity performance measuredby EVM metric and the PA efficiency.
Analytical trade-off that ensures a good linearity withreasonable efficiency by combining PAPR reduction andPredistortion.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Linearity considering PAPR reduction and Predistortion
1 Background and motivation
2 Linearity considering PAPR reduction and PredistortionPredistortion error ε definitionExpressions of 1st and 2nd order moment of εLinearity performance measured by EVM
3 PA efficiency considering PAPR reduction and Predistortion
4 Joint combination of PAPR reduction and Predistortion
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Error ε definition
Simplified transmission scheme
)(0)()( tjetrtx θ= )(11
1)(~)(~ tjetrtx θ=
]~[ 1rp ]~[ 2rh
)(22
1)(~)(~ tjetrtx θ=PAPR
reduction Predistortion POWER AMPLIFIER
)(3
1)(~)( tjetrty θ=
h(r) is PA’s characteristic and p(r) the predistorter’s function:
h(r) =r(
1 +(rA
)2b) 12b
, p(r) =r(
1−(rA
)2a) 12a
, r ∈ [0, A[,
a and b are “knee factors”; A the maximum output amplitude.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Error ε definition
Simplified transmission scheme
)(0)()(tj
etrtx
)(
111)(~)(~ tj
etrtx
]~[ 1rp ]~[ 2rh
)(
221)(~)(~ tj
etrtx
PAPR reduction
Predistortion POWER AMPLIFIER
)(
31)(~)(
tjetrty
measure
Predistortion error ε:
ε (t) = |x1 (t)− y (t)| = |r1 (t)− r3 (t)|
Upper bound considered (closed form)[1]:
ε (t) ≤ r1 (t)∣∣∣1− 2
b−a2ab
∣∣∣[1] O. A. Gouba and Y. Louet “Predistortion Performance considering Peak to Average Power Ratio
Reduction in OFDM context”, in IEEE WCNC 2012, Paris, France, Apr. 2012.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Error ε definition
Simplified transmission scheme
)(0)()(tj
etrtx
)(
111)(~)(~ tj
etrtx
]~[ 1rp ]~[ 2rh
)(
221)(~)(~ tj
etrtx
PAPR reduction
Predistortion POWER AMPLIFIER
)(
31)(~)(
tjetrty
measure
OFDM signal x(t) is a stationary complex Gaussian process soits amplitude r(t) converges to Rayleigh Distribution:
pr (r) =2r
Pre
−r2Pr
The distribution of the signal after PAPR reduction is neededfor the calculation of 1st or 2nd order moment of ε.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
1st and 2nd order moment of the Predistortion error
1st order moment of ε
m1 , E [ε (r1)]
2nd order moment of ε
m2 ,E[|ε (r1)|2
]The distribution of the signal after PAPR reduction is neededfor the calculation of 1st or 2nd order moment of ε.
The signal distribution depends on the PAPR reduction method.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
1st and 2nd order moment of the Predistortion error
1st order moment of ε
m1 , E [ε (r1)]
2nd order moment of ε
m2 ,E[|ε (r1)|2
]The distribution of the signal after PAPR reduction is neededfor the calculation of 1st or 2nd order moment of ε.
The signal distribution depends on the PAPR reduction method.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
1st and 2nd order moment of the Predistortion error
3 top categories of PAPR reduction methods[2]:
PAPR reduction methods
Adding signal methods Probabilistic methods Coding methods
[2] C. Langlais, S. Haddad, Y. Louet and N. Mazouz “Clipping noise mitigation with the capacityapproaching FEC codes for PAPR reduction of OFDM signals”, in MC-SS 2011, Herrshing, Germany, May 2011.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
1st and 2nd order moment of the Predistortion error
3 top categories of PAPR reduction methods[2]:
PAPR reduction methods
Adding signal methods Probabilistic methods Coding methods
Data
bits
Coding
I
F
F
T
Mapping
Serial /
Parallel
S/P
Example of
(1-3)Reed Muller
kX nx
Coding methods use structuredsequences of frequency symbols thatare no longer independent identicallydistributed, therefore the resultedsignal is not Gaussian.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
1st and 2nd order moment of the Predistortion error
3 top categories of PAPR reduction methods[2]:
PAPR reduction methods
Adding signal methods Probabilistic methods Coding methods
S
E
L
E
C
T
I
O
N
IFFT
IFFT
IFFT
1
kV
2
kV
P
kV
kX nx
Side
information
Selected Mapping principle
Probabilistic methods proceed basicallyto a linear transformation by multiplyingthe data symbols by a deterministicvector send as side information, thereforethe resulted signal remains Gaussian.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
1st and 2nd order moment of the Predistortion error
3 top categories of PAPR reduction methods[2]:
PAPR reduction methods
Adding signal methods Probabilistic methods Coding methods
N
IFFT
N
IFFT
0X
1X
1NX
0C
1C
1NC
)(tc
)(tx )()( tctx
Adding signal technique
Adding signal methods depend on theadditive signal, therefore, the resultedsignal is not Gaussian anymore.
For our study, we consider Amplitudeclipping with the clipping ratio givenby γ =
Aclip√Pr
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
1st and 2nd order moment of the Predistortion error
3 top categories of PAPR reduction methods[2]:
PAPR reduction methods
Adding signal methods Probabilistic methods Coding methods
Distribution of the signal after clipping[3]:
υ (r) = pr (r) 1r≤Aclip + Pr{r > A}δ (r −Aclip)
Probability that r larger than clipping threshold Aclip:
Pr{r > Aclip} =
∫ +∞
Aclip
pr (r) dr = e−A2
clipPr .
[3] P. Banelli, G. Leus, and G. B. Giannakis, “Bayesian Estimation of Clipped Gaussian Processes withApplication to OFDM”, in Proc. EUSIPCO, vol.1, pp.181-184, Sep. 2002.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
1st and 2nd order moment of the Predistortion error
Probabilistic case[1]
m(prob)1 , E [ε (r1)] =
∫ rmax
rmin
ε (r) pr (r) dr
• Considering ε upper bound and ρ =r21
Pr1:
m(prob)1 max =
√Pr1
∣∣∣1− 2b−a2ab
∣∣∣ [Γinc(3
2, ρ
)]ρ=ρmaxρ=ρmin
,∀ρmin
• For ρmin = 0 :
m(prob)1 max =
√Pr1
∣∣∣1− 2b−a2ab
∣∣∣Γinc(3
2, PAPRr1
)• with :
Γinc (z, a) =
∫ a
0xz−1e−xdx
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
1st and 2nd order moment of the Predistortion error
Probabilistic case[1]
m(prob)2 , E [|ε (r1)|2] =
∫ rmax
rmin
|ε (r) |2pr (r) dr.
• Considering ε upper bound and ρ =r21
Pr1:
m(prob)2 max = Pr1
(1− 2
b−a2ab
)2 [(ρ+ 1) e−ρ
]ρ=ρminρ=ρmax
, ∀ρmin
• For ρmin = 0 :
m(prob)2 max = Pr1
(1− 2
b−a2ab
)2 (1− (PAPRr1 + 1) e−PAPRr1
)
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
1st and 2nd order moment of the Predistortion error
0.8 0.9 1 1.1 1.2 1.3
−70
−60
−50
−40
−30
−20
−10
Error after Selected Mapping with {Vk}={±1,± j}, P=10 and IBO=7dB
a/b
Err
or [d
B]
m1 simulated(10)
m2 simulated(14)
m1_max(11)
m1_max(13),ρmin=0
m2_max(15)
m2_max(16),ρmin=0
1st and 2nd order moments ofε with Selected Mapping(SLM) as PAPR reductionmethod.
m(prob)1 max =
√Pr1
∣∣∣∣1 − 2b−a2ab
∣∣∣∣Γinc ( 3
2, PAPRr1
)
m(prob)2 max = Pr1
(1 − 2
b−a2ab
)2 (1 −
(PAPRr1 + 1
)e−PAPRr1
)10/24
Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
1st and 2nd order moment of the Predistortion error
Amplitude clipping case[1]
m(clip)1 , E [ε (r1)] =
∫ rmax
rmin
ε (r) υ (r) dr.
• Considering ε upper bound and ρclip =A2clip
Pr1:
m(clip)1 max =
√Pr
∣∣∣1− 2b−a2ab
∣∣∣ [Γinc(3
2, γρ
)]ρ=ρclipρ=ρmin
+ ε (Aclip) e−γρclip .
• For ρmin = 0 :
m(clip)1 max =
√Pr
∣∣∣1− 2b−a2ab
∣∣∣Γinc(3
2, γPAPRr1
)+ ε (Aclip) e
−γPAPRr1 .
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
1st and 2nd order moment of the Predistortion error
Amplitude clipping case[1]
m(clip)2 , E
[|ε (r1) |2
]=
∫ rmax
rmin
|ε (r) |2υ (r) dr
• Considering ε upper bound and ρclip =A2clip
Pr1:
m(clip)2 max = Pr
[1− 2
b−a2ab
]2 [(γρ+ 1) e−γρ
]ρ=ρminρ=ρclip
+ |ε (Aclip) |2e−γρclip
• For ρmin = 0 :
m(clip)2 max =
Pr1γ
(1− 2
b−a2ab
)2 (1− e−γPAPRr1
)10/24
Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
1st and 2nd order moment of the Predistortion error
0.8 0.9 1 1.1 1.2 1.3
−70
−60
−50
−40
−30
−20
−10
Error after clipping, CR= 3dB, IBO=6dB
a/b
Err
or [d
B]
m1 simulated(17)
m2 simulated(20)
m1_max(18)
m1_max(19),ρmin=0
m2_max(21)
m2_max(22),ρmin=0
1st and 2nd order moments ofε with amplitude clipping asPAPR reduction method.
mclip1 max =
√Pr
∣∣∣∣1 − 2b−a2ab
∣∣∣∣Γinc ( 3
2, γPAPRr1
)+ ε
(Aclip
)e−γPAPRr1
m(clip)2 max =
Pr1
γ
(1 − 2
b−a2ab
)2 (1 − e
−γPAPRr1)
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Expressions of EVM of the amplified signal
Linearity metric EVM represents Error Vector Magnitude.
EVM expressions deducted from m2:
EVM =
√√√√√ E[|ε(t)|2
]E[|x1(t)|2
]=
√m2
Pr1.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Expressions of EVM of the amplified signal
Probabilistic case[4]
EVM (prob)max =
∣∣∣1− 2b−a2ab
∣∣∣√1− (PAPRr1 + 1) e−PAPRr1 .
Amplitude clipping case[4]
EVM (clip)max =
∣∣∣1− 2b−a2ab
∣∣∣√(1
γ
)(1− e−γPAPRr1
).
[4] O. A. Gouba and Y. Louet “Theoretical analysis of the trade-off between efficiency and linearity of theHigh Power Amplifier in OFDM context”, in European Wireless 2012, Poznan, Poland, Apr. 2012.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Expressions of EVM of the amplified signal
EVM metric depending of the“knee factors” ratio a/b whenamplitude clipping is used asPAPR reduction technique
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Expressions of EVM of the amplified signal
EVM metric depending of the“knee factors” ratio a/b whenSLM is used as PAPRreduction technique
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Expressions of EVM of the amplified signal
EVM metric depending onPAPRr1 for a/b = 0.65,0.875 and 0.975 whenAmplitude Clipping is used
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Expressions of EVM of the amplified signal
Recap
Theoretical expressions are relatively closed to the simulationaccordingly to the upper bound of the Predistortion error ε.
The linearity measured by EVM depends mainly onPredistortion performance but also on PAPR reduction.
Linearity (EVM equals zero) is achieved for an effective PAPRreduction and a perfect Predistortion (a = b).
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
PA efficiency considering PAPR reduction and Predistortion
1 Background and motivation
2 Linearity considering PAPR reduction and Predistortion
3 PA efficiency considering PAPR reduction and PredistortionDefinition of PA efficiencyExpression of the power efficiency
4 Joint combination of PAPR reduction and Predistortion
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
PA efficiency
Power budget of a power amplifier
POWER AMPLIFIER
Pin
Input power Pout
Output power
PDC
DC power
Plost
Dissipated power
PA efficiency definition:
ηDC =PoutPDC
Expression of PA efficiency[5]:
ηDC = G · exp (−g · PAPRr1)
Examples of power efficiencyparameters[5]
Class G [%] gA 58.7 0.1247B 90.7 0.1202
[5] D. Wulich, “Definition of efficient PAPR in OFDM”, IEEE Com. Letters, vol. 9, n. 9, p. 832 - 834, sept.2005.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
PA efficiency
Power efficiency depending ofPAPRr1 for classes A and BPA
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
PA efficiency
PA’s behavior to high peaks signals
IBO*
Signal to be amplified
PA efficiency mainly depends on PAPR reduction performance.
The maximum possible efficiency is achieved when the peakpower of amplified signal coincides with the saturation power.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Joint combination of PAPR reduction and Predistortion
1 Background and motivation
2 Linearity considering PAPR reduction and Predistortion
3 PA efficiency considering PAPR reduction and Predistortion
4 Joint combination of PAPR reduction and PredistortionDiscussion and analysisSimulations and results
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Discussion and analysis
EVM expression depends on signal PAPR and the “kneefactors” a and b.
Efficiency expression depends mainly on signal PAPR.
Relationship between EVM and PA efficiency is carried out bysubstituting these two expressions[4]:
EVM (prob)max =
∣∣∣1− 2b−a2ab
∣∣∣√
1−(ηDCG
) 1g
(1− 1
gln(ηDCG
))
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Discussion and analysis
EVM metric depends on thepower efficiency of class A PAfor different values of the“knee factors” ratio a/b whenSLM is considered as PAPRreduction technique
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Discussion and analysis
Recommendations for PAPR reduction and Predistortioncombination:
High PAPR reduction gain and minimum drawbacks
Effective Predistortion designed taking into account PAPRreduction (maximum linearity)
Input Back-Off (IBO) of the PA equal to the signal’s PAPR(maximum efficiency)
Adaptive Predistortion can also be considered.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Simulations and results
1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
60
IBO[dB]
EV
M [%
]
EVM metric measured between the amplified signal and the PAPR reduced signal
Clipping+Predistortion+PA with PAPRtarget=5dB
SLM+Predistortion+PA with PAPRtarget=5dB
class A power efficiency
Good trade−off betweenefficiency and linearity
Trade-off between linearity andpower efficiency whenamplitude clipping and SLMare used with Predistortion andSSPA Class A power amplifier.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Simulations and results
Recap
The main goal of our trade-off analysis is to ensure goodlinearity with reasonable efficiency.
Relationship between EVM and PA efficiency.
Optimal combination of PAPR reduction and Predistortion.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Conclusion
EVM = f (PAPR, a, b)
The quality in term of linearity and efficiency of thetransmitters depends on PAPR reduction and Linearization.
The trade-off in OFDM context can be estimated without theneed of extensive simulations
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
References I
[1] O. A. Gouba and Y. Louet “Predistortion Performanceconsidering Peak to Average Power Ratio Reduction in OFDMcontext”, in IEEE WCNC 2012, Paris, France, Apr. 2012.
[2] C. Langlais, S. Haddad, Y. Louet and N. Mazouz “Clippingnoise mitigation with the capacity approaching FEC codes forPAPR reduction of OFDM signals”, in MC-SS 2011,Herrshing, Germany, May 2011.
[3] P. Banelli, G. Leus, and G. B. Giannakis, “BayesianEstimation of Clipped Gaussian Processes with Application toOFDM”, in Proc. EUSIPCO, vol.1, pp.181-184, Sep. 2002.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
References II
[4] O. A. Gouba and Y. Louet “Theoretical analysis of thetrade-off between efficiency and linearity of the High PowerAmplifier in OFDM context”, in European Wireless 2012,Poznan, Poland, Apr. 2012.
[5] D. Wulich, “Definition of efficient PAPR in OFDM”, IEEECom. Letters, vol. 9, n. 9, p. 832 - 834, sept. 2005.
[6] O. A. Gouba and Y. Louet, “Joint study PAPR reduction andHPA predistortion”, URSI GASS 2011, Istanbul, Turkey, Aug.2011.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Thank for your attention.
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Background and motivation Linearity performance PA efficiency study Joint combination Conclusion References
Thank for your attention.
Questions?Abel.Gouba@supelec.fr
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