Helsinki University of Technology
T-72.333 Postgraduate Course in Radio Communications
RF Distortion Analysis for OFDM WLAN (part I)
Hafeth [email protected]
/RF Distortion Analysis for OFDM WLAN/ 07.04.2004 [email protected] 2
Outline
Amplifier NonlinearityPre-distortion TechniquesOFDM and PAPRConclusions
/RF Distortion Analysis for OFDM WLAN/ 07.04.2004 [email protected] 3
Next . . .
Amplifier NonlinearityPre-distortion TechniquesOFDM and PAPRConclusions
/RF Distortion Analysis for OFDM WLAN/ 07.04.2004 [email protected] 4
Amplifier Non-Linearity
Amplifier non-linearity leads toHarmonic DistortionIntermodulation Distortion / Spectral RegrowthCross ModulationSNR DegradationConstellation Deformation
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Harmonic Distortion
Harmonics distortion comes because of the amplifier non-linear transfer characteristics
2 3 41 2 3 4o i i i iv a v a v a v a v= + + + +…
Every nonlinear term (n > 1) generates a new harmonic component at nf1 and nf2
Harmonics can be filtered out without degrading the system performance, since they are far away from the fundamental frequency
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Intermodulation Distortion (1/2)Intermodulation Distortion (IMD) is a result of amplifier nonlinear terms (n > 1)
generates Intermodulation products (IMP) at fim = m f1 - n f2Distortion order = n + m
In-band components (odd-order)
2fc 3fcfc0 Frequency
Am
plitu
de
2
2
4
3 3
5 5 22 2
4 4 5 53 3
3 3
3rd IMD (IM3)FundamentalHarmonicsSum IMPsDifference IMPs
Fundamental zone
2nd Harmonic zone
3rd Harmonic zoneDC zone
IMD ratio
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Intermodulation Distortion (2/2)
IMD is a serious problem in RF systems, especially the third-order IMD (IM3)
At 2 f2 - f1 and 2 f1 - f2IM3 is the strongest and the most closest to the fundamental frequency componentsIMD products appear regularly on either side of each carrierOdd-order products introduce in-band distortionEven-order products introduce out-of-band distortion
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Cross Modulation
The crossmodulation comes as a result of the amplifier nonlinearity
For the input
The 3rd order term is
New modulation term at fc1
V a
( )( )1 21 2
cos(2 ) 1 cos(2 )in c cV V f t V m t f tπ π= + +
( ) ( )( ) 12 33 1 23 1 2 cos(2 )2o c
VV m t m t f tπ= + +
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Spectral Regrowth
Also called “Adjacent Channel Interference”
IM3 energy leaks to the adjacent channelsACLR (Adjacent Channel Leakage Ratio)
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Constellation Deformation
16-QAM signal
Input signal Output signal
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Measuring Nonlinearity
Most common measures of nonlinearity1-dB compression pointIntercept pointsAM/AM and AM/PM conversion
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1-dB Compression Point
The point where the output signal gain has dropped by 1dB from the ideal linear characteristics
Input amplitude
Out
put a
mpl
itude
1 dB drop
Dynamic Range
1-dB compression point
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3rd Order Intercept Point (IIP3)
The interception point between the the extrapolated linear fundamental component and 3rd distortion product
Linear
gain
3rd h
armo
nic
Fundam
ental
Input Voltage (peak)
Out
put V
olta
ge (p
eak)
3rd order intercept
point
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Amplifier Dynamic Range
Noise floorGkTeB
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Distortion in Power Amplifiers
There are two reasons for power amplifiers distortionDistortion due to the amplifier nonlinear characteristics
Small signal distortion
Distortion due to the amplifier saturationLarge signal distortion
The impact of the large-signal-distortion is more sever than that of small-signal-distortion
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Amplifier Back-Off
Input Back-Off (IBO)
Output Back-Off (OBO)
,
,
10 log sat inavg in
PIBO
P
=
,
,
10 log sat outavg out
POBO
P
=
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Next . . .
Amplifier NonlinearityOFDM and PAPRPre-distortion TechniquesConclusions
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OFDM Problems
There are some obstacles when using OFDM
High sensitivity to the frequency errors
Intercarrier Interference (ICI) between the subcarriers
OFDM signal exhibits very high Peak to Average Power Ratio (PAPR)
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PAPR of OFDM Signals
The complex envelope of the OFDM signal, over T second interval is given by
1
0( ) ( ), 0
N
c n nn
S t A w t t Tϕ−
=
= > >∑Where
is the carrier amplitude, andis the data vector
And the orthogonal carriers are
where
cAnw
2( ) nj f tn t eπϕ =
1 1( )2n
Nf t nT
− = −
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PAPR Definition
The PAPR is defined as ( )( )2
2
0
max ( )
1 ( )
tNT
s
S tPAPR S t
E S t dtNT
=
∫
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Quantifying PAPR
As N becomes larger, the imaginary and real parts of S(t) becomes Gaussian distributed (central limit theory)
The amplitude of PAPR has a Rayleigh distribution, with zero mean and variance N times of one complex sinusoid
Assuming mutually uncorrelated symbols, the CDF of PAPR per OFDM symbol is given by
{ } ( )( )Pr 1 1 NPAPR eγγ> = − −
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PAPR Properties
From the pervious two slides, we can conclude the following PAPR properties
PAPR results from the superposition of large number of subcarriersThe PAPR follows the Rayleigh distributionThe large peaks do not occur very often
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Next . . .
Amplifier NonlinearityOFDM and PAPRPre-distortion TechniquesConclusions
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Predistortion Techniques
Attempts to compensate for the nonlinear distortions by modifying the input signal characteristics
These modifications can be either non-adaptive or adaptive
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Amplitude Clipping
Limits the peak envelope of the input signal to a predefined value
The amplitude clipping introduces additional distortion, which can be viewed as a clipping noise
In-band noise for Nyquist sampled signalsOut-of-band noise for oversampled signals
arg( )
,( )
,j xx x A
L xAe x A
≤= >
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Clipping Ratio
Clipping Ratio (CR) The ratio of peak value (A) to the RMS value of the OFDM signal
PSD
(dB
)
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Clipping Noise
Clipped and Filtered OFDM signals
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Next . . .
Amplifier NonlinearityOFDM and PAPRPre-distortion TechniquesConclusions
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Conclusions
Clipping is the simplest and most common non-adaptive predistortion techniqueAlthough clipping helps limits the peak amplitude of the input signal, it also introduces an additional noise source called clipping noiseClipping noise can greatly degrade the BER performance of the system
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Thank You!
/RF Distortion Analysis for OFDM WLAN/ 07.04.2004 ha[email protected] 31
References
J. Heiskala and J. Terry, “OFDM Wireless LAN: A Theoretical and Practical Guide”, SAM Publishing, 2001Peter B. Kenington, “High Linearity RF Amplifier Design”, Artech House, 2002
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Exercise
Clipping is one method to overcome the PAPR in OFDM. List three other methods, and give a two lines description for each.
Hint.There are around 9 popular PAPR reduction methods. You may google the internet with “PAPR Reduction”
RF Distortion Analysis for OFDM WLAN (part I)OutlineNext . . .Amplifier Non-LinearityHarmonic DistortionIntermodulation Distortion (1/2)Intermodulation Distortion (2/2)Cross ModulationSpectral RegrowthConstellation DeformationMeasuring Nonlinearity1-dB Compression Point3rd Order Intercept Point (IIP3)Amplifier Dynamic RangeDistortion in Power AmplifiersAmplifier Back-OffNext . . .OFDM ProblemsPAPR of OFDM SignalsPAPR DefinitionQuantifying PAPRPAPR PropertiesNext . . .Predistortion TechniquesAmplitude ClippingClipping RatioClipping NoiseNext . . .ConclusionsReferencesExercise