Exploring the Limits of
Digital Predistortion
P. Draxler, I. Langmore*, D. Kimball*, J. Deng*, P.M. Asbeck*
QUALCOMM, Inc. & UCSD – HSDG
*University of California, San Diego, HSDG
September 14th, 2004
Predistortion with Memory Model
Original measurement
with DPD incl. memory
AM/AM (K*volts) Measured (blue dots) Ideal (red) Curvefit (green)
AM/AM (K*volts) Measured (blue dots) Ideal (red) Curvefit (green)
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Blue points – instantaneous Vout vs. Vin
Purple line – gain target
Green line – expected value of gain
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Outline
• Introduction
• Contraction approximation for nonlinear systems
• Memory effect compensation – model based
• Error Vector Magnitude (EVM) metric
• Memory effect compensation – measurement based
• Results from 2 RF Power Amplifiers
• Conclusions
System Block Diagram
ec(i-1)
y'ni
xpni
PA
DPD
xn
eci
Ideal
Gain
yn
• DPD is the digital predistortion block
• PA is the power amplifier (model or device)
• Ideal Gain block sets system performance target
Notation and Relationships
ec(i-1)
• n is the sample index
xpni
• i is compensated waveform
DPD
iteration index
xn
• x: vectors are denoted with
Ideal
underbars
Gain
• {} curly brackets denote
multiple signals in an ensemble
• yn=Go xn is output of the “Ideal Gain” block (the
target output of the system)
• y’n=Gn(xn) is the output of the “PA” block (with
memory)
y'ni
PA
eci
yn
Waveforms Identified
• xn is the input waveform
• xpni is the input waveform
after digital pre-distortion
• y’ni is the output waveform
• yn is the target output
waveform
• eci is the current error
waveform
• ec(i-1) is the past error
waveform
ec(i-1)
y'ni
xpni
PA
DPD
xn
eci
Ideal
Gain
yn
e  y '  yn
i
c
i
n
Contraction approximation
G ( xn )  E (Gn ( x n ))
Memoryless gain
Gn ( x n )  G ( xn )  (1   ( x n )) Gain with memory effects
xpni  xpn( i 1)  xn( i 1)
x
( i 1)
n

  ec( i 1)
( i 1)
Gn ( xpn
xpni correction equation
Δx adjustment equation
)
Specific Application –
Model Based
• Generate xpni
• Evaluation of model
– Compare modeled vs.
measured for xpni
• Quantify the predictive
accuracy of the model
ec(i-1)
xpni
y ni
PA
Model
DPD
xn
Ideal
Gain
eci
Specific Application –
Model Based
Error Vector Magnitude
• Over all sample points, n,
of a single measurement:
– Normalize average power
of signals to unity: xα , yα
• Generate the rms
difference between the
normalized vectors
x 
2x
 ( x0 )
2
n
n
y 
2y
 ( y0 )
2
n
n
 ( y  x )
2
EVM rms 
n
n
Experimental values of alpha: α
– Memoryless nonlinearity
– Memory effect
nonlinearity
– Noise and chaotic
amplifier behavior
– Baseband envelope
DAC/ADC quantization
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Magnitude of EVM
• Identify vector Δxn
• Sweep α and evaluate
for optimal EVM.
• Function of:
Memoryless predistortion EVM over factor
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0.045
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del factor
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•
Ensemble Average
Error Vector Magnitude
x  Ex, y  E y
Perform an ensemble average
0
over many measurements:
E{.}
x 
0
2  x0
 ( x0 )
2
n
• Over all sample points: n
– Normalize average power of
both signals to unity: xα , yα
• Generate the rms difference
between the normalized
vectors
n
y 
2  y0
 ( y0 )
2
n
n
 ( y  x )
2
EVM rms 
n
n
Typical EVM histogram with
Ensemble EVM (N=16)
• Ensemble EVM is
typically in the lower
range of the histogram
members.
• As E{eci} becomes
small, more ensemble
members are needed to
have confidence in the
ensemble means and
variances.
Simple Test Amplifier
• Inexpensive catalog amplifier.
• WCDMA waveform used – amplifier
configured for narrowband operation.
• Severe ACPR asymmetry which switched
sides and didn’t improve after memoryless
predistortion.
Specific Application –
Experiment Based
Original I/O performance
Memoryless correction
AM/AM (K*volts) Measured (blue dots) Ideal (red) Curvefit (green)
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AM/AM (K*volts) Measured (blue dots) Ideal (red) Curvefit (green)
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Specific Application –
Experiment Based
Original I/O performance
Correction with memory
compensation
AM/AM (K*volts) Measured (blue dots) Ideal (red) Curvefit (green)
AM/AM (K*volts) Measured (blue dots) Ideal (red) Curvefit (green)
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Non-optimal RF Power Amplifier
EER Amplifier
• Power Amplifier
– Motorola LDMOS
– Vdd amplifier included
– PAE: 31.5%
• Signal
–
–
–
–
WCDMA signal
>9dB peak to average
Pin: 3.35 Watts
Pout: 29.0 Watts
ec(i-1)
xpni
y ni
PA
DPD
xn
Ideal
Gain
eci
RF Power Amplifier using Envelope
Elimination and Restoration (EER)
Conclusions
• A new metric – ensemble average EVM – has been
defined to separate out the deterministic EVM
components from the random EVM components.
• An measurement based algorithm has been realized that
enables one to compensate for deterministic components
of the output waveform.
• This metric and compensation technique is insightful
during:
–
–
–
–
component evaluation and characterization of amplifiers,
amplifier modeling and model evaluation,
identification of optimal performance targets,
in support of development of real time adaptive blocks…