Wideband Linearization: Feedforward plus DSP

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Wideband LinearizationFeedforward plus DSP
Workshop WMD

• Jim Cavers and Thomas Johnson
• Engineering Science, Simon Fraser University
• 8888 University Dr., Burnaby, BC V5A 1S6
• Canada

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• Why linearize RF power amps?
• Power-efficient amps are nonlinear.
• Nonlinearity causes a signal to expand
• beyond its allotted bandwidth.

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A single-carrier example
The IM, viewed as additive distortion, is
uncorrelated with the signal.
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So linearize the amplifier.
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• The linearizer menu
• Cartesian feedback simple, power efficient,
  limited bandwidth.
• digital predistortion - power efficient,
  moderate bandwidth.
• LINC power efficiency? bandwidth?
• feedforward moderate power efficiency, high
  bandwidth.

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• Two big advantages of classic feedforward
• independent of amplifier model
• reasonably wide bandwidths

• But practical issues limit its bandwidth
• delay differences between parallel branches
• frequency dependence of components

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• A genuinely wideband feedforward linearizer rests
  on
• a novel multibranch RF architecture
• and the DSP to back it up.
• Well look at both of them.

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1. Classic FF and DSP

• The traditional feedforward linearizer

is sensitive to ?, ? misadjustments needs
adaptation.
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• A common adaptation loop uses a bandpass
  correlator. Stochastic gradient.
• Problems
• Accurate wideband mixing is hard.
• DC offset misadaptation.

Focus is on signal cancellation circuit, but all
remarks apply equally to error cancellation
circuit.
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• DSP solution
• use slices a few tens of kHz wide
• inexpensive ADCs
• no DC offset
• no wideband variation
• a partial correlation.

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• By tuning LO1, we get partial correlations at
  strategically selected frequencies
• on strong desired signals to drive the signal
  cancellation circuit
• on IM alone no desired signals to drive the
  error cancellation circuit
• For correlation across the entire band, sum the
  successive partial correlations at the selected
  frequencies.

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2. Multibranch Feedforward

• Q Whats wrong with the classic FF (other than
  power efficiency)? A Limited bandwidth.
• Signals dont cancel perfectly at the subtraction
  point, because of
• Delay mismatch between parallel branches
• Frequency dependence of components

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Virtually every component has some frequency
dependence. Summarize the filter action from
input to error signal by He(f,a). Suppress the
signal. (In error cancelln circuit, suppress
the IM.)
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Choose coefficient a to minimize the error filter
power
where B is linearization bandwidth, W(f ) is a
non-negative weighting function. If W(f ) is
uniform, the optimum He(f )2 has a null in the
center of the band. Other useful weight functions
are possible, e.g., W(f ) is signal power
spectrum to minimize error signal power.
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Great signal suppression, but at a single
frequency. Gradual degradation away from
center with increasing mismatch between
branches. A partial correlator is sufficient for
whole-band optimum.
Tilt describes frequency dependence the dB
variation of branches across the band.
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A new feedforward architecture compensates for
delay mismatch and frequency dependence.
Think of it as a time-shifting interpolator or as
an FIR filter at RF.
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The criterion is the same - minimize the error
filter power
with respect to a0 and a1. The resulting
He(f,a0,a1)2 has two nulls in the band.
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Two-branch matching greatly improves IM
suppression. Multibranch is even better.
The whole-band optimum can again be achieved with
partial correlators at specific frequencies.
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In the minimization criterion
the uniform weight function (whole band) and a
two-delta weight function have the same effect.
Use
with appropriately selected frequencies.
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• Summary
• The multibranch feedforward architecture gives
  greater IM suppression or greater bandwidth
  through compensation.
• Modular - just add branches to get the required
  linearized bandwidth.
• The architecture rests on DSP-implemented
  partial correlations.
• But DSP is required for more than correlations

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3. Adapting Multibranch FF

• Multibranch feedforward has several coefficients
  to adapt.
• How do we do it?

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Straightforward? Adapt the coefficients
independently, like the classic LMS algorithm.
Each partial correlator visits both (or all)
frequencies.
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The problem? The branch 0 and 1 signals are
highly correlated, since Dt B ltlt 1.
Large eigenvalue spread in the correlation matrix
means sloooow convergence performance is no
better than single branch.
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The solution decorrelate the branch signals
first.
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For two branches, decorrelate by forming sum and
difference.
Aggregate the slices across the band, as usual.
For more branches, use eigenvector matrix or
inverse square root of correlation matrix.
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This approach leads to variants of decorrelated
stochastic gradient (like decorrelated LMS) or to
RLS. An eigendecomposition requires a sample
correlation matrix, so some learning is required.
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Decorrelation is important
simulated no decorrn
measured no decorrn
measured decorrn
simulated decorrn
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• Summary
• Multibranch feedforward needs decorrelation.
• Decorrelation needs DSP.
• DSP needs frequency slices and partial
  correlations.

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4. Ancillary Algorithms and Architectures

• To finish a working multibranch design, we need
• a little housekeeping software
• simplified hardware

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Fast, stable adaptation decorrelated or basic
requires accurate knowledge of internal phase and
amplitude relationships. Its hopeless otherwise.
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Self-calibration of amplitudes/phases can be
achieved through prior correlations in DSP.
No extra hardware needed for this, provided PA
can be put into standby and complex gains set to
0.
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Bonus accurate self calibration allows
simplified, cheaper hardware only one sdc on
the input side, not one per branch.
Branch 0, 1, relationships are already known
pretty well through self calibration.
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5. Performance and Applications

• At present
• Several working prototypes constructed.
• Linearized bandwidth of 40 MHz, 60 MHz, 100 MHz
  and beyond but who needs it?

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Decorrelation improves converged IM suppression.
Early measurements
Two branches 1 no decorr, simn 2 no decorr,
meast 3 decorr, meast 4 decorr, simn
Slice (subband) separation 36 MHz.
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Slice (subband) separation affects IM suppression
and linearized bandwidth. Later measurements
Two-branch prototype. Add another branch for
more bandwidth or more suppression.
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With two CW carriers and five narrowband
modulated carriers
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6. Applications

• Many 10s of MHz and more linearized
• bandwidth.
• Deep IM suppression over smaller bands.
• Multicarrier systems DVB?
• What else???

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7. Conclusions

• Combine wide bandwidth of analog technology and
  signal manipulation of DSP.
• Modular architecture can linearize over huge
  bandwidths.
• Technology package is available.
• Applications?

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8. References

• J.K. Cavers, "Adaptive Feedforward Linearizer
  for RF Power Amplifiers", U.S. Pat. 5,489,875,
  February 6, 1996.
• A.M. Smith and J.K. Cavers, A Wideband
  Architecture for Adaptive Feedforward Amplifier
  Linearization, IEEE Veh Technol Conf, Ottawa,
  May 1998.
• T. Johnson, J. Cavers, M. Goodall, Multibranch
  
• Feedforward Power Amplifier Linearization
  Techniques, Proc. Commun. Design Conf., 2002.
• J.K. Cavers and T.E. Johnson, Self-calibrated
  power amplifier linearizers, U.S. Pat.
  6,734,731, May 11, 2004.
• T.E. Johnson and J.K. Cavers, Reduced
  architecture for multibranch feedforward power
  amplifier linearizers, U.S. Pat. 6,683,495 ,
  January 27, 2004.

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• J.K. Cavers, Adaptive linearizer for RF power
  amplifiers, U.S. Pat. 6,414,546, July 2, 2002.
• J.K. Cavers, Adaptive linearizer for RF power
  amplifiers, U.S. Pat. 6,208,207, March 27, 2001.
• T.E. Johnson, Calibration and Adaptation of a
  Two Branch Feedforward Amplifier Circuit With a
  Decorrelated Block Based Least Mean Square
  Algorithm, M.A.Sc. Thesis, Simon Fraser
  University, July 2001.