Workshop WMD. Wideband Linearization: Feedforward plus DSP. Jim Cavers and Thomas Johnson Engineering Science, Simon Fraser University 8888 University Dr., Burnaby, BC V5A 1S6 Canada. Why linearize RF power amps? Power-efficient amps are nonlinear.
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The IM, viewed as additive distortion, is uncorrelated with the signal.
The traditional feedforward linearizer
is sensitive to , misadjustments – needs adaptation.
A common adaptation loop uses a bandpass correlator. Stochastic gradient.
Focus is on signal cancellation circuit, but all remarks apply equally to error cancellation circuit.
By “tuning” LO1, we get partial correlations at strategically selected frequencies:
Q: What’s wrong with the classic FF (other than power efficiency)? A: Limited bandwidth.
Signals don’t cancel perfectly at the subtraction point, because of:
Summarize the filter action from input to error signal by He(f,a).
Suppress the signal.
(In error cancell’n circuit, suppress the IM.)
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.
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.
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.
with respect to a0 and a1. The resulting |He(f,a0,a1)|2 has two nulls in the band.
Two-branch matching greatly improves IM suppression. Multibranch is even better.
The whole-band optimum can again be achieved with partialcorrelators at specific frequencies.
the uniform weight function (whole band) and a “two-delta” weight function have the same effect. Use
with appropriately selected frequencies.
Multibranch feedforward has several coefficients to adapt.
How do we do it?
Straightforward? Adapt the coefficients independently, like the classic LMS algorithm.
Each partial correlator visits both (or all) frequencies.
The problem? The branch 0 and 1 signals are highly correlated, since Dt B << 1.
Large eigenvalue spread in the correlation matrix means sloooow convergence – performance is no better than single branch.
Aggregate the slices across the band, as usual.
For more branches, use eigenvector matrix or inverse square root of correlation matrix.
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.
simulated – no decorr’n
measured – no decorr’n
measured – decorr’n
simulated – decorr’n
To finish a working multibranch design, we need:
Fast, stable adaptation – decorrelated or basic – requires accurate knowledge of internal phase and amplitude relationships. It’s hopeless otherwise.
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.
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.
Decorrelation improves converged IM suppression. Early measurements:
1: no decorr, sim’n
2: no decorr, meas’t
3: decorr, meas’t
4: decorr, sim’n
Slice (subband) separation 36 MHz.
Slice (subband) separation affects IM suppression and linearized bandwidth. Later measurements:
Add another branch for more bandwidth or more suppression.
J.K. Cavers, “Adaptive linearizer for RF power amplifiers,” U.S. Pat. 6,414,546, July 2, 2002.