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## Wideband Linearization: Feedforward plus DSP

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### Wideband Linearization:Feedforward plus DSP

Jim Cavers and Thomas Johnson

Engineering Science, Simon Fraser University

8888 University Dr., Burnaby, BC V5A 1S6

Canada

- Power-efficient amps are nonlinear.
- Nonlinearity causes a signal to expand
- beyond its allotted bandwidth.

The IM, viewed as additive distortion, is uncorrelated with the signal.

- Cartesian feedback – simple, power efficient, limited bandwidth.
- digital predistortion - power efficient, moderate bandwidth.
- LINC – power efficiency? bandwidth?
- feedforward – moderate power efficiency, high bandwidth.

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

A genuinely wideband feedforward linearizer rests on

- a novel multibranch RF architecture
- and the DSP to back it up.
- We’ll look at both of them.

1. Classic FF and DSP

The traditional feedforward linearizer

is sensitive to , misadjustments – needs adaptation.

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.

- use slices a few tens of kHz wide
- inexpensive ADCs
- no DC offset
- no wideband variation
- a “partial correlation.”

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.

2. Multibranch Feedforward

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:

- Delay mismatch between parallel branches
- Frequency dependence of components

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 cancell’n circuit, suppress the IM.)

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.

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.

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.

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.

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.

- 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…

3. Adapting Multibranch FF

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.

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.

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

- Multibranch feedforward needs decorrelation.
- Decorrelation needs DSP.
- DSP needs frequency slices and partial correlations.

4. Ancillary Algorithms and Architectures

To finish a working multibranch design, we need:

- a little housekeeping software
- simplified hardware

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.

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?

Decorrelation improves converged IM suppression. Early measurements:

Two branches

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:

Two-branch prototype.

Add another branch for more bandwidth or more suppression.

6. Applications

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

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?

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.

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.

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