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## Wideband Linearization: Feedforward plus DSP

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**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. • Nonlinearity causes a signal to expand • beyond its allotted bandwidth.**A single-carrier example:**The IM, viewed as additive distortion, is uncorrelated with the signal.**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.**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.**DSP solution:**• 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.**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.**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…**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.**Decorrelation is important:**simulated – no decorr’n measured – no decorr’n measured – decorr’n simulated – decorr’n**Summary:**• 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.**With two CW carriers and five narrowband modulated carriers:****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.