1. 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 14 th, 2004

2. Predistortion with Memory Model Blue points – instantaneous V out vs. V in Purple line – gain target Green line – expected value of gain Original measurement with DPD incl. memory

3. 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

4. System Block Diagram DPD is the digital predistortion block PA is the power amplifier (model or device) Ideal Gain block sets system performance target

5. Notation and Relationships n is the sample index i is compensated waveform iteration index x: vectors are denoted with underbars {} curly brackets denote multiple signals in an ensemble y n =G o x n is output of the “Ideal Gain” block (the target output of the system) y’ n =G n (x n ) is the output of the “PA” block (with memory)

6. Waveforms Identified x n is the input waveform xp n i is the input waveform after digital pre-distortion y’ n i is the output waveform y n is the target output waveform e c i is the current error waveform e c (i-1) is the past error waveform

7. Contraction approximation Memoryless gain Gain with memory effects xp n i correction equation Δx adjustment equation

8. Specific Application – Model Based Generate xp n i Evaluation of model –Compare modeled vs. measured for xp n i Quantify the predictive accuracy of the model Model

9. Specific Application – Model Based

10. Error Vector Magnitude Over all sample points, n, of a single measurement: –Normalize average power of signals to unity: x α, y α Generate the rms difference between the normalized vectors

11. Experimental values of alpha: α Identify vector Δx n Sweep α and evaluate for optimal EVM. Function of: –Memoryless nonlinearity –Memory effect nonlinearity –Noise and chaotic amplifier behavior –Baseband envelope DAC/ADC quantization

12. Ensemble Average Error Vector Magnitude Perform an ensemble average over many measurements: E{.} Over all sample points: n –Normalize average power of both signals to unity: x α, y α Generate the rms difference between the normalized vectors

13. Typical EVM histogram with Ensemble EVM (N=16) Ensemble EVM is typically in the lower range of the histogram members. As E{e c i } becomes small, more ensemble members are needed to have confidence in the ensemble means and variances.

14. 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.

15. Specific Application – Experiment Based Memoryless correctionOriginal I/O performance

16. Specific Application – Experiment Based Correction with memory compensation Original I/O performance

17. Non-optimal RF Power Amplifier

18. 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

19. RF Power Amplifier using Envelope Elimination and Restoration (EER)

20. 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…