Exploring the Limits of Digital Predistortion

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 14th, 2004

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

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 • yn=Goxn is output of the “Ideal Gain” block (the target output of the system) • y’n=Gn(xn) is the output of the “PA” block (with memory)

6. Waveforms Identified • xn is the input waveform • xpni is the input waveform after digital pre-distortion • y’ni is the output waveform • yn is the target output waveform • eci is the current error waveform • ec(i-1) is the past error waveform

7. Contraction approximation Memoryless gain Gain with memory effects xpni correction equation Δx adjustment equation

8. Model Specific Application – Model Based • Generate xpni • Evaluation of model • Compare modeled vs. measured for xpni • Quantify the predictive accuracy of the 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: xα, yα • Generate the rms difference between the normalized vectors

11. Experimental values of alpha: α • Identify vector Δxn • 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: xα, yα • 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{eci} 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 correction Original 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…