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### 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

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

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

System Block Diagram

- DPD is the digital predistortion block
- PA is the power amplifier (model or device)
- Ideal Gain block sets system performance target

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)

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

Contraction approximation

Memoryless gain

Gain with memory effects

xpni correction equation

Δx adjustment equation

Specific Application – Model Based

- Generate xpni
- Evaluation of model
- Compare modeled vs. measured for xpni
- Quantify the predictive accuracy of the model

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

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

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

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.

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.

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

RF Power Amplifier using Envelope Elimination and Restoration (EER)

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…

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