Subject: [NEXTEL-1] Digital Baseband Predistortion of Non-Linear Power Amps using Orthogonal Polynominals.

From: [email-masked]
Date: Tue, 26 Aug 2003 02:18:12 -0400

The following is a White Paper on Digital Baseband Predistortion of Non-Linear
Power Amps using Orthogonal Polynominals.

Baseband predistortion (BPD) is a technique used in power amplifiers to reduce
power consumption and increase efficiency. BPD is also used to reduce adjacent
channel interference, it also provides a lower Bit Error Rate for digital
algorithms. Orthogonal polynomial is a algebraic theory systems of perpendicular
(orthogonal) polynomials can be constructed, that span a so called function space.
Orthogonality has the meaning of being zero of the inproducts. This function
inproduct is defined as a integral, where w (x) is called the weight function ( So
they say).  Orthogonal Polynominals is one of the most favored models for use in
baseband predistrotion.

The people from G-Tech claim their theory differs from previously published
models. They claim their calculations to be more precise and require fewer
resources. Previously calculations were taxing on resources and often subject to
errors.

Nortel has experimented with this model for their base radios for PCS/Celluar
service
(see http://groups.yahoo.com/group/NEXTEL-1/message/10802 ). Nortel will be
rolling out their first Baaseband predistortion amplifier in 03Q4. If all goes
well we will see cellsites that can operate 50%-60% longer that their
predecessors. This will prove extremely useful  in emergency situations when power
efficiency is the key to survival.  This method combined with Forward Power
Control could  extend cellsite battery life substantially and reduce
interference.  This paper is well worth the read.

===================================================================

DIGITAL BASEBAND PREDISTORTION OF NONLINEAR POWER AMPLIFIERS
USING ORTHOGONAL POLYNOMIALS
Raviv Raich, Hua Qian, and G. Tong Zhou _
Georgia Institute of Techonology
School of Electrical and Computer Engineering
Atlanta, GA 30332-0250, USA

ABSTRACT

The polynomial model is commonly used in predistorter
design. However, the conventional polynomial model ex-
hibits numerical instabilities when high-order terms are in-
cluded. In this paper, we introduce a novel set of orthog-
onal polynomial basis functions for predistorter modeling.
Theoretically, the conventional and the orthogonal polyno-
mial models are \equivalent" and thus should have the same
performance. In practice, however, the two approaches can
perform quite differently in the presence of quantization
noise and with infinite precision processing. Simulation re-
sults show that the orthogonal polynomials can alleviate the
numerical instability problem associated with the conven-
tional polynomials and generally yield better predistortion
linearization performance.

INTRODUCTION

 Power amplier (PA) is a major source of nonlinearity in a
communication system. To increase efficiency, PAs are of-
ten driven into their nonlinear region, thus causing spectral
regrowth (broadening) as well as in-band distortion. PA lin-
earization is often necessary to suppress spectral regrowth,
contain adjacent channel interference, and to reduce bit er-
ror rate (BER).

Among all linearization techniques, digital baseband pre-
distortion is one of the most cost effective. A predistorter,
which (ideally) has the inverse characteristic of the PA, is
used to compensate for the nonlinearity in the PA. To lin-
earize a memoryless nonlinear PA, the polynomial model is
a common choice and is widely used in predistorter model-
ing [1, Sec. 3.3]. In practice, however, the polynomial model
may experience numerical di_culties when high-order poly-
nomial terms are included [1, p. 86]. Volterra series and
certain special cases of the Volterra series, for example, the
Hammerstein model [2] and the memory polynomial model
[3], have been proposed for predistorter design that includes
memory effects.

To the best of our knowledge, [4, 5] are the only published
results on orthogonal polynomials for predistorter design.
Our approach is different and has the following advantages:
(i) Our orthogonal polynomial basis functions are expressed
in closed form (non-iterative), and the coe_cients are free of
round-o_ errors. (ii) Our basis functions are pre-determined
and can be implemented with little demand on the compu-
tation resources. In [4, 5], the basis functions are calculated
online and iteratively, thus requiring much more computa-
tional power. (iii) Our basis set consists of both even and
odd-order terms whereas that of [4, 5] allows odd-powered
series only. Moreover, our basis function expressions are for
generally complex-valued baseband data; their application
to nonlinear systems with memory is also prescribed.
In Section 2, we describe the conventional polynomial
model and point out its de_ciencies. In Section 3, we derive
novel orthogonal polynomial basis functions which are nu-
merically more stable than the conventional one. In Section

4, simulation results are presented to illustrate the bene-
_ts of the orthogonal polynomials. Finally, conclusions are
drawn in Section 5.

http://users.ece.gatech.edu/~qianhua/publications_files/Hua_ICASSP03.pdf

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