Eduardo G. Lima

Validation and Physical Interpretation of the Power-Amplifier Polar Volterra Model

Although the Cartesian signal decomposition has been the preferred representation in baseband polynomial power-amplifier (PA) behavioral models, this is not the only 2-D reference frame that could be considered for representing the input complex envelope signal. Indeed, in this paper, we demonstrate that, if the alternative polar representation is considered, the resulting Volterra series model is much more adequate to model the physical behavior of PA devices. This is the feature that supports the design of an innovative PA model, denominated the Polar Volterra model, which is more flexible and general than the traditional Volterra series commonly used in PA baseband modeling. The closeness of the new model formulation with the PA physical operation enabled, for the first time in PA low-pass equivalent behavioral modeling, the theoretical derivation of a Volterra series model directly from the PA circuit analysis. In fact, as the proposed model directly isolates such PA physical characteristics, a significant reduction of the number of model coefficients is achieved when compared with the traditional Cartesian Volterra model. Finally, validation results that highlight the advantages of the Polar Volterra model are presented. These were based on the laboratory measurements performed on two PAs with distinct architectures: a conventional class-AB amplifier and a polar transmitter.

Base-band derived volterra series for power amplifier modeling

This paper proves that the traditional way of deriving power amplifier low-pass equivalent complex-signal Volterra models from their original band-pass RF real-signal Volterra models is too restrictive, and so does not lead to an optimal model. Then, it proposes a much richer alternative approach. Instead of deriving the base-band Volterra model from the RF Volterra model, we started by a general Volterra series expansion of a complex-signal to only then impose the restrictions of odd parity required by the low-pass equivalent polynomial approximation. This way, not only we prove that the theoretical reticence that was raised to similar approaches previously proposed for the memoryless polynomial and the memory polynomial were unfounded, as experimental results fully justified this novel approach.

A Physically Meaningful Neural Network Behavioral Model for Wireless Transmitters Exhibiting PM–AM/PM–PM Distortions

Artificial neural networks (ANNs) have been widely used to model wireless transmitter low-pass equivalent behavior. However, previously proposed ANNs either do not account for PM-AM and PM-PM distortions or do not satisfy a fundamental constraint imposed by the bandpass nature of wireless transmitters. The purpose of this work is twofold. First, it is shown that PM-AM and PM-PM distortions observed in wireless transmitters excited by wideband signals can have a significant impact on the performance of their behavioral models. Second, a novel ANN topology for wireless transmitter behavioral modeling is proposed. Contrary to previously published ANNs, this one only generates physically meaningful contributions as well as retaining the ability of accounting for PM-AM and PM-PM distortions. The accuracy of the proposed ANN is then compared with two commonly used ANNs of the same computational complexity and for fitting experimental data measured on a GaN-based class-AB amplifier chain. Improvements of up to 7 dB in NMSE and ACEPR results are achieved if the proposed ANN is used instead of a commonly used ANN that neglects the PM-AM and PM-PM distortions. Furthermore, improvements as high as 16 dB in NMSE and ACEPR are achieved by the proposed ANN in comparison with a traditional ANN that also accounts for the PM-AM and PM-PM distortions but does not satisfy the fundamental odd-parity constraint imposed by the bandpass nature of wireless transmitters.

Low-pass equivalent feedback topology for Power Amplifier modeling

In [1], Pedro et al. have presented an RF feedback model that was conceived to match the physical behavior of a general Power Amplifier (PA) circuit. Unfortunately, a procedure for the extraction of this model’s parameters has not yet been presented, because of the difficulties introduced by its recursive topology and the limited frequency band that is accessible in both the PA input and output ports. Nevertheless, this model has been used by various research groups as a design basis of new PA behavioral models, which generally approximate the feedback structure by a non-recursive Volterra series topology. This paper presents a new model whose parameters are easy to extract, and that keeps the original topological information of [1] by maintaining a feedback structure.

Rational function-based model with memory for power amplifier behavioral modeling

Polynomials have been extensively used to model power amplifier (PA) behavior because of their linearity in the parameters, which eases their identification. However, these models are inherently local, being unable to extrapolate the PA behavior for conditions not considered during model extraction. This paper presents a model which, based on the ratio of two polynomials, avoids the catastrophic error degradation of polynomials (being thus suitable for large-signal behavior prediction) but still can be extracted using linear regression techniques. This model is tested with measured data from a class-AB PA.

A polar-oriented Volterra model for power amplifier characterization

This paper addresses power amplifier (PA) behavioral models that are based on the low-pass equivalent Volterra series approach. As the PA is a band-pass system, the model that processes the complex envelope of the input signal is restricted to the generation of only the first zone output components. It is shown here that such restriction has been interpreted in a too conservative way in the conventional Volterra series based models. Alternatively, we propose a new model formulation which incorporates the band-pass restriction in a more suitable way, significantly increasing the flexibility of the Volterra-based PA models in general.

Low-Pass Equivalent Behavioral Modeling of RF Power Amplifiers Using Two Independent Real-Valued Feed-Forward Neural Networks

Feed-forward artiflcial neural networks (ANNs) can provide the adequate model required for the linearization of power ampliflers (PAs) used in wireless communication systems. A common characteristic of previously available ANN-based models for linearization purposes is the use of a single real-valued ANN having two outputs. The contribution of this work is to report the beneflts of performing such behavioral modeling based on two independent real-valued ANNs, where each network has a unique output. The proposed ANN-based model is applied to the behavioral modeling of a GaN HEMT class AB PA, and its accuracy is compared to previous approaches in two difierent scenarios. First, in case of similar number of network parameters, it is observed that the proposed ANN-based model can reduce the normalized mean-square error (NMSE) by up to 1.3dB. Second, in a situation of comparable modeling accuracy (NMSE = i40dB), it is observed that the proposed ANN-based model can reduce the number of network parameters by up to 40% (from 62 to 38 real-valued parameters).

PM-AM/PM-PM distortions in wireless transmitter behavioral modeling

This paper addresses the impact of PM-AM and PM-PM distortions observed in wireless transmitters excited by wideband signals on the performance of their behavioral models. The origins of PM-AM and PM-PM distortions in these are first identified and then the necessary conditions for their accurate representation are theoretically discussed and experimentally assessed based on experimental data measured on a complete transmitter chain. Improvements of almost 10dB in NMSE and ACEPR results are achieved when a general behavioral model that takes into account the PM-AM and PM-PM distortions is used, instead of common behavioral models that neglect such distortions.

A new predistorter model based on power amplifier physical knowledge

This paper presents a new power amplifier (PA) linearizer model whose topology has support on the physical recursive behavior of the general PA electronic circuit. The resulting model presents a topology that, in its essence, is non recursive, which makes it suited for an easy implementation on digital hardware devices (such as FPGAs and DSPs). Validation tests were performed on a 900 MHz PA excited with WCDMA-3GPP signals and comparison with other linearizer models demonstrated its excellence. Due to its support on the PA physical behavior, the proposed predistorter model has the potential to be an adequate linearizer for a wide range of PA device technologies and excitation signals.

A Modified Real-Valued Feed-Forward Neural Network Low-Pass Equivalent Behavioral Model for RF Power Amplifiers

This work addresses the low-pass equivalent behavioral modeling of radio frequency (RF) power amplifiers (PAs) for modern wireless communication systems. Similar to a previous approach, here the PA behavioral modeling is based on two independent real-valued feed-forward artificial neural networks (ANNs). A careful analysis is first presented to show that the nonlinear training algorithm for the previous ANN-based approach can be easily trapped into local minima, especially for the ANN that estimates the polar angle component of a complex-valued signal. Then, a modified ANN-based model is proposed to eliminate the local minimum problem, in this way significantly improving the modeling accuracy. Indeed, in the proposed model the two real-valued ANNs are responsible for estimating the in-phase and quadrature components of a complex-valued base-band signal. When applied to the behavioral modeling of a GaN HEMT class AB PA, the proposed ANN-based model reduces normalized mean-square error (NMSE) by up to 2.2 dB, in comparison with the previous ANN-based model having an equal number of network parameters.