Magnus Isaksson

A comparative analysis of behavioral models for RF power amplifiers

A comparative study of nonlinear behavioral models with memory for radio-frequency power amplifier (PAs) is presented. The models are static polynomial, parallel Hammerstein (PH), Volterra, and radial basis-function neural network (RBFNN). Two PAs were investigated: one was designed for the third-generation (3G) mobile telecommunication systems and one was designed for the second-generation (2G). The RBFNN reduced the total model error slightly more than the PH, but the error out of band was significantly lower for the PH. The Volterra was found to give a lower model error than did a PH of the same nonlinear order and memory depth. The PH could give a lower model error than the best Volterra, since the former could be identified with a higher nonlinear order and memory depth. The qualitative conclusions are the same for the 2G and 3G PAs, but the model errors are smaller for the latter. For the 3G PA, a static polynomial gave a low model error as low as the best PH and lower than the RBFNN for the hardest cross validation. The models with memory, PH, and RBFNN, showed better cross-validation performance, in terms of lower model errors, than a static polynomial for the hardest cross validation of the 2G PA

A Comparative Analysis of the Complexity/Accuracy Tradeoff in Power Amplifier Behavioral Models

A comparative study of state-of-the-art behavioral models for microwave power amplifiers (PAs) is presented in this paper. After establishing a proper definition for accuracy and complexity for PA behavioral models, a short description on various behavioral models is presented. The main focus of this paper is on the modeling accuracy as a function of computational complexity. Data is collected from measurements on two PAs-a general-purpose amplifier and a Doherty PA designed for WiMAX-for different output power levels. The models are characterized in terms of accuracy and complexity for both in-band and out-of-band error. The results show that, among the models studied, the generalized memory polynomial behavioral model has the best tradeoff for accuracy versus complexity for both PAs, and can obtain high performance at half of the computational cost of all other models analyzed.

Wide-band dynamic modeling of power amplifiers using radial-basis function neural networks

A radial-basis function neural network (RBFNN) has been used for modeling the dynamic nonlinear behavior of an RF power amplifier for third generation. In the model, the signals envelope is used. The model requires less training than a model using IQ data. Sampled input and output signals were used for identification and validation. Noise-like signals with bandwidths of 4 and 20 MHz were used. The RBFNN is compared to a parallel Hammerstein (PH) model. The two model types have similar performance when no memory is used. For the 4-MHz signal, the RBFNN has better in-band performance, whereas the PH is better out-of-band, when memory is used. For the 20-MHz signal, the models have similar performance in- and out-of-band. Used as a digital-predistortion algorithm, the best RBFNN with memory suppressed the lower (upper) adjacent channel power 7 dB (4 dB) compared to a memoryless nonlinear predistorter and 11 dB (13 dB) compared to the case of no predistortion for the same output power for a 4-MHz-wide signal.

Comparison of evaluation criteria for power amplifier behavioral modeling

In this paper different evaluation criteria for power amplifier behavioral modeling are studied and evaluated using measuremed data. The figure-of-merits are calculated from complex-envelope data of a sampled power amplifier intended for 3G. Both time- and frequency domain methods are included in the study. It is found that a model evaluation criterion should have ability to capture both the linear and nonlinear distortion as well as the memory effects in the power amplifier. The normalized mean square error (NMSE) and the weighted error-to-signal power ratio (WE-SPR) are found to be the strongest candidates for capturing the in-band and the out-of-band errors, respectively. Both are also independent of power amplifier technology and stimuli input.

A Kautz-Volterra Behavioral Model for RF Power Amplifiers

A new type of behavioral power amplifier (PA) model, a discrete-time Kautz-Volterra (KV) model, is presented. In the model a priori knowledge of the system properties in terms of different poles for different nonlinear orders is used, which is needed for modeling nonlinear and linear memory effects in PAs. An accurate model can thus be achieved with a small number of parameters. Simulated results of parallel Hammerstein and Wiener structures and from modeling the behavior of a PA are presented

Nonlinear behavioral modeling of power amplifiers using radial-basis function neural networks

A radial-basis function neural network (RBFNN) is proposed for modeling the dynamic nonlinear behavior of RF power amplifiers. In the model the signals envelope is used. The model requires less training than a model using both IQ-data. Sampled input and output signals from a power amplifier for 3G were used in the identification and validation. The RBFNN is compared with a parallel Hammerstein model. For a memory depth of one sample the RBFNN gives a better model, in- and out-of-band; for three samples the RBFNN reduces the in-band error more while the Hammerstein model reduces the error out-of-band more.

Extension of the hammerstein model for power amplifier applications

Due to the use of modem digital modulation methods power amplifiers are nowadays subjected to signals having a considerable bandwidth and a fast changing envelope. This means that traditional quasi-memoryless AMAM and AMPM characteristics are no longer enough to describe and model the behavior of power amplifiers [I]-[2], neither can they be successfully used for linearization. Instead, different models with memory have been introduced to accurately model power amplifiers over the bandwidth of interest [3]-[SI. In most cases the identification of the system parameters is done using multiple swept CW or two-tone measurements. An altemative approach is to extract the model parameters from sampled input output data as in [6]-[8]. The latter is the approach taken here.

Three-Tone Characterization of Nonlinear Memory Effects in Radio-Frequency Power Amplifiers

A stepped three-tone measurement technique based on digitally modulated baseband signals is used in characterizing radio-frequency power amplifiers (PAs). The bandwidths of the stepped measurement were 8.8 MHz for the input signal and 26.4 MHz for the output signal. A PA designed for third-generation mobile telecommunication system was analyzed. The amplitude and phase of the third-order Volterra kernel were determined from the identified intermodulation products. The properties of the Volterra kernel along certain paths in the 3-D frequency space were analyzed and compared to some box models for nonlinear systems. The main symmetry of the third-order Volterra kernel of this PA was found to be of the type given by the cascaded quadratic nonlinearities with a linear filter in between (a Hammerstein-Wiener system), and frequency dependence, i.e., memory effects, was found to be due to the effects at the baseband.

A general evaluation criteria for behavioral power amplifier modeling

In this paper a new goodness measure for behavioral complex envelope power amplifier models is defined in the frequency domain. The measure can be calculated for any input signal using the same formulas, which makes it general and easy to use. The results will however be dependent on the input signal. The total model error, or normalized mean-square error, for power amplifier models are normally dominated by the in-band error, often mainly caused by the linear distortion. The new measure is aimed at capturing the nonlinear modeling performance of the amplifier model. This is of interest since it is most often the nonlinear, rather than the linear, distortion that causes most harm in real-life power amplifier applications.

Noise impact on the identification of digital predistorter parameters in the indirect learning architecture

The indirect learning architecture (ILA) is the most used methodology for the identification of Digital Predistorter (DPD) functions for nonlinear systems, particularly for high power amplifiers. The ILA principle works in black box modeling relying on the inversion of input and output signals of the nonlinear system, such that the inverse is estimated. This paper presents the impact of disturbances, such as noise in the DPD identification. Experiments were performed with a state-of-art Doherty power amplifier intended for base station operation in current telecommunication wireless networks. As expected, a degradation in the performance of the DPD (measured in normalized mean square error (NMSE)) is found in our experiments. However, adjacent channel power ratio (ACPR) can be a misleading figure of merit showing improvement in the performance for wrongly estimated DPD functions.