Characterization and Identification Techniques
In the previous chapters, a thorough review of behavioral models proposed for the modeling and predistortion of wideband power amplifiers (PAs) and transmitters was presented. All these models can be seen as mathematical functions for which a set of coefficients needs to be identified. These coefficients are derived, using identification techniques, from measurements data acquired through the characterization of the device under test (DUT). Thus, the validity of a behavioral model and its accuracy will greatly depend, among others, on the characterization step. In fact, since the behavioral model coefficients are calculated solely from input and output measured data, the obtained model is able to take into consideration only the effects that are observed during the characterization step. For example, if measurements are performed with a test signal for which a DUT has a memoryless behavior, then a model derived from these measurements will be unable to predict the memory effects that will be present in the DUT if a wider bandwidth signal is used. This is true even if the model structure incorporates memory effects (such as the memory polynomial model). The accuracy of the model also depends on the model structure that is adopted and its ability to mimic all aspects of the observed behavior. As matter of fact, if the DUT exhibits memory effects during the measurements, the appropriate model structure should be used to ensure that the model reproduces these memory effects. For instance, a memoryless model cannot predict the memory effects of the DUT even if it is identified using measurements that include memory effects.
Accordingly, choosing the adequate model structure is certainly required but definitely not enough to guarantee accurate behavioral modeling and high performance digital predistortion (DPD). To better recognize the factors affecting the performance of a behavior model, the flow chart of behavioral modeling and DPD processes
Behavioral Modeling and Predistortion of Wideband Wireless Transmitters, First Edition. Fadhel M. Ghannouchi, Oualid Hammi and Mohamed Helaoui.
© 2015 John Wiley & Sons, Ltd. Published 2015 by John Wiley & Sons, Ltd.
Figure 8.1 Flow chart of behavioral modeling and digital predistortion processes
is illustrated in Figure 8.1. First, the type of the drive signal to be used in the characterization of the DUT is selected. This encompasses continuous wave (CW), two-tones, multi-tones, as well as standard compliant and synthetic test signals. Then, the measurement data are acquired at the input and the output of the DUT. The raw measurements need to be processed to de-embed the signals from the measurement reference planes to the DUT reference planes. Next, the behavioral model and/or digital predistorter structure is selected, its parameters (i.e., nonlinearity order, memory depth,...) defined, and its coefficients identified. Finally, the performance of the behavioral model and/or digital predistorter is assessed. The performance of a behavioral model is evaluated by comparing the predicted and the measured output signals of the DUT and quantifying the similarity between these two signals using the metrics defined in Chapter 3. The performance of a digital predistorter is quantified in frequency domain by the adjacent channel leakage ratio measured at the output of the linearized DUT, and in modulation domain by evaluating the error vector magnitude at the output of the linearized DUT. Based on the performance of the model/DPD, the model parameters can be adjusted, or if needed, a different model structure can be selected.
This chapter focuses on the types of test signals that can be used to characterize the behavior of power amplifiers and wireless transmitters, and the impact of these test signals on the observed behavior of the DUT. Emphasis is then given to the use of standard compliant test signals and the steps required for processing the measured data under such conditions, as well as the identification techniques that can be applied to calculate the model coefficients.