Digital Predistortion Boot Camp
Juan A. Becerra and María J. Madero-Ayora
Departamento de Teoría de la Señal y Comunicaciones
Universidad de Sevilla, Spain
In this short course, the fundamentals underlying the digital predistortion (DPD) concept are explained. It will be shown how the nonlinearities present in communication systems produce both in-band and out-of-band distortion that degrades their performance. This effect will be reviewed in time, frequency and constellation domains of modulated signals along with commonly employed linearity indicators such as the normalized mean square error, adjacent channel power ratio and error vector magnitude. An important number of modern wireless communication standards employ spectrally efficient modulation schemes such as the orthogonal frequency division multiplexing (OFDM). The generation and demodulation of OFDM signals will be discussed and the challenges posed by their high peak-to-average power ratio will be illustrated. The representation of nonlinear systems with memory by means of the Volterra series will be introduced, involving scenarios for the modeling of a power amplifier and also for its linearization through DPD. In order to train the DPD, two possible architectures will be compared: the indirect learning architecture and the direct learning architecture. The construction of widely-used models as the memory polynomial and generalized memory polynomial will be examined together with the regression of models to identify their coefficients. Based on them, we can exemplify how rapid the number of coefficients grows as the nonlinear order and memory depth are increased, a problem referred to as the curse of dimensionality. This leads to the idea of pruning the model structures in order to reduce their complexity, for which a priori or a posteriori approaches can be followed. Through the a posteriori pruning approach, several coefficient selection techniques that exploit the sparsity in the regression process will be analyzed to provide a reduced-order model with equivalent accuracy. Throughout this short course, the explanations will be covered theoretically and with sample code to provide practical hands-on experience.
The following topics will be covered:
- Basics of nonlinearities: effects in time, frequency and constellation domains.
- Orthogonal frequency division multiplexing (OFDM) signals generation.
- Volterra series in power amplifier (PA) modeling.
- Volterra series and digital predistortion (DPD). Indirect learning (ILA) and direct learning (DLA) architectures.
- Basic models: the memory polynomial (MP) and the generalized memory polynomial (GMP).
- Fundamentals of Volterra models: the curse of dimensionality, regression, and a priori versus a posteriori pruning.
- Coefficient selection techniques.