# Power Amplifier Predistortion Using Reduced Sampling Rates in the Forward and Feedback Paths
## 1 Introduction
Other techniques such as those presented in [20; 21; 22; 23] approach the sampling rates challenges in digital predistortion systems differently by directly under-sampling the feedback signal and allowing some aliasing to occur. The under-sampled feedback signal is then manipulated to cancel out the aliasing effect, and an appropriate DPD model is utilized. Nevertheless, such methods still suffer from similar shortcomings as previously discussed. Furthermore, another approach presented is spectrum stitching [24; 25] by which the full bandwidth of the feedback signal is stitched together from several narrow band feedback signals. However, this increases the time required to train a DPD model, as the original feedback signal needs to first be reconstructed. Hence, all of the methodologies presented above focus on relaxing the feedback path's sampling rate whilst maintaining a higher sampling in the forward path. On the other hand, to address the sampling requirements of the forward path, RF predistortion [26; 27] and hybrid predistortion [28; 29] have been suggested. RF predistortion entails applying the predistortion function in the analog domain at radio frequencies. However, implementing RF predistortion requires more hardware components, and due to its analog nature, its flexibility is quite limited when compared to hybrid and digital predistortion counterparts. On the other hand, hybrid predistortion entails utilizing both digital and analog signal processing to implement a predistortion algorithm. An example of that is to have a hybrid two-box model where each box is in a separate domain. This effectively reduces the forward path's DAC sampling rate requirement, as some of the linearization is implemented in the analog domain. Furthermore, some of the flexibility of DPD is still maintained, as a significant part of the linearization is performed in the digital domain. One example of this is the work presented by [PERSON] et al. in [29]. The predistortion function was divided into two boxes, namely, a memory-based nonlinear box and a memoryless nonlinear box. The main contribution was related to the fact that the memoryless nonlinear function can be implemented in the analog domain to effectively alleviate the linearization effort required in the digital domain. Hence, this allows for utilizing relaxed sampling rates in the forward path as coarse linearization can be obtained by using the analog domain predistor. This work aims to extend the work proposed in [29] by simultaneously relaxing the sampling rate in both the feedback and the forward paths, and to realize a complete sampling rate reduction. In this paper, the challenges related to the use of predistortion systems in wideband applications are discussed. It is shown that analog predistortion implementation suffers from poor linearization performance and complex implementation while having the advantage of reducing the sampling rate requirements in the digital-to-analog converter used in the signal's forward path of digital predistortion systems. Conversely, digital predistortion allows for flexible implementation of the predistortion function and hence is able to reach better linearization performance than the analog predistortion technique. However, this comes at the cost of higher sampling rate requirements on the digital-to-analog converter in the forward path. To achieve a better tradeoff between performance and complexity, a hybrid digital predistortion system is proposed along with reduced sampling rates in the forward and feedback paths. It is shown that the system level architecture, in which the predistortion function is carefully split between the analog and digital domains, allows for relaxed sampling rates in both the forward and feedback paths without compromising the linearization capability of the predistorter.