# Power Amplifier Predistortion Using Reduced Sampling Rates in the Forward and Feedback Paths
## 2 On the Challenges of Predistortion Systems Design
Moreover, using the signals \(x_{out\_APD}\) and \(x_{out\_PA}\) for the identification of the predistortion function does not capture any impairments that occur within the forward path's frequency up-conversion stage. This limitation is compounded with the need for two frequency down-conversion stages and two analog-to-digital converters, which constitutes a major complexity overhead in analog predistortion systems when compared to digital predistortion systems. Accordingly,  
Figure 1: Simplified functional block-diagram of a digital predistortion system. Figure 2: Simplified functional block-diagram of an analog predistortion system. with respect to the accurate characterization of the power amplifier behavior, the analog predistortion architecture presents a single advantage related to the relaxed sampling rate requirements in the DAC of the forward path. However, this comes at the cost of an additional down-conversion and digitization block in the feedback path. A key difference between digital predistortion and analog predistortion systems is related to the implementation of the predistortion function. For digital domain implementation, a plethora of models exist and can be used to accurately synthesize a predistortion function that will lead to a quasi-perfect match between the nonlinear characteristics of the DPD and that of the power amplifier, hence, ensuring optimal linearization performance and spectrum regrowth cancellation. However, the use of analog implementation of the predistortion function significantly limits the options available. In fact, analog predistortion mainly uses analog nonlinear devices/circuits that operate as distortion generators or a very limited set of analytically defined functions such as look-up tables, and the envelope memory polynomial. This results in reduced linearization performance when compared to digital predistortion systems, especially in the case of highly nonlinear power amplifiers exhibiting memory effects. Accordingly, digital predistortion offers a significant advantage in terms of performance. In addition to its ability to synthesize accurate predistortion profiles, digital predistortion functions are easy to implement through an update of their coefficients and parameters. On the other hand, the update of the analog predistortion functions is very tedious and does not offer the same degree of flexibility observed in digital predistortion systems. From the discussion above, it appears that digital predistortion as well as analog predistortion systems each suffer from several key limitations, as summarized in Table 1. These limitations are at the origin of the motivation behind this work in which a hybrid predistortion function that allies the advantages of digital and analog systems is proposed. As summarized in Table 1, the proposed hybrid predistorter which employs a digital predistortion function and an analog predistortion function aims at taking advantage of the reduced sampling rate in the forward path, which is characteristic of analog predistortion systems, while avoiding the limitations associated with the analog implementation by augmenting it with a digital predistortion function. The digital predistortion function enables the use of high accuracy adaptive predistortion functions.