# Power Amplifier Predistortion Using Reduced Sampling Rates in the Forward and Feedback Paths
## 2 On the Challenges of Predistortion Systems Design  
Predistortion relies on applying a complementary nonlinear function prior to the nonlinear amplifier, such that the cascade of both nonlinear functions is equivalent to a linear one. The amplifier's complementary nonlinear function is commonly implemented either in digital domain (as it is the case in digital predistortion techniques), or in the analog domain (as it is the case in analog predistortion techniques). The linearization performance of predistortion systems heavily relies on two key aspects, which are the accurate characterization of the amplifier's nonlinear behavior and the precise synthesis of the desired predistortion function that will perfectly complement the nonlinear behavior of the power amplifier. Despite being considered a mature technology, predistortion systems require continuous efforts to enhance their performance and cope with the evolution of wireless communication standards. In [4], a thorough study of predistortion systems and their challenges is presented with an emphasis on emerging 5G and beyond applications especially at millimeter waves. A simplified functional block diagram of a digital predistortion system is reported in Figure 1. Conversely, Figure 2 depicts a simplified block diagram of an analog predistortion system. In the digital predistortion system of Figure 1, since the signal is predistorted in the digital domain, the DAC is being fed with the signal \(x_{out\_DPD}\). This predistorted signal typically has a bandwidth that is five times that of the input signal \((x_{in})\) due to the nonlinear distortions generated by the predistortion function. Therefore, the DAC needs to be able to handle such a bandwidth. Similarly, the signal at the output of the amplifier \((x_{out\_PA})\) is also expected to have a bandwidth that is five times that of the input signal to capture the full extent of the spectral regrowth caused by nonlinear distortions. Hence, the ADC in the feedback path needs to be able to handle such a bandwidth. These constraints on the bandwidth of the signals being fed to the digital-to-analog and the analog-to-digital converters in the forward and the feedback paths, respectively, represent a bottleneck for digital predistortion systems, especially in the case of wideband signals. In digital predistortion systems, the signals used for the predistortion function identification are the predistorted signal \(x_{out\_DPD}\) (already in the digital domain) and the amplifier's output signal \(x_{out\_PA}\) which is in the analog RF domain. Hence, only one feedback path is needed in order to down-convert and digitize the amplifier's output signal. An inherent advantage of this approach relies on the fact that the signals used for the predistortion function identification include the power amplifier nonlinearities as well as any possible impairments caused by the frequency up-conversion stage. A closer look at the block diagram of Figure 2 shows that in analog predistortion systems, the signal at the input of the DAC in the forward path is the original signal and not the predistorted one. This alleviates the requirements on the DAC sampling rate in the forward path. Conversely, the signal at the output of the amplifier still requires a sampling rate commensurate to five times the bandwidth of the input signal. Therefore, the ADC sampling rate requirements in the feedback path of analog predistortion systems is identical to that of digital predistortion systems. Moreover, since the predistortion function is applied just before the power amplifier, the signals used for the identification of the predistortion function, that is, the predistorted signal \((x_{out\_APD})\) and the amplifier's output signal \((x_{out\_PA})\), are both in the analog RF domain. Hence, two frequency down-conversion and digitization paths are needed for the feedback path.