# Power Amplifier Predistortion Using Reduced Sampling Rates in the Forward and Feedback Paths
## 3 Proposed Predistortion System  
### Proposed Predistortion System Description  
In this work, a hybrid digital/analog predistortion system is considered. The proposed system builds upon conventional digital predistortion systems (such as the one reported in \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature** & \begin{tabular}{c} **Digital Predistortion** \\ **System** \\ \end{tabular} & \begin{tabular}{c} **Analog Predistortion** \\ **System** \\ \end{tabular} & \begin{tabular}{c} **Proposed Hybrid** \\ **Predistortion System** \\ \end{tabular} \\ \hline \begin{tabular}{c} Sampling rate in the \\ forward path \\ \end{tabular} & High (✗) & Moderate (✓) & Moderate (✓) \\ \hline \begin{tabular}{c} Sampling rate in the \\ feedback path \\ \end{tabular} & High (✗) & High (✗) & Moderate (✓) \\ \hline \begin{tabular}{c} Feedback path \\ complexity \\ \end{tabular} & Moderate (✓) & High (✗) & Moderate (✓) \\ \hline \begin{tabular}{c} Predistortion \\ function accuracy \\ \end{tabular} & High (✓) & Limited (✗) & High (✓) \\ \hline \
\begin{tabular}{c} Predistortion \\ function update \\ \end{tabular} & Simple (✓) & Complex (✗) & Simple (✓) \\ \hline
\begin{tabular}{c} Linearization \\ capability \\ \end{tabular} & High (✓) & Limited (✗) & High (✓) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of key features of digital predistortion systems, analog predistortion systems, and the proposed hybrid predistortion system. Figure 3) by adding a second predistortion function in the analog domain, as illustrated in the block diagram of Figure 4. Comparing the block diagrams of Figure 3 and that of Figure 4, it appears that adding a predistortion function in the analog domain leads to several benefits that make the hybrid predistortion system superior to its fully digital and fully analog counterparts. These competitive advantages will be discussed in this section and corroborated with the experimental results derived in the next section. Typical power amplifiers nonlinearity results in spectral regrowth that spans over five times the bandwidth of the input signal. Predistortion techniques that are used to linearize such amplifiers will result in a similar (in terms of bandwidth) spectral regrowth. Therefore, in common predistortion systems (such as the one depicted in Figure 3), the signals \(x_{out\_DPD}\) and \(x_{out\_PA}\) are expected to have five times the bandwidth of the input signal \(x_{int}\). Hence, the forward path's DAC and the feedback path's ADC are expected to operate at a sufficiently high sampling rate to accommodate signals with a bandwidth equal to \(5\times BW\), where \(BW\) refers to the bandwidth of the input signal. Several solutions have been proposed to relax the sampling rate of the ADC used in the feedback path [18; 19; 20; 21; 22; 23; 24; 25]. This is possible since the in-band frequency range includes information about higher order distortions [8]. However, to the best of the author's knowledge, there was no reported attempt to simultaneously reduce the sampling rates of the forward path's DAC and the ADC used in the feedback path. In the proposed hybrid predistorter, this major limitation of digital predistortion systems is addressed by adding a second predistortion function in the analog domain. The analog predistortion function's main purpose is to perform a coarse linearization of the device under test with a focus on the strongly nonlinear memoryless distortions. The  
Figure 4: Proposed hybrid digital/analog predistortion system architecture detailing signal bandwidths. Figure 3: Generic digital predistortion system architecture detailing signal bandwidths. analog predistortion function is optimized for simplicity and will be made of a simple memoryless look-up table (LUT), hence avoiding the implementation complexity typically associated with analog predistorters.