# Power Amplifier Predistortion Using Reduced Sampling Rates in the Forward and Feedback Paths
## 3 Proposed Predistortion System
### Proposed Predistortion System Description
The analog predistortion function is computed by the predistortion functions identification block which is responsible of synthesizing the look-up table of the analog predistorter (APD) and the memory polynomial function of the DPD. The parameters computed by the predistortion function's identification block are fed to the two predistortion functions. Moreover, since the analog predistorter will perform a coarse compensation of the highly nonlinear memoryless distortions of the PA, the cascade made of the APD, and the PA will behave as a nonlinear system with mild nonlinearity. However, the memory effects exhibited by the PA will also be observed since they are not compensated for using the APD. Hence, the digital predistortion function will be almost linear as it will be mainly compensating for the mildly nonlinear residual distortions that remain following the application of the analog predistortion function. The analog predistortion function preferred implementations include several options such as the use of an RF vector multiplier, a variable gain amplifier, or a variable attenuator. The update of the analog predistortion function refers to the update of the look-up table function and not the hardware of the analog predistorter itself. In fact, the update is applied to the mapping function that translates the output of the digital predistorter into the control signals that need to be applied to the analog predistortion function to result in the desired APD gain. This mapping is a function of the transfer characteristics of the analog predistorter used. Moreover, in all cases, the analog predistortion function is subject to imperfections associated with analog domain implementations. These can include delay misalignment between the control signal and the RF signal, as well as limited resolution and accuracy in the implementation of the gain values. These issues are commonly observed in analog predistorters. The use of a second predistortion function, which will be applied to linearize the cascade made of analog predistorter and the device under test, is expected to partially compensate for such imperfections. It is important to note here that these imperfections are observed in analog predistorters in general and are not specific to the proposed predistorter. The digital predistortion function is derived from the signals \(x_{out\_DPD}\) and \(x_{out\_PA}\), yet, it is performed when the APD function is being applied. Hence, the \(x_{out\_DPD}\) and \(x_{out\_PA}\) will be the input and output waveforms of a mildly nonlinear system. Since the nonlinearity order of the system being linearized by the DPD function is less than that of the PA alone, the spectral regrowth caused by the DPD function in the case of the proposed hybrid predistortion system will be less than that observed in the case of the conventional digital predistortion system. Consequently, it is anticipated that the bandwidth of the signal at the output of the DPD will be \(K\times BW\) with \(K<5\). This will result in a sampling rate reduction for the DAC used in the signal's forward path. Accordingly, the architecture of the proposed hybrid predistorter is suitable for reducing the sampling rate in the forward and feedback paths through the use of the analog predistortion function in conjunction with the digital predistortion function. Moreover, the procedure used to identify the two predistortion functions lessens the accuracy requirements on the APD function, and hence reduces its implementation complexity. Here, it is important to note that the reduction in the sampling rate of the forward path's DAC and that of the feedback path's ADC can be independent.