# Reduced Complexity Sequential Digital Predistortion Technique for 5G Applications
## 2 Sequential Digital Predistortion Using Under-Sampled Feedback Signals
### Proposed Sequential Digital Predistortion
Furthermore, the step related to the data de-embedding needed in the conventional identification approach is avoided in the proposed system and is replaced by the second characterization. Hence, the sequential characterization approach  
Figure 3: Simplified reverse TNTB predistorter block diagram. Figure 2: Flow chart of conventional two-box DPD identification process. eliminates the data de-embedding step, and allows for the use of reduced sampling rates in the feedback path without causing a loss of performance for the proposed DPD as it will be demonstrated through the experimental validation section. The flow chart summarizing the identification process of the proposed sequential DPD system is presented in Figure 4.  
From an implementation point of view, the proposed sequential DPD does not involve any additional circuitry in the analog domain. The detailed block diagram presented in Figure 5 shows that a single feedback loop is used for both characterization steps. This feedback path provides access to the power amplifier's output signal. The output of the power amplifier is down-converted and then digitized using an analog to digital converter (ADC) operating at lower sampling rate. The signal at the output of the ADC is fed to a digital signal-processing block which mainly implements the up-sampling of the acquired PA output signal in order to have consistent sampling rates between the input and output waveforms being fed to the delay alignment blocks. The identification of the LUT-based DPD sub-function includes a fine delay alignment (FDA) block. Conversely, a coarse delay alignment (CDA) block is used for the identification of the memory polynomial DPD sub-function. From a hardware perspective, the proposed DPD is identical to conventional DPDs in the sense that only a single feedback path is required. However, this feedback  
Figure 4: Flow chart of proposed two-box S-DPD identification process. (Solid boxes refer to steps that are also in the conventional approach. Dashed boxes refer to steps specific to the proposed S-DPD). path operates at reduced sampling rate in the proposed DPD. In the digital domain, the proposed DPD includes two loops. The first loop (shown in red color in Figure 5) is used to identify the LUT DPD function. It includes a fine-delay alignment block (FDA) followed by a model identification block (MIB) which calculates the model coefficients or in this case the LUT entries. In the second loop (shown in blue color in Figure 5), a coarse delay alignment (CDA) is first performed, then the coefficients of the MP function are identified using the MIB block. Depending on which predistortion sub-function is being identified, the output of the digital signal processing block is channeled to position 1 or 2. The output of the LUT DPD is fed into a digital to analog converter (DAC) which generates the analog signal to be up-converted by the frequency up-conversion stage before being applied at the input of the power amplifier. In the scheme depicted in Figure 5, the DPD update is performed using the signal to be transmitted and does not require any synthetic test signal. Hence, it can be performed online while the PA is operating and does not require any down time. Compared to conventional identification techniques of two-box models, the proposed sequential DPD eliminates the need for data de-embedding needed to calculate the memory polynomial function, but requires an additional delay alignment step. However, the complexity of this step is reduced by using a coarse delay alignment algorithm. In fact, it was shown in [25] that the identification of static nonlinear distortions requires sub-sample delay resolution for satisfactory modelling accuracy, while the identification of the memory polynomial function is robust to delay misalignment. Therefore, in the proposed DPD, when the static nonlinear function is being identified, a sub-sample accurate delay estimation and alignment algorithm is used.