# Reduced Complexity Sequential Digital Predistortion Technique for 5G Applications
## 3 Performance Assessment of the Proposed Digital Predistortion System
This is anticipated since a more accurate reconstruction of the output signal waveform sampled at 100 MSa/s will  
Figure 8: Measured instantaneous gain characteristics of the device under test: (a) AM/AM characteristic; (b) AM/PM characteristic. Figure 9: Spectra at the output of the amplifier following partial linearization using LUT–DPD. translate into a more accurate model of the DUT, and hence a more optimal memoryless LUT. However, even though the performances of the DPDs derived from low-sampling-rate data acquisitions are not as good as the one derived from 100 MSa/s measurement, they lead to noticeable spectrum regrowth cancellation ranging from 10 dB to 20 dB for the 25 MSa/s and the 50 MSa/s data acquisitions, respectively. More importantly, this spectrum regrowth cancellation reduces the bandwidth of the signal at the output of the device under test, which will reduce the impact of the limited observation bandwidth on the performance of the DPD. Accordingly, the use of the low-sampling-rate data acquisitions for the synthesis of the second predistortion sub-function (the memory polynomial block) is anticipated to further enhance the capabilities of the predistorter. The last step in the validation of the proposed S-DPD system is to assess the performance of the complete two-box DPD for each value of the sampling rates used in the signal observation path. First, the benchmark data corresponding to a data acquisition at sampling rate of 100 MSa/s was used to determine the required dimensions for the memory polynomial block of the two-box DPD. The memory polynomial predistortion function is given by  
\[x_{out\_MP}(n)=\sum_{k=1}^{K}\sum_{m=0}^{M}a_{km}x_{in\_MP}(n-m)|x_{in\_MP}(n-m )|^{k-1}, \tag{3}\]  
where \(x_{in\_MP}\) and \(x_{out\_MP}\) are the input and the output of the MP function, respectively. \(a_{km}\) are the complex-valued model coefficients. \(K\) and \(M\) represent the memory polynomial's nonlinearity order and memory depth, respectively. For the considered DUT, it was found that the MP sub-function needed to have a nonlinearity order \(K=7\) and a memory depth \(M=5\). This setting (nonlinearity order and memory depth) of the MP sub-function was kept the same for all MP sub-functions derived from the under-sampled output waveforms. For each acquisition, a new set of coefficients was calculated. For the 25 MSa/s data acquisition, the signal at the output of the amplifier linearized using the memoryless LUT derived from the same sampling rate was used along with the LUT's input signal to build the memory polynomial sub-function of the predistorter. This sub-function, also derived from data acquired at 25 MSa/s, aims at linearizing the cascade made of the LUT predistorter and the power amplifier. The same test was repeated for the 30 MSa/s, 40 MSa/s and 50 MSa/s acquisitions as well as the 100 MSa/s benchmark. The spectra obtained at the output of the power amplifier following the use of the cascade made of the memory polynomial and the LUT DPDs are reported in Figure 10 for all considered sampling rates. This figure clearly shows that the use of the proposed sequential DPD technique can result in excellent linearization without performance deteriorations as the sampling rate is reduced by a factor of four from 100 MSa/s to 25 MSa/s. This is mainly due to the fact that despite the imperfections of the LUT DPD, it still reduces the bandwidth of the partly linearized output signal, and the fact that the MP DPD is derived to linearize the cascade made of the LUT and DUT in a second iteration.