## 2 Principle of the CMUDPD Technique
In other words, the gain vs. input power curves of PA\({}_{i}\) and PA\({}_{j}\) have a similar shape, and the gains of PA\({}_{i}\) and PA\({}_{j}\) (i.e., \(G_{i}\) and \(G_{j}\)) feature the following relationship:  
\[G_{j}=G_{i}\cdot 10^{\alpha/20}, \tag{4}\]  
where \(\alpha\) is a vertical constant as indicated in Figure 3b. In this situation, the actual output of PA\({}_{j}\) can be written as  
\[y_{j}(t)\approx G_{i}\cdot g_{i}\Big{(}x_{i}(t)\cdot 10^{-\beta/20}\Big{)} \cdot 10^{\alpha/20}, \tag{5}\]  
Figure 2: The system architecture of non-uniform amplitude excitation arrays with the proposed CMUDPD linearization technique. Figure 4: Schematic diagram of the simulation circuit. Figure 5: Advanced Design System (ADS) simulated AM/AM curves of the GaN PA: (**a**) \(V_{\text{DD}}\) = 28 V, (**b**) \(V_{\text{DD}}\) = 20 V, (**c**) \(V_{\text{DD}}\) = 12 V, and AM/PM curves; (**d**) \(V_{\text{DD}}\) = 28 V, (**e**) \(V_{\text{DD}}\) = 20 V, and (**f**) \(V_{\text{DD}}\) = 12 V.  
in both \(V_{\text{GG}}\) (\(-2.3\), \(-2.5\), and \(-2.7\) V) and \(V_{\text{DD}}\) (\(28\), \(20\), and \(12\) V) are applied. Then, in the next step, the CMUDPD simulations were conducted based on the two groups, as mentioned above. A 10 MHz LTE signal with a carrier frequency of 3.5 GHz was used as the input signal. The average input power \(P_{\text{in}}\) was set to the 1 dB compression point of the selected modes. The error vector magnitude (EVM) and adjacent channel power ratio (ACPR) were used to evaluate the in-band and out-band distortions, respectively. The definition of EVM is given by  
Figure 2.0  
where \(P_{\text{error}}\) represents the average power of the error vector and \(P_{\text{reference}}\) represents the average power of the reference signal [27]. The ACPR is defined as  
Figure 2.1  
where \(P_{\text{main}}\) is the main channel power, and \(P_{\text{adjacent}}\) is the average power of the lower adjacent channel and upper adjacent channel [41]. The simulated drain efficiency values are shown in Table 2, where the values were calculated as an average of 10,000 samples. It can be seen that the drain efficiencies of all studied operation modes improved after the CMUDPD. The detailed simulation procedures were as follows:  
* Step 1: Drive the PAs to one of the different operation modes while working at the 1 dB compression point. * Step 2: Select an operation mode \(i\) in the low-sidelobe active antenna array, as shown in Figure 2, to obtain the output signal for pre-distortion. * Step 3: According to the output signal obtained in step 2, model the PAs in the array in MATLAB. Collect the coefficient of CMUDPD using MPM, and the obtain pre-distorted input signal. * Step 4: Load the pre-distorted signal into the CMUDPD block of ADS. Then change the PA's operating mode according to Figure 2.2 After the CMUDPD, obtain the linearized outputs of PAs. * Step 5: Plot the normalized power spectral density (PSD) and calculate EVM and ACPR. In step 3, a traditional MPM was used to model the power amplifier, which can be expressed as follows:  
Figure 2.3 \begin{table}
\begin{tabular}{c c c c c c} \hline
**Mode \(i\)** & \(P_{\text{in}}\) & \(V_{\text{DD}}\) & \(V_{\text{GG}}\) & **Drain Eff. (\%)** & \(\varepsilon\) **(dB)** \\ \hline mode a1 & 13.6 dBm & 28 V & \(-2.9\) V & 14.54/20.23 & \(-54.84\) \\ mode a2 & 14.0 dBm & 20 V & \(-2.9\) V & 17.81/30.50 & \(-53.82\) \\ mode a3 & 15.3 dBm & 12 V & \(-2.9\) V & 34.15/38.13 & \(-52.40\) \\ mode b1 & 23.3 dBm & 28 V & \(-2.3\) V & 42.48/43.11 & \(-50.76\) \\ mode b2 & 21.0 dBm & 20 V & \(-2.5\) V & 27.45/29.64 & \(-47.63\) \\ mode b3 & 18.2 dBm & 12 V & \(-2.7\) V & 18.04/22.98 & \(-45.45\) \\ \hline \end{tabular}
\end{table} 
Table 2: Different modes setup of Group A (mode a1, mode a2, and mode a3) and Group B (mode b1, mode b2, and mode b3). Format of the drain efficiency (eff.) column: without CMUDPD and with CMUDPD. where \(M\), \(K\), and \(a_{mk}\) denote the memory depth, the order of memory polynomial, and the coefficient of memory polynomial, respectively.