## 4 \(N_{g}\) Determination and Related System Structure  
In this Section, we propose how to determine \(N_{g}\) in an antenna group-based RS overhead reduced massive MIMO. Based on analysis in Section 3, ZF and MF precoded SE, \(SE_{ZF}\) and \(SE_{MF}\) can be approximated as follows: \begin{table}
\begin{tabular}{c c c c} \hline \(\boldsymbol{\gamma_{k,MF}^{ref}}\) & \(\boldsymbol{\gamma_{k,ZF}^{ref}}\) & \(\hat{\gamma}_{k,MF}\) & \(\hat{\gamma}_{k,ZF}\) \\ \hline \(\frac{N_{t}}{K}\left(\frac{\rho_{r}}{\rho_{r}+1}\right)\) & \(\frac{N_{t}-K}{K}\left(\rho_{r}\right)\) & \(\frac{N_{t}}{K}\left(\frac{\xi^{2}\rho_{r}}{\rho_{r}+1}\right)\) & \(\frac{N_{t}-K}{K}\left(\frac{\xi^{2}\rho_{r}}{(1-\xi^{2})\rho_{r}+1}\right)\) \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of approximated SINRs. \[SE_{ZF}\approx\left\{ \begin{array}{ll}\left(1-\frac{\frac{\eta_{CRS}+(N_{t}+K \cdot\Phi)}{\eta_{R_{bat}}N_{S}}}\right)\cdot K\cdot\left[\log_{2}\left(1+\frac{ (N_{t}-K)\xi\left(1-\frac{N_{g}}{\epsilon}\right)\rho_{r}}{k\left(\left(1-\xi \left(1-\frac{N_{g}}{\epsilon}\right)\right)\rho_{r}+1\right)}\right)\right],& \left(1-\frac{\eta_{CRS}+(N_{t}+K\cdot\Phi)}{\eta_{R_{bat}}N_{S}}\right)>0.5\\ 0.5\cdot K^{\prime}\cdot\left[\log_{2}\left(1+\frac{N_{t}^{\prime}-K^{\prime} \right)\xi\left(1-\frac{N_{g}^{\prime}}{\epsilon}\right)\rho_{r}}{k\left( \left(1-\xi\left(1-\frac{N_{g}}{\epsilon}\right)\right)\rho_{r}+1\right)} \right)\right],&\left(1-\frac{\eta_{CRS}+(N_{t}+K\cdot\Phi)}{\eta_{R_{bat}}N_{S} }\right)\leq 0.5\end{array} \right. \tag{28}\]  
\[SE_{MF}\approx\left\{ \begin{array}{ll}\left(1-\frac{\eta_{CRS}+(N_{t}+K\cdot \Phi)}{\eta_{R_{bat}}N_{S}}\right)\cdot K\cdot\left[\log_{2}\left(1+\frac{N_{t }\xi\left(1-\frac{N_{g}}{\epsilon}\right)\rho_{r}}{k\left(\rho_{r}+1\right)} \right)\right],&\left(1-\frac{\eta_{CRS}+(N_{t}+K\cdot\Phi)}{\eta_{R_{bat}}N_{ S}}\right)>0.5\\ 0.5\cdot K^{\prime}\cdot\left[\log_{2}\left(1+\frac{N_{t}^{\prime}\xi\left(1- \frac{N_{g}^{\prime}}{\epsilon}\right)\rho_{r}}{k\left(\rho_{r}+1\right)} \right)\right],&\left(1-\frac{\eta_{CRS}+(N_{t}+K\cdot\Phi)}{\eta_{R_{bat}}N_{ S}}\right)\leq 0.5\end{array} \right. \tag{29}\]  
where \(K^{\prime}\), \(N_{t}^{\prime}\), and \(N_{g}^{\prime}\) are corresponding \(K\), \(N_{t}\), and \(N_{g}\) when \(\left(1-\frac{\eta_{CRS}+(N_{t}+K\cdot\Phi)}{\eta_{R_{bat}}N_{g}}\right)=0.5\). A few observations are in order. Observation 1:As \(N_{g}\) increases, bandwidth increases due to RS overhead reduction. Observation 2:As \(N_{g}\) increases, SINR decreases due to channel estimation error. Increasing \(N_{g}\) is beneficial to the system when system is working in bandwidth limited regime, but if system is working in power limited regime and/or interference limited regime, increasing \(N_{g}\) worsens system performance. Two strategies can be considered to choose \(N_{g}\). First, \(N_{g}\) can be determined to maximize SE which can be represented as follows for ZF precoding and MF precoding respectively. \[\max_{N_{g}}\left(\Theta\cdot\sum_{k=1}^{K}E\left[\log_{2}\left(1+ \frac{(N_{t}-K)\xi\left(1-\frac{N_{g}}{\epsilon}\right)\rho_{r}}{K\left(\left( 1-\xi\left(1-\frac{N_{g}}{\epsilon}\right)\right)\rho_{r}+1\right)}\right) \right]\right) \tag{30}\] \[s.t. \Theta\geq 0.5\] \[\rho_{r}\leq\rho_{r,\max},\]  
\[\max_{N_{g}}\left(\Theta\cdot\sum_{k=1}^{K}E\left[\log_{2}\left(1+ \frac{N_{t}\xi\left(1-\frac{N_{g}}{\epsilon}\right)\rho_{r}}{K(\rho_{r}+1)} \right)\right]\right) \tag{31}\] \[s.t. \Theta\geq 0.5\] \[\rho_{r}\leq\rho_{r,\max},\]  
where \(\Theta=\left(1-\frac{\eta_{CRS}+(N_{t}+K\cdot\Phi)}{\eta_{R_{bat}}N_{S}}\right)\) and \(\rho_{r,\max}\) is the maximum SNR which reflect the maximum allowable TX power. This is a typical setting for wireless communication systems up to now. However, to support distributed sensors and/or sensor networks, energy efficiency can be more important than SE depending on applications. In a certain application, sensor devices do not require high data rate, but maintaining moderate data rate can be enough.