precoder aided massive MIMO system. This result brings new insights into the question of how to enhance the system sum rate performance. Then, a pair of low-complexity user selection schemes are proposed based on the attained approximation of the sum rate.

Sum Rate Approximation in the Large-System Regime
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We first evaluate the value of $\text{SINR}_k$ for the scenario where $M\text{ and }K$ go to infinity with a finite ratio $M/K>0$. Then, the approximation of the ergodic sum rate is derived.

Applying RMT-based large-system analysis, we reveal that $\text{SINR}_k$ may be characterized by (please see Appendix for the detailed derivation) $$\label{eq_sinr_1}
\text{SINR}_k\xrightarrow{a.s.}\frac{1}{\sum_{i=1}^Kd_i^{\alpha}\left(A(K,M)+B(K,M)d_k^{-\alpha}\right)},$$where $$\label{eq_ab_0}\begin{split}
A(K,M)&=\frac{1}{1-\rho}\frac{\sigma_n^2}{Pc\phi M},\\
B(K,M)&=\frac{\rho}{1-\rho}\frac{\psi}{M\phi^2-K\psi}.
\end{split}$$In , $\phi$ is the unique solution of the equation $$\phi=\frac{1}{M}\text{tr}\left(\mathbf{R}\left(\mathbf{I}_M+\frac{K}{M}\frac{1}{\phi}\mathbf{R}\right)^{-1}\right)$$and $\psi$ is defined as $$\psi=\frac{1}{M}\text{tr}\left(\mathbf{R}^2\left(\mathbf{I}_M+\frac{K}{M}\frac{1}{\phi}\mathbf{R}\right)^{-2}\right).$$

Exploiting and , the ergodic sum rate $\text{E}[\mathcal{R}]$ in large-system regime can be formulated as $$\label{eq_lb_0}\begin{split}
\text{E}[\mathcal{R}]&=\left(1-\frac{K}{T}\right)\text{E}_{d_1,\cdots,d_K}\left[\sum_{k=1}^K\log_2(1+\text{SINR}_k)\right]\\
&\geq\tilde{\mathcal{R}},
\end{split}\nonumber$$in which $\tilde{\mathcal{R}}$ is defined as $$\label{eq_rsim_0}\tilde{\mathcal{R}}=\left(1-\frac{K}{T}\right)\sum_{k=1}^K\text{E}_{d_k}\left[\log_2(1+\widetilde{\text{SINR}}_k)\right],$$and “$\geq$” is obtained by applying Jensen’s inequality$$\text{E}\left[\log_2\left(1+\frac{1}{x}\right)\right]\geq \log_2\left(1+\frac{1}{\text{E}[x]}\right).$$Additionally, $\widetilde{\text{SINR}}_k$ is given by $$\widetilde{\text{SINR}}_k=\frac{1}{T_1d_k^{\alpha}+T_2d_k^{-\alpha}+T_3},$$where $$\label{eq_t123_0}\begin{split}
T_1&=A(K,M),\\
T_2&=B(K,M)\sum_{i=1,i\neq k}^K\text{E}_{d_i}[d_i^{\alpha}],\\
T_3&=A(K,M)\sum_{i=1,i\neq k}^K\text{E}_{d_i}[d_i^{\alpha}]+B(K,M).
\end{split}$$

In this paper, we employ the lower bound $\tilde{\mathcal{R}}$ defined by as an approximation of the system sum rate. It should be emphasized that $\tilde{\mathcal{R}}$ is independent of the SSF CSI of UEs, 