As a result, the computational complexity is approximately $\mathcal{O}(1)$, which is just the same as that of the conventional RUS scheme.

Performance Analysis for the Special Case of $\rho=0,\delta=0$\[sub:Performance-Analysis\]
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All the above investigations are subject to the general case, i.e., in the context of the systems with imperfect CSI and transmit antenna correlation. In this subsection, we consider a special case in which there exists neither channel estimation error nor transmit antenna correlation, i.e., $\rho=0,\delta=0$. In this context, because we can obtain clearer insights into how the system performance is affected by different user selection schemes.

For $\rho=0,\delta=0$, we have $$\begin{split}
A(K,M)&=\frac{\sigma_n^2}{Pc(M-K)},\\
B(K,M)&=0.
\nonumber\end{split}$$Substituting them into and , the approximate sum rates can be calculated. Nevertheless, the integrals of logarithmic functions in and degrade the intelligibility of the results.

Here, a new method, which is different from those adopted in Section \[sub:Random–User\] and Section \[sub:-Based-Location-Dependant-User\], is developed for finding a much simpler expression of the ergodic sum rate approximation in this special case. In what follows we apply Jensen’s inequality in a slightly different manner for the sake of finding a more concise expression of the system sum rate approximation. More specifically, we have $$\begin{split}
\text{E}[\mathcal{R}]&=\left(1-\frac{K}{T}\right)\text{E}_{d_1,\dots,d_K}\left[\sum_{k=1}^{K}\log_2(1+\text{SINR}_k)\right]\\
&\geq\left(1-\frac{K}{T}\right)K\log_2(1+\widetilde{\widetilde{\text{SINR}}}),
\end{split}\nonumber$$where $$\widetilde{\widetilde{\text{SINR}}}=\frac{Pc(M-K)}{\sigma_n^2\sum_{k=1}^K\text{E}_{d_k}[d_k^{\alpha}]}.$$The 