namely the $K^*$-LUS is developed in this subsection. In $K^*$-LUS, we select an appropriate number of UEs in descending order of the LSF coefficients (i.e., in ascending order of the BS-UE distances) for simultaneous data transmissions.

Inspired by $K^*$-RUS, let us first investigate the optimal number of active-UEs in LUS, which is denoted by $K^*_{\text{LUS}}$. We assume that $K$ UEs are selected and the distances between the selected UEs and the BS satisfy $d_1\leq d_2\leq\cdots\leq d_K$. Let $(r_k,\theta_k)$ represent the $k$-th active-UE according to the distance in ascending order. According to , we can get the PDF of the order statistic $d_k,k=1,\dots,K$ in LUS as $$\label{eq_df_3}\begin{split}
f_{d_k}^{\text{LUS}}\!(r_k)\!
&\!=\!\frac{1}{\text{B}(k,N\!-\!k+1)}F_R^{(k-1)}(r_k)[1\!-\!F_R(r_k)]^{N-k}f_R(r_k)\\
&\!=\!\frac{2r_k(R_{\max}^2-r_k^2)^{N-k}(r_k^2-R_{\min}^2)^{k-1}}{\text{B}(k,N-k+1)(R_{\max}^2-R_{\min}^2)^N},
\end{split}$$in which $\text{B}(x,y)$ represents the Beta function with parameters $x\text{ and }y$. Then, we have $$\label{eq_t123_4}
\text{E}_{d_k}[d_k^{\alpha}]=R_{\min}^{\alpha}{}_2F_1\left(k,-\frac{\alpha}{2};N+1;1-\frac{R_{\max}^2}{R_{\min}^2}\right)$$and $$\label{eq_rlus_0}\begin{split}
&\text{E}_{d_k}\left[\log_2(1+\widetilde{\text{SINR}}_k)\right]\\
&=\int_{R_{\min}}^{R_{\max}}\log_2\left(1+\frac{1}{T_1r_k^{\alpha}+T_2r_k^{-\alpha}+T_3}\right)f_{d_k}^{\text{LUS}}(r_k)dr_k,
\end{split}$$where ${}_2F_1(\cdot)$ is the ordinary hypergeometric function[@gauss_F12]. Therefore, $\tilde{\mathcal{R}}_{\text{LUS}}$ can be formulated with the aid of , , , and , as shown in on the next page.

$$\label{eq_lus_final}\begin{split}
&\tilde{\mathcal{R}}_{\text{LUS}}\\
&=\Gamma_2(T,M,K,R_{\min},R_{\max},P,c,\sigma_n^2,\rho,\alpha,\delta)\\
&=\left(1-\frac{K}{T}\right)\sum_{k=1}^K
\int_{R_{\min}}^{R_{\max}}\frac{2r_k(R_{\max}^2-r_k^2)^{N-k}(r_k^2-R_{\min}^2)^{k-1}}{\text{B}(k,N-k+1)(R_{\max}^2-R_{\min}^2)^N}
\log_2\Bigg(1+\\
&\quad\frac{1-\rho}{\frac{\sigma_n^2}{Pc\phi M}\left(r_k^{\alpha}+R_{\min}^{\alpha}{}_2F_1\left(k,-\frac{\alpha}{2};N+1;1-\frac{R_{\max}^2}{R_{\min}^2}\right)\right)+\frac{\rho\psi}{M\phi^2-K\psi}\left(r_k^{-\alpha}R_{\min}^{\alpha}{}_2F_1\left(k,-\frac{\alpha}{2};N+1;1-\frac{R_{\max}^2}{R_{\min}^2}\right)+1\right)}\Bigg)dr_k.
\end{split}$$

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If the system parameters are fixed, we are capable of solving for the optimal number $K^*_{\text{LUS}}$ maximizing $\tilde{\mathcal{R}}_{\text{LUS}}$ offline relying on standard line search algorithms, i.e.,$$\label{eq_lus_0}\begin{split}
&K^*_{\text{LUS}}\\
&=\mathop{\arg\max}_{K\in\{1,\dots,M-1\}}\Gamma_2(T,M,K,R_{\min},R_{\max},P,c,\sigma_n^2,\rho,\alpha,\delta).
\end{split}$$As long as we find 