and }\delta$.

Given these system parameters, the optimal number $K^*_{\text{RUS}}$ in the sense of $\tilde{\mathcal{R}}_{\text{RUS}}$ maximization can be obtained efficiently with an one-dimensional search over the candidate set $\{1,2,\dots,M-1\}$, i.e., $$\label{eq_krus_0}\begin{split}
&K^*_{\text{RUS}}\\
&=\mathop{\arg\max}_{K\in\{1,\dots,M-1\}}\Gamma_1(T,M,K,R_{\min},R_{\max},P,c,\sigma_n^2,\rho,\alpha,\delta).
\end{split}$$Obviously, $K^*_{\text{RUS}}$ is independent of any instantaneous CSI, which makes it possible to find $K^*_{\text{RUS}}$ offline.

After obtaining $K^*_{\text{RUS}}$, the only online operation in the proposed $K^*$-RUS scheme is to randomly select $K^*_{\text{RUS}}$ UEs for simultaneous data transmissions. Therefore, little extra computational complexity is imposed on the proposed $K^*$-RUS compared to the conventional RUS.

The authors of [@wanger_large_2012; @zhao_performance_2013] and [@jung_optimal_2013] also discussed the optimal number of UEs for the ZF precoding, but they treated the LSF coefficients of UEs as deterministic values, which limit the generality of $K^*$. In other words, $K^*$ has to be updated whenever any LSF CSI of the system changes. By contrast, we take random UE locations into account for obtaining a more general and practical $K^*$. As long as the statistical properties of the system remain unchanged, our $K^*$ keeps its current value for arbitrary LSF and SSF channel realizations.

$K^*$-Based Location-Dependant User Selection ($K^*$-LUS)\[sub:-Based-Location-Dependant-User\]
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In order to enhance the sum rate performance further, a $K^*$-based location-dependant user selection scheme, 