which constitute the basis for our designs.

The results obtained above are invalid for the scenario of $K=M$ due to mathematical intractability. Fortunately, as shown by our simulation results that are given in Section \[sub:Sum-Rate-Performance\], $K=M$ is rarely beneficial for enhancing the performance of the considered massive MIMO system. This phenomenon was also observed by[@bjornson_optimal_2014] and [@wanger_large_2012]. Therefore, in this section we focus on the sum rate approximation for $K<M$.

$K^*$-Based Random User Selection ($K^*$-RUS)\[sub:Random–User\]
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In this subsection, we develop a novel RUS scheme, namely $K^*$-RUS, for the sake of improving the system sum rate and ensuring the fairness among candidate-UEs. Specifically, compared with the conventional RUS scheme in which $M$ UEs are selected for simultaneous data transmissions at each coherence slot, we modify the number of active-UEs to a more appropriate value $K^*$, which is decided according to the system parameters (e.g., the transmit power $P$ of the BS) and the statistical information of the channel (e.g., the probability distributions of SSF CSI and LSF CSI).

![The diagram of UE locations.[]{data-label="fig_ue"}](sys2){width="5cm"}

In order to obtain $K^*_{\text{RUS}}$, we need to consider the user distribution, which facilitates characterizing the effects of LSF. As shown in Fig. \[fig\_ue\], in this paper 