the conventional RUS and LUS, and then further develop two low-complexity user selection schemes. Our numerical results are provided in Section IV. Finally, the conclusions are drawn in Section V.

*Notations:* We use uppercase and lowercase boldface letters to denote matrices and vectors, respectively. $(\cdot)^H$, $(\cdot)^\dagger$ and $\textnormal{tr}(\cdot)$ denote the conjugate transpose, the pseudo-inverse, and the trace operations, respectively. $\text{E}_x[\cdot]$ represents the expected value with respect to $x$. $\mathcal{CN}(\mathbf{m},\mathbf{\Theta})$ denotes the circularly symmetric complex Gaussian distribution with mean vector $\mathbf{m}$ and covariance matrix $\mathbf{\Theta}$. Finally, $\xrightarrow{a.s.}$ denotes the *almost sure* convergence.

System Model \[sec:System-Model\]
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![The downlink of a TDD based massive MIMO system, which is composed of an $M$-antenna BS and $N$ single-antenna candidate-UEs. Among all the candidate-UEs, $K$ UEs are selected to be simultaneously served, which are regarded as the active-UEs.](sys1){width="6cm"}

\[FIG 1\]

We consider the downlink of a TDD based massive MIMO system consisting of an $M$-antenna BS and $N$ single-antenna candidate-UEs ($N\geq M$). We assume that $N$ and $M$ are of the same order. $K$ UEs $(K<M)$ are selected for simultaneous data transmissions at each coherence slot. The composite channel matrix $\mathbf{G}\in\mathbb{C}^{K\times M}$ from the BS to the $K$ active-UEs characterizes LSF, SSF and transmit correlation[^2], 