## 2 System Model  
This paper considers a multi-user massive MIMO communication system, as illustrated in Figure 1a. The base station is equipped with \(N_{t}\) transmit antennas, and there are \(U\) single-antenna users. To reduce energy consumption and hardware cost while improving the system rate in a multi-user scenario, antenna selection and user scheduling are employed. The original transmitted signal consists of \(U\) user information signals, denoted by \(\mathbf{s}\in\mathbb{C}^{U\times 1}\). User selection is realized through a switch array, which disables part of the data streams and retains only \(K\) streams for transmission, forming the signal \(\mathbf{x}\in\mathbb{C}^{K\times 1}\). This selected signal is then digitally precoded to eliminate inter-user interference. The precoded signal is converted from digital to analog by \(N_{RF}\) RF chains, where \(K\leq N_{RF}\). Finally, the signal is delivered to the transmit antennas through an RF switch array, which deactivates part of the antennas and only retains \(N_{RF}\) active antennas for communication. In this way, antenna selection and user scheduling are jointly accomplished. We define the group of selected transmitting antennas as \(\mathcal{A}\) and the group of scheduled users as \(\mathcal{S}\). The use of switch-based hardware in the system design is due to its compact size, high integration,and reliability, which make it a practical solution for selectively disabling data streams and deactivating antennas. Figure 1b illustrates a conventional fully digital system. In this system, neither user scheduling nor antenna selection is performed. The absence of user scheduling prevents the exploitation of multi-user diversity gain, resulting in a degradation of the average system throughput. Moreover, if the users' channels are highly correlated, transmitting signals to multiple users simultaneously will lead to severe inter-user interference. The absence of antenna selection implies that each antenna in the system is connected to a dedicated RF chain, i.e., \(N_{RF}=N_{t}\), resulting in an extremely high hardware cost and power consumption. In contrast, in the system shown in Figure 1a, only the selected antennas are equipped with complete RF chains (e.g., digital-to-analog converters/analog-to-digital converters, amplifiers), while the remaining antennas can be ignored, i.e., \(N_{RF}\ll N_{t}\). This reduces the number of RF chains, thereby lowering hardware cost, reducing power consumption, and simplifying signal processing complexity. Furthermore, when certain antennas suffer from hardware faults or poor channel conditions, the system can still maintain robust performance by selecting antennas in better states, thereby improving overall system robustness. In the antenna selection and user scheduling system, \(\mathbf{x}=\left[x_{1},x_{2},\ldots,x_{K}\right]\) denotes the data streams sent to \(K\) scheduled users. After user scheduling and antenna selection, the received signal for \(K\) users could be represented as  
\[\mathbf{y}=\mathbf{H}\mathbf{W}\mathbf{x}+\mathbf{n}, \tag{1}\]  
\(\mathbf{H}=\left[\mathbf{h}_{1}^{T},\mathbf{h}_{2}^{T},\ldots,\mathbf{h}_{K} ^{T}\right]^{T}\) is the channel matrix formed by all scheduled users and the selected antennas, where \(\mathbf{h}_{i}\in\mathbb{C}^{1\times N_{RF}}\) stands for the channel state response between the  
Figure 1: Multi-user massive MIMO system model: (**a**) antenna selection and user scheduling system; (**b**) traditional fully digital system. base station and the scheduled user \(i\). \(\mathbf{h}_{i}\) is considered to be an independent and identically distributed Rayleigh fading channel. To reduce the interference among different users, the forced-zero precoding is used [25]. \(\mathbf{W}=\left[\mathbf{w}_{1},\mathbf{w}_{2},\ldots,\mathbf{w}_{k}\right]\) is the precoding matrix and \(\mathbf{W}=\mathbf{H}\big{(}\mathbf{H}^{H}\mathbf{H}\big{)}^{-1}\). \(\mathbf{n}\) denotes the noise vector, \(\mathbf{n}\sim\mathcal{CN}(\mathbf{0},\mathbf{I}_{K})\).