## 1 Introduction
In contrast, joint optimization can more effectively exploit spatial resources by selecting the optimal subsets of users and antennas under limited resources (e.g., RF chains, transmit power), thereby maximizing the system's sum rate. Successive elimination is a commonly used antenna selection method [15; 16; 17; 18]. It starts by assuming that all antennas are involved in communication and then eliminates one antenna with the least contribution to the system in each iteration until the desired number of antennas is achieved. [PERSON] et al. propose a joint strategy of base station antenna selection and user allocation in large-scale MIMO broadcast channel, aiming to optimize the total system throughput [15]. By successively eliminating the antennas with the least contribution to the system and using semi-orthogonal user selection (SUS) algorithm to obtain a set of optimal users simultaneously, a sum rate performance close to the exhaustive search method can be achieved with very low complexity. The user scheduling algorithm is changed in reference [16]. First, users whose channel singular values are greater than the preset threshold are selected to ensure communication efficiency. Then, a detailed user scheduling is carried out in this user group. The user with the largest singular value is the first scheduled user, and the remaining scheduling users are selected according to the principle of low orthogonality with all the selected users. In reference [17], a low-complexity suboptimal user allocation approach assisted by a matrix Gaussian elimination method (MGEM) is proposed. The user scheduling scheme is integrated with norm-maximized antenna selection to optimize the sum rate, subject to the constraints of a maximum number of served users and limited transmission power. In reference [18], a set of transmitting antennas and a group of users which can generate maximum channel matrix eigenvalues are selected at first. Then, the antennas and users are iteratively updated. The worst antenna or user is eliminated at each time and replaced by the antenna or user that contributes most to the sum rate. Finally, a maximum system sum rate can be achieved. The difference in this scheme lies in selecting a suboptimal user group and antenna group in the beginning. The user group and antenna group are constantly optimized to approach the optimal scheme. In reference [19], the antennas are pre-divided into multiple antenna groups, with the antennas within each group working cooperatively. A greedy strategy is employed to select the optimal group from the candidate antenna groups, while simultaneously scheduling the user group that best matches the selected antenna group. Compared to the traditional per-antenna selection approach, this method significantly reduces the search space. The primary focus of the above studies is to achieve favorable system sum rate with low computational complexity. In addition, there are studies on different channel state information as well as system models. When only part of channel state information (CSI) is known, a joint antenna selection and user allocation algorithm on the base station side using the partially observable Markov decision processes (POMDP) framework is designed in reference [20]. At the start of every frame, the transmitter schedules the users participating in communication and selects the corresponding antenna subset to serve each group of users. For massive MIMO downlink time-varying fading channels, [PERSON] et al. study the problem of weighted average sum rate maximization, while guaranteeing the lowest average sum rate for users [21]. Adaptive scheduling of antennas and users is implemented through dual and randomized subgradient approach, with a heuristic algorithm applied in each time slot to minimize computational complexity. In a multi-cell large-scale MIMO scenario, a resource-efficient joint antenna and user selection technique leveraging the Adaptive Markov Chain Monte Carlo (AMCMC) algorithm is reported in reference [22].