# Improved Branch-and-Bound Antenna Selection Algorithm for Massive MIMO
###### Abstract
This method leverages MCTS's heuristic search to balance exploration and exploitation, while a linear regression model extracts channel norm and correlation features from the CSI, generating prior probabilities to accelerate search convergence. Their work introduces two key innovations. First, it pioneers the integration of the MCTS and self-supervised learning for antenna selection, enabling closed-loop optimization through online training sample generation. Second, it proposes a computational efficiency framework that combines incremental channel capacity calculation with ternary correlation approximation. Despite its advantages, this approach has three key limitations. First, the linear regression model has limited representational capacity, potentially struggling to extract discriminative channel features in complex propagation conditions. Second, the data migration and parallelization mechanisms introduce significant hardware implementation overheads. Finally, its scalability remains unverified for ultra-large-scale antenna arrays (more than 64 transmit or receive antennas), particularly concerning computational resource allocation and real-time decision latency. In recent years, machine learning and deep learning have been increasingly applied to antenna selection algorithm design. [PERSON] et al. [PERSON] et al. (2018) proposed a deep learning-based antenna selection algorithm leveraging Convolutional Neural Networks (CNNs). This approach formulates antenna selection as a classification problem, using CNNs to extract features from the channel matrix and directly predict the optimal antenna subset. The CNN model is trained offline on a large dataset of channel samples and exhaustive search results, enabling it to learn the mapping between the CSI and optimal subsets. This method marks the first application of CNNs in large-scale antenna selection, significantly reducing real-time computational overheads through an \"offline training-online inference\" paradigm. Despite its potential, this approach faces several challenges. First, label generation relies on an exhaustive offline search, making data generation and model training increasingly complex as the number of antennas grows. Additionally, the CNN model considers only channel amplitude, neglecting phase information, which may lead to the loss of important channel features. Finally, its generalization ability remains limited, with performance in non-uniform arrays or correlated channels requiring further validation. A Branch and Bound (BAB) search, a method capable of effectively reducing the search space, was first proposed by [PERSON] and [PERSON] in 1977 ([PERSON] and [PERSON], 1977). In 2015, [PERSON] et al. (2015) first proposed the application of the BAB search for antenna selection, which selects the antenna subset that maximizes the minimum singular value (MSV) of the channel sub-matrix, thereby maximizing the post-processing signal-to-noise ratio (SNR) and reducing the BER. In 2018, [PERSON] et al. (2018) reapplied the BAB algorithm for antenna selection, with the notable distinction that their methodology adopted a channel capacity maximization criterion. Commencing from an empty set, the researchers iteratively incorporated the antenna providing the maximum incremental channel capacity gain into the optimal subset. The existing literature demonstrates that in the application of Branch and Bound (BAB) algorithms to antenna selection, researchers have systematically reduced the computational complexity by implementing three pivotal mechanisms: (1) The establishment of monotonic criteria to ensure progressive optimization, (2) the development of pruning strategies to eliminate non-viable search branches, and (3) the dynamic updating of lower bounds throughout the search process to maintain solution quality. [PERSON] et al.