# Improved Branch-and-Bound Antenna Selection Algorithm for Massive MIMO
###### Abstract
(2018) similarly demonstrated the superiority of the BAB algorithm in complexity reduction for antenna selection, though it should be noted that the computational complexity of the BAB-based antenna selection algorithm remains dependent on the initial ordering strategy, exhibiting exponential growth with an increasing number of antennas in worst-case scenarios. Building on the research on antenna selection algorithms, we observe that different selection strategies significantly impact the performance of large-scale MIMO systems. While each of the aforementioned algorithms optimizes specific performance metrics, they all have inherent limitations and fail to comprehensively enhance the MIMO system performance. Therefore, a more robust and versatile antenna selection algorithm is needed to achieve optimization without compromising other key performance aspects. This paper proposes the Improved Branch-and-Bound (I-BAB) algorithm for antenna selection. By introducing a monotonicity criterion and constructing an optimized search tree, the algorithm iteratively eliminates antennas that contribute the least to performance gain from the candidate set of receiving antennas, ultimately identifying the optimal antenna subset. Simulation results demonstrate that the I-BAB algorithm significantly reduces computational complexity while maintaining channel capacity performance comparable to the traditional Branch-and-Bound (BAB) algorithm. Notably, I-BAB's unique ability to generate optimal subsets for all possible antenna subset sizes within a user-defined range eliminates the traditional requirement for predetermined subset sizes, greatly enhancing operational flexibility. In future research on antenna selection algorithms, innovative approaches incorporating cutting-edge technologies such as dynamic optimization, energy complementarity, and machine learning could be explored for algorithm advancement ([PERSON] et al. proposed a machine learning model based on a Support Vector Machine (SVM) [22]. The SVM achieves classification by identifying an optimal hyperplane to separate samples from different classes while maximizing the inter-class margin. For nonlinear problems, the SVM employs kernel functions (e.g., a polynomial kernel) to map data into a high-dimensional space for linear separation, enabling high-accuracy classification. This model demonstrates strong noise resistance through filtering and dimensionality reduction operations to effectively process noise. It provides a valuable reference framework for future antenna selection algorithms employing machine learning techniques. However, the dimensionality reduction operations incur high computational resource demands, and the model requires a substantial number of labeled samples for training. The remainder of the paper is organized as follows. Section 2 presents the most representative antenna selection algorithms and introduces their search mechanisms and operational processes in detail. Section 3 describes our enhanced Branch-and-Bound (I-BAB) algorithm, providing its system model, mathematical framework, and new search strategy. In Section 4, a comprehensive numerical simulation comparing I-BAB with existing algorithms is conducted. Finally, Section 5 concludes the paper.