# Improved Branch-and-Bound Antenna Selection Algorithm for Massive MIMO
## 3 Efficient Antenna Selection via Enhanced Branch-and-Bound Optimization
### Branch-and-Bound Antenna Selection
However, the observed throughput in Table 4 demonstrates a performance gap from the aggregate capacity, primarily attributable to practical limitations in the USRP N310-based 4 \(\times\) 8 MIMO system, including the inherent protocol overhead, BER impacts, and hardware efficiency constraints. Notably, the measured throughput of BAB and I-BAB algorithms reaches 249.1 Mbps and 247.72 Mbps, respectively, exhibiting a marginal difference of 1.38 Mbps. This comparative analysis reveals that both the BAB anI-BAB maintain comparable throughput performances under identical hardware constraints, which aligns with the simulation results obtained in ideal channel conditions. Simultaneously, the proposed I-BAB algorithm achieves a latency of 31.75 ms, merely 13% of the BAB algorithm's latency, further demonstrating its marked effectiveness in reducing computational complexity. Due to practical equipment cost constraints, the application of the I-BAB algorithm for performance validation in large-scale systems with higher antenna counts was not implemented; this will be addressed through subsequent research endeavors where we will create necessary conditions to conduct further explorations. Table 5 presents the actual throughput of the BAB algorithm and I-BAB algorithm under different SNR conditions. As demonstrated in the table, the throughput of the I-BAB marginally exceeds that of the BAB at SNR = 5 dB. When the SNR reaches or exceeds 15 dB, the BAB's throughput becomes consistently lower than the I-BAB's. These results align with the conclusions derived from the simulation data in Figure 6. In the high SNR region, although the throughput gap between the I-BAB and BAB remains marginal with a relatively low growth rate of disparity, the problem of further enhancing the throughput performance of the I-BAB algorithm under high SNR conditions still warrants further investigation in future research. ## 5 Conclusions

This paper proposes an improved BAB search algorithm (I-BAB) under the assumption of independent and identically distributed (i.i.d.) Rayleigh flat-fading channels. Extensive simulations are conducted to evaluate the channel capacity and computational complexity performance of antenna selection using the I-BAB algorithm. Experimental results demonstrate that as the number of antennas at the receiver increases, the channel capacity achieved by the I-BAB algorithm remains comparable to that of the conventional BAB algorithm, while exhibiting significantly higher search efficiency than both the BAB and exhaustive search methods. This validates the theory that the I-BAB algorithm can substantially reduce computational complexity without sacrificing channel capacity, thereby achieving comprehensive performance enhancement for massive MIMO systems. Conceptualization, Y.G., C.-O.C., W.R.W. ; Methodology, Y.G., C.-O.C., W.R.W. ; Investigation, Y.G., C.-O.C. ; Data Curation, Y.G., W.R.W. ; Formal Analysis, Y.G., C.-O.C. ; Validation, C.-O.C., W.R.W. ; Writing (Original Draft), Y.G. ; Writing (Edit and Review), C.-O.C., W.R.W. ; Supervision: C.-O.C., W.R.W. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Data Availability Statement: The original data presented in the study are openly available in [[https://github.com/Yuki-GY/IBAB](https://github.com/Yuki-GY/IBAB)]([https://github.com/Yuki-GY/IBAB](https://github.com/Yuki-GY/IBAB)) (accessed on 13 April 2025). ## Conflicts of Interest: The authors declare no conflicts of interest.