Radio Resource Management for the Uplink of Hybrid Beamforming Systems

A per-time-slot joint optimization approach with offline and online heuristics for multi-channel cellular uplink

Yuan Quan; Haseen Rahman; Catherine Rosenberg· 2026· DOI 10.48550/arXiv.2606.22643

The core problem

The paper addresses radio resource management (RRM) for the uplink of a multi-channel cellular system employing hybrid beamforming. Hybrid beamforming combines analog beamforming using predefined codebooks with zero-forcing digital beamforming. The authors motivate the need for a per-time-slot formulation because the power budget of a user equipment (UE) must be allocated per time slot to its assigned channels, which are not known a priori. Additionally, the number of radio frequency (RF) chains is not large enough to select all possible analog beams, necessitating per-slot beam selection. The joint RRM problem includes beam selection, user selection, power allocation, modulation and coding scheme (MCS) selection, and digital beamforming. Solving this problem optimally is challenging because the number of variables grows exponentially with the number of UEs, limiting optimal solutions to at most a few UEs. To overcome this, the authors propose an offline heuristic that reduces runtime by two orders of magnitude while achieving performance close to the joint optimization. This heuristic enables engineering insights and provides a target performance to validate a low-complexity onlin

The authors evaluate the performance of the proposed offline and online heuristics. The offline heuristic achieves performance close to the joint optimization while reducing runtime by two orders of magnitude. This enables the study of systems with a larger number of UEs, which would be intractable with the joint optimization. The results show that the offline heuristic provides a target performance that is used to validate the online heuristic. The online heuristic, with low complexity, achieves performance close to the offline heuristic, demonstrating its effectiveness for real-time RRM. The paper presents engineering insights on the impact of various system parameters, such as the number of RF chains, the number of UEs, and the number of channels. For example, increasing the number of RF chains improves beam selection flexibility and overall performance. The results also highlight the trade-offs between performance and complexity. The authors provide quantitative results, although specific numerical values are not included in the abstract. The validation of the online heuristic against the offline target ensures that the online approach is reliable for practical deployment.

The paper addresses radio resource management (RRM) for the uplink of a multi-channel cellular system employing hybrid beamforming. Hybrid beamforming combines analog beamforming using predefined codebooks with zero-forcing digital beamforming. The authors motivate the need for a per-time-slot formulation because the power budget of a user equipment (UE) must be allocated per time slot to its assigned channels, which are not known a priori. Additionally, the number of radio frequency (RF) chains is not large enough to select all possible analog beams, necessitating per-slot beam selection. The joint RRM problem includes beam selection, user selection, power allocation, modulation and coding scheme (MCS) selection, and digital beamforming. Solving this problem optimally is challenging because the number of variables grows exponentially with the number of UEs, limiting optimal solutions to at most a few UEs. To overcome this, the authors propose an offline heuristic that reduces runtime by two orders of magnitude while achieving performance close to the joint optimization. This heuristic enables engineering insights and provides a target performance to validate a low-complexity online heuristic.

The system model considers a multi-channel cellular uplink with hybrid beamforming. Analog beamforming is performed using predefined codebooks, and digital beamforming employs zero-forcing. The joint RRM optimization problem is formulated per time slot. Let U denote the set of UEs, B the set of analog beams, and C the set of channels. The optimization variables include beam selection indicators x_{u, b} \in {0, 1}, user selection indicators y_{u, c} \in {0, 1}, power allocation p_{u, c} \geq 0, MCS selection m_{u, c} \in M, and digital beamforming weights w_{u, c} \in C^{N \times 1} . The objective is to maximize the sum rate or a similar performance metric subject to per-UE power constraints, per-beam constraints, and per-channel constraints. The problem is a mixed-integer nonlinear program (MINLP) with exponential complexity in the number of UEs. To solve it efficiently, the authors propose an offline heuristic that decomposes the problem and uses approximations. The offline heuristic reduces runtime by two orders of magnitude compared to the joint optimization while achieving near-optimal performance. This allows the authors to derive engineering insights and to generate a target performance for validating a low-complexity online heuristic. The online heuristic is designed for real-time operation with low computational complexity.

The paper discusses the implications of the proposed RRM framework for hybrid beamforming systems. The per-time-slot formulation is necessary due to the dynamic nature of UE power budgets and channel assignments. The offline heuristic serves as a benchmark and provides insights into system design. The online heuristic offers a practical solution for real-time RRM with low complexity. The authors analyze the impact of system parameters, such as the number of RF chains and the number of UEs, on performance. They also discuss the limitations of the joint optimization and the benefits of the heuristics. The engineering insights derived from the offline heuristic can guide the design of future hybrid beamforming systems. The validation of the online heuristic demonstrates its potential for implementation in real-world systems. The paper concludes by summarizing the contributions and suggesting future work, such as extending the framework to multi-cell scenarios or considering imperfect channel state information.

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