# A Bipartite Graph Neural Network Approach for Scalable Beamforming Optimization

arXiv: https://arxiv.org/abs/2207.05364 · HTML: https://mlsanity.com/paper/2207.05364/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 12 Jul 2022.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Deep Learning in Mobile and Wireless Networking: A Survey](https://mlsanity.com/paper/1803.04311/) (2018)
- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks](https://mlsanity.com/paper/1909.01865/) (2019)
- [Graph Neural Networks for Scalable Radio Resource Management: Architecture Design and Theoretical Analysis](https://mlsanity.com/paper/2007.07632/) (2020)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Unfolding WMMSE using Graph Neural Networks for Efficient Power Allocation](https://mlsanity.com/paper/2009.10812/) (2020)
- [Gated Graph Recurrent Neural Networks](https://mlsanity.com/paper/2002.01038/) (2020)
- [Towards Optimal Power Control via Ensembling Deep Neural Networks](https://mlsanity.com/paper/1807.10025/) (2018)
- [Wireless Networks Design in the Era of Deep Learning: Model-Based, AI-Based, or Both?](https://mlsanity.com/paper/1902.02647/) (2019)
- [EdgeNets:Edge Varying Graph Neural Networks](https://mlsanity.com/paper/2001.07620/) (2020)
- [Learning to Reflect and to Beamform for Intelligent Reflecting Surface with Implicit Channel Estimation](https://mlsanity.com/paper/2009.14404/) (2020)
- [Deep Learning for Distributed Optimization: Applications to Wireless Resource Management](https://mlsanity.com/paper/1905.13378/) (2019)
- [Scalable Power Control/Beamforming in Heterogeneous Wireless Networks with Graph Neural Networks](https://mlsanity.com/paper/2104.05463/) (2021)
- [Deep Learning Methods for Universal MISO Beamforming](https://mlsanity.com/paper/2007.00841/) (2020)
- [Graph Neural Network based Channel Tracking for Massive MIMO Networks](https://mlsanity.com/paper/2004.08738/) (2020)
- [Learning Robust Beamforming for MISO Downlink Systems](https://mlsanity.com/paper/2103.01602/) (2021)
- [Learning Optimal Fronthauling and Decentralized Edge Computation in Fog Radio Access Networks](https://mlsanity.com/paper/2103.11284/) (2021)
- [Learning Autonomy in Management of Wireless Random Networks](https://mlsanity.com/paper/2106.07984/) (2021)

## Built on by (most cited first, 7 of 7)

- [Machine Learning for Large-Scale Optimization in 6G Wireless Networks](https://mlsanity.com/paper/2301.03377/) (2023)
- [ENGNN: A General Edge-Update Empowered GNN Architecture for Radio Resource Management in Wireless Networks](https://mlsanity.com/paper/2301.00757/) (2022)
- [Edge Graph Intelligence: Reciprocally Empowering Edge Networks with Graph Intelligence](https://mlsanity.com/paper/2407.15320/) (2024)
- [Learning Resource Allocation Policy: Vertex-GNN or Edge-GNN?](https://mlsanity.com/paper/2307.12480/) (2023)
- [A Semi-amortized Lifted Learning-to-Optimize Masked (SALLO-M) Transformer Model for Scalable and Generalizable Beamforming](https://mlsanity.com/paper/2510.13077/) (2025)
- [Quantum spatial best-arm identification via quantum walks](https://mlsanity.com/paper/2509.05890/) (2025)
- [Self-Evolving In-Context Learning for Direct Pilot-to-Beamformer Design in MU-MISO Systems](https://mlsanity.com/paper/2607.11970/) (2026)

## Abstract (arXiv)

Deep learning (DL) techniques have been intensively studied for the optimization of multi-user multiple-input single-output (MU-MISO) downlink systems owing to the capability of handling nonconvex formulations. However, the fixed computation structure of existing deep neural networks (DNNs) lacks flexibility with respect to the system size, i.e., the number of antennas or users. This paper develops a bipartite graph neural network (BGNN) framework, a scalable DL solution designed for multi-antenna beamforming optimization. The MU-MISO system is first characterized by a bipartite graph where two disjoint vertex sets, each of which consists of transmit antennas and users, are connected via pairwise edges. These vertex interconnection states are modeled by channel fading coefficients. Thus, a generic beamforming optimization process is interpreted as a computation task over a weight bipartite graph. This approach partitions the beamforming optimization procedure into multiple suboperations dedicated to individual antenna vertices and user vertices. Separated vertex operations lead to scalable beamforming calculations that are invariant to the system size. The vertex operations are realized by a group of DNN modules that collectively form the BGNN architecture. Identical DNNs are reused at all antennas and users so that the resultant learning structure becomes flexible to the network size. Component DNNs of the BGNN are trained jointly over numerous MU-MISO configurations with randomly varying network sizes. As a result, the trained BGNN can be universally applied to arbitrary MU-MISO systems. Numerical results validate the advantages of the BGNN framework over conventional methods.