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Joint Beamforming Design and Port Selection in Fluid Antenna-Assisted Multi-Cell Networks: A Personalized Federated Learning Approach
Liwen Gao, Li Zheng, Xing Hao, Ziru Chen, Lin X. Cai
TL;DR
Multi-cell FAS networks require joint optimization of coupled beamforming and discrete port selection under interference and heterogeneous cell preferences. The paper combines FedRep with a position-aware dual-branch DNN to learn these variables, and simulations report higher WSR than conventional FL and benchmark port-selection schemes.
Problem
Joint beamforming and discrete FA-port selection in multi-cell FAS networks remains an unexplored federated-learning problem despite their coupling through intra-cell and inter-cell interference.
Method
A FedRep framework shares beamforming-related parameters globally while retaining local port-selection heads, and a PA-DNN uses CSI and positional encoding with differentiable dual-branch outputs.
Results
The proposed scheme achieves higher WSR than conventional FL and port-selection benchmarks, including 1.57 bps/Hz for PA-DNN and 1.34 bps/Hz for FedRep in the reported scenarios.
Takeaways & Limitations
Explicitly decoupling global beamforming from local port selection supports decentralized training and improves performance, particularly in heterogeneous multi-cell environments.
Abstract
from arXiv · showhide
This paper investigates joint beamforming and port selection in multi-cell fluid antenna-assisted (FAS) networks. In such networks, active beamforming and discrete FA port selection are coupled through intra-cell and inter-cell interference and are jointly optimized to maximize the weighted sum-rate (WSR). We develop a federated representation learning (FedRep) framework with a position-aware dual-branch deep neural network (PA-DNN). The PA-DNN uses channel state information and port positional encoding as inputs, and jointly outputs beamforming vectors and port selections through two task-specific branches. To support decentralized training across heterogeneous cells, the FedRep framework shares global beamforming-related parameters among base stations while keeping port-selection parameters local for cell-specific adaptation. Simulation results show that the proposed scheme achieves a higher weighted sum-rate than conventional FL and port-selection benchmark schemes.
I. INTRODUCTION
Fluid antenna systems provide reconfigurable spatial degrees of freedom, but existing multi-user and joint beamforming-port-selection studies do not address decentralized, heterogeneous multi-cell settings. The paper introduces a personalized federated framework with position-aware joint learning to optimize both variables.
- Fluid antennas dynamically adjust their effective radiating positions within compact regions to exploit spatial channel diversity and mitigate interference.
- Prior FAS studies establish that selecting suitable ports improves link reliability, received signal quality, and interference management through spatial diversity.
- Existing multi-user FAS work largely remains limited to single-cell scenarios, while centralized multi-cell approaches cannot accommodate per-base-station preferences such as user-specific WSR weights.
- Conventional federated learning uses one global model, whereas personalized methods separate shared representations from local heads to address heterogeneous cell data.
- The proposed FedRep framework shares beamforming-related parameters globally while keeping port-selection parameters local, and its PA-DNN jointly learns both through CSI and positional encoding.
A. Channel Model
The channel model represents multi-cell BS-user links using fixed transmit antennas, movable fluid-antenna ports, multipath propagation, and spatially defined phase responses. It distinguishes serving and inter-cell interfering channels at each candidate port.
- Each BS-user link contains fixed transmit-antenna and fluid-antenna-port positions described in local three-dimensional Cartesian coordinates.
- The model includes L propagation paths whose complex gains are independently modeled as αi,m,k,ℓ∼CN(0, 1).
- Receive and transmit phase differences are defined from the arrival and departure azimuth and elevation angles for each propagation path.
- The channel representation uses receive and transmit field-response vectors to describe links between each BS and user.
- At each candidate FA port, the serving channel and inter-cell interfering channel are represented separately for the user’s selected location.
B. System Model
The system model describes downlink transmission through per-cell beamforming and symbol matrices, with each user activating one FA port. Achievable rates depend on the resulting SINR under desired, interfering, and noise components.
- The transmitted signal matrix is formed from the beamforming matrix Wm and the per-cell symbol matrix Sm.
- Each user can activate only a single FA port for data reception at any given time.
- The received signal model leads to an SINR expression that accounts for the user’s downlink transmission conditions.
- The achievable user rate is computed from the SINR as Rm,k = log2 (1 + ζm,k).
C. Problem Formulation
The optimization maximizes weighted sum-rate over BS beamforming matrices and user FA-port selections. It imposes per-BS transmit-power limits and requires each user to select one available port.
- The objective maximizes the weighted sum-rate over all cells and users by jointly optimizing beamforming matrices and FA-port selections.
- Each BS must satisfy the transmit-power constraint ∥Wm∥2 F ≤ PT.
- The user weights ωm,k represent priorities, while PT denotes the maximum transmit power available at each BS.
- The port-selection constraint requires every user to activate one port from the available set P.
III. PROPOSED SOLUTION
This section presents the PA-DNN architecture and then introduces the FedRep-based training framework.
- The proposed solution first describes the PA-DNN architecture.
- It then presents a FedRep-based training framework.
- The section is organized around the network design followed by federated training.
1) Input and Output:
The PA-DNN input fuses channel state information with spatial positional encoding, while parallel outputs represent beamforming and port-selection decisions.
- Input: The input combines a CSI matrix with a positional encoding matrix.CSI contains real and imaginary channel gains across users and ports; positional encoding maps physical 3D coordinates through multi-frequency sine and cosine functions.
- Input: Positional encoding maps relative spatial distances into feature distances so the network can learn similarities between closely spaced ports.
- Output: The network outputs the beamforming matrix and port selections in parallel.
- Backbone: A shared MLP backbone extracts high-dimensional spatial information from the fused input.
2) Neural Network Architecture:
The PA-DNN uses sinusoidal hidden-layer representations and two task-specific branches to produce constrained beamforming and differentiable port selections.
- Shared backbone: SIREN hidden layers preserve high-frequency spatial features introduced by positional encoding.The sine activation is used to prevent these features from decaying or becoming oversmoothed in deeper layers.
- Dual-branch architecture: A shared latent representation is processed by two task-specific branches in parallel.
- Beamforming branch: The beamforming branch generates an unnormalized matrix and applies a deterministic power projection to enforce the per-BS power constraint.
- Port-selection branch: The port-selection branch produces per-user logits, converts them to one-hot port choices, and uses STE-Gumbel for gradient computation.The forward pass uses hard one-hot selection, while the backward pass uses a continuous Gumbel-Softmax relaxation.
- Dual-branch architecture: The dual-branch design provides end-to-end differentiability while addressing mixed-integer constraints.
B. FedRep-Based PFL
FedRep separates globally shared beamforming representation parameters from locally retained port-selection parameters, enabling coordinated learning with cell-specific adaptation.
- Parameter partitioning: FedRep partitions PA-DNN parameters into a global representation and a local head.
- Global representation: Beamforming parameters are shared across base stations to learn spatial features common to all cells.
- Local head: Port-selection parameters remain local for adaptation to each cell’s user distribution and instantaneous interference conditions.
- Interference handling: Inter-cell interference is fixed during local optimization, updated at each global round, and iteratively refined from the evolved global beamforming model.
- Local training: During each round, base stations jointly optimize both parameter sets for E local epochs.
- Federated aggregation: Only updated global representations are uploaded, while updated local port-selection branches are retained at their originating base stations.
IV. SIMULATION RESULTS
The simulations compare PA-DNN and federated-learning strategies across multi-cell FAS scenarios, showing higher WSR and different convergence behavior under varying interference and heterogeneity.
- PA-DNN versus port-selection baselines: 1.57 bps/Hz: PA-DNN achieves the highest WSR against baseline port-selection strategies in the K = 7 multi-cell scenario.The comparison uses (K1, K2, K3) = (2, 2, 3) users.
- PA-DNN versus port-selection baselines: PA-DNN requires 150 epochs to fully converge, while its longer training period is associated with steady long-term capacity gains.The reported computational overhead is described as marginal.
- Federated-learning comparison: 1.34 bps/Hz: FedRep reaches the highest WSR among federated-learning frameworks, while EM-based PFL reaches 1.29 bps/Hz.The comparison uses (K1, K2, K3) = (2, 3, 4) users.
- Federated-learning comparison: Traditional FL plateaus at 0.9 bps/Hz, whereas pFedMe converges after 200 epochs and EM-based PFL ranks second overall in the reported comparison.The passage attributes the benchmark limitations to a common model or shared parameter optimization.
- Per-BS performance: FedRep achieves 0.42 bps/Hz at BS1, the highest reported per-BS WSR in the low-heterogeneity, simple-topology setting.EM-based PFL follows at 0.41 bps/Hz.
- Per-BS performance: At BS3, FedRep reaches 0.31 bps/Hz by epoch 100, but pFedMe later achieves 0.32 bps/Hz around epoch 170.The setting has moderate heterogeneity and severe interference.
V. CONCLUSION
The paper concludes that FedRep with PA-DNN jointly optimizes beamforming and port selection in multi-cell FAS while decoupling global and local parameters. It reports higher WSR than traditional baselines, particularly in heterogeneous networks.
- Conclusion: FedRep with PA-DNN jointly optimizes beamforming and port selection in multi-cell FAS using decentralized training.The design decouples global and local parameters and uses port positional encoding.
- Conclusion: The proposed scheme clearly outperforms traditional baselines, particularly in heterogeneous network environments.The conclusion attributes the reported effectiveness to explicit decoupling and position-aware learning.