Joint Beamforming Design and Port Selection in Fluid Antenna-Assisted Multi-Cell Networks: A Personalized Federated Learning Approach

• Fluid antennas dynamically adjust their effective radiating positions within compact regions to exploit spatial channel diversity and mitigate interference.Source: §I · p. 1
• Prior FAS studies establish that selecting suitable ports improves link reliability, received signal quality, and interference management through spatial diversity.Source: §I · p. 1
• 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.Source: §I · p. 1
• Conventional federated learning uses one global model, whereas personalized methods separate shared representations from local heads to address heterogeneous cell data.Source: §I · pp. 1–2
• 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.Source: §I · p. 2

• Each BS-user link contains fixed transmit-antenna and fluid-antenna-port positions described in local three-dimensional Cartesian coordinates.Source: A. Channel Model · p. 2
• The model includes L propagation paths whose complex gains are independently modeled as αi,m,k,ℓ∼CN(0, 1).Source: A. Channel Model · p. 2
• Receive and transmit phase differences are defined from the arrival and departure azimuth and elevation angles for each propagation path.Source: A. Channel Model · p. 2
• The channel representation uses receive and transmit field-response vectors to describe links between each BS and user.Source: A. Channel Model · p. 2
• At each candidate FA port, the serving channel and inter-cell interfering channel are represented separately for the user’s selected location.Source: A. Channel Model · p. 2

• The transmitted signal matrix is formed from the beamforming matrix Wm and the per-cell symbol matrix Sm.Source: B. System Model · p. 2
• Each user can activate only a single FA port for data reception at any given time.Source: B. System Model · p. 3
• The received signal model leads to an SINR expression that accounts for the user’s downlink transmission conditions.Source: B. System Model · p. 3
• The achievable user rate is computed from the SINR as Rm,k = log2 (1 + ζm,k).Source: B. System Model · p. 3

• The objective maximizes the weighted sum-rate over all cells and users by jointly optimizing beamforming matrices and FA-port selections.Source: C. Problem Formulation · p. 3
• Each BS must satisfy the transmit-power constraint ∥Wm∥2 F ≤ PT.Source: C. Problem Formulation · p. 3
• The user weights ωm,k represent priorities, while PT denotes the maximum transmit power available at each BS.Source: C. Problem Formulation · p. 3
• The port-selection constraint requires every user to activate one port from the available set P.Source: C. Problem Formulation · p. 3

• The proposed solution first describes the PA-DNN architecture.Source: §III · p. 3
• It then presents a FedRep-based training framework.Source: §III · p. 3
• The section is organized around the network design followed by federated training.Source: §III · p. 3

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.Source: 1) Input and Output · p. 3
• Positional encoding maps relative spatial distances into feature distances so the network can learn similarities between closely spaced ports.Source: 1) Input and Output · p. 3

Output

• The network outputs the beamforming matrix and port selections in parallel.Source: 1) Input and Output · p. 3

Backbone

• A shared MLP backbone extracts high-dimensional spatial information from the fused input.Source: 2) Neural Network Architecture · p. 4

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.Source: 2) Neural Network Architecture · p. 4

Dual-branch architecture

• A shared latent representation is processed by two task-specific branches in parallel.Source: 2) Neural Network Architecture · p. 4

Beamforming branch

• The beamforming branch generates an unnormalized matrix and applies a deterministic power projection to enforce the per-BS power constraint.Source: 2) Neural Network Architecture · p. 4

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.Source: 2) Neural Network Architecture · p. 4

Dual-branch architecture

• The dual-branch design provides end-to-end differentiability while addressing mixed-integer constraints.Source: 2) Neural Network Architecture · p. 4

Parameter partitioning

• FedRep partitions PA-DNN parameters into a global representation and a local head.Source: B. FedRep-Based PFL · p. 4

Global representation

• Beamforming parameters are shared across base stations to learn spatial features common to all cells.Source: B. FedRep-Based PFL · p. 4

Local head

• Port-selection parameters remain local for adaptation to each cell’s user distribution and instantaneous interference conditions.Source: B. FedRep-Based PFL · p. 4

Interference handling

• Inter-cell interference is fixed during local optimization, updated at each global round, and iteratively refined from the evolved global beamforming model.Source: B. FedRep-Based PFL · p. 4

Local training

• During each round, base stations jointly optimize both parameter sets for E local epochs.Source: B. FedRep-Based PFL · p. 4

Federated aggregation

• Only updated global representations are uploaded, while updated local port-selection branches are retained at their originating base stations.Source: B. FedRep-Based PFL · p. 4

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.Source: §IV · p. 5
• 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.Source: §IV · p. 5

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.Source: §IV · p. 5
• 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.Source: §IV · p. 5

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.Source: §IV · p. 5
• 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.Source: §IV · p. 6

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.Source: §V · p. 6
• 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.Source: §V · p. 6