Decentralized Cooperative Beamforming Framework

• Decentralized cooperative beamforming frameworks are distributed methods where wireless nodes jointly design beamforming vectors using local CSI and lightweight coordination.
• They employ optimization algorithms such as ADMM, consensus protocols, and federated learning to achieve near-centralized performance with reduced signaling overhead.
• These frameworks are applied in cellular, satellite, ad hoc, ISAC, and IRS-aided networks, with experimental SDR validations confirming robust SNR gains.

Decentralized cooperative beamforming frameworks enable distributed sets of wireless nodes—such as access points, satellites, relays, or user devices—to jointly design transmit or receive beamforming vectors in a fully or partially decentralized manner. These architectures exploit local information, lightweight coordination protocols, and scalable distributed optimization to approach the performance of centralized beamforming with reduced signaling, computational cost, and improved scalability in large networks. Key models include decentralized consensus and ADMM-based optimization, federated learning-based beamforming, relay phase alignment, and pathloss-coupled coordination, with application in cellular, satellite, ad hoc, ISAC, and IRS-aided systems.

1. Cluster and Network Architectures

Decentralized cooperative beamforming is realized under diverse architectures:

• Relay-assisted clusters: In distributed receive beamforming, a single node acts as the final receiver while $N$ neighboring nodes function as amplify-and-forward relays. Each relay applies a controllable phase shift to its retransmission so that the over-the-air sum at the Rx is constructively combined. This architecture transforms the problem into distributed transmit beamforming for phase-aligned relays, leveraging local links for low-latency over-the-air combining (Quitin et al., 2015).
• Dense wireless and Cloud-RAN: Large networks of multi-antenna access points (APs) serve many users. Each AP stores only its own local channel state information (CSI) and power budget, and updates its local beamforming vectors in parallel with exchanges of low-dimensional dual variables over the backhaul. Coordinated multibase approaches in multicell and Cloud-RAN scenarios use such decentralizedization to enable scalability as user/AP density grows (Shi et al., 2014, Asgharimoghaddam et al., 2018).
• Cell-free/IRS-aided/topology-agnostic networks: For distributed cell-free MIMO or with IRS enhancement, each AP or BS optimizes its own beamforming and power allocation using locally held CSI plus dynamic scalar variables exchanged with a central server (for partial decentralization) or with neighbors via consensus protocols. System architectures may include clusters of APs, IRS panels, or even fully distributed interconnects without any master coordinator (Huang et al., 2020, Zafari et al., 1 Aug 2025).
• LEO satellite constellations: In large-scale satellite networks, each satellite performs local beamformer updates using statistical CSI, exchanges small coupled variables with neighbors over arbitrary topologies (e.g., ring, star, mesh), and applies consensus or dual decomposition to ensure scalable, feasible cooperative downlink (Zhang et al., 21 Dec 2025).
• Ad hoc and guided arrays: In wireless ad hoc networks and UAV swarms, every node computes its beamforming weight locally, based on instantaneously measured or statistically averaged CSI. In the absence of a central controller, collaborative protocols support multi-destination multicast and throughput-optimized MAC/PHY layering (0708.0805, Hanna et al., 2021).

2. Distributed Phase and Frequency Alignment

Phase alignment is critical for coherent combining in decentralized architectures:

• One-bit feedback phase synchronization: Relays iteratively perturb their transmit phase by small random steps, with a scalar feedback (increase/decrease) from the destination guiding each relay’s phase towards maximized received signal strength. The process converges to optimal alignment in $O(N)$ iterations when memory length $K \rightarrow \infty$, supporting robust alignment under oscillator drift and phase noise (Quitin et al., 2015).
• Consensus-based frequency/phase syntonization: In distributed phased arrays, nodes implement average consensus protocols to align their local oscillators’ carrier frequencies by recursive averaging of frequencies with their graph neighbors. The converged consensus error is bounded and, under typical oscillator drift and realistic connectivity, yields phase errors within $18^\circ$, preserving at least $90\%$ of the ideal beamforming gain (Ouassal et al., 2019).
• Destination-feedback-free approaches: Guided directionality leverages mobility and internal synchronization instead of direct destination feedback; one node acts as a guide, moving spatially to calibrate the beam while the others phase-align to it by measuring inter-node channels (Hanna et al., 2021).

3. Decentralized Optimization Frameworks

Distributed cooperative beamforming relies on various decentralized optimization methods:

• ADMM-based decentralized optimization: Problems such as max-min fair beamforming or weighted sum-rate maximization are reformulated in an ADMM-compliant structure, often via matrix-stuffing or consensus splitting. Each AP solves a small quadratic (or QCQP) subproblem with closed-form auxiliary variable and dual updates, communicating only low-dimensional dual variables to enforce coupling/consensus (Shi et al., 2014, Huang et al., 2020, Zafari et al., 1 Aug 2025).
• Block coordinate descent (BCD): For block-separable objectives (e.g., joint admission and beamforming), BSs iteratively solve local SDPs using only updated interference footprints from other BSs. Convergence to a stationary point is guaranteed under mild smoothness conditions, and the entire deflation loop for user selection proceeds efficiently (Wai et al., 2012).
• Federated learning for beamforming: Vertical FL (VFL) leverages a central server to aggregate per-BS DNN model outputs and compute joint gradients under a global loss (based on full network sum-rate). Horizontal FL (HFL) eliminates all CSI/model exchange beyond model weights, instead using local leakage-penalty losses at each BS and distributed SGD. Both protocols provide scalable convergence to near-centralized performance for ISAC and multicell problems (Jiang et al., 28 Jan 2025, Xiao et al., 2020).
• Penalty dual decomposition (PDD) and consensus-ADMM: In distributed satellite or cell-free networks, consensus constraints on coupled variables (e.g., effective channel or beamforming metrics) are enforced via ADMM or PDD. Local updates admit closed-form or low-dimensional line search, and consensus is achieved over generic topologies without scaling communication with antenna size (Zhang et al., 21 Dec 2025, Kim et al., 2 Jun 2025).

4. SNR/Rate Scaling, Analytical Models, and Performance

• Scaling laws: Under perfect phase alignment, the aggregate SNR at the destination scales linearly with the number of cooperative relays or APs, i.e., $\mathrm{SNR}_{\mathrm{total}} = N\rho_1$ for single-relay average SNR $\rho_1$ (Quitin et al., 2015).
• Beamforming under phase noise: The phase noise due to relay delay and inter-cycle drift is analytically modeled as a Gaussian process with variance

$$\sigma_\phi^2 = \omega_c^2 q_1^2 T_d + \frac{\omega_c^2 q_2^2 T_d^3}{3} + \omega_c^2 q_2^2 T_d^2 T_c,$$

affecting steady-state RSS and ultimately limiting the achievable beamforming gain for a given feedback/processing design (Quitin et al., 2015).

• Convergence guarantees: For convex consensus and ADMM formulations, convergence to the global minimum or KKT points is established under standard conditions (e.g., closed convex cones, full row-rank of consensus matrices). The number of iterations scales logarithmically in the norm of the initial error and inversely with the spectral gap of the mixing matrix for consensus-based methods (Ouassal et al., 2019, Shi et al., 2014).
• Empirical performance: Measurements from SDR implementations confirm the predicted SNR/RSS gains, matching the theoretical coherent sum of amplitudes across multi-relay or multi-AP clusters. The distributed algorithms consistently approach the centralized sum-rate or power-minimization benchmarks within 0.5–1 dB under practical signaling overhead, even in large-scale/LEO networks (Quitin et al., 2015, Kim et al., 2 Jun 2025, Zhang et al., 21 Dec 2025).

5. Coordination Overhead and Implementation Tradeoffs

• Coordination overhead: Most decentralized beamforming algorithms exchange only a small set of scalars (dual variables, consensus parameters, or local metrics) per local iteration, with complexity and communication load dominated by the number of users, clusters, or beams—not antenna array size. Algorithms that exchange full CSI or beamformers scale poorly; thus, advanced consensus and federated learning strategies localize parameter exchange for practical signaling budgets (Jiang et al., 28 Jan 2025, Shi et al., 2014, Zhang et al., 21 Dec 2025).
• Synchronization strategies: Implicit frequency and timing synchronization are exploited by time-division of long and short links and narrowband signaling, eliminating the need for explicit frequency references or GPS timing across the cluster (Quitin et al., 2015). Fine-grained phase/frequency alignment is enforced via iterative consensus or phase-perturbation protocols, robust to oscillator drift and time-varying topology (Ouassal et al., 2019). Overhead trade-offs are explicit in satellite topologies: ring architectures incur sequential update latency but balance signaling, while star architectures centralize consensus but can bottleneck at the hub node (Kim et al., 2 Jun 2025, Zhang et al., 21 Dec 2025).
• Practical SDR/PHY validations: SDR-based implementations demonstrate feasibility with typical USRP platforms at 900 MHz, with experimentally observed SNR/beamforming gains stable in time and matching predicted values for 2–4 relay/cluster node configurations, even under significant oscillator drift (Quitin et al., 2015, Hanna et al., 2021).

6. Extensions and Limitations

• Joint design for ISAC: Decentralized frameworks are extended to simultaneous communication and sensing via weighted-sum objectives, local beamforming nulling, penalty consensus, and federated learning losses controlling interference leakage for both communication users and radar receivers. ISAC frameworks leverage power and SINR tradeoff parameters to operate along the communication–sensing Pareto frontier (Jiang et al., 28 Jan 2025, Zafari et al., 1 Aug 2025).
• Admission, scheduling, and QoS: Slack variable-based joint optimization allows user admission and scheduling to be handled jointly with beamforming under decentralized operation, addressing practical QoS constraints and infeasible settings with embedded soft violation penalties (Antonioli et al., 2021, Wai et al., 2012).
• Limitations: Phase/Frequency consensus protocols require initial topology connectivity and bounded oscillator drift to guarantee sub-$18^\circ$ error. One-bit feedback schemes require feedback SNR above a critical threshold for convergence. Federated learning-based methods are robust to CSI/model error but may converge slower or have higher per-round communication in very large networks. Fully decentralized architectures may trade off convergence speed for signaling economy, especially under strong coupling or severe interference (Quitin et al., 2015, Ouassal et al., 2019, Jiang et al., 28 Jan 2025).
• Open problems: Non-LOS or strongly scattered channels remain difficult for location-based guideless DBF. Fast mobility/topology change and dynamic multi-beam steering challenge practical implementations in ad hoc and UAV swarms (Hanna et al., 2021). Potential directions include secure aggregation for privacy, integration with RIS, full-duplex extension, and hybrid architectures with partial centralization.