Topology-Agnostic Decentralized Beamforming

• The paper pioneers a protocol where nodes compute beamforming weights using only local channel statistics and consensus variables, achieving scalable and robust performance without global topology details.
• It leverages advanced optimization frameworks like consensus-based ADMM and WMMSE, ensuring low-overhead communication and convergence within a few iterations.
• The methodology significantly reduces signaling overhead while maintaining near-centralized performance across dynamic, large-scale wireless networks.

A topology-agnostic decentralized beamforming algorithm refers to any distributed beamforming protocol or optimization strategy whose operation, update laws, and convergence properties do not depend on global knowledge of the physical or logical network graph, node numbering, or connectivity details, and whose performance and correctness are maintained across arbitrary, possibly dynamic network topologies. These algorithms have gained significance in wireless communication, sensing, satellite constellations, acoustic sensor networks, and large-scale distributed MIMO/ISAC, enabling scalable, robust, and low-overhead coordinated transmission under realistic signaling and computational constraints.

1. Fundamental Principles and Definition

Topology-agnostic decentralized beamforming denotes any multi-agent/wireless array protocol in which each agent (node, AP, BS, satellite, or sensor) computes its local beamforming weights and control variables using only locally available CSI/statistics, messages from direct neighbors (or minimal global summaries), and generic update rules that do not rely on explicit knowledge of the network’s full connectivity structure. Consensus or coordination constraints, when present, are enforced through low-dimensional variables (e.g., consensus scalars, dual multipliers, summary interference parameters) rather than explicit exchange of full channel or topology maps.

This decoupling from network topology ensures that the protocol can scale, self-adapt, and be deployed in large and/or dynamically changing networks without requiring central reconfiguration or knowledge of the global node graph (Zafari et al., 1 Aug 2025, Zhang et al., 21 Dec 2025, Asgharimoghaddam et al., 2018, Xiao et al., 2020, Antonioli et al., 2021, Hojatian et al., 2021, Lakshminarayana et al., 2015, 0910.2771, Ouassal et al., 2019).

2. Algorithmic and Optimization Frameworks

Topology-agnostic decentralized beamforming algorithms fall into several classes, among which the most important are:

• Consensus-based ADMM (Alternating Direction Method of Multipliers): Each node maintains local copies of global variables and enforces consensus constraints by dual variables and consensus steps; communication is limited to a few summary statistics (e.g., local SINR floor, noise terms, or interference profiles) (Zafari et al., 1 Aug 2025, Zhang et al., 21 Dec 2025).
• WMMSE (Weighted Minimum Mean Square Error) Decomposition: Distributed WMMSE/dual decomposition transforms the global nonconvex beamforming/rate/sum-power problem into per-node convex/quadratic subproblems with minimal inter-node coupling via consensus or price variables; partial dualization ensures locality (Zhang et al., 21 Dec 2025, Antonioli et al., 2021).
• Deterministic Equivalent & Interference Coordination: Nodes exchange deterministic equivalents of aggregate inter-cell interference (ICI) or interference covariances, computed from slowly varying channel statistics or pathloss values, instead of full CSI—allowing for non-iterative, topology-agnostic operation (Asgharimoghaddam et al., 2018, Lakshminarayana et al., 2015).
• Federated Learning and Decentralized Stochastic Optimization: Random-walk or gossip-based distributed ADMM with inexact/first-order updates enables consensus on beamforming model parameters (e.g., ELM weights) in UAV swarms, with only token-based peer-to-peer exchange on dynamic graphs (Xiao et al., 2020).
• Unsupervised Deep Neural Networks: Fully local (or partially clustered) DNNs are trained offline to map local observations (RSSI, SSB matrices) to beamformer outputs, eliminating any explicit need for topology or CSI exchange at inference (Hojatian et al., 2021).
• Decentralized Interference Pricing: Interference-temperature variables and dual prices for local interference constraints are updated in primal/dual iterations using only neighbor-to-neighbor signaling; global convergence and Pareto-optimality are maintained without global graph awareness (0910.2771).

3. Decentralized Update Laws and Consensus Mechanisms

At the operational level, topology-agnostic decentralized beamforming algorithms share several core update mechanisms:

• Local primal/dual optimization: Each agent solves a local quadratic or convex subproblem using its own CSI/observation data and a small set of globally coupled (consensus or price) variables received from the minimal neighbor set (Zafari et al., 1 Aug 2025, Zhang et al., 21 Dec 2025, Asgharimoghaddam et al., 2018). Updates are scalable, fully parallel, and amenable to line-search or closed-form evaluations in low-complexity variants (Zhang et al., 21 Dec 2025).
• Consensus variable exchange: Nodes exchange only low-dimensional scalars (e.g., min-SINR, interference summaries, average frequency offsets, or model parameter tokens). Communication per iteration is independent of the antenna count or user density, and scales as $\mathcal{O}(\text{number of streams or users})$ (Zafari et al., 1 Aug 2025, Zhang et al., 21 Dec 2025, Ouassal et al., 2019).
• Robustification and auxiliary variables: To maintain correctness under channel uncertainty, estimation errors, or incomplete topology information, robust penalty or slack variables are introduced (e.g., to account for RATF estimation errors, TAD errors, or consensus drift) (Koutrouvelis et al., 2017, Xiao et al., 2020).
• Neighbor-adaptive signaling: No global neighbor list or explicit routing table is needed; each node dynamically discovers and exchanges information with only those neighboring nodes/users with non-negligible interference or statistical coupling (0910.2771, Antonioli et al., 2021).

4. Application Domains and System Models

The topology-agnostic paradigm has been developed and empirically validated across multiple canonical and emerging system architectures:

System Class	Main Model/Features	Reference(s)
Cell-Free Massive MIMO/ISAC	Arbitrary-distributed APs, local-only CSI, consensus	(Zafari et al., 1 Aug 2025, Hojatian et al., 2021)
LEO Satellite Constellations	Fully parallel satellites, ISL graph arbitrary	(Zhang et al., 21 Dec 2025)
Acoustic Sensor Networks	Arbitrary/wireless topologies, distributed constraints	(Koutrouvelis et al., 2017)
Multi-cell Cellular MIMO	Multi-cell BS, only large-scale stats needed	(Lakshminarayana et al., 2015, Asgharimoghaddam et al., 2018)
MISO Interference Channels	Local interference-pricing, arbitrary interference	(0910.2771)
UAV Swarms	Random-walk FL with dynamic graph	(Xiao et al., 2020)
Distributed Phased Arrays	Frequency/phase consensus in dynamic graphs	(Ouassal et al., 2019)

For all these cases, convergence and performance equivalence to centralized or fully informed designs are theoretically established or empirically confirmed, provided weak conditions on graph connectivity and exchange of consensus variables.

5. Communication, Complexity, and Scalability

Topology-agnostic decentralized schemes are characterized by:

• Communication efficiency: Per-iteration overhead is constant or linear in user/AP count, not in antenna or network size; overhead is dramatically lower than full-CSI centralized schemes (e.g., 10–1,000× reduction) (Zhang et al., 21 Dec 2025, Zafari et al., 1 Aug 2025, Hojatian et al., 2021, Antonioli et al., 2021, Lakshminarayana et al., 2015).
• Computational scalability: Local per-agent convex subproblems admit low-complexity (occasionally closed-form) solutions—quasi-closed-form line search is available for the LEO context (Zhang et al., 21 Dec 2025). Training/inference complexity in DNN-based designs grows only linearly with local resource count (Hojatian et al., 2021).
• Robustness to network dynamics: As operation is independent of global topology, agents can be added/dropped, links can fluctuate, and the same protocol persists without network-wide reconfiguration (Ouassal et al., 2019, Xiao et al., 2020).
• Convergence rate and optimality: Consensus or dual variables typically converge in 5–30 iterations; performance within 0.1–5% of centralized optimum is consistently achieved in both simulation and theory (Zafari et al., 1 Aug 2025, Zhang et al., 21 Dec 2025, Antonioli et al., 2021).

6. Performance and Empirical Results

Extensive simulation studies and analytical performance bounds have established that topology-agnostic decentralized beamforming can closely approach (within statistical error bounds) the sum-rate, power-minimization, and SINR-feasibility performance of their centralized or globally coordinated counterparts under a variety of metrics, including minimum per-user SINR, system sum-rate, convergence speed, and operational power budgets (Zafari et al., 1 Aug 2025, Zhang et al., 21 Dec 2025, Asgharimoghaddam et al., 2018, Xiao et al., 2020, Antonioli et al., 2021, Hojatian et al., 2021, Lakshminarayana et al., 2015). The trade-off between reduced consensus variable dimensionality and slight suboptimality vs. full-CSI centralized methods is quantitatively documented.

Scalability and adaptability across mesh, ring, and star topologies in LEO satellites is demonstrated, with particular reductions in signaling overhead for sparser (non-mesh) ISL configurations (Zhang et al., 21 Dec 2025). In dynamic graphs and time-varying acoustic or UAV networks, convergence is maintained provided sufficient average connectivity (Ouassal et al., 2019, Xiao et al., 2020). For cell-free ISAC and MIMO, the trade-off parameter between communication and sensing SINR utility can be tuned in decentralized consensus (Zafari et al., 1 Aug 2025).

7. Limitations and Future Directions

Topology-agnostic frameworks assume (and require) local graph connectivity (possibly time-varying but jointly connected over time). Full network disconnection or prolonged partitioning can lead to loss of consensus or degraded performance. Methods relying on statistical CSI or slow-fading pathloss are subject to error if those statistics become rapidly varying relative to the algorithm timescale (Asgharimoghaddam et al., 2018, Lakshminarayana et al., 2015).

Emerging directions include topology-agnostic joint beamforming and resource/scheduling integration, learning-based consensus under model drift, hybrid layered designs for integrated sensing/communication in LEO, and explicit incorporation of ISL or wireless link failures in the cooperative protocol (Zhang et al., 21 Dec 2025, Zafari et al., 1 Aug 2025).

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The topology-agnostic decentralized beamforming algorithm framework provides a scalable, flexible, and robust class of protocols for coordinated transmission across distributed, large-scale, and dynamic multi-agent wireless systems without reliance on global network mapping or centralized control, with rigorous performance guarantees and proven efficiency in diverse domains (Zhang et al., 21 Dec 2025, Zafari et al., 1 Aug 2025, Antonioli et al., 2021, Asgharimoghaddam et al., 2018, Hojatian et al., 2021, Xiao et al., 2020, 0910.2771).