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Robust Distributed Collaborative Beamforming for WSANs in Dual-Hop Scattered Environments with Nominally Rectangular Layouts

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We introduce a robust distributed collaborative beamforming (RDCB) approach for addressing channel estimation challenges in dual-hop transmissions within wireless sensor and actuator networks (WSANs) of K nodes. WSANs enhance wireless communication by reducing data transmission, latency, and energy consumption while optimizing network load through integrated sensing and actuation. The source S transmits signals to the WSAN, where nodes relay them to the destination D using beamforming weights to minimize noise and preserve signal integrity. These weights depend on channel state information (CSI), where estimation errors degrade performance. We develop RDCB solutions for three first-hop propagation scenarios—monochromatic [line-of-sight (LoS)] or “M”, bichromatic (moderately scattered) or “B”, and polychromatic (highly scattered) or “P”—while assuming a monochromatic LoS or “M” link for the second hop between the nodes and the far-field destination. Termed MM-RDCB, BM-RDCB, and PM-RDCB, respectively (“X” and “Y” in XY-RDCB—for X (Formula presented.) and Y (Formula presented.) —refer to the chromatic natures of the first- and second-hop channels, respectively, to which a specific RDCB solution is tailored), these solutions leverage asymptotic approximations for large K values and the nodes’ geometric symmetries. Our distributed solutions allow local weight computation, enhancing spectral and power efficiency. Simulation results show significant improvements in the signal-to-noise ratio (SNR) and robustness versus WSAN node placement errors, making the solutions well suited for emerging 5G and future 5G+/6G and Internet of Things (IoT) applications for different challenging environments.

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Funding Information: This work was supported by the Discovery Grants (DGs) and CREATE PERSWADE (<www.create-perswade.ca>) Programs of NSERC. Publisher Copyright: © 2025 by the authors.

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5G+/6G Angular spread (AS) Channel mismatch Deterministic WSAN Distributed collaborative beamforming (DCB) Geometrical grids IoT Localization Robust DCB (RDCB) Synchronization Wireless sensor and actuator network (WSAN) Instrumentation Computer Networks and Communications Control and Optimization SDG 7 - Affordable and Clean Energy

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