Abstract
We propose a new collaborative beamforming (CB) solution robust (i.e., RCB) against major channel estimation impairments over dual-hop transmissions through a wireless sensor network (WSN) of K nodes. The source first sends its signal to the WSN. Then, each node forwards its received signal after multiplying it by a properly selected beamforming weight. The latter aims to minimize the received noise power while maintaining the desired power equal to unity. These weights depend on some channel state information (CSI) parameters. Hence, they have to be estimated locally at each node, thereby, resulting in channel estimation errors that could severely hinder CB performance. Exploiting an efficient asymptotic approximation at large K, we develop alternative RCB solutions that adapt to different implementation scenarios and wireless propagation environments ranging from monochromatic (i.e., scattering-free) to polychromatic (i.e., scattered) ones. Besides, in contrast to existing techniques, our new RCB solutions are distributed (i.e., DCB) in that they do not require any information exchange among nodes, thereby dramatically improving both WSN spectral and power efficiencies. Simulation results confirm that the proposed robust DCB (RDCB) techniques are much more robust in terms of achieved signal-to-noise ratio (SNR) against channel estimation errors than best representative CB benchmarks.
Highlights
We propose a new robust distributed CB (DCB) (RDCB) solution robust against major channel estimation impairments, namely phase synchronization, localization, direction-of-arrival (DoA), and/or channel scatterers/coefficients estimation errors over dual-hop transmissions from a source to a destination communicating through a wireless sensor network (WSN) of K nodes
We notice that the ASNR and average signal to average noise ratio (ASANR) curves remain very close for K ≤ 8 or coincide almost perfectly otherwise, thereby proving the insightfulness of the ASANR metric
We observe from these figures that monochromatic RDCB (M-RDCB) largely outperforms both benchmarks for any given K, σψ, σr, and σα
Summary
Collaborative beamforming (CB) stands out today as a key technique that offers tremendous capacity, coverage, and power gains [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. WSN nodes find their extremely limited computing and power capabilities severely burdened and quickly exhausted or depleted Their robustness very often deteriorate drastically in the presence of large channel estimation errors and, become unsuitable for hostile wireless environments. We propose a new RDCB solution robust against major channel estimation impairments, namely phase synchronization, localization, direction-of-arrival (DoA), and/or channel scatterers/coefficients estimation errors over dual-hop transmissions from a source to a destination communicating through a WSN of K nodes. Simulations results confirm that the proposed RDCB techniques are much more robust in terms of achieved signal-to-noise ratio (SNR) against channel estimation errors than the nominal optimal CB solution (i.e., optimized without being aware of and, accounting for impairments) and RDCB in [32] benchmarks, yet at much lower complexity, power cost, and overhead, making them suitable for WSN deployment in the harsh environments that characterize operation in real-world conditions. E{.} stands for the statistical expectation and J1 (.) is the first-order Bessel function of the first kind
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