Dual-Hop Robust Distributed Collaborative Beamforming Over Nominally Rectangular WSNs in Slightly to Moderately Scattered Environments : (Invited Paper)

propose a new distributed collaborative beam-forming (DCB) solution that is robust (i.e., RDCB) against major channel estimation impairments over dual-hop transmissions through a wireless sensor network (WSN) of K nodes with a nominally deterministic geometry, presumably rectangular (or a fortiori square). The source S first sends its signal to the WSN. Then, each node forwards its received signal to the destination D after multiplying it by a properly selected beamforming weight. The latter aims to minimize the received noise power while maintaining the desired one equal to unity at the destination D. These weights depend on some channel state information (CSI) parameters. Hence, they have to be estimated locally at each node or fed back to it; resulting in either case in channel parameter estimation or feedback errors that could severely hinder DCB performance. Due to lack of space, we only account here for nodes location placement errors which would always amount to some additional phase error. Accounting for the massive connectivity characterizing new 5G and future 5G+/6G wireless technologies and the Internet of things (IoT), we develop alternative RDCB solutions that properly adapt both to monochromatic [i.e., line-of-sight (LoS)] and bichromatic (i.e., slightly to moderately scattered) propagation scenarios over the first hop while always assuming a LoS link over the second; referred to hereafter as MM-RDCB and BM-RDCB, respectively. We do so by exploiting i) very efficient asymptotic approximations at large numbers K of the WSN nodes and ii) the nominal geometric symmetries of their deterministic (rectangular or square) grid shapes. Furthermore, our new MM-RDCB and BM-RDCB solutions are distributed since their weights can be locally computed at every terminal, thereby dramatically improving both spectral and power efficiencies of the WSN. Simulation results show considerable gains and robustness of the proposed techniques in terms of achieved signal-to-noise ratio (SNR) against nodes location placement errors.