Distributed Collaborative Beamforming for Real-World WSN Applications

In this paper, we consider a collaborative beamformer (CB) design that achieves a dual-hop communication from a source to a receiver in highly-scattered environments, through a wireless sensor network (WSN) comprised of independent and autonomous sensor nodes. The weights of the considered CB design at these nodes, derived to maximize the received signal-to-noise ratio (SNR) subject to constraint over the nodes total transmit power, have expressions that inevitably depend on some form of the channel state information (CSI). Only those requiring the local CSI (LCSI) available at their respective nodes lend themselves to a truly distributed implementation. The latter has the colossal advantage of significantly minimizing the huge overhead resulting otherwise from non-local CSI (NLCSI) exchange required between nodes, which becomes prohibitive for large and/or high Doppler. We derive the closed-form expression of the SNR-optimal CB (OCB) and verify that it is a NLCSI-based design. Exploiting, however, the polychromatic (i.e., multi-ray) structure of scattered channels as a superposition of impinging rays or chromatics, we propose a novel LCSI-based distributed CB (DCB) design that requires a minimum overhead cost and, further, performs nearly as well as its NLCSI-based OCB counterpart. Furthermore, we prove that the proposed LCSI-based DCB outperforms two other DCB benchmarks: the monochromatic (i.e., single-ray) DCB and the bichromatic (i.e., two-ray) DCB (B-DCB).