Distributed Collaborative Beamforming Design in Scattered-Environments

In this paper, we consider a collaborative beamforming (CB) technique to achieve a dual-hop communication from a source surrounded by $M_I$ interferences to a receiver, through a wireless network comprised of $K$ independent terminals. The CB weights are designed so as to minimize the interferences plus noises´ powers while maintaining the received power from the source to a constant level. We show, however, that they are intractable in closed-form due to the complexity of the polychromatic channels arising from the presence of scattering in real-world environments. By recurring to a two-ray channel approximation proved valid at relatively low angular spread (AS) values, we are able to derive the new optimum weights and prove that they could be locally computed at each terminal, thereby complying with the distributed feature of the network of interest. The so-obtained bichromatic distributed collaborative beamforming (B-DCB) is then analyzed and compared in performance to the monochromatic CB (MCB), whose design does not account for scattering, and the optimal CSI-based CB (OCB). It is shown that the proposed B-DCB outperforms its counterparts in real-world environments.