Distributed Collaborative Beamforming Design for Maximized Throughput in Interfered and Scattered Environments

In this paper, we consider a dual-hop communication from a source surrounded by M_I interferences to a receiver, through a wireless network comprised of K independent terminals. In the first time slot, all sources send their signals to the network, whereas in the second time slot, the terminals multiply the received signal by their respective beamforming weights and forward the resulting signals to the receiver. We design these weights 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. By resorting 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). Comparisons are made under both ideal and real-world conditions where we account for implementation errors and the overhead incurred by each CB solution. They reveal that the proposed B-DCB always outperforms MCB in practice; and that it approaches OCB in lightly to moderately scattered environments under ideal conditions and outperforms it under real-world conditions even in highly scattered environments. In such conditions, indeed, the B-DCB operational regions in terms of AS values over, which it is favored against OCB could reach until 50° and hence cover about the entire span of AS values.