Distributed Zero-Forcing Amplify-and-Forward Beamforming for WSN Operation in Interfered and Highly Scattered Environments

In this paper, amplify-and-forward beamforming (AFB) is considered to establish a communication, through wireless sensor networks (WSNs) of $K$ sensor nodes, from a source to a receiver in the presence of both scattering and interference. All sources send their data to the WSN during the first time slot, while the nodes forward a properly weighted version of their received signals during the second slot. These weights are properly selected to maximize the desired power while completely canceling the interference signals. We show, however, that they depend on information locally unavailable at each node, making the zero-forcing beamformer (ZFB) unsuitable for WSNs, due to the prohibitive data exchange overhead and the power depletion it would require. To address this issue, we exploit the asymptotic expression at large $K$ of the ZFB weights that is locally computable at every node and, further, well-approximates their original counterparts. The performance of the resulting new distributed ZFB (DZFB) version is analyzed and compared with the conventional ZFB and two other distributed AFB benchmarks: the monochromatic (i.e., single-ray) AFB whose design neglects the presence of scattering and the bichromatic AFB which relies on an efficient two-ray channel approximation valid only for low angular spread (AS). We show that the proposed DZFB outperforms its monochromatic and bichromate counterparts while incurring much less overhead and power depletion than ZFB. We show also that it is able to provide optimal performance even in highly scattered environments as in the latter.