Energy-Efficient distributed amplify-and-forward beamforming for wireless sensor networks

In this paper, we consider an amplify-and-forward (AF) beamformer that achieves a dual-hop communication from a source to a receiver in highly-scattered environments, through a wireless sensor network (WSN) comprised of K independent and autonomous nodes. The AF beamforming weights are derived to maximize the received signal-to-noise ratio (SNR) subject to a constraint over the nodes' total transmit power. We verify that the so-obtained SNR-optimal AF beamformer (OB) implementation requires from the small-battery powered WSN nodes a prohibitive power cost. Exploiting the polychromatic structure of scattered channels, we develop a novel polychromatic (i.e., multi-ray) distributed AF beamformer (P-DB) that performs nearly as well as OB while requiring much less power consumption at each node. Furthermore, we prove that the proposed P-DB always outperforms two other benchmarks: the monochromatic (i.e., single-ray) DB (M-DB) which neglects scattering, and the bichromatic (i.e., two-ray) DB (B-DB) which relies on an efficient polychromatic channel approximation by two rays that is valid for small angular spreads (AS).