Distributed collaborative beamforming design in highly-scattered environments

Abstract

In this paper, we consider a collaborative beam-former (CB) design that achieves a dual-hop communication from a source to a receiver in highly-scattered environments, through a wireless network comprised of K independent terminals. The weights of the considered CB design at these terminals, derived to maximize the received signal-to-noise ratio (SNR) subject to constraint over the terminals' 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 terminals 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 terminals, which becomes prohibitive for large K 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 L 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 (M-DCB) whose design ignores the presence of scattering and the bichromatic (i.e., two-ray) DCB (B-DCB) which relies on an efficient polychromatic-channel approximation by two rays when the angular spread is relatively small.