Widely-Linear Distributed Beamforming for Weak-Sense Non-Circular Sources Based on Relay Power Minimization

In this paper, we present a widely-linear (WL) distributed beamforming algorithm that takes full advantage of weak-sense second-order (SO) non-circular source signals. We consider a single-antenna source-destination pair in an ad-hoc relay network that suffers from strong interference. Assuming that perfect channel state information (CSI) is available at the receiver, we design our algorithm based on the total relay transmit power minimization subject to a signal-to-interferenceplus-noise ratio (SINR) constraint after applying WL processing at the relays. We find key properties, analyze the computational complexity, and show by simulations that the proposed WL distributed beamforming algorithm provides a substantial relay power reduction compared to its linear counterpart for different degrees of non-circularity.