Opportunistic collaborative beamforming with one-bit feedback

An energy-efficient opportunistic collaborative beamformer with one-bit feedback is proposed for ad hoc sensor networks transmitting a common message over independent Rayleigh fading channels to a relatively distant destination node. In contrast to conventional collaborative beamforming schemes in which each relay node uses channel state information (CSI) to pre-compensate for its channel phase and local carrier offset, the relay nodes in the proposed beamforming scheme do not perform any phase precompensation. Instead, the destination node broadcasts a relay node selection vector to the pool of available relay nodes to opportunistically select a subset of relay nodes whose transmitted signals combine in a quasicoherent manner at the destination. Since the selection vector only indicates which relay nodes are to participate in the collaborative beamformer and does not convey any CSI, only one bit of feedback is required per relay node. Theoretical analysis shows that the received signal power obtained with the proposed opportunistic collaborative beamforming scheme scales linearly with the number of available relay nodes under a fixed total power constraint. Since computation of the optimal selection vector is exponentially complex in the number of available relays, three low-complexity sub-optimal relay node selection rules are also proposed. Simulation results confirm the effectiveness of opportunistic collaborative beamforming with the low-complexity relay node selection rules.