When Do Non-Regenerative Two-Hop Relaying Networks Require a Global Phase Reference?

We consider a distributed wireless multiuser network with non-regenerative relays, where the gain factors are computed from channel estimates. They are to be chosen such that multiple signal paths add up coherently at the destinations (´distributed coherent beamforming´). In the presence of channel estimation errors, coherency is generally destroyed because the gain factors cannot be computed correctly. In this work, the channel estimates are assumed to be noiseless, but exhibit phase errors due to random and unknown local oscillator (LO) phases at the terminals. Without global phase reference at the nodes, the phase errors depend on the direction in which the individual point-to-point channels are measured. In some cases, coherency is completely destroyed while in others the system performance is not affected. We will still call the latter cases ´coherent´, even if perfect channel state information (CSI) is not available. Based on this observation we derive a framework to determine which nodes in a two-hop network require a global phase reference in order to allow for coherent distributed beamforming. We consider four traffic patterns that differ in the utilization of the direct link and discuss all combinations of directions in which the single-hop channel matrices can be estimated.