Robust gain allocation against phase uncertainty at the relays for multiuser cooperative networks

We consider a coherent multiuser relaying network, where a number of source-destination pairs communicate concurrently over the same physical channel and a set of amplify-and-forward relays assist them. It has been shown recently that distributed phase synchronization can be avoided in coherent forwarding schemes. However, the uplink and downlink channel estimates at the relays used for gain allocation, so as the signal-to-noise plus interference ratios (SINRs) at the destinations, are severely affected by the uncertainty at the local oscillator phase offsets, which are modeled as Gaussian random variables. We propose a worst-case robust design for relay gain allocation assuming that the phase uncertainties at the relays are bounded within a defined range, which is determined according to the desired probability of assurance. The corresponding quasi-convex optimization problem is formulated as a semidefinite program. It has been shown by the simulations that the robust design provides a substantial SINR gain over the non-robust approach.