Worst-Case Based Robust Distributed Beamforming for Two-Way Relay Networks

In this paper, we consider a worst-case based robust beam forming approach for two-way relay networks that consist of two transceivers and multiple relays. Both the transceiver-to relay channels are assumed to have norm-bounded channel estimation errors. The worst case of the problem in a norm defined error set is optimized to guarantee the performance of the actual case. The resultant beam forming problem minimizes the worst-case total relay transmit power subject to the constraints of quality of service (QoS) of both receivers. We show that the robust beam forming problem can be formulated to a second-order-cone programming (SOCP) problem and can be solved efficiently using interior point method. Simulation results show that the proposed robust beam forming method guarantees no QoS outage at the price of 2 dB of total relay transmit power.