  We reduce the problem of optimal beamforming for two-way relay (TWR) systems
with perfect channel state infomation (CSI) that use analog network coding
(ANC) to a pair of algebraic equations in two variables that can be solved
inexpensively using numerical methods. The solution has greatly reduced
complexity compared to previous exact solutions via semidefinite programming
(SDP). Together with the linearized robust solution described in (Aziz and
Thron, 2014), it provides a high-performance, low-complexity robust beamforming
solution for 2-way relays.
