Power allocation for two-way amplify-forward relaying with receive channel knowledge

The power allocation problem corresponding to the communication of two sources via a relay with amplify-forward capability is studied from the outage probability perspective. Analog network coding is considered for half-duplex nodes with perfect channel state information at the receiver side. Under a sum-power constraint on the transmit powers of the nodes, an optimal power allocation strategy that minimizes the high signal-to-noise ratio approximation of the outage probability is derived and shown to improve the performance significantly. As a reference for comparison, a cut-set type bound is also optimized for the setup.