Power Allocation for a Single-Frequency Fixed-Gain Relay Network

We study a wireless two-hop relaying network where a destination node receives a superposition of direct link and relayed signals, because the same physical channel is employed for both transmissions. We assume fixed-gain amplify-and-forward operation in the relay and develop a power allocation technique that requires only slowly varying channel state information. The optimal power allocation maximizes the end-to-end signal- to-noise ratio under total transmit power constraint. Furthermore, we propose a nearly optimal power allocation that can be determined using closed-form expressions.