Power optimization for an amplify-and-forward half-duplex two-way relay system

In this paper, we consider an amplify and forward half-duplex two-way-relay wireless communication system. For such a system, we estimate the channel information using a particular test signal set. The actual transmitted signal from a normalized square QAM constellation is then detected by choosing the symbol in the QAM constellation closest in distance to it. We derive an error probability which is found to be signal dependent for this system. An optimum design problem under a transmission power constraint based on this signal dependent asymptotic formula is then formulated leading to the optimum transmission power condition. Simulations show that under this optimum power transmission condition the system indeed yields optimum performance.