Power control for physical-layer network coding in fading environments

In a three-node wireless relay network, two nodes, BS1 and BS2, exchange information through a relay node, RL. Suppose time division duplex is used, physical network coding (PNC) uses two time slots for the information exchange instead of four time slots needed by the conventional method. In the first time slot, both BS1 and BS2 transmit simultaneously to RL. The relay node, RL does a PNC mapping based on the received signal and broadcast the mapped signal back to BS1 and BS2 simultaneously during the second time slot. The nodes, BS1 and BS2 are able to decode their desired information based on the received mapped signal and the signal which they had transmitted during the first time slot. In this paper, we analyze the average BER of the information exchanged between the two nodes in Rayleigh fading environments. We also derive the average BER of the mapped signal at the relay during the first time slot. With the derived BER of the mapped signal at RL, we propose to use power control at BS1 and BS2 to minimize the instantaneous BER of the mapped signal at RL. The proposed technique improves the BER of the desired information decoded at the two nodes. The solution turns out to be channel inversion based power control at both BS1 and BS2. The proposed power control technique improves both the average BER of the mapped signal at RL and the desired information at BS1 and BS2.