Optimal power adaption for NAF relaying with channel side information

In this paper, we develop optimal power adaptation schemes by means of power amplification coefficients at the relay for the half-duplex single-relay non-orthogonal amplify-and-forward (NAF) system with channel side information (CSI) available at the relay. In particular, assuming that the relay has full knowledge of the channel gains, optimal power adaptation schemes are established in closed-form using both the mutual information (MI) and pairwise error probability (PEP) criteria with Gaussian inputs at the source. The proposed solutions can be understood as a multi-dimensional (multi-D) distributed water-filling in time and space. Numerical results show that the proposed power amplification methods provide a significant improvement over conventional schemes using either channel distribution information (CDI) or channel inversion (CI). The gain is observed with regard to both the MI with Gaussian inputs and the bit error rate (BER) performance using finite constellations such as quadrature amplitude modulation (QAM).