Joint constellation size, energy allocation and relay location optimisation for energy-efficient DF relaying

Energy efficiency is a major issue in the energy-constrained wireless sensor network to ensure longer battery life. In this study, minimisation of total energy per bit for multi-hop decode-and-forward network employing M-ary quadrature amplitude modulation is considered. An average bit error rate (ABER) requirement at the destination over an independent Rayleigh fading channel is assumed. A realistic energy model is considered. The authors have proposed joint optimisation of constellation size, energy allocation per bit and relay location assuming fixed end-to-end distance. The authors have considered two scenarios: one, that each hop employs the same constellation size per hop and two, it adapts independently to take different constellation size. A novel solution is implemented following least square method to find the approximate closed-form solution of the optimal constellation size, which otherwise would not have been possible. It is observed that joint optimisation technique where the constellation size adapts independently per hop outperforms the one where the constellation size is same. Least amount of total energy is consumed per bit for balanced link. Finally, the analysis shows that for a realistic energy model, the dual hop network provides significant energy saving of 58% at 10 − 4 ABER over multi-hop network with four hops.