Energy Consumption Analysis and Optimization of BER-Constrained Amplify-and-Forward Relay Networks

In this paper, we first develop an analytical framework for the total energy consumption of an amplify-and-forward (AF) multihop network employing M-ary quadrature amplitude modulation (MQAM) while satisfying an average bit error rate (BER) requirement at the destination over Rayleigh fading channels. Based on this framework, we then establish the conditions under which a dual-hop relay network is always more energy efficient when compared with a reference single-hop network. Moreover, the impact of the relay's location and the energy resource allocation between the relay and the source on the possible energy savings is also analyzed. Since a realistic power consumption model is considered, it is shown that there exists an optimal number of relays for the linear multihop relay network and that the maximum energy efficiency (EE) is obtained through the joint optimization of the number of relays and the constellation size. Considering this fact, we first formulate the optimization problem, and then, this problem is transformed into a convex form by relaxing constraints to be defined over the real numbers (instead of taking only discrete values). The new closed-form optimal solution that involves only elementary functions is derived for this relaxed problem. It is also demonstrated that the optimized multihop network has the potential not only to reduce the total energy consumption but to satisfy the peak-power constraint simultaneously at the expense of more delay as well. Finally, our analysis shows that significant energy savings are possible through joint optimization not only for delay-tolerant networks but for delay-limited networks as well, and up to about 55% energy savings are achievable over the optimized single-hop system.