The paradigm of upcoming 5G and beyond is the massive machine type communications (mMTC), where a large number of devices automatically operate wireless communications. Due to their automatic and energy-intensive operations, energy efficiency (EE) becomes crucial, but there is a lack of

investigation for EE of random access networks, which is the underlying platform for mMTC. In this paper, we focus on the EE of carrier sense multiple access-based non-orthogonal multiple access (NOMA) random access networks. We first construct mathematical models. Instead of investigating all combinations regarding successful decoding events as in previous works, by pivoting around the decoding process of a specific signal, a hidden pattern of NOMA decoding process is unveiled, which can largely decrease analytical complexity. Then, together with this feature, by adopting Markov chain and Q-function approximation, closedform formulation for EE is derived. Subsequently, to efficiently solve the complicated non-convex EE maximization problem built via the constructed models, we employ an approach that unifies complementary geometric programming (CGP) and difference of convex programming (DCP) to optimize all the controllable parameters at device side, namely, transmission probability, power, and data rate, with a tightest lower bound strategy to guarantee seamless EE improvement and very fast convergence to local optimal points even in the worst case. Simulation experiments verify the accuracy of mathematical models and efficiency of optimization scheme.