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In 5G and beyond 5G networks, the new cell-less radio access network architecture is adopted to overcome the extreme network capacity challenges generated by massive wireless devices used for diverse scenarios and various applications. At the same time, the evolution of mobile communications faces the important challenge of increased network power consumption. To fulfill user demands for various user densities and meanwhile reduce the power consumption, we present a novel energy-efficiency enhancement scheme, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(3\times E)$ </tex-math></inline-formula> to increase the transmission rate per energy unit, with stable performance within the cell-less radio access network (RAN) architecture. Our proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(3\times E)$ </tex-math></inline-formula> scheme activates two-step sleep modes (i.e., certain phase and conditional phase) through the intelligent interference management for temporarily switching access points (APs) to sleep, optimizing the network energy efficiency (EE) in highly loaded scenarios, as well as in scenarios with lower load. An intelligent control over underutilized/unused APs is considered, taking their interference contribution into account as the primary main criteria in addition to load-based conditional criteria. Therefore, our proposed scheme assures a stable performance enhancement and maintains an efficient power saving when the number of UEs increases, improving existing works not addressing this performance stability in peak-traffic hours. Simulation results show that the network EE is improved up to 30% compared to the reference algorithm and up to 60% with respect to the baseline algorithm in which all APs are active all the time.