Proactively pushing content to users has emerged as a promising technology to cope with the explosively growing traffic demands of next-generation mobile networks. Yet, it is unclear whether content pushing can improve the energy efficiency (EE) of delay-constrained communications. With pushing, the energy consumption can be reduced by extending transmission time. However, if the user never needs the pushed content, pushing may incur wasted energy. Based on the random content request delay, this paper studies the maximization of EE subject to a hard delay constraint in an additive white Gaussian noise channel with pushing. In the scenarios of fixed and variable transmit powers, we propose transmission policies to allocate power based on difference of convex functions programming and dynamic programming. Moreover, the lower and upper bounds on EE are derived, and the user request probability thresholds are provided to determine whether or not to push a file for these two cases. It is shown that the EE of systems with pushing can be significantly improved with increasing content request probability and target transmission rate, compared with the on-demand scheme. Furthermore, pushing with variable power is found to bring extra EE gain at the expense of computational complexity.
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