In this paper, using stochastic geometry, we investigate the average energy efficiency (AEE) of the user terminal (UT) in the uplink of a two-tier heterogeneous network (HetNet), where the two tiers are operated on separate carrier frequencies. In such a deployment, a typical UT must periodically perform inter-frequency small cell discovery (ISCD) process in order to discover small cells in its neighborhood and benefit from the high data rate and traffic offloading opportunity that small cells present. We assume that the base stations (BSs) of each tier and UTs are randomly located and we derive the average ergodic rate and UT power consumption, which are later used for our AEE evaluation. The AEE incorporates the percentage of time a typical UT missed small cell offloading opportunity as a result of the periodicity of the ISCD process. In addition to this, the additional power consumed by the UT due to the ISCD measurement is also included. Moreover, we derive the optimal ISCD periodicity based on the UT’s average energy consumption (AEC) and AEE. Our results reveal that ISCD periodicity must be selected with the objective of either minimizing UT’s AEC or maximizing UT’s AEE.
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