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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, where the two tiers are operated on separate carrier frequencies. In such a deployment, a typical UT must periodically perform the interfrequency small-cell discovery (ISCD) process 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 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 that a typical UT missed small-cell offloading opportunity as a result of the periodicity of the ISCD process. The additional power consumed by the UT due to the ISCD measurement is also included …