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This paper investigates energy efficient uplink communications for battery-constrained mobile terminals (MTs). We consider a heterogeneous wireless medium where MTs communicate with base stations (BSs) and access points (APs) of different networks with overlapped coverage. Unlike the existing research, we develop a joint bandwidth and power allocation framework that maximizes energy efficiency for a set of MTs, in different service areas, with best effort service and multi-homing capabilities. The problem formulation captures the heterogeneity of the medium, in terms of different service areas, channel conditions, available resources at BSs/APs of different networks, and different available maximum power at the MTs. In addition, the framework is implemented in a decentralized manner which is desirable in a case that different networks are operated by different service providers. Simulation results are …