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Abstract-Driven by green communications, energy-efficient transmission is becoming an important design criterion for wireless systems, aiming to extend the life cycle of batteries in mobile devices. In this paper, we tackle the energy efficiency (EE) issue in uplink virtual multiple-input multiple-output (MIMO) systems, which requires the optimization of two interlaced parameters: the number of constituent mobile users in the virtual MIMO and their corresponding power allocation. The former parameter is a structural parameter defining the size of the virtual MIMO (usually known as the transmission mode) and its optimization relies on the method of enumeration. The difficulty is further aggravated by the fact that the EE is a nonconvex function of power, even for a given transmission mode. By exploiting the fact that increasing the number of active users can increase the number of contributors to the total EE on one hand but reducing the diversity order for each single user on the other, we can show the existence of an optimal transmission mode and find a simple way for its search. Through in-depth analysis, we show the existence of a unique globally optimal power allocator for the case without power constraints under the assumption of zero-forcing receivers, and further reveal the impact of power constraints upon power allocation, as compared to its global counterpart, aiming to provide a powerful means for power-constrained EE optimization. Finally, we establish theories, for isometric networks, to narrow down the search range for possible transmission modes, leading to a significant reduction of computational complexity in optimization. Simulation results are presented to substantiate the proposed schemes and the corresponding theories.

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