Energy Efficient Power and Channel Allocation in Underlay Device to Multi Device Communications

In this paper, we optimize the energy efficiency (bits/s/Hz/J) of device-to-multi-device (D2MD) wireless communications. While the device-to-device scenario has been extensively studied to improve the spectral efficiency in cellular networks, the use of multicast communications opens the possibility of reusing the spectrum resources also inside the groups. The optimization problem is formulated as a mixed integer nonlinear joint optimization for the power control and allocation of Resource Blocks (RB's) to each group. Our model explicitly considers resource sharing by letting co-channel transmission over a RB (up to a maximum of r transmitters) and/or transmission through s different channels in each group. 

We use an iterative decomposition approach, using first matching theory to find a stable even if sub-optimal channel allocation, to then optimize the transmission power vectors in each group via fractional programming. Additionally, within this framework, both the network energy efficiency and the max-min individual energy efficiency are investigated. We characterize numerically the energy-efficient capacity region, and our results show that the normalized energy efficiency is nearly optimal (above 90% of the network capacity) for a wide range of minimum-rate constraints. This performance is better than that of other matching-based techniques previously proposed.