Multi-hop, multi-route power minimisation in ad hoc network

This paper studies the problem of finding the optimal route of a stream between the transmitter and the receiver in an ad hoc network while minimizing the total power consumption. The criterion is the minimum power, and the fact that the stream must reach its destination is used as a constraint. Compared to previous approaches, we introduce more flexibility by allowing the stream to be split between several intermediate destinations, and we do not use the specific approximations (mainly high SNR) required to make the problem convex. Therefore, the main difficulty is due to the non convexity of the problem. In this contribution, we address a simple situation (flat fading channels, constant during the optimization process, simple transmitters and receivers) in order to demonstrate some properties of the problem. Finally, we propose an algorithm which, at least in some cases, is able to overcome the non convexity. Illustrations of the path followed by the algorithm demonstrates that it is able to find the global optimum even is difficult cases.