Robotic router formation - A bit error rate approach

In this paper we consider the problem of robotic router formation, where a node needs to maintain its connectivity to a fixed station by using a number of mobile routers. While most literature on this topic optimizes the formation of the routers by maximizing the Fiedler eigenvalue of the resulting graph, we take a different approach and consider the true reception quality. By following a transmission of a bit from the transmitter to the receiver, we formulate the probability of bit error of the reception as a function of the positions of the routers. Then, we formulate an optimization problem that aims at minimizing the probability of bit error in the receiver while considering the environmental constraints. We consider two cases of multihop and diversity, for which we characterize the optimum configuration under certain conditions. We show that the robotic router graph formed by considering the true reception quality may not be the same as the one found by maximizing the Fiedler eigenvalue. Furthermore, only maximizing the Fiedler eigenvalue, without considering the reception quality, can result in a performance loss.