Relay placement for reliable ranging in cooperative mm-Wave Systems

We study millimeter wave-based ranging of randomly located terminal nodes (TNs) using fixed relay nodes (RNs) deployed around a central node (CN). This setting may correspond to a disaster-relief scenario where the rescuers require positioning information in the absence of a global positioning system (GPS). We derive the Bayesian Cramer-Rao lower bound (BCRLB) for the TNs range estimation from the CN as well as from the RNs in this network using a stochastic geometry framework. Contrary to existing studies, we take the effect of link-blockages into account while deriving the BCRLB, and thereby present a more accurate bound on the ranging error. For the special case of no blockages, we formulate a convex problem for obtaining the optimal relay positions. Our results provide the operator a guideline for initial deployment planning, in terms of number and location of RNs to be deployed in order to achieve an accurate ranging.