Snapshot Capacity of Multi Hop Ad Hoc Networks

This paper studies the single power vector (snap-shot) capacity of the multi hop ad hoc networks. In a previous work, we introduced the concept of snapshot capacity region and studied it extensively for the case of single hop ad hoc networks. Here, we extend the snapshot capacity region idea to the more general and practical case of multi hop ad hoc networks with the partial successive interference cancellation technique. First, we prove the existence of a minimal power vector for each rate matrix and then we find the necessary and sufficient conditions of the rate matrices to be on the border of the snapshot capacity region. At the end, a novel iterative algorithm is proposed to produce the border of the snapshot capacity region. This algorithm can be used as an admission control algorithm to achieve the snapshot capacity region with some modifications.