Determinate bounds of design parameters for critical connectivity in wireless multi-hop line networks

Connectivity is a crucial performance parameter for wireless multi-hop networks, which is affected by factors like the communication radius, the node density as well as the link quality. In this paper, we solve the critical communication radius problem in wireless multi-hop line networks with unstable links. Specifically, we deduce determinate upper and lower bounds of the critical radius, and validate them by extensive simulations. The range of the critical radius for a line network of n nodes with link connection probability p is (ln n)/n ≤ r_c ≤ (2 ln n)/np.