Asymptotic connectivity properties of cooperative wireless ad hoc networks

Extensive research has demonstrated the potential improvement in physical layer performance when multiple radios transmit concurrently in the same radio channel. We consider how such cooperation affects the requirements for full connectivity and percolation in large wireless ad hoc networks. Both noncoherent and coherent cooperative transmission are considered. For one-dimensional (1-D) extended networks, in contrast to noncooperative networks, for any path loss exponent less than or equal to one, full connectivity occurs under the noncoherent cooperation model with probability one for any node density. Conversely, there is no full connectivity with probability one when the path loss exponent exceeds one, and the network does not percolate for any node density if the path loss exponent exceeds two. In two-dimensional (2-D) extended networks with noncoherent cooperation, for any path loss exponent less than or equal to two, full connectivity is achieved for any node density. Conversely, there is no full connectivity when the path loss exponent exceeds two, but the cooperative network percolates for node densities above a threshold which is strictly less than that of the noncooperative network. A less conclusive set of results is presented for the coherent case. Hence, even relatively simple noncoherent cooperation improves the connectivity of large ad hoc networks.