Connectivity with Noncoherent Cooperation in Extended Wireless Networks

Abstract— The connectivity and capacity of large ad hoc networks have been studied extensively under standard point-to-point physical layer assumptions. However, extensive recent research has demonstrated the improvement in performance possible when multiple radios concurrently transmit in the same radio channel. In this paper, we consider how such physical layer cooperation improves the connectivity in wireless ad hoc networks. In particular, for noncoherent power summing of signals on the physical channel, we consider conditions on the node density λ (or, equivalently, the transmit power) for full connectivity and percolation for large networks in various dimensions and with various path loss exponents α. For the one-dimensional (1-D) case, in contrast to noncollaborative networks, we demonstrate that full connectivity can be realized for certain conditions. In particular, for any node density with α < 1, or for node density λ > 2 when α = 1, full connectivity occurs with probability one in extended networks. Conversely, we demonstrate that there is no percolation with probability one when α > 1. In two-dimensional (2-D) extended networks, for any node density with α < 2, or for node density λ > 5 when α = 2, full connectivity is achieved. Conversely, there is no full connectivity with probability one when α > 2, but we prove that, for α 6 4, the percolation threshold of the noncoherent collaborative network is strictly less than that of the noncollaborative network. Hence, even relatively simple physical layer collaboration in the form of noncoherent power summing can substantially improve the connectivity of large ad hoc networks.— The connectivity and capacity of large ad hoc networks have been studied extensively under standard point-to-point physical layer assumptions. However, extensive recent research has demonstrated the improvement in performance possible when multiple radios concurrently transmit in the same radio channel. In this paper, we consider how such physical layer cooperation improves the connectivity in wireless ad hoc networks. In particular, for noncoherent power summing of signals on the physical channel, we consider conditions on the node density λ (or, equivalently, the transmit power) for full connectivity and percolation for large networks in various dimensions and with various path loss exponents α. For the one-dimensional (1-D) case, in contrast to noncollaborative networks, we demonstrate that full connectivity can be realized for certain conditions. In particular, for any node density with α < 1, or for node density λ > 2 when α = 1, full connectivity occurs with probability one in extended networks. Conversely, we demonstrate that there is no percolation with probability one when α > 1. In two-dimensional (2-D) extended networks, for any node density with α < 2, or for node density λ > 5 when α = 2, full connectivity is achieved. Conversely, there is no full connectivity with probability one when α > 2, but we prove that, for α 6 4, the percolation threshold of the noncoherent collaborative network is strictly less than that of the noncollaborative network. Hence, even relatively simple physical layer collaboration in the form of noncoherent power summing can substantially improve the connectivity of large ad hoc networks.