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Connectivity in cooperative wireless ad hoc networks

Connectivity and capacity are two measures for the performance of mobile ad hoc networks that have been studied extensively under standard point-to-point physical layer assumptions. However, extensive recent research at the physical layer 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, with noncoherent cooperation at the physical layer, 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 one-dimensional (1-D) extended networks, in sharp contrast to noncooperative networks, we demonstrate that full connectivity can be realized under certain conditions. In particular, for any node density with path loss exponent α < 1, or for node density λ > 2 when α = 1, full connectivity occurs with probability one. Conversely, we demonstrate that, under noncoherent cooperation, there is no full connectivity with probability one when α < 1. In two-dimensional (2-D) extended networks with noncoherent cooperation, for any node density with α < 2, or for node density λ Ū 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 ≥ 4, the percolation threshold of the noncoherent cooperative network is strictly less than that of the noncooperative network. Analogous results are presented for dense networks. Hence, the main conclusion is that even relatively simple physical layer cooperation in the form of noncoherent power summing can substantially improve the connectivity of large ad hoc networks.