Broadcast Analysis for Large Cooperative Wireless Networks
  The capability of nodes to broadcast their message to the entire wireless network when nodes employ cooperation is considered. We employ an asymptotic analysis using an extended random network setting and show that the broadcast performance strongly depends on the path loss exponent of the medium. In particular, as the size of the random network grows, the probability of broadcast in a one-dimensional network goes to zero for path loss exponents larger than one, and goes to a nonzero value for path loss exponents less than one. In two-dimensional networks, the same behavior is observed for path loss exponents above and below two, respectively. 
Cagatay Capar, Dennis Goeckel, Don Towsley
cs.IT cs.NI math.IT