Abstract—We consider a collection of battery-operated, lowpower sensors randomly deployed within a geographic region for the purpose of sensing/monitoring the environment. We assume that a transmitting sensor broadcasts messages to receiver nodes over a randomly varying(fading) wireless channel. With the intention of maximizing overall network lifetime in such a setting, we propose a protocol that allows the receivers to sleep (power off) most of the time and turn on (activate) according to a function that depends on their link distance from the transmitter. We first derive the optimum density of link distances assuming N (fixed) nodes to be awake such that the distance to the farthest successful receiver is maximized. We then extend our analysis to networks where the number of nodes are distributed according to the Poisson distribution. In particular, we utilize this optimal density function to derive a simple expression for the conditional probability that a node turns on, given its distance from the transmitter. We also derive the minimum node density and scaling constant that meets the constraint on the average number of nodes that are awake to listen to a transmission. We compare the performance of our protocol with a simpler protocol that turns on all the nodes around the transmitter upto a certain distance. For fairness in comparison, the average number of nodes that activate is kept the same in both the protocols. I.