Coverage problem of wireless sensor networks

In this paper we study the limiting achievable coverage problems of sensor networks. For the sensor networks with uniform distributions we obtain a complete characterization of the coverage probability. For the sensor networks with non-uniform distributions, we derive two different necessary and sufficient conditions respectively in the situations that the density function achieves its minimum value on a set with positive Lebesgue measure or at finitely many points. We propose also an economical scheme for the coverage of sensor networks with empirical distributions.