In this paper, we address a new unexplored problem

- what are the optimal patterns to achieve connected coverage in

wireless networks with directional antennas. As their name implies,

directional antennas can focus their transmission energy in

a certain direction. This feature leads to lower cross-interference

and larger communication distance. It has been shown that with

proper scheduling mechanisms, directional antennas may substantially

improve networking performance in wireless networks.

In this paper, we propose a set of optimal patterns to achieve

full coverage and global connectivity under two different antenna

models, i.e., the sector model and the knob model. We also

introduce with detailed analysis several fundamental theorems

and conjectures. Finally, we examine a more realistic sensor

model, where sensing range and communication range may both

vary randomly. Results show that our designed patterns work

well even in unstable and fickle physical environment.