The Optimal Node Placement for Long Belt Coverage in Wireless Networks

The optimal node placement for a very large plane without boundary effect has been proven to be the regular triangular-lattice pattern in 1939. However, the regular triangular-lattice placement may not be optimal in a long belt with an upper and lower boundary. This paper proposes an optimal node deployment pattern to minimize the number of nodes for completely covering a long belt. The optimal pattern uses shifted node strips for belt coverage, and we compute the best node distance, strip offset, and strip distance for different belt heights. Mathematical analysis are provided to prove its optimality in terms of the minimum node density for belt coverage. Numerical computations are used to show its superiority, compared with other well-known placement patterns and our previously proposed equipartition placement.