  In this paper, we propose a selection region based multihop routing protocol
with directional antennas for wireless mobile ad hoc networks, where the
selection region is defined by two parameters: a reference distance and the
beamwidth of the directional antenna. At each hop, we choose the nearest node
to the transmitter within the selection region as the next hop relay. By
maximizing the expected density of progress, we present an upper bound for the
optimum reference distance and derive the relationship between the optimum
reference distance and the optimum transmission probability. Compared with the
results with routing strategy using omnidirectional antennas in
\cite{Di:Relay-Region}, we find interestingly that the optimum transmission
probability is a constant independent of the beamwidth, the expected density of
progress with the new routing strategy is increased significantly, and the
computational complexity involved in the relay selection is also greatly
reduced.
