Connectivity is a crucial issue in wireless networks. Gupta and Kumar show that with omnidirectional antennas, the critical transmission range for a wireless network to achieve asymptotic connectivity is O({the square root of}(log n/n)) if n nodes are uniformly and independently distributed in a disk of unit area. In this paper, we investigate the connectivity problem when directional antennas are used. We find that there also exists a critical transmission range, which corresponds to a critical transmission power. We show that in the same propagation environment, when directional antennas use the optimal antenna pattern, the critical transmission power could be much smaller than that in networks using omnidirectional antennas. Moreover, to achieve asymptotic connectivity, it is known that each node has to have O(log n) neighbors when using omnidirectional antennas. We show that even using the transmission power level at which each node has only O(1) neighbors when using omnidirectional antennas, we can still achieve the asymptotic connectivity with directional antennas.
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机译：连接是无线网络中的一个至关重要的问题。 Gupta和Kumar表明，通过全向天线，如果n个节点均匀且独立地分布在单元的盘中，则无线网络实现渐近连接的关键传输范围是O（{}的平方根））（}（log n / n））区域。在本文中，我们研究了使用定向天线时的连接问题。我们发现还存在关键的传输范围，其对应于临界传输功率。我们示出在相同的传播环境中，当方向天线使用最佳天线图案时，临界传输功率可能远小于使用全向天线的网络中的。此外，为了实现渐近连接，已知每个节点必须在使用全向天线时具有O（log n）邻居。我们表明，即使使用每个节点的传输功率电平仅在使用全向天线时只有O（1）邻居，我们仍然可以实现与定向天线的渐近连接。
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