Capacity of Hybrid Wireless Networks with Directional Antenna and Delay Constraint

We study the throughput capacity of hybrid wireless networks with a directional antenna. The hybrid wireless network consists of n randomly distributed nodes equipped with a directional antenna, and m regularly placed base stations connected by optical links. We investigate the ad hoc mode throughput capacity when each node is equipped with a directional antenna under an L-maximum-hop resource allocation. That is, a source node transmits to its destination only with the help of normal nodes within L hops. Otherwise, the transmission will be carried out in the infrastructure mode, i.e., with the help of base stations. We find that the throughput capacity of a hybrid wireless network greatly depends on the maximum hop L, the number of base stations m, and the beamwidth of directional antenna \theta. Assuming the total bandwidth W bits/sec of the network is split into three parts, i.e., W_1 for ad hoc mode, W_2 for uplink in the infrastructure mode, and W_3 for downlink in the infrastructure mode. We show that the throughput capacity of the hybrid directional wireless network is \Theta(\frac{nW_1}{\theta^2L\log n})+\Theta(mW_2), if L=\Omega(\frac{n^{1/3}}{\theta^{4/3}\log^{2/3} n}); and \Theta((\theta^2L^2\log n)W_1)+\Theta(m W_2), if L=o(\frac{n^{1/3}}{\theta^{4/3}\log^{2/3} n}), respectively. Finally, we analyze the impact of L, m and \theta on the throughput capacity of the hybrid networks.