Capacity of Wireless Ad Hoc Networks Using Practical Directional Antennas

Capacity is one fundamental problem in wireless Ad hoc networks. Deploying directional antennas to wireless networks can reduce interference among concurrent transmissions and increase spatial reuse, while the technology of multi-channel can separate concurrent transmissions. Therefore, combining these two technologies into one wireless network is capable of great improvement on the network capacity. Recent studies proposed a multi-channel network architecture that equips each wireless node with multiple directional antennas, which is called MC-MDA network. The capacity in MC-MDA network is derived under arbitrary and random placements. However, they only used a simplified directional antenna model. For approaching the more accurate capacity in real scenario, in this paper, we consider a hybrid antenna model, which takes the effect of side lobe and back lobe into account. We derive the capacity upper-bounds of MC-MDA networks in arbitrary and random network with the hybrid model to find the effect of back lobe and side lobe. We show that the network capacity is closely related to $s$ the ratio of the radiuses of side lobe to main lobe. The capacity decreases when $s$ increases. Moreover, we compare the network capacity of MC-MDA using the simplified antenna model with our results. When considering the factor of interference constraint, the capacity gain using the hybrid antenna model is $sqrt{frac{theta^{2}}{theta^{2}+(4pi^{2}-theta^{2})s}}$ over the one with the simplified model.