Imperfect sector antenna diversity in slotted ALOHA mobile network

In a wireless network with path loss and fading channels, receiver capture is known to substantially enhance the performance of the slotted ALOHA random access protocol. The efficiency of narrowband slotted ALOHA radio networks can be enhanced further by using sector antennas, each receiving signals from a particular segment of the network area. This paper investigates the effect of realistic, Le., partially overlapping antenna patterns and the resulting correlation of received power levels at different receiver branches. A method is derived for computing the joint throughput from two base station receivers with overlapping antennas patterns. The a posteriori information provided by the event of one message capturing one antenna is used to find conditional probabilities of capturing the other antennas as well. The paper shows that any overlap in the antenna patterns decreases the throughput, but transmissions from the overlapping area may face a larger probability of capture than signals from directions in which one antenna has maximum gain.