Capacity Bounds for Large Scale Wireless Ad Hoc Networks Under Gaussian Channel model

Abstract—We study the capacity for both random and arbitrary wireless network under Gaussian Channel model, i.e., all wireless nodes have the same constant transmission power P and the transmission rate is determined by Signal to Interference plus Noise Ratio (SINR). During the transmission, the power decays along path with attenuation exponent β> 2. We consider extended networks, where n wireless nodes {v1, v2, · · · , vn} are randomly or arbitrarily distributed in a square region Ba with side-length a. We randomly choose ns multicast sessions. For each source node vi, we randomly select k points pi,j (1 ≤ j ≤ k) in Ba and the node which is closest to pi,j will serve as a destination node of vi. The per-flow unicast(multicast) capacity is defined as the minimum data rate of all unicast(multicast) sessions in this network. We derive the achievable upper bounds on unicast capacity and a upper bound(partial achievable) on multicast capacity of the wireless networks under Gaussian Channel model. We found that the unicast(multicast) capacity for wireless networks under Gaussian Channel model has three regimes. Index Terms—Wireless networks, capacity, unicast, multicast, Gaussian channel