Capacity in arbitrary wireless ad hoc networks with MIMO and power constraint

In this paper, we consider a general scenario where tphe wireless network is modeled as a rectangle with side lengths √n and n^1/2-β, where 0 ≤ β ≤ 1/2 is a variance independent of n. n source-destination pairs are randomly located in the network, with their communication subject to the short-distance SNR, the long-distance SNR and the path loss. Based on these conditions, we identify the scaling laws of capacity for the network. The upper bound of the capacity is derived for the network, with the adoption of Multiple Input Multiple Output (MIMO) technology. Furthermore, we propose three different schemes, i.e., multihop, MIMO and hybrid schemes to achieve the upper bound. The capacity performance exhibits distinctive intriguing results as the side length of the network varies. Moreover, our results capture the impact of network shape on capacity and can unify the previous capacity results obtained in square networks.