Spatial Degrees of Freedom of Large Distributed MIMO Systems and Wireless Ad Hoc Networks

We consider a large distributed MIMO system where wireless users with single transmit and receive antenna cooperate in clusters to form distributed transmit and receive antenna arrays. We characterize how the capacity of the distributed MIMO transmission scales with the number of cooperating users, the area of the clusters and the separation between them, in a line-of-sight propagation environment. We use this result to answer the following question: can distributed MIMO provide significant capacity gain over traditional multi-hop in large adhoc networks with n source-destination pairs randomly distributed over an area A? Two diametrically opposite answers [24] and [26] have emerged in the current literature. We show that neither of these two results are universal and their validity depends on the relation between the number of users n and v root A/lambda, which we identify as the spatial degrees of freedom in the network lambda is the carrier wavelength. When root A/lambda >= n, there are n degrees of freedom in the network and distributed MIMO with hierarchical cooperation can achieve a capacity scaling linearly in n as in [24], while capacity of multihop scales only as root n. On the other hand, when root A/lambda