The Capacity of Wireless Networks: Information-Theoretic and Physical Limits

Abstract

Abstract-It is shown that the capacity scaling of wireless networks is subject to a fundamental limitation which is independent of power attenuation and fading models. It is a degrees of freedom limitation which is due to the laws of physics. By distributing uniformly an order of n users wishing to establish pairwise independent communications at fixed wavelength inside a two-dimensional domain of size of the order of n, there are an order of n communication requests originating from the central half of the domain to its outer half. Physics dictates that the number of independent information channels across these two regions is only of the order of p n, so the per-user information capacity must follow an inverse square-root of n law. This result shows that information-theoretic limits of wireless communication problems can be rigorously obtained without relying on stochastic fading channel models, but studying their physical geometric structure.Index Terms-Ad hoc networks, capacity, network information theory, scaling laws, wireless networks.

Hierarchical beamforming for large one-dimensional wireless networks

“…The recent work [6], however, reveals that degrees of freedom in a wireless network can be limited by physical constraints in the spatial channel. This can be thought of as the spatial channel introducing correlation between pairwise gains.…”

“…In the regime when the available degrees of freedom in the network are very few (determined by the area of the network and the carrier wavelength [8]), they can be readily achieved by multi-hop. This makes multi-hop scaling optimal for such networks in the high SNR regime [6]. However, at low SNR, the performance is determined by the power transfer in the network and it is not clear whether any of the existing architectures achieves the optimal scaling of the capacity.…”

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

“…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 √ A/λ, which we identify as the spatial degrees of freedom in the network.…”

“…λ is the carrier wavelength. When √ A/λ ≥ 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 √ n. On the other hand, when √ A/λ ≤ √ n as in [26], there are only √ n degrees of freedom in the network and they can be readily achieved by multihop. Our results also reveal a third regime where…”

“…In regimes where power is not a limiting factor [25], the capacity can scale almost linearly with n implying a constant rate per user. 2) The scaling of the capacity is upper bounded by √ n due to the spatial constraints imposed by the physical channel [26]. Nearest-neighbor multi-hop already achieves this scaling and more sophisticated cooperation is useless.…”