On Information-Theoretic Scaling Laws for Wireless Networks

In the development of large wireless networks, scaling law studies can provide fundamental insights. For example, is it possible to build an arbitrarily large wireless network without a wired infrastructure while maintaining a constant communication rate for each user? This is equivalent to asking if a linear scaling law is achievable for wireless networks. Whether too ambitious a goal or not, this question has attracted intensive research but still remains open. Among many proposals, the hierarchical scheme is impressive in exploiting the MIMO gain with a bootstrapping strategy. In this paper, a careful analysis of the hierarchical scheme exposes the potential influence of the pre-constant in deriving scaling laws. It is found that a modified hierarchical scheme can achieve a throughput up to an arbitrary factor higher than the original one, although it is still short of linear scaling. This study demonstrates the essential importance of the throughput formula itself, rather than the scaling laws consequently derived.