Throughput Scaling in Random Wireless Networks: A Non-Hierarchical Multipath Routing Strategy

Franceschetti et al. [1] have recently shown that per-node throughput in an extended (i.e., geographically expanding), ad hoc wireless network with Θ(n) randomly distributed nodes and multihop routing can be increased from the Ω( 1 √ n log n ) scaling demonstrated in the seminal paper of Gupta and Kumar [2] to Ω( 1 √ n ). The goal of the present paper is to understand the dependence of this interesting result on the principal new features it introduced relative to Gupta-Kumar: (1) a capacity-based formula for link transmission bit-rates in terms of received signal-to-interference-and-noise ratio (SINR), instead of the threshold model that positive bit-rate W is attainable when SINR lies above some threshold, and zero bit-rate otherwise; (2) hierarchical routing from sources to destinations through a system of communal highways, instead of individual direct routes from each source to the corresponding destination; and (3) cell-based routes constructed by percolation rather than by simply interconnecting all cells touched by a straightline between two end points. The conclusion of the present paper is that the improved throughput scaling is principally due to the percolation-based routing, which enables shorter hops and, consequently, less interference. This is established by showing that throughput Ω( 1 √ n ) can be attained by a system that does not employ highways, but instead uses percolation to establish, for each source-destination pair, a set of Θ(log n) routes within a narrow routing corridor running from source to destination. As a result, highways are not essential. In addition, it is shown that throughput Ω( 1 √ n ) can be attained with the original threshold transmission bit-rate model, provided that node transmission powers are permitted to grow with n. Thus, the benefit of the capacity bit-rate model is simply to permit the power to remain bounded, even as the network expands.