Capacity of multi-channel wireless networks with random (c, f) assignment

With the availability of multiple unlicensed spectral bands, and potential cost-based limitations on the capabilities of individual nodes, it is increasingly relevant to study the performance of multi-channel wireless networks with channel switching constraints. To this effect, some constraint models have been recently proposed, and connectivity and capacity results have been formulated for networks of randomly deployed single-interface nodes subject to these constraints. One of these constraint models is termed random (c, f) assignment, wherein each node is pre-assigned a random subset of f channels out of c (each having bandwidth W<over>c), and may only switch on these. Previous results for this model established bounds on network capacity, and proved that when c=O(logn), the per-flow capacity is O(Wp _rnd<over>nlogn) and (Wf<over>cnlogn) (where p _rnd = 1 - (1-f<over>c)(1-f<over>c-1)...(1-f<over>c- f+1) 1-^-f2<over>^c). In this paper we present a lower bound construction that matches the previous upper bound. This establishes the capacity as (Wp_rnd<over>nlogn). The surprising implication of this result is that when f=(c), random (c, f) assignment yields capacity of the same order as attainable via unconstrained switching. The routing/scheduling procedure used by us to achieve capacity requires synchronized route-construction for all flows in the network, leading to the open question of whether it is possible to achieve capacity using asynchronous procedures.