Capacity of Multi-Channel Wireless Networks

The issue of transport capacity of a randomly deployed wireless network under random (c, f ) channel assignment was considered by us in [1]. We showed in [1] that when the number of available channels is c = O(logn), and each node has a single interface assigned a random f subset of channels, the capacity is Ω(W √ f cn logn ) and O(W √ prnd n logn ), and conjectured that capacity is Θ(W √ prnd n logn ). We now present a lower bound construction that yields capacity Ω(W √ prnd n logn ) for all c = O(logn) and 2 ≤ f ≤ c. This establishes the capacity under random (c, f ) assignment as Θ(W √ prnd n logn ). The surprising implication of this result is that when f = Ω( √ c), random (c, f ) assignment yields capacity of the same order as attainable via unconstrained switching. Also of interest is the routing/scheduling procedure we utilize to achieve capacity, which marks a significant point of departure from the construction used to obtain the previous lower bound of Ω(W √ f cn logn ). This procedure 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 routing/scheduling procedures.