Capacity of Multi-Channel Wireless Networks with Random Channel Assignment: A Tight Bound

This paper studies how the capacity of a static multichannel network scales as the number of nodes, n, increases. Gupta and Kumar have determined the capacity of single channel networks, and those bounds are applicable to multichannel networks as well, provided each node in the network has a dedicated interface per channel. In this work, we establish the capacity of general multichannel networks wherein the number of interfaces, m, may be smaller than the number of channels, c. We show that the capacity of multichannel networks exhibits different bounds that are dependent on the ratio between c and m. When the number of interfaces per node is smaller than the number of channels, there is a degradation in the network capacity in many scenarios. However, one important exception is a random network with up to O (log n) channels, wherein the network capacity remains at the Gupta and Kumar bound of Θ