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

摘要

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(log n), and each node has a single interface assigned a random f subset of channels, the capacity is Omega(W x square root of f/cn log n) and O(W x square root of Prnd/n log n), and conjectured that optimal capacity was Theta(W x square root of Prnd/N log n). We now present a lower bound construction that yields capacity Omega(W x square root of Prnd/n log n) whenever f > 10(1 + log 192/5 + log c/f). Thus for values of c and f that satisfy f > 10(1 + log 192/5 + log c/f), the optimal capacity under random (c,f) assignment is proved to be Theta(W x square root of Prnd/n log n). n log n. We conjecture that this would be the case for all 2.