On the capacity of κ-MPR wireless networks

The capacity of wireless ad hoc networks is mainly restricted by the number of concurrent transmissions. Recent studies found that multi-packet reception (MPR) can increase the number of concurrent transmissions and improve network capacity. This paper studies the capacity of 2-D wireless networks wherein each node can decode at most k simultaneous transmissions within its receiving range. We call such networks k-MPR wireless networks. For comparison, we call traditional networks 1-MPR wireless networks. Suppose that the number of nodes in a wireless network is n and each node can transmit at W bits/sec. For arbitrary k-MPR wireless networks, we show that when k = O(n), the capacity gain over 1-MPR networks is Theta(radickappa). When k = Omega(n), the capacity is Theta(W n) bit-meters/sec and the network is scalable. For random k-MPR wireless networks, we show that when k = O(radic(log n)), the capacity upper bound and lower bound match and the capacity gain over 1-MPR networks is Theta(kappa). When k = Omega(radic(log n)), even the lower bound has a capacity gain of Theta(radic(log n)) over 1-MPR networks. From these results, we conclude that the main constraints for k-MPR wireless networks to utilize MPR ability are the limited number of transmitters and the limited number of flows served by each node.