On the Capacity of Ad Hoc Networks Under Random Packet Losses

We consider the problem of determining asymptotic bounds on the capacity of a random ad hoc network. Previous approaches assumed a link layer model in which if a transmitter-receiver pair can communicate with each other, i.e., the signal to interference and noise ratio (SINR) is above a certain threshold, then the transmitted packet is received error-free by the receiver thereby. Using this model, the per node capacity of the network was shown to be $Theta left ( {{ 1}over { sqrt {nlog {n}}}}right )$. In reality, for any finite link SINR, there is a nonzero probability of erroneous reception of the packet. We show that in a large network, as the packet travels an asymptotically large number of hops from source to destination, the cumulative impact of packet losses over intermediate links results in a per-node throughput of only $Oleft ( {{ 1}over { n}}right )$ under the previously proposed routing and scheduling strategy. We then propose a new scheduling scheme to counter this effect. The proposed scheme provides tight guarantees on end-to-end packet loss probability, and improves the per-node throughput to $Omega left ( {{ 1}over { sqrt {n} left ({log {n}}right )^{{ alpha {+2}}over { 2(alpha -2)}}}}right )$ where $alpha >2$ is the path loss exponent.