On the Connectivity and Multihop Delay of Ad Hoc Cognitive Radio Networks

TL;DR

This paper studies the multihop delay in ad hoc cognitive radio networks, revealing how connectivity type and spectrum availability influence delay scaling with distance, using advanced probabilistic theories.

Contribution

It establishes the scaling laws of multihop delay in cognitive radio networks considering spectrum availability and connectivity, highlighting differences between instantaneous and intermittent connectivity.

Findings

Delay is independent of distance in instantaneously connected networks.

Delay scales linearly with distance in intermittently connected networks.

Small propagation delays significantly reduce delay in instantaneously connected networks.

Abstract

We analyze the multihop delay of ad hoc cognitive radio networks, where the transmission delay of each hop consists of the propagation delay and the waiting time for the availability of the communication channel (i.e., the occurrence of a spectrum opportunity at this hop). Using theories and techniques from continuum percolation and ergodicity, we establish the scaling law of the minimum multihop delay with respect to the source-destination distance in cognitive radio networks. When the propagation delay is negligible, we show the starkly different scaling behavior of the minimum multihop delay in instantaneously connected networks as compared to networks that are only intermittently connected due to scarcity of spectrum opportunities. Specifically, if the network is instantaneously connected, the minimum multihop delay is asymptotically independent of the distance; if the network is only intermittently connected, the minimum multihop delay scales linearly with the distance. When the propagation delay is nonnegligible but small, we show that although the scaling order is always linear, the scaling rate for an instantaneously connected network can be orders of magnitude smaller than the one for an intermittently connected network.