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Uncoordinated Frequency Hopping (UFH) and Collaborative UFH (CUFH) are viable countermeasures for jamming attacks without dependency on pre-shared secret keys. In this work we analytically evaluate their communication efficiency in large-scale networks, where the number of nodes n is large and may even exceed the number of channels C. Such a large-system analysis is pertinent to emerging complex networks and systems, and helps us reveal the scaling behavior of the system performance with respect to the network size and other important system parameters. In particular, we show that the average network broadcast delay incurred by UFH scales as O(Clnn) , while that incurred by CUFH scales as O(lnn) when C=o(lnn). This demonstrates a significant improvement achieved by cooperative relays and the feasibility of UFH-based schemes in large-scale networks. In large-scale networks, the number of relays in CUFH needs to be carefully controlled for best performance. In this study the optimal number of relays in CUFH is derived such that the packet reception rate is maximized, and the optimal cooperation gain achieved by CUFH over UFH is quantified. To facilitate the implementation of CUFH, a suboptimal protocol, CUFH-p, is proposed, which achieves the optimal cooperation gain asymptotically. As an intermediate step, we also study an ideal cooperative network, whose results may be of independent interest. Our analytical results are well substantiated by simulations, and our analytical methodology applies largely to general anti-jamming broadcast in multi-channel networks.
Date of Publication: Oct. 2012