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In a frequency hopping (FH) scheme users communicate simultaneously using FHsequences defined on the same set of frequency channels. An FH sequencespecifies the frequency channel to be used as communication progresses. Much ofthe research on the performance of FH schemes is based on either pairwisemutual interference or adversarial interference but not both. In this paper, weevaluate the performance of an FH scheme with respect to both group-wise mutualinterference and adversarial interference (jamming), bearing in mind that morethan two users may be transmitting simultaneously in the presence of a jammer.We establish a correspondence between a cover-free code and an FH scheme. Thisgives a lower bound on the transmission capacity. Furthermore, we specify ajammer model and consider what additional properties a cover-free code shouldhave to resist the jammer. We demonstrate that a purely combinatorial approachis inadequate against such a jammer, but that with the use of pseudorandomness,we can have a system that has high throughput as well as security againstjamming.

A Combinatorial Model of Interference in Frequency Hopping Schemes