A Combinatorial Model of Interference in Frequency Hopping Schemes

In a frequency hopping multiple access (FHMA) system a set of users communicate simultaneously using frequency hopping sequences defined on the same set of frequency channels. A frequency hopping sequence specifies which channels to use as communication progresses. A set of frequency hopping sequences used in an FHMA is called a frequency hopping scheme (FHS). Much of the research on the performance of FHS is based on either pairwise mutual interference or adversarial interference but not both. In this paper, we evaluate the performance of an FHS with respect to both group-wise mutual interference and adversarial interference (jamming), bearing in mind that more than two users may be transmitting simultaneously in the presence of an adversary. We point out a correspondence between a cover-free code and a frequency hopping scheme. Cover-free codes give a lower bound on the transmission capacity of the FHS. Furthermore, we specify a jammer model and consider what additional properties a cover-free code should have to resist the jammer. We show that a purely combinatorial approach is inadequate against such a jammer, but that with the use of pseudorandomness, we can have a system that has high throughput as well as secure against jamming.