A Combinatorial Approach for Frequency Hopping Schemes

Abstract

In a frequency hopping (FH) scheme users communicate simultaneously using FH sequences defined on the same set of frequency channels. An FH sequence specifies the frequency channel to be used as communication progresses. An inherent problem for an FH scheme is interference, unintentional and intentional. Much of the existing research on the performance of FH schemes in the presence of interference is based on either pairwise mutual or adversarial interference (jamming), but not both. In this thesis, we develop a new model for evaluating the performance of an FH scheme with respect to both group-wise mutual interference and jamming, bearing in mind that more than two users may be transmitting simultaneously in the presence of a jammer.We then analyse existing constructions of FH schemes in the new model proposedin this thesis. The FH schemes considered are optimal in the well-known Lempel-Greenberger or Peng-Fang bounds. We estimate the group-wise mutual interference using pairwise mutual interference to determine the performance of these FH schemes. Further, we note that these FH schemes do not withstand a jammer for a long period of time.An FH scheme in which we can determine the minimum number of places an FHsequence can be successfully used in the presence of mutual interfering FH sequences can be designed from a cover-free code. We study and specify a jammer model for cover-free codes. We examine necessary and desirable additional properties of cover-free codes that can mitigate against jamming. We conclude that while MDS codes are ideal cover-free codes for mitigating against jamming, MDS codes also do not withstand a jammer for an extended period.Finally, we propose an ecient and secure FH scheme. We consider the use of pseudo-randomness in an FH scheme based on Latin squares and how it affects the resistance of an FH scheme against a jammer. We conclude that in order to have a guarantee of transmission, as well as withstand a jammer for a long time, FH schemes should minimize group-wise mutual interference and possess some form of pseudo-randomness