Academic Papers

A New Class of Optimal Frequency Hopping Sequences with Applications to Secure Communication Waveforms

Frequency hopping (FH) is a spread spectrum technique used to protect against detection, interception, location, and jamming. FH is an interference mitigation strategy wherein the transmission frequency is changed in a seemingly random manner, occupying a given frequency band for a very short amount of time. FH systems provide low probability of intercept (LPI) mainly by using large hop bandwidths. Using large portions of spectrum is beneficial because it makes it potentially more difficult for a third party to monitor the entire bandwidth at once. 

A popular way to implement FH is through the use of specially designed pseudorandom sequences known only to intended users. The pseudorandom sequences must be designed according to certain mathematical properties in order to guarantee that an attacker cannot learn the hopping sequence and defeat the protection. Prior research has revealed an interesting equivalence relation between mathematically optimal FH sequences and partitioned difference families in cyclic groups. 

Using this relationship, we provide a method that yields new families of optimal FH sequences, inequivalent to known ones. The resulting FH sequence families contain several members whose underlying pseudorandom sequences (waveforms) possess high linear span, thereby making them desirable for secure communications. For periodic sequences, linear span is the standard measure of its predictability. The higher the linear span, the harder it is for an adversary to jam or intercept messages. To intercept a waveform, one must capture enough to fully reproduce the sequence. If the linear span is L, then the entire sequence can be determined by 2L successive elements of it. So after capturing 2L elements, an attacker can fully reproduce the waveform. If they can reproduce it, they can jam it. Our proof-of-concept research shows exponential growth (Fibonacci in dimension d of the underlying m-sequences/LFSR) of the linear span, which is a significant increase in security over the state of the art (SOA). As larger values of d are used, the security benefits of our sequences become more and more pronounced in comparison with SOA.

• Year: 2023
• Tag: Wireless communication, Geometry, Time-frequency analysis, Bandwidth, Spread spectrum communication, Electromagnetic spectrum, Security
• Author: K. T. Arasu, Michael R. Clark, Timothy M. McManus
• Released: 2023 33rd International Telecommunication Networks and Applications Conference