Asynchronous channel hopping systems from difference sets

作者：Chen, Xiaotian; Zhou, Yue^*

来源：Designs, Codes and Cryptography, 2017, 83(1): 179-196.

DOI：10.1007/s10623-016-0221-8

• Difference set
• Hopping sequence
• Projective plane
• Blind rendezvous
• Cognitive radio network

In cognitive radio networks, the process for any two unlicensed (secondary) users (SU) to establish links through a common channel is called a rendezvous. It is hard to employ a common control channel to solve the rendezvous problem, because of the bottleneck of the single control channel. Asynchronous channels hopping (ACH) systems have been proposed and investigated to guarantee rendezvous without requirement of global synchronization and common control channels. An ACH system with N channels can be mathematically interpreted as a set of sequences of the same period T on the alphabet satisfying certain rotation closure properties. For each , each and any two distinct sequences , in an ACH system H, if there always exists i such that the i-th entries of and are both identical to j where denotes the cyclic shift of by l, then H is called a complete ACH system, which guarantees rendezvous between any two SUs who share at least one common channel. In this paper, we prove some properties of such systems. Moreover, we investigate the complete ACH systems, in each of which all SUs repeat the same (global) sequence associated with the system. One challenging research problem is to construct such ACH systems of period such that is as small as possible. By applying mathematical tools such as group rings and (relative, relaxed) difference sets from combinatorial design theory, we obtain two constructions of them in which respectively. Finally, we also present a simple and powerful approach to combining known ACH systems to produce new ones.

• 出版日期2017-4
• 单位中国人民解放军国防科学技术大学