Asynchronous Channel-Hopping Sequences With Maximum Rendezvous Diversity and Asymptotic Optimal Period for Cognitive-Radio Wireless Networks

In this paper, two new families of asynchronous channel-hopping (CH) sequences—Symmetric Maximum-Length CH (SML-CH) Sequences and Relaxed Difference Set (RDS) of Maximum-Length CH (RDSML-CH) Sequences—are constructed. For the first time, the maximum-length sequences (also called as m-sequences) are used to create 2-D CH matrices with a reduced number of “jump” columns. The two new constructions carry the desirable properties of maximum rendezvous diversity (MRD) and even channel use (ECU) and, more importantly, have the shortest periods in their categories of constructions. Another contribution is on the embedment of optical orthogonal codes (OOCs) to eliminate “stay” columns in the RDSML-CH matrices, thus resulting in the first and only family of the asynchronous CH sequences that can asymptotically achieve the theoretical period lower bound. To support the RDSML-CH construction, a new shortened RDS algorithm for creating the OOCs with smaller weight-to-length ratios than the existing ones is proposed. Numerical and simulation analyses show that the two new constructions have a good balance of short period, MRD, ECU, short time-to-rendezvous (TTR) mean, small TTR variance, and short maximum-TTR, thus more suitable for practical CR wireless networks than the existing constructions.