Abstract
In this paper, one family of identification-(ID)-based and one family of non-ID-based asynchronous channel-hopping (CH) sequences are constructed for supporting cognitive-radio wireless networks (CRWNs) in a homogeneous channel setting. The novelty lies in the use of two-dimensional (2-D) algebraic algorithms to properly arrange the linear- and quadratic-congruence sequences in the prime field; channel rendezvous are guaranteed to occur among all the elements (i.e., licensed channels) in at least one of the columns between any two CH matrices. As a result, the new asynchronous CH sequences always have uniform time-to-rendezvous (TTR) structures and satisfy the desirable design criteria of short periods, full degree-of-rendezvous (DoR), and even channel use (ECU). The studies show that the new constructions have the best balance between the full DoR, ECU, short period, small TTR mean and variance, and shortest maximum-time-to-rendezvous (MTTR) and maximum-first-time-to-rendezvous (MFTTR) in their respective categories of constructions. A short period can save memory in small sensors and mobile devices and are suitable for the Internet-of-Things and device-to-device communications. A short MTTR/MFTTR and a small TTR mean/variance can improve the rendezvous frequency and shorten the latency, thus enhancing and stabilizing the throughput.
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