On the Theoretical Gap of Channel Hopping Sequences with Maximum Rendezvous Diversity in the Multichannel Rendezvous Problem
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In the literature, there are several well-known periodic channel hopping (CH) sequences that can achieve maximum rendezvous diversity in a cognitive radio network (CRN). For a CRN with N channels, it is known that the period of such a CH sequence is at least N^2. The asymptotic approximation ratio, defined as the ratio of the period of a CH sequence to the lower bound N^2 when N →∞, is still 2.5 for the best known CH sequence in the literature. An open question in the multichannel rendezvous problem is whether it is possible to construct a periodic CH sequence that has the asymptotic approximation ratio 1. In this paper, we tighten the theoretical gap by proposing CH sequences, called IDEAL-CH, that have the asymptotic approximation ratio 2. For a weaker requirement that only needs the two users to rendezvous on one commonly available channel in a period, we propose channel hopping sequences, called ORTHO-CH, with period (2p +1)p, where p is the smallest prime not less than N.
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