Systematic construction of common channel hopping rendezvous strategies in cognitive radio networks

EURASIP Journal on Wireless Communications and Networking

Table 1 Summary of representative rendezvous protocols

Protocol	ETTR	MTTR	MCTTR	Asymmetric	Maximum	Strategy
				model support	rendezvous diversity
ACH(RB) [17]	Unknown	Unknown	Unknown	\(\checkmark \)	\(\checkmark \)	RB
A-MOCH [15]	Unknown	N ²−N+1	N ²	\(\checkmark \)	\(\checkmark \)	RB
SRB [18]	\(\frac {N-1}{2}\)	N−1	Unknown			RB
ARCH [19]	Unknown	2N−1^⋆	N ^2⋆	\(\checkmark \)	\({\checkmark }^{\star }\)	RB
ASYN-ETCH [21]	\(\frac {2N^{2}+N}{N-1}\)	Unknown	Unknown	\(\checkmark \)	\(\checkmark \)	Hybrid
GOS [22]	\(\frac {N^{4}+2N^{2}+6N-3}{3N^{2}+3N}\)	N(N+1)	Unknown			CS
MC [22]	\(\frac {2P^{2}}{P-1}\)	Unknown	Unknown			Hybrid
MMC [22]	Unknown	Unknown	Unknown	\(\checkmark \)		Hybrid
DRSEQ [23]	Unknown	2N+1	Unknown			CS
CRSEQ [24]	Unknown	Unknown	P(3P−1)	\(\checkmark \)		CS
RW2 [25]	\((N-1)(\ln ^{n}+\frac {1}{2})\)	n(N−1)	2n(N+1−G)(N−1)	\(\checkmark \)		Hybrid
JS [26]	\(\frac {5P}{3}+3\)	3P	3N P(P−G)+3P	\(\checkmark \)	\(\checkmark \)	Hybrid
EJS [27]	\(\frac {3P}{2}+3\)	4P	4P(P+1−G)	\(\checkmark \)	\(\checkmark \)	Hybrid
FRCH [16]	Unknown	2N+1	N(2N+1)^⋆⋆	\(\checkmark \)		CS
SSB [28]	\(\frac {2(N-1)^{2}}{2N-1}\)	2N−2	(N−1)(2N−1)	\(\checkmark \)		CS
RPS ^⋆⋆⋆ [29]	(1)	(2)	Unknown	\(\checkmark \)	\(\checkmark \)	Hybrid

N, number of available channels. P, smallest prime greater or equal than N for MC and CRSEQ, but N+1 for JS and EJS. n, number of nodes in the network. G, number of common available channels for two-user scenario. ^⋆These results are valid when N is even, please see Table one in [19] for further details. ^⋆⋆This expression is only valid for some values of N, please see [16] for further details. ^⋆⋆⋆In the RPS algorithm, each SU is equipped with more than one radio. (1): ETTR \( = \left \lceil \frac {P}{\max {(u,v)}-1}\right \rceil +\frac {\left (\left \lceil \frac {P}{\max {(u,v)}-1}\right \rceil -1\right)^{2}}{2\left \lceil \frac {P}{\min {(u,v)}-1}\right \rceil }\). (2): MTTR\( \,= \left \lceil 2\left \lceil \frac {P}{\max {(u,v)}}\right \rceil -1\right \rceil \). u,v, number of radios of SUs attempting to rendezvous. ARCH(RB), asynchronous channel hopping (role based). A-MOCH, asynchronous maximum overlapping channel hopping. SRB, simple role-based. ARCH, asynchronous rendezvous channel hopping. ASYN-ETCH, asynchronous efficient channel hopping. GOS, generated orthogonal sequences. MC, modular clock. MMC, modified modular clock. DRSEQ, deterministic rendezvous sequence. CRSEQ, channel rendezvous sequence. RW2, ring walk 2. JS, jump stay. EJS, enhanced jump stay. FRCH, fast rendezvous channel hopping. SSB, short sequence-based. RPS, role-based parallel sequence.