A Quasi-random Algorithm for Anonymous Rendezvous in Heterogeneous Cognitive Radio Networks

The multichannel rendezvous problem that asks two secondary users to rendezvous on a common available channel in a cognitive radio network (CRN) has received a lot of attention lately. Most rendezvous algorithms in the literature focused on constructing channel hopping (CH) sequences that guarantee finite maximum time-to-rendezvous (MTTR). However, these algorithms perform rather poorly in terms of the expected time-to-rendezvous (ETTR) even when compared to the simple random algorithm. In this paper, we propose the quasi-random (QR) CH algorithm that has a comparable ETTR to the random algorithm and a comparable MTTR to the best bound in the literature. Our QR algorithm does not require the unique identifier (ID) assumption and it is very simple to implement in the symmetric, asynchronous, and heterogeneous setting with multiple radios. In a CRN with $N$ commonly labelled channels, the MTTR of the QR algorithm is bounded above by $9 M \lceil n_1/m_1 \rceil \cdot \lceil n_2/m_2 \rceil$ time slots, where $n_1$ (resp. $n_2$) is the number of available channels to user $1$ (resp. 2), $m_1$ (resp. $m_2$) is the number of radios for user $1$ (resp. 2), and $M=\lceil \lceil \log_2 N \rceil /4 \rceil *5+6$. Such a bound is only slightly larger than the best $O((\log \log N) \frac{n_1 n_2}{m_1 m_2})$ bound in the literature. When each SU has a single radio, the ETTR is bounded above by $\frac{n_1 n_2}{G}+9Mn_1n_2 \cdot (1-\frac{G}{n_1 n_2})^M$, where $G$ is the number of common channels between these two users. By conducting extensive simulations, we show that for both the MTTR and the ETTR, our algorithm is comparable to the simple random algorithm and it outperforms several existing algorithms in the literature