Efficient Encoding of User IDs for Nearly Optimal Expected Time-To-Rendezvous in Heterogeneous Cognitive Radio Networks

The multichannel rendezvous problem in cognitive radio networks (CRNs) has been a hot research topic lately. One of the most challenging settings of the multichannel rendezvous problem is the oblivious rendezvous problem in heterogeneous CRNs, where: 1) there are no distinguishable roles of users; 2) users' clocks are not synchronized; 3) users may have different available channel sets; and 4) there is no universal labelling of the channels. Most existing works in the literature focus on achieving deterministic bounds for the maximum conditional time-to-rendezvous (MCTTR) and perform poorly (in comparison with the random algorithm) for the expected time-torendezvous (ETTR) due to the "stay" modes in these works. In this paper, we tackle the oblivious rendezvous problem by taking both MCTTR and ETTR into consideration. In order to have guaranteed rendezvous, we only make two assumptions: (A1) there is at least one common available channel and (A2) there is a unique ID for each user. We first propose a new class of strong symmetrization mappings to encode user IDs for speeding up the rendezvous process. Two efficient and yet simple encoding schemes are proposed by utilizing the C-transform and the existing 4B5B encoding. Based on the new class of strong symmetrization mappings, we propose the twoprime modular clock algorithm for the two-user rendezvous problem. The ETTR of our algorithm is almost the same as that of the random algorithm and its MCTTR is also comparable to the best existing bound. We also extend the two-prime modular clock algorithm for multiuser rendezvous by proposing the stick together algorithm and the spread out algorithm. One interesting finding for the multiuser rendezvous problem is that the spread out algorithm is not always better than the stick together algorithm as commonly claimed in the literature.