Toeplitz-structured Sequences for Rendezvous in Dynamic Spectrum Access

This work addresses the problem of asynchronous rendezvous in dynamic spectrum access (DSA) networks. Considering channel-hopping techniques in this context, two (or more) users scan through a list of available channels as to detect and establish communication with each other. In this work, we propose a new rendezvous sequence based on the vectorization of a Toeplitz matrix built from a list of channels available for rendezvous. We provide results showing that the proposed sequence ensures rendezvous, has low mean time to rendezvous (TTR) for two users, and a bounded maximum TTR. For the proposed sequence, we show that the mean TTR, maximum TTR, and the probability of rendezvous on each of the available channels have exact closed-form expressions.