Due to the changing network topology and the time and location varying spectrum availability in Cognitive Radio Networks (CRNs), there is a need of on-demand searching for a control traffic channel by CR users in order to be able to initiate a communication. This neighborhood discovery phase, also referred to as a rendezvous (RDV) phase, is challenging due to the dynamics of CRNs. There are a number of different proposed solutions (pseudo-random or systematic approaches such as quorum systems) to tackle this issue, however, not so many elaborate on the asynchronous character of CRNs, and even less taking into account channel heterogeneity in terms of quality. In this study, on the one hand, we propose a novel quorum system -based neighborhood discovery protocol, which operates on channels having different priorities, on the other hand, we perform an analysis of the effect of asynchronism on the proposed protocol. We analyze the behavior of the protocol in terms of rendezvous opportunities, time-to-rendezvous, and the measured error margins for both, for different asynchronous offsets. We show that an asynchronism can bring noticeable profits over the slot synchronized case.