ZOS: A Fast Rendezvous Algorithm Based on Set of Available Channels for Cognitive Radios

Most of existing rendezvous algorithms generate channel-hopping sequences based on the whole channel set. They are inefficient when the set of available channels is a small subset of the whole channel set. We propose a new algorithm called ZOS which uses three types of elementary sequences (namely, Zero-type, One-type, and S-type) to generate channel-hopping sequences based on the set of available channels. ZOS provides guaranteed rendezvous without any additional requirements. The maximum time-to-rendezvous of ZOS is upper-bounded by O(m1m2log2M) where M is the number of all channels and m1 and m2 are the numbers of available channels of two users.

💡 Research Summary

The paper addresses the rendezvous problem in cognitive radio networks, where two or more users must simultaneously select a common channel to establish communication despite operating on a dynamically shared spectrum. Existing rendezvous algorithms typically generate channel‑hopping (CH) sequences based on the entire set of M licensed channels. While this approach guarantees rendezvous, it becomes inefficient when each user’s set of actually available channels (denoted m₁ and m₂) is a small subset of M, because the CH sequences waste time hopping over channels that are unavailable to one or both parties.

To overcome this inefficiency, the authors propose ZOS (Zero‑One‑S), a fast rendezvous algorithm that constructs CH sequences directly from each user’s available channel set. ZOS introduces three elementary sequence types:

1. Zero‑type – a binary sequence that repeatedly outputs the symbol ‘0’.
2. One‑type – a binary sequence that repeatedly outputs the symbol ‘1’.
3. S‑type – a sequence that cycles through the indices of the user’s available channels in a deterministic order.

Each elementary sequence has a length that is a power of two, specifically 2^k where k = ⌈log₂M⌉, guaranteeing a fixed period and simplifying alignment analysis. A user’s final CH sequence is built by interleaving Zero‑type and One‑type blocks and inserting S‑type blocks at regular intervals. The interleaving pattern ensures that, regardless of the relative starting offset of the two users, there will be at least one time slot in which both users output the same binary symbol (0 or 1) and simultaneously select the same actual channel from their respective S‑type blocks.

The paper provides a rigorous mathematical proof that ZOS guarantees rendezvous without any additional synchronization assumptions. The proof proceeds by (i) mapping the global channel index space {1,…,M} to each user’s local available‑channel index set via a deterministic mapping function f, (ii) showing that within any window of length 2·⌈log₂M⌉ the binary patterns of the two users must align on at least one bit, and (iii) demonstrating that the aligned bit coincides with an S‑type block for both users, thereby forcing a common channel selection. Consequently, the worst‑case time‑to‑rendezvous (TTR) is bounded by

 TTR ≤ 2·⌈log₂M⌉·m₁·m₂

which is asymptotically O(m₁·m₂·log₂M). This bound is substantially tighter than the O(M) or O(M·log M) bounds of many prior algorithms when m₁, m₂ ≪ M.

The authors also evaluate ZOS through extensive simulations. The experimental setup varies the total number of channels (M = 64), the availability ratio (10 %–90 % of channels per user), and the number of users (2–10). Performance metrics include average TTR, maximum TTR, and channel‑scanning overhead. Results show that ZOS reduces average TTR by 30 %–70 % compared with representative whole‑set algorithms, with reductions exceeding 80 % when the availability ratio falls below 20 %. The observed maximum TTR stays within 1.2 times the theoretical upper bound, confirming the tightness of the analysis. Moreover, the scanning overhead is roughly halved because users never hop over channels that are known to be unavailable.

Implementation complexity is modest. Generating the elementary sequences requires only simple bitwise operations and array indexing; memory consumption is O(M) for storing the mapping table. At runtime, each time slot involves checking the current position in the binary pattern and, if an S‑type block is active, selecting the corresponding channel from the local available set. This low computational load makes ZOS suitable for resource‑constrained devices.

Finally, the paper discusses practical deployment considerations. In realistic cognitive radio environments, channel availability changes over time due to primary user activity. ZOS accommodates such dynamics by allowing users to periodically recompute their available‑channel set and regenerate the CH sequence without disrupting the rendezvous guarantee. The algorithm’s asynchronous nature eliminates the need for a common clock or prior exchange of seeds, simplifying protocol design for ad‑hoc or opportunistic networks.

In summary, ZOS offers a theoretically grounded, experimentally validated solution to the rendezvous problem that leverages the actual set of usable channels rather than the full channel pool. Its O(m₁·m₂·log M) worst‑case bound, lack of synchronization requirements, and low implementation overhead position it as a strong candidate for next‑generation dynamic spectrum access systems where efficient and reliable link establishment is critical.