[Paper Review] A Quasi-random Algorithm for Anonymous Rendezvous in Heterogeneous Cognitive Radio Networks

Cheng‐Shang Chang, Yeh-Cheng Chang+1 more|arXiv (Cornell University)|Feb 19, 2019

Cognitive Radio Networks and Spectrum Sensing19 references4 citations

TL;DR

This paper proposes a quasi-random (QR) channel-hopping algorithm for anonymous rendezvous in heterogeneous cognitive radio networks, enabling symmetric, asynchronous, and multi-radio operation without unique identifiers. The algorithm achieves expected time-to-rendezvous (ETTR) comparable to random algorithms and maximum time-to-rendezvous (MTTR) close to the theoretical lower bound, outperforming existing schemes in both metrics under diverse network conditions.

ABSTRACT

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 $9 M \lceil n_1/m_1 ceil \cdot \lceil n_2/m_2 ceil$ 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 $M=\lceil \lceil \log_2 N ceil /4 ceil *5+6$. 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.

Motivation & Objective

• To address the limitations of existing rendezvous algorithms in cognitive radio networks that exhibit poor expected time-to-rendezvous (ETTR) despite good maximum time-to-rendezvous (MTTR) bounds.
• To design a simple, anonymous, and robust channel-hopping scheme suitable for symmetric, asynchronous, and heterogeneous environments with multiple radios.
• To achieve ETTR performance comparable to the random algorithm while maintaining MTTR close to the best-known theoretical bound in the literature.
• To eliminate reliance on unique identifiers (IDs), enhancing resilience against jamming attacks in distributed settings.

Proposed method

• The QR algorithm uses a deterministic yet quasi-random sequence generation based on a modified 4B5B encoding scheme to produce channel-hopping patterns with low correlation and uniform coverage.
• It ensures that each secondary user (SU) generates a sequence that maximizes the probability of overlapping on a common available channel, even without prior synchronization or unique IDs.
• The algorithm bounds the MTTR by analyzing the worst-case overlap using parameters: $ n_1, n_2 $ (available channels per SU), $ m_1, m_2 $ (number of radios), and $ M = \lceil \lceil \log_2 N \rceil / 4 \rceil \cdot 5 + 6 $.
• The ETTR is derived using probabilistic analysis, showing it is bounded by $ \frac{n_1 n_2}{G} + 9M n_1 n_2 \cdot \left(1 - \frac{G}{n_1 n_2}\right)^M $, where $ G $ is the number of common channels.
• The scheme is designed to be oblivious, meaning no learning from failed rendezvous attempts, and is compatible with multi-radio operation.
• The algorithm is evaluated via extensive simulations across varying network parameters: number of channels, common channels, and radios.

Experimental results

Research questions

• RQ1 Can a rendezvous algorithm achieve ETTR performance comparable to the simple random algorithm while maintaining a bounded MTTR in heterogeneous, anonymous, and asynchronous cognitive radio networks?
• RQ2 How does the proposed QR algorithm perform in terms of MTTR and ETTR when compared to existing state-of-the-art algorithms like GCR, AMRR/M, FMRR, and JS/I?
• RQ3 To what extent does the absence of unique identifiers affect the performance and robustness of the rendezvous algorithm?
• RQ4 How do the number of available channels, common channels, and number of radios influence the MTTR and ETTR of the QR algorithm?

Key findings

• The QR algorithm achieves an ETTR that is nearly identical to the random algorithm across all simulation settings, significantly outperforming deterministic schemes in expected performance.
• The MTTR of the QR algorithm is bounded above by $ 9M \lceil n_1/m_1 \rceil \cdot \lceil n_2/m_2 \rceil $, which is only slightly larger than the best-known $ O((\log \log N) \frac{n_1 n_2}{m_1 m_2}) $ bound in the literature.
• In simulations with fixed common channels ($ G=2 $), the MTTR of QR remains comparable to GCR, AMRR/M, FMRR, and random algorithms, while significantly outperforming JS/I, which has $ O(N^3) $ MTTR.
• When the number of common channels scales with $ N $, the QR algorithm maintains low ETTR and MTTR, with ETTR remaining nearly indistinguishable from the random algorithm.
• Increasing the number of radios ($ m_1, m_2 $) consistently reduces both MTTR and ETTR, confirming the positive impact of multi-radio capability.
• The algorithm demonstrates robustness in heterogeneous settings without requiring unique identifiers, making it resilient to jamming and suitable for real-world deployment.