在無線感知網路中，多通道會面的問題一直是至今最炙手可熱的題目之一，而其中一項最具有挑戰性的環境設置莫過於在異質的無線感知網路中的遺忘式會面問題，囊括了以下四項特徵：使用者之間並沒有特定的角色之分、使用者本身已知的時間沒有同步、使用者可能有不同的可用頻道集合、每個頻道並沒有統一的標籤。至今大部分的文獻多著重在於實現最大條件會面時間的決定性區間，卻在平均會面時間表現的要比隨機演算法來的要差，而這樣的結果主要是因為這些文獻提出的演算法很多都包含了停留模式。在這篇論文中，我們在應對遺忘式會面問題時將最大條件會面時間和平均會面時間都納入考慮，而為了要確保在一定時間下能夠會面，我們做出了以下兩個假設：(A1) 至少存在一個頻道是所有使用者可以使用的；(A2) 每個使用者都有一個唯一的編號。首先，我們提出了新版本的強對稱映射法來對使用者編號做編碼以加速會面的過程，包括兩種既有效率又簡易的編碼方案被推出，一是使用C-transform，一是使用已存在的4B5B 編碼。基於這種新版本的強對稱映射編碼法，我們提出了雙質數模數時鐘演算法來應對兩個使用者的會面問題，這個演算法除了與隨機演算法有非常近似的平均會面時間之外，在最大條件會面時間也能和現有文獻旗鼓相當。我們也將其推廣成兩種可以用在多使用者會面問題的雙質數模數時鐘演算法，包括使用者在會面後會走在一起的聚合演算法，以即使用者在會面後會分頭尋找其他人的發散演算法。其中，在多使用者會面問題我們有項十分有趣的發現，發散演算法在某些情況下不一定會比聚合演算法還來的好，這是與目前文獻上的一般認知是相悖的。

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 (i) there are no distinguishable roles of users, (ii) users' clocks are not synchronized, (iii) users may have different available channel sets, and (iv) 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-to-rendezvous (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 two-prime 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.

Contents 1
List of Figures 4
1 Introduction 5
2 Two-user rendezvous 12
2.1 Deterministic modular clock algorithm . . . . . . . . . . . . . . . . . . . 14
2.2 Strong symmetrization mapping . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 4B5B encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Two-prime modular clock algorithm . . . . . . . . . . . . . . . . . . . . . 24
3 Multiuser rendezvous 31
4 Experiments 36
4.1 Simulation settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2 Two-user rendezvous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3 Multiuser rendezvous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5 Conclusion

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