在本論文中，我們考慮在感知無線電網路中的多通道交會問題，並且假設兩個使用者同時間跳到共同一個通道時會成功交會的機率會根據通道的狀態。我們用隨機程序去代表在任意時間下所有的通道狀態。對兩個使用者而言，他們只能夠知道通道狀態的分布狀況，並不能夠看到在任一時間下通道確切的狀態為何。

我們考慮兩個通道模型:(i)快速時變通道模型 (ii)慢速時變通道模型。在快速時變通道模型中，假設在不同的時間下，通道狀態是獨立地且相同地分布。在慢速時變通道模型中，假設通道狀態隨著時間保持不變。兩個使用者會依照每個通道的選擇機率在每個時間下隨機地選擇通道，透過這個交會方法，我們證明在快速時變模型中，能夠得到最小交會時間期望值所需的最佳通道選擇策略就是讓使用者在每個時間總是去選擇狀態最好的通道，這樣的交會方法又稱為單一通道選擇策略。

然而對慢速時變通道模型來說，要找到一個最佳的通道選擇策略是非常困難的事情。因此在假設所有通道狀態皆符合可交換性之下，我們透過優化排序推導出交會時間期望值的上下界。根據交會時間期望值的上下界，我們提出幾個近似演算法。最後透過許多的數值運算去驗證提出的近似演算法計算得到的結果確實能夠接近最佳解。

In this paper, we consider the multichannel rendezvous problem in cognitive radio networks (CRNs) where the probability that two users hopping on the same channel have a successful rendezvous is a function of channel states.
The channel states are modelled by stochastic processes with joint distributions known to users. However, the exact state of a channel at any time is not observable. We consider two channel models: (i) the fast time-varying channel model (where the channel states are assumed to be independent and identically distributed in each time slot), and (ii) the slow time-varying channel model (where the channel states remain unchanged over time).
Among the classes of the blind rendezvous policies that randomly hop on channels according to certain channel selection probabilities, we show the optimal channel selection policy that minimizes the expected time-to-rendezvous (ETTR) is the single selection policy that hops on the ``best'' channel all the time in the fast time-varying channel model. However, for the slow time-varying channel model, it is much more difficult to find the optimal channel selection policy. By using the majorization ordering, we derive a lower bound and an upper bound for the ETTR under the assumption that the channel states are exchangeable random variables.
Bases on these bounds, we then propose various approximation algorithms.The effectiveness of our approximation algorithms are further verified by extensive numerical experiments.

Contents 1
List of Figures 2
1 Introduction 3
2 System Model 7
3 The Fast Time-Varying Channel Model 9
4 The Slow Time-Varying Channel Model 11
4.1 A slow time-varying channel model with two channels 12
4.2 Change of probability vectors 18
4.3 Majorization ordering and bounds for the ETTR 20
4.4 Approximation solutions 23
5 Conclusion 37

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