# Decentralized Blind Spectrum Selection in Cognitive Radio Networks Considering Handoff Cost
## 3 Problem Formulation and Policies
Secondly, the \(k\)th-UCB1 policy can distinguish the order-optimal arm from other arms more precisely than the \(\varrho^{\text{PRE}}\) policy by comparing the action histogram of Figure 3a,b, in which the number of arm 9 selected by the \(k\)th-UCB1 policy is smaller than that of policy \(\varrho^{\text{PRE}}\). The regret of policy SL(K) in Figure 3c is largest, which means it has the largest leading constant in the logarithmic order. We also investigated the regret of the three policies with varying handoff cost \(H\) as shown in \[\sum_{t=1}^{T}S^{*}(t)=T\sum_{i\in\mathcal{O}_{M}^{*}}\Theta_{i}. \tag{2}\]1 As handoff cost is meaningless when the value is larger than 0.5, an \(H\) between 0 and 0.5 is chosen. From Figure 4, we see that the regret increases as \(H\) increases. Moreover, the growth rates of the three policies are all small when \(H<0.3\), which shows that these policies perform well. However, they become considerably large when \(H>0.3\). Intuitively, this is because a large \(H\) causes the arms to become indistinguishable. ## 5 Conclusions

In this work, we studied the blind spectrum selection in a decentralized cognitive radio networks in the MAB framework considering the handoff delay as a fixed handoff cost. We formulate this problem and investigate three representative policies and prove the uniform goodness of these policies for our scenario. Through simulation, we further show that, despite the inclusion of the fixed handoff cost, \(\varrho^{\text{PRE}}\), SL(K), and \(k\)th-UCB1 achieve the same asymptotic performance as they do without handoff cost. Through comparison of these three policies, we found that the \(k\)th-UCB1 policy has better overall performance. **Acknowledgments: This work was supported by the International S & T cooperation Program of China under grand No. 2013 DFA12460 and partially supported by the Zhejiang Provincial Natural Science Foundation of China under Grant No. LY16F010015 and by a grant from Public Projects of Wenzhou Science & Technology Bureau (Grant No. G20150020 & No. G20160007). **

**Author Contributions: [PERSON] and [PERSON] conceived and designed the experiments; [PERSON] and [PERSON] analyzed the data; [PERSON] and [PERSON] wrote the paper. **

**Conflicts of Interest: The authors declare no conflict of interest. **

\[\sum_{t=1}^{T}S^{*}(t)=T\sum_{i\in\mathcal{O}_{M}^{*}}\Theta_{i}. \tag{2}\]2 The regret with handoff cost (\(H\)). ## References

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