# Decentralized Blind Spectrum Selection in Cognitive Radio Networks Considering Handoff Cost
## 1 Introduction  
In cognitive radio networks (CRNs), secondary users (SUs) may access a potentially large number of frequency bands or channels that are not occupied by primary users (PUs) at given time and space. Therefore, the coexistence of PUs and SUs becomes one of the key challenges while accessing the same part of the spectrum [1]. In an ideal condition, SUs must sense all channels before deciding which channel to access based on accessing strategy. However, in actuality, because of wide-band spectrum and hardware constraints, it is difficult for SUs to sense the entire operating spectrum band (300 GHz) in a given period of time. Although compressive sensing is adopted as a wideband spectrum sensing technology for CRNs to solve this problem [2, 3], little research has been done to implement feasible wide band spectrum sensing, as it is especially difficult to perform compressive sensing when prior knowledge of the primary signals is lacking. In fact, spectrum statistical information as a priori knowledge may not always be separable in a decentralized cognitive radio network. Hence, the blind sub-Nyquist wideband sensing is still an open issue in the field of compressive sensing for CRNs [4]. Some efforts [5] have been made to solve this problem. Cognitive compressive sensing has been formulated as a restless multi-armed bandit (rMAB) problem, which makes compressive sensing adaptive and cognitive.  
In this paper, we investigate the blind spectrum selection problem for classical narrow-band spectrum sensing technology considering the handoff cost. In a decentralized CRN, prior knowledge of spectrum statistical information maybe not acquiable; in this context, many scholars have developed the multi-armed bandit (MAB) framework for opportunistic spectrum access (OSA) of CRN [6; 7; 8; 9]. [PERSON] et al. [8] proposed a distributed algorithm named \(\varrho^{\text{PRE}}\) policy based on the \(\varepsilon_{n}\)-greedy policy [10]. [PERSON] et al. [9] proposed a SL(K) subroutine and then established the prioritized access policy (DLP) and fair access policy (DLF) based on SL(K) and a pre-allocation order. [PERSON] et al. [11] then proposed \(k\)th-UCB1 policy combined the \(\varepsilon_{n}\)-greedy and UCB1 policy and evaluated its performance both for real-time applications and best-effort applications. All of them achieve logarithmic regret in the long run.  
Due to the spectrum varying nature of CRN, SUs are required to perform proactive spectrum handoffs when the spectrum band is occupied by PUs in the MAB framework, which results in a handoff delay consisting of RF reconfiguration or negotiation between transceiver In the above work [9; 10; 11], the handoff delay is not taken into consideration in their paper, i.e., the spectrum handoff is assumed to be costless. In this paper, by including a fixed handoff delay, SUs have to make the choice of either staying foregoing spectrum with low availability or handing off to a spectrum with higher availability and tolerating the handoff delay. We formulate this problem and investigate the performance of the above policies, i.e., \(\varrho^{\text{PRE}}\), SL(K), and \(k\)th-UCB1. To the best of our knowledge, the influence of the handoff delay on the above policies in the MAB framework has not been investigated yet.  
The rest of this paper is organized as follows: Section 2 describes the system model, which is similar to related works [9; 12] except that the handoff delay is included as a handoff cost. In Section 3, we formulate the problem and present the three policies. In Section 4, we examine the proposed scheme through simulation. Finally, the paper concludes with a summary in Section 5.