# Channel-Hopping Using Reinforcement Learning for Rendezvous in Asymmetric Cognitive Radio Networks
## 2 System Model and Related Works  
### System Model  
We examine a cognitive radio network (CRN) where a limited number of secondary users (SUs) and primary sers (PUs) are spread across a single contention area. The available spectrum is divided into N non-overlapping orthogonal channels, numbered 1, 2,..., N, and these channel numbers are well known to all SUs. Each SU, equipped with a half-duplex transceiver, can switch to any channel but can only operate on one channel at a time. We assume a self-configuring network where SUs can communicate with each other if they are within range. In the current framework, PUs are the licensed owners of the spectrum bands and access the channels in a synchronized time-slot manner. All channels have identical bandwidth and are identified by their central frequency. Each channel maintains equal bandwidth spacing from its neighboring channels, similar to most wireless systems (e.g., IEEE 802.11).  
A channel is accessible to an SU if there is no interference during transmission. Using an appropriate sensing technique, SUs can detect available channels from the N options before starting the rendezvous process. Here, we consider an asymmetric model, meaning that all SUs in the same area have different sets of channels. However, there is always an overlap between these sets, making rendezvous feasible. On the other hand, PUs can randomly select a channel for data transmission on a slot-by-slot basis. As a result, multiple PUs can choose the same channel at the same time, leading to scenarios where a channel may be unavailable for rendezvous at any given moment. This indicates that some channels in the overall channel set may be inaccessible.  
We consider an asynchronous network model, meaning that there is no global time synchronization among SUs. However, the duration of a time-slot should be long enough to complete the rendezvous process. For simplicity in analysis, we assume that the clock difference between two SUs is a random integer number of mini-slots. In this study, we explore reliable active scanning (RAS), which is straightforward and effective in detecting lost probe requests and quickly retransmitting or switching to the next channel. However, the successful transmission of a probe request is unpredictable due to the possibility of collisions and the lack of acknowledgment. In this active scanning approach, an SU broadcasts a probe request and expects to receive a probe response from any neighboring SU.  
Figure 1 illustrates the fundamental structure of the rendezvous process considered in this study. At time \(t=1\), both SUs A and B are on channel 1 and they are in communication range of each other. Therefore, [PERSON] and [PERSON] discover each other at time \(t=1\) on channel 1. These two SUs are now time-synchronized and attempt to rendezvous with other nodes such that both of them do not attempt at the same time-slot. Hence, at time \(t=2\), when [PERSON] attempts to rendezvous on channel 2, [PERSON] holds. Similarly, at time \(t=3\), [PERSON] attempts to rendezvous on 3 and [PERSON] holds its attempt now. [PERSON] and C achieve a rendezvous at \(t=5\) on channel 4. Hereafter, all three SUs are rendezvoused and now they follow the same procedure to rendezvous with the rest.  
In a cognitive radio environment, when a connection is desired, channels currently in use by other users are considered unavailable to avoid interference. Therefore, it is reasonable to generalize the scenario to a two-user case. As a result, the problem can be addressed by assuming a two-user situation where the total number of channels available to each user is not identical [12].