## 2 System Model  
This section describes the system model and parameters adopted for this research. The network is assumed to be static, consisting of \(N\) non-mobile homogenous fully functional cognitive radio sensor nodes capable of performing complex tasks. The number of SUs in the network exert a significant impact on energy consumption and on sensing performance. For instance, in a fixed size cluster, the cooperative probability of detection increases along with the increase in the number of cooperative SUs. The network area is partitioned into \(q\) clusters, each cluster can be seen as a small cell network comprising a clusterhead and a few member nodes, as shown in Figure 1. Partitioning the network area into clusters has a significant effect on the network energy consumption. If the number of clusters in the network is too small, spectrum sensing, reporting and data communication consume a large amount of energy owing to large number of member nodes per cluster. On the other hand, if the number of clusters is too many, the number of member nodes would be too small and hence the energy consumption per cluster would be low but a large amount of energy would be consumed for inter-cluster communication. Therefore, the optimal number of clusters is extremely important. The nodes are uniformly distributed in a two-dimensional square area \(\mathrm{N_{A}}\) of \(\mathrm{L}\times\mathrm{L}\) square meters and each node is battery powered. This means sensor nodes' energy cannot be recharged, therefore, nodes' energy consumption need to be minimized to extend the lifetime of the network. Each node can operate either as a clusterhead or member node. The member nodes MNs sense a set of licensed channels to detect vacant channels, report local sensing decisions to clusterheads for cooperative decision-making and also sense the environment to detect events. The clusterheads perform additional tasks which include decision fusion on the sensing results, controlling access to free channels for data communication and coordinating channel sensing. These additional tasks drain more energy from the battery of the clusterhead, therefore the role of clusterhead will be reassigned to other member nodes within a cluster when the energy depletes below a threshold. It is further assumed that all member nodes lie within the radio range of their respective clusterheads (\(d<R_{max}\)) and communicate directly with the clusterheads in a single-hop manner. This means that member nodes require only low transmissions power and at least one common vacant channel to communicate their data to clusterheads since the distance between them is short. The operation of the SUs are divided into time slots \(\tau\) of durations, \(\tau^{cs}\) is the time allocated for sensing channels, \(\tau^{rp}\) is the time duration for reporting the results, and \(\tau^{dt}\) is duration over which the SU can access the free channel for data transmission. There are \(n_{z}\) heterogeneous licensed channels in which each channel may exhibit different bandwidth and channel conditions. Larger bandwidth requires longer sensing time which translates into higher energy consumption and poor channel conditions resulting in inaccurate local decisions. An energy detection technique is employed to detect the presence  
Figure 1: Clustered cooperative channel sensing. of PUs on the licensed channels, since the PUs' signals are assumed to be unknown, coupled with the unique resource constraint features of the CR-WSN which requires less complex spectrum sensing techniques. The Proposed Energy Efficient Spectrum Aware Reinforcement Learning Based Clustering (EESA-RLC) Algorithm  
This section presents modelling and algorithms for our energy-efficient reinforcement learning-based clustering scheme. The algorithms basically comprise of initialization, set-up and coordination phases. The initialization phase precedes the reinforcement learning process; it involves election of clusterheads.