## 2 System Model
### Cognitive Radio Wireless Sensor Network Energy Consumption Model
#### 3.3.4 Transceiver Unit Energy Consumption  
The transceiver unit enables communication between the member nodes MNs and the clusterheads CHs as well as between the CHs and the BS. Each \(MN_{i}\) transmits its reading data to any of the selected clusterheads \(CH_{j}\) through the available licensed channels. Since all MNs are within the radio range of their neighboring clusterheads, adjacent MNs can send their data to the \(CH_{j}\) without intermediary nodes. Energy consumption E\({}_{tM}\) for transmitting \(B_{dt}\)-bits packet to \(CH_{j}\) over a distance \(d_{i,j}\) can be expressed as:  
\[\text{E}_{tM}(B_{dt},d_{i,j})=\ B_{dt}(E_{ec}+E_{am}\ d_{i,j}) \tag{20}\]  
The \(CH_{j}\) aggregates the data received from the MNs and then forwards the aggregated data either through some intermediate neighbouring clusterhead \(CH_{g}\) or directly to the BS. Energy consumption E\({}_{rM}\) for receiving \(B_{dt}\)-bits packet from member node \(MN_{i}\) can be expressed as:  
\[\text{E}_{rM}(B_{dt})=\ B_{dt}E_{ec} \tag{21}\]  
Let \(CH_{g}\)denote the immediate neighbouring clusterhead through which the aggregated data packets \(B_{pk}\) will be routed to the BS, \(E_{mp}\) denotes the energy consumption for amplifying the signal and \(d_{j,g}\) denotes the distance between clusterhead \(CH_{j}\) and the immediate neighbouring clusterhead \(CH_{g}\) or the BS. The energy consumption E\({}_{tH}\) for transmitting the aggregated data packets \(B_{pk}\) to the immediate neighboring clusterhead \(CH_{g}\) or the BS over a distance \(d_{j,g}\) can be expressed as:  
\[\text{E}_{tH}\big{(}B_{pk},d_{j,g}\big{)}=\ B_{pk}\big{(}E_{ec}+E_{mp}\ d_{j,g} \big{)} \tag{22}\]  
Energy consumption for receiving the aggregated data packets \(B_{pk}\) from neighbouring clusterhead \(CH_{g}\) for onward transmission is given as:  
\[\text{E}_{rH}(B_{pk})=\ B_{pk}E_{ec} \tag{23}\]  
The source of power consumption in the RF-front end is mainly dominated by power amplifier which boosts the transmission power to a certain level depending on the type of the amplifier and the application. The power amplifier's power consumption \(P_{am}\) which is a function of transmission distance \(d\) largely depends on many factors which include operating frequency, DC supply voltage, output power, hardware technology and load characteristic. The total power consumption for running the power amplifier is equal to the DC input power \(P_{dc}(P_{am}=P_{dc})\)[44]. The ability of the power amplifier to convert the DC input power \(P_{dc}\) into RF signal power \(P_{tx}\) is referred to as drain efficiency. This efficiency can be expressed as the ratio of signal power to DC power given as:  
\[\eta=\frac{P_{tx}}{P_{dc}} \tag{24}\]  
Communication over the wireless medium is susceptible to propagation impairments such as multi-path, fading and attenuation. If \(P_{tx}\) denotes the RF signal power from the transmitter's power amplifier delivered to the receiver node's antenna, and \(G\) is a parameter that defines the characteristic of the transmitting and receiving antenna, then the RF signal power \(P_{rx}\) received at the receiving sensor node can be expressed as:  
\[P_{rx}=\frac{P_{tx}}{(G\ d\theta)} \tag{25}\]Therefore, from Equations (24) and (25), the minimum power consumption of RF power amplifier to amplify transmission signals is given by \(P_{am}=\mu/\eta\), where \(\mu=P_{rx}\)\(G\) is a constant given by the received RF signal power P\({}_{rx}\) and the antenna characteristic G [44]. The parameter value \(\mu\) is a function of radio environment and can be set to a single-hop maximum transmission power value _i.e._, 6.3 mW instead of absolute value as in [44]. The energy consumption for data transmission comprises of energy cost for intra-cluster and inter-cluster data communication. In intra-cluster data communication, distance between the MNs and their prospective CHs is presumably short and therefore, the channel between them follows the Friis free space path loss model with signal power attenuation of \(\beta=2\) power loss [30].