## 3 ROR: Reliable Opportunistic Routing for CRSN
### System and Network Model  
In cognitive radio sensor networks, like in CR networks, generally, primary users have more privileges to spectrum usage than the secondary users; in this case, the CRSN nodes. Thus, the secondary user (SU) nodes dynamically sense the spectrum holes (channels) and switch to a negotiated channel, which is free of primary user (PU) transmission or interference for data transfer. Nodes are assumed to be location-aware via an on-board GPS or by running a localization algorithm [33]. No specific topology is assumed, and nodes are assumed to be stationary. The nodes are also assumed to have a single half-duplex CR transceiver that can be tuned to any licensed channel. The PU or SU transmit power decays with distance based on the free-space path loss model. The considered model is according to the probabilistic wireless network simulator [34], which considers the signal-to-noise ratio (SNR) for each receiver and transmitter pair and a value of receiver noise variance (RNV). A signal can only be received or detected if the power limit from both neighbors (_i.e._, SUs) and primary users (PUs) is above a threshold, \(\lambda_{su}\) and \(\lambda_{pu}\), respectively. It is assumed that the energy detection sensing mechanism is used in a non-fading environment for PU detection. Thus, when the SU performs spectrum sensing to detect the PU activity, the nature of the received signal, \(S\), can be represented as follows [35]:  
\[S_{rec}^{su}= \begin{cases}n(t),&\text{if }H_{0}.\\ n(t)+S^{p}(t),&\text{if }H_{1}.\end{cases}  \tag{1}\]where \(H_{0}\) represents the PU hypothetical ideal state, while \(H_{1}\) represents the active state. \(n(t)\) is a zero-mean additive white Gaussian noise (AWGN) and \(S^{p}(t)\) represents the PU signal waveform. Accordingly, the probability of the SU detecting the PU, \(P_{d}\) and the probability of a false alarm, \(P_{f}\), is computed as [35]:  
\[P_{d} =\Pr\left\{Y>\lambda_{pu}\left|H_{1}\right.\right\} \tag{2}\] \[P_{f} =\Pr\left\{Y>\lambda_{pu}\left|H_{0}\right.\right\} \tag{3}\]  
where \(Y\) represents the decision statistic obtained from the energy detection algorithm and \(\lambda_{pu}\) is the decision threshold. It thus implies that a low value of \(P_{d}\) increases the probability of PU interference, while a high value would result in low spectrum utilization, because false alarms increase the number of missed opportunities. It is assumed that PUs are available in the network area and that they make use of the licensed spectrum according to a probabilistic model. The PU activity is modeled according to an ON and OFF Poisson state transition model [36, 37], in which both states represent the arrival or absence of the primary user, respectively, with \(\tau_{on}\) seconds for the ON state and \(\tau_{off}\) for the OFF state. These states are exponentially distributed, because the PU arrival is independent [36]. The ON state transits to the OFF state with a probability, \(P_{on}\), and reverses from the OFF state with a probability, \(P_{off}\). When the licensed user arrives, it stays for a time period of \(T_{PU}^{off}\). \[P_{on}=\frac{\tau_{on}}{\tau_{on}+\tau_{off}} \tag{4}\]  
It thus derives that, when the value of \(P_{on}\) is high, there is more PU activity in the licensed spectrum and less opportunity for SU transmission. When \(P_{on}\) is low, which also translates to a high value for \(P_{off}\), this means the SU has more opportunity to make use of the licensed spectrum. The probability of being in an OFF state is calculated as:  
\[P_{off}=1-P_{on} \tag{5}\]  
At the data channel, once the SU has commenced transmission; it completes sending its packet before releasing the channel, and any interference that might arise thereof is controlled by adopting suitable SU transmission power [38]. For simplicity, we assume that a specific frequency band is chosen as the operation area for the sensors with \(N\) channels having same bandwidth. All control negotiations is carried out via a dedicated common control channel (CC).