## 3 ROR: Reliable Opportunistic Routing for CRSN
### Channel Selection and Route Request Initiation  
It is assumed that an event occurs in an event area with an event radius of \(r_{evt}\) meters, and each source node is expected to report its event information to the sink. An event in this case can be motion activated sensors strategically positioned to monitor an area of interest. They are expected to transmit their data, which could be pictures, temperature, humidity or a combination of all to a remote sink. In order to locate all possible routes from the source to the sink, the source nodes located at the event area compete to initiate the route request operation. Once one successfully sends its route request, all other nodes in the event area refrain from sending and participate in the route request phase. Thus, the source node broadcasts the route request (RREQ) packet, which carries the source address, the sink address and the RREQ identification. The source node then sets a timer, \(\overline{T_{r}}\), which is the maximum route negotiation time, within which it expects a route reply packet via the control channel. However, if no reply is received by the source node and it time-outs, then another RREQ is sent. The route request payload carries the important quality of service requirements needed to service the traffic at hand. These include the minimum required data rate required to service the available packets, as stipulated by the application layer. It is pertinent to mention that a high value of \(v_{i}(t)\) does not imperatively mean that the channel can service the application at hand. This is because the \(v_{i}(t)\) does not consider other metrics, like bandwidth and spectrum sensing error, which are very important metrics to be considered, especially for quality of service-specific applications. Thus, it is necessary to confirm the data rate of the chosen channel to be sure it can support the application. The requisite data rate is defined as the achievable data rate, \(R\), on any channel at any time instant, \(t\). This is the sum of the rate, \(R_{s}\left(t\right)\), when a channel is detected as idle with the possibility of the appearance of the PU during the packet transmission period, \(T_{su}\), with the rate achieved, \(R_{f}\left(t\right)\), as a result of false channel availability. In both cases, the interference among SUs, \(I_{su}\), has to be considered. Thus, when the PU is inactive, and there is no false alarm  
Figure 1: Spectrum quality initiative scaling. of inferring the received signal as a PU transmission. The attainable data rate at a truly detected idle channel is:  
\[b_{s}(t)=\beta log_{2}\left(1+\frac{S_{rec}^{su}}{n(t)+I_{su}}\right)\]  
\[R_{s}(t)=\left(P_{off}-P_{f}\right)\frac{T_{su}-\overline{T_{s}}-\overline{T_{r }}}{T_{su}}b_{s}(t) \tag{6}\]  
However, a PU can arrive at any time instant during the time, \(T_{su}\), thus causing interference that eventually converges to \(\left(1-P_{off}\right)T_{su}\) with the probability \(1-e^{-\theta\frac{T_{su}}{\tau_{on}}}\), where \(\theta\) is the scaling factor. On the other hand, the achievable data rate,\(R_{s}(t)\), in the situation where PU is active, but it is not detected by the SU, due to spectrum sensing error, is:  
\[b_{f}(t)=\beta\mathrm{log}_{2}\left(1+\frac{S_{rec}^{su}}{n(t)+S^{p}(t)+I_{su}}\right)\]  
\[R_{f}(t)=\left(P_{on}-P_{d}\right)\frac{T_{su}-\overline{T_{s}}-\overline{T_{r }}}{T_{su}}b_{f}(t) \tag{7}\]  
Thus, the achievable data rate, \(R\), on any channel at any time instant, \(t\), is:  
\[R\left(t\right)=e^{-\theta\frac{T_{su}}{\tau_{on}}}R_{s}\left(t\right)+\left(1 -e^{-\theta\frac{T_{su}}{\tau_{on}}}\right)R_{f}\left(t\right) \tag{8}\]  
where \(e^{-\theta_{1}\frac{T_{su}C}{\tau_{on}}}\) is the probability that the PU remains active on the channel over the entire packet transmission time \(T_{su}\). Hence, the source node places the minimum required data rate needed to service the packets at any instance in the route request payload. Along with this, it also includes its distance to the sink and its data channel of choice in the payload.