## 3 The Proposed Routing Protocol--CRD
### The Proposed Routing Protocol--CRD
#### 3.4.1 The Proposed Sending Channel Based Focus Region Selection Algorithm--CFS  
**Focus region.** A focus region in Reference [26] is defined as follows. We assume that each node can know the location of a destination. Consider a straight line \(SD\) from a node \(S\) to a destination \(D\). The region with transmission radius \(R=250\) m, centered at the location of the node \(S\), extends up to a angular spread of \(\theta\) on either side of \(SD\) and gives a focus region for node \(S\).  
We now propose necessary definitions for the CFS algorithm. If \(v\) is a mobile node, \(\theta_{v}(c)\) can be denoted as the angle of focus region of node \(v\) with channel \(c\). The angle \(\theta_{v}(c)\) can be mathematically expressed as  
\[\theta_{v}(c)=\max_{u\in N(v)}\{\measuredangle uvD\mid(\measuredangle uvD\leq\pi/2) \text{ and }(\text{the receiving channel of node $u$ is $c$})\}. \tag{9}\]  
A pair \((v,c)\) is not affected by PU if the pair \((v,c)\) satisfies one of the following conditions: (p1): node \(v\) is not in PU region and (p2): node \(v\) is in PU region and PU does not use the channel \(c\).  
**Best neighbor.** Let node \(u\) be a neighbor of node \(v\). Node \(u\) is called a best neighbor of node \(v\) if node \(u\) is calculated by  
\[u=\arg\min_{u\in N(v)}\{\measuredangle uvD\mid\text{node $u$ and $v$ satisfy (b1) and (b2)}\}, \tag{10}\]  
where the conditions (b1) and (b2) are presented as follows. (b1): pair \((v,c_{u})\) is not affected by PU and (b2): node \(u\) is not in PU region. We can see that a best neighbor \(u\) of node \(v\) is not in PU region and the angle \(\measuredangle uvD\) is the smallest angle.  
**Good neighbor.** If we cannot find a best neighbor, a node \(u\) is called a good neighbor of node \(v\) if node \(u\) is also calculated by (10) without condition (b2). Thus, a good neighbor \(u\) of node \(v\) is inside PU region and the angle \(\measuredangle uvD\) is the smallest angle.  
Based on the angle \(\theta_{v}(c)\), we propose the CFS algorithm, as shown in Algorithm 4, to determine a focus region with a sending channel of a node \(v\). Algorithm 4 can be explained as follows. First, if there exists a node \(u\) which is the best neighbor of node \(v\), node \(v\) chooses the sending channel as \(c_{u}\) and the angle of focus region as \(\theta_{v}(c_{u})\). On the other hand, if node \(v\) has a good neighbor \(u\), node \(v\) will choose the sending channel \(c_{u}\) and the angle of focus region \(\theta_{v}(c_{u})\) to transmit its packets.  
Furthermore, the CFS algorithm can be described in Figure 6 as follows. When CH\({}_{1}\) receives a RREQ packet, it chooses channel 1 as the sending channel because GW\({}_{2}\) is not in the PU region and \(\measuredangle(\text{GW}_{2})(\text{CH}_{1})(D)\) is the smallest angle. Moreover, GW\({}_{1}\) also uses channel 1, thus CH\({}_{1}\) chooses \(\theta=\max\{\measuredangle(\text{GW}_{2})(\text{CH}_{1})(D),\measuredangle(\text{GW }_{1})(\text{CH}_{1})(D)\}\) as the sending angle. When \(CH_{2}\) receives a RREQ packet, it chooses \(\theta=\measuredangle(\text{GW}_{4})(\text{CH}_{2})(D)\) as a sending angle and channel 2 as a sending channel to forward the RREQ to GW\({}_{4}\) because GW\({}_{5}\) is in the PU region.