# A Stable Backup Routing Protocol for Wireless Ad Hoc Networks
## 2 Stable Backup Routing Scheme (SBR)  
### System Model  
In the SBR, backup routes are classified into three categories based on hop counts or path length. As shown in Figure 3, there are three backup paths in the topology. The hop counts of the backup route through B-E decrease by one compared with that of main route, and such a path is called a decreased  
Figure 2: A fish bone structure formed in AODV-backup routing (BR).  
backup route (DBR). Similarly, because of the equal hop counts to that of the main route, the backup route through B-F-E is called an equal backup route (EBR). With regard to the backup route through B-G-C, whose length is larger than that of main route by one, it is named the increased backup route (IBR).  
From Figure 3, we can see that \"IBR\" has the longest route to destination whereas \"DBR\" has the shortest path. Thus, one can select a different type of backup route to deliver packets according to practical application requirements. For instance, if real-time traffic (music or video streams) that require Quality of Service (QoS) support is being transmitted in Ad hoc networks, \"DBR\" or \"EBR\" should be chosen to meet the low delay requirement. For the purpose of shortening transmission delay, in SBR, \"DBR\" has the highest priority due to its smallest hop counts and the priority of \"IBR\" is the lowest.  
To estimate link stability, the bit error rate (BER) is introduced which depends on the Signal to Noise Ratio (SNR) obtained from physical layer [32]. In this paper, the wireless Additive White Gaussian Noise (AWGN) channel and the Binary Phase Shift Keying (BPSK) digital modulation are used. Then the BER can be given by [33]  
\[\text{BER}= \frac{1}{2}erfc\left(\sqrt{\frac{\text{P}_{\text{r}}\cdot\text{B}}{ \text{P}_{\text{N}}\cdot\text{T}_{\text{b}}}}\right) \tag{1}\]  
where \(\text{P}_{\text{r}}\) denotes the received power, B is the channel bandwidth, \(\text{P}_{\text{N}}\) represents the noise power, \(\text{T}_{\text{b}}\) is the transmission bit rate and _erfc_ is the complementary error function.  
Denote the link between node \(i\) and \(j\) by \((i,j)\), the successful rate on link \((i,j)\), named \(p^{(i,j)}\) is defined as:  
\[p^{(i,j)}=\left(1-\text{BER}^{(i,j)}\right)^{l}, \tag{2}\]  
where \(l\) is packet length and \(\text{BER}^{(i,j)}\) is the bit error rate of \((i,j)\) calculated by (1). It is assumed that the channel is symmetric in this paper, i.e., \(p^{(i,j)}=p^{(j,\,j)}\). As we know, data transmissions in adjacent links interfere with each other, which can be avoided by the MAC layer's RTS/CTS mechanism. The success rate \(p^{(i,j)}\) here refers to the probability that a packet is received correctly by node \(j\) after being sent by node \(i\). Hence, the path successful rate is then the product of all passing links' successful rates. Essentially, path successful rate defined here is a metric for evaluating the path quality, which indicates the probability for a certain packet to pass through a piece of route successfully. Note that, in addition to AWGN and BPSK, our proposed SBR can also be applied to other noise models and modulation methods without losing generality.  
Figure 3: Three types of backup routes.