## 4 RACAA: Reliability-Aware Cooperative Routing with Adaptive Amplification
#### Cooperative Routing with Adaptive Amplification  
In cooperative routing, data packets are broadcasted by a source node \(S\) and are received by a relay node \(R\) and a destination node \(D\). At least a single relay node \(R\) between \(S\) and \(D\) also receives the broadcasted information. Such information is then transferred from \(R\) to \(D\) that combines the two copies of information to extract the desired information [20]. A data symbol \(x\) broadcasted by \(S\) is received by \(D\) as [20]  
\[y_{SD}=h_{SD}x+n_{SD} \tag{6}\]  
where \(y_{SD}\) is the signal received at \(D\), \(h_{SD}\) is the gain of the channel from \(S\) to \(D\) and \(n_{SD}\) represents the additive white Gaussian noise (AWGN) along the \(S-D\) link. The source broadcasted data symbol \(x\), when received by \(R\), is given as [20]  
\[y_{SR}=h_{SR}x+n_{SR} \tag{7}\]  
where \(y_{SR}\) is the signal received at \(R\), \(h_{SR}\) is the gain of the channel from \(S\) to \(R\) and \(n_{SR}\) is the AWGN along the \(S-R\) link. Adaptive amplification implies that at \(R\), the received signal is amplified before transferring it to \(D\) when the error probability is above 50% (a certain threshold) and is given by [20]  
\[y_{RD}=A^{2}h_{RD}y_{SR}+n_{RD} \tag{8}\]  
where \(y_{RD}\) is the signal that \(D\) receives from \(R\), \(h_{RD}\) is the gain of the channel along the along the \(R-D\) link and \(n_{RD}\) is the AWGN along the \(R\) to \(D\) link. The symbol \(A^{2}\) denotes the factor by which the \(y_{SR}\) signal is amplified by \(R\) and is mathematically defined by [20]  
\[A^{2}=\frac{\rho}{P_{s}h_{SR}^{2}+\sigma^{2}} \tag{9}\]  
where the constant \(\rho\) equals either unity or the transmit power \(P_{R}\) of the relay \(R\). The proposed scheme takes \(\rho=P_{R}\) and adjusts \(P_{R}\) according to the bit error probability computed above. If the bit error probability of the packets at \(R\) is above 50%, this indicates unfavorable channel conditions. Therefore, the relay increases its transmit power to the maximum, otherwise it forwards packets to \(D\) with normal power. The increase in power of the relay helps in mitigating the the channel effects by increasing the SNR and, therefor, decreasing the bit error probability. For the accomplishment of cooperative routing, at least three nodes are necessary to exist. They are: source, relay and destination nodes. Packets are generated and broadcasted by the source, which are received by the relay and destination. In RAR scheme, the destination node was not involved. Instead, data packets were broadcasted by a source and received by a relay, which further forwarded it towards end destination. The choice of relay node was made by source, which used to choose a lowest depth neighbor node as a relay. However, with cooperative routing in RACAA, source chooses a lowest depth neighbor as an intermediate destination. The relay node in RACAA is the one that has the lowest depth after the destination node and be a mutual neighbor of the source-destination pair. In RACAA, the source broadcasted data packets are received by the destination and relay nodes. The relay node then waits for the destination node to receive a request whether or not to forward the same data packets to destination. The destination checks the error probability in data packets. If this probability is below the threshold, the destination does not request the relay node. The relay node knows this by not receiving a request from the destination node within the predefined interval of time that leads to timer expiration of the relay node. The timer of the relay node (for receiving a request from the destination node) starts as soon as the relay node receives the data packets from the destination node. Relay and destination nodes are selected by the source node using the vital information of nodes obtained by the exchange of hello packets. Figure 3 is the flow chart of RAR and RACAA schemes that indicates the way packets are transferred to the water surface.