# Cooperative Opportunistic Pressure Based Routing for Underwater Wireless Sensor Networks
## 3 Our Proposed Work
### Throughput Maximization  
In this section, we have formulated an objective function to maximize the network throughput, the purpose of this model is to show that the minimization of energy consumption did not compromise the throughput of the network in our proposed schemes is comparatively still better than the compared existing scheme (Hydrocast). In our proposed schemes (Co-Hydrocast, improved-Hydrocast, and Co-improved Hydrocast), data packets are received via cooperative routing or with out cooperation. The network throughput is, the total number of data packets received successfully at the sink. The SNR check is performed at each link to ensure that data packets arrived the destination are within the SNR, if the data packet received at the destination have SNR within the predefined threshold then the data packet is considered in throughput. Therefore, based on these considerations, an objective function is formulated that is given in Equation (41). \[Max\sum_{r=1}^{r=max}TP(r)\ \ \forall\ r\in R \tag{41}\]  
where TP(r) denotes total number of data packets received in r (rounds) and TP is computed as given in Equation (42). It shows number of packets (P) those meet the \(SNR_{th}\). \[TP=\sum_{P=1}^{P_{max}}SNR\times P\ \ \forall\ P\in TP \tag{42}\]  
Equation (43) shows that a packet is only counted as a successful transmission when SNR of a signal is 1, if the received signal SNR is not within the threshold value then \(TP=(0\times P)\). \[SNR=\left\{ \begin{array}{ll}1&\text{if }SNR\geq SNR_{th}\\ 0&\text{if }SNR<SNR_{th}\end{array} \right. \tag{43}\]  
such that;  
\[E_{tx,xx}\leq E_{i}^{max}\ \ \forall\ i\in N \tag{44}\]  
Figure 10: Feasible Region of Energy Minimization. \[E_{(tx,rx)}\geq E_{(i)}^{min}\ \ \forall\ i\in N \tag{45}\]  
\[SNR\geq SNR_{th}\ \ \forall\ SNR\in N \tag{46}\]  
\[D_{s}^{d}\leq D_{s}^{d_{max}}\ \ \forall\ s,d\in N \tag{47}\]  
\[D_{s}^{d}\leq D_{s}^{d_{min}}\ \ \forall\ s,d\in N \tag{48}\]  
\[Max\sum_{CN=1}^{CN_{max}}CN_{B}\ \ \forall\ CN_{B}\in N \tag{49}\]  
\[Min\sum_{NC=1}^{NC_{max}}NC_{B}\ \ \forall\ NC_{B}\in N \tag{50}\]  
Our main objective is to maximize the network throughput (that is Equation (41)) by meeting all the given constraints. Equations (42) and (43) ensures that all packets received at the destination are meeting the predefined SNR threshold (\(SNR_{th}\)) will be accounted as a successful data packet. Constraints defined in Equations (44) and (45), make that \(E_{tx},E_{rx}\) should not exceed the maximum and the minimum limits. These restrictions are set to avoid the wastage of energy. SNR constraint is defined in Equation (46) to ensure the reception of error free packets at the sink and to conserve the energy and avoid a packet loss over long distances and minimize the number of hops for maximizing network lifetime and reducing propagation delay (Equations (47) and (48) are defined). Similarly, to avoid buffer overflow of sensor nodes, two constraints Equation (49) and Equation (50) are used to allocate a desired bandwidth as per requirement. Let suppose, the total available bandwidth (KHz) be \(T_{B}\), such that,  
\[T_{B}=CN_{B}+NC_{B} \tag{51}\]  
where \(CN_{B}\) and \(NC_{B}\) denote cooperative nodes bandwidth and non cooperative nodes bandwidth, respectively. \(CN_{B}\) is computed as follows:  
\[CN_{B}=T_{B}(i)\times(N_{n})^{p}\ \ \forall\ i\in N \tag{52}\]  
\(T_{B}(i)\) is the total available bandwidth for a cooperative node i, \(N_{n}\) number of nodes present in its transmission range for the relay cooperation, \(C_{N}\) represents the number of times the cooperation is performed, \(NC_{B}\) is the total available bandwidth for non cooperative nodes, and \(p=[0,1]\) is a probability of relay node existence. Figure 10:0  
Figure 10:1  
Here, it can be noted that the bandwidth allocation during data collection provides the encouraging results in the response to the objective function given in Equation (25). **Graphical analysis**: Let suppose, we have a scenario in which \(T_{B}=282\) KHz to \(300\) KHz, \(N=100\), \(N_{n}=3\), and \(C_{N}=3\).