## 4 Proposed 3D-UWSN Design
### Data Gathering  
Data gathering is the key process in a UWSN performed by an AUV. The data from cluster members are collected by the CH and then delivered to the AUV. The CH is appointed with a waiting time for the arrival of AUV. Once the sensors' data are transmitted and stored at the level of each CH in the different clusters, and in order to minimize the CH energy consumption due to data overload and the data collection delay that can be caused due to a long waiting time for the AUV arrival, this operation must be performed according to pre-defined CH waiting time deadlines. If this waiting time is exceeded, then the CH requests for a route to the gateway and performs inter-cluster routing. A gateway is used as a communication and organization entity with nodes that aim to forward the data between the CHs in different clusters through an optimal, selected route designed in the inter-cluster routing process. Searching for a route with limited knowledge of other CHs tends to consume more energy and cause a delay, so the gateway is employed. A three-step, inter-cluster routing method is incorporated based on the three steps: route discovery, longer route elimination and validation of filtered routes. The gateway, having the knowledge of all the CHs in \(L_{1}\) and \(L_{2}\), constructs an undirected graph from which the route is selected towards the AUV. The undirected graph \(G=(S,e)\) represents the set of CH sensor nodes \(S\) and their edges \(e\). All the possible routes are extracted from \(G\) and then the routes with a longer distance and higher hop counts are eliminated. This filtration is performed to ensure faster transmission of data. The increase in distance and hop counts tends to increase end-to-end delay, and, hence, the routes are eliminated in the second step. Then, a route is selected from the filtered route after validation by the fuzzy-LeNet method. The route validation is handled based on the computation of average energy consumption, fairness, synthesis speed and node efficiency. LeNet is a convolution neural network (CNN) that is combined with fuzzy for accurate results in route validation. The LeNet is composed of a convolutional block and fully connected block. The convolutions block is fed with the input parameters, i.e., a node's average energy consumption, fairness, synthesis speed and node efficiency, based on which, fuzzy membership functions are created. The LeNet is developed with seven layers: three convolutional layers, two pooling layers, one fully connected layer and one output layer. In the pooling layer, the input parameters computed are crisp values which are converted into the fuzzy set for processinginto the fuzzy membership function. In the fully connected layer, each neuron is connected to all the neurons that are present in the next layer. The input for the fully connected layer is the individual parameters of each sensor, which are converted into a single-vector value using the membership function. Then, the output from the fully connected layer is the probability values of each route. The input for the fuzzy-LeNet is the filtered route in which the CHs in the route are computed with the above, discussed parameters. Figure 2 depicts the model of the proposed fuzzy-LeNet for inter-cluster route validation. The average energy consumption of the sensor node is formulated based on its packet transmission with other sensor nodes. The average energy consumption (\(A_{EC}\)) of a node is given as:  
\[A_{EC}=\frac{EC_{To}}{R_{p}} \tag{12}\]  
Of the terms used above, \(EC_{To}\) and \(R_{p}\) are the total energy consumption and received number of packets. The route fairness (\(RF_{s}\)) is mathematically formulated based on [PERSON]'s fairness index, which is represented as:  
\[RF_{s}=\frac{\left(\sum_{i=1}^{nCH}tp_{i}\right)^{2}}{nCH\left(\sum_{i=1}^{nCH }tp_{i}^{2}\right)} \tag{13}\]  
This fairness index is formulated for a route in which the number of CHs in a route is \(nCH\), and their throughput is \(tp_{i}\).