## 4 System Model
### Huiwst  
There are three types of entities in the considered HUWST framework (Figure 1). They respectively are the base station (BS), sink node (SN), and sensor. Among them, several sensors and an SN form a cluster, where the SN acts as a cluster head, and the sensor acts as a cluster member. Further, the cluster head is responsible for all the sensors in the cluster. Each sensor belongs to only one cluster, and the sensors hand over the collected data to the cluster head SN. The cluster head SN transmits the data to the BS uniformly. We detail the differences of three types of entities as follows. 1. Sensors: The sensors have data acquisition capability and data transmission capability. They are used to collect underwater data and transmit the collected data to the cluster head SN of their cluster. 2. SNs: The SNs are used to receive the data transmitted by the sensors in their cluster and transmit the received data to the BS in a unified way. In particular, SN has certain computing power, which supports it to perform computational processing (e.g., data mining and analysis) on the received data. 3. BS: The BS can be a ship or surface monitoring station to receive data transmitted by underwater devices. Figure 1: HUWST framework. In the considered HUWST framework (Figure 1), we divide the network into n layers, in the vertical direction, each h meters as a layer. In HUWST, the SN has two choices for data transmission: 1 Transmit data to the SNs of the upper layer (non-layer hopping transmission); 2 Transmit data directly to the BS. To counterbalance the different energy consumption between different sensors, the sensor simply passes the task to the SN for further processing. The sensors' energy consumption is thus assumed to be similar, so we do not discuss the transmission problem of sensors. The SN transmission model of the considered HUWST framework is shown in Figure 2 (The black dots in Figure 2 represent the omitted layers in the middle). Therefore, the data transmission paradigm of each SN can be divided into four modes, which are:  
1. Transmit data directly to the BS;
2. Transmit to the SN of the upper layer, to handle the data task further by the upper-layer SN;
3. Transmit the calculation result directly to BS after calculating;
4. After calculating and processing, transmit the calculation result to the SN of the upper layer, then the SN of the upper layer transmits it to the BS. Because SNs typically have low data rates and suffer from selective fading in both time and frequency domains, we consider our novel HUWST framework based on the orthogonal frequency division multiplexing (OFDM) scheme. The OFDM scheme has the advantages of resisting frequency selective attenuation and improving frequency band utilization. Therefore, underwater OFDM systems have already become an essential choice for UWSNs [24; 25]. For the underwater OFDM system, the total bandwidth is divided into multiple orthogonal sub-channels, and each sub-channel can be assigned to at most one sensor node. Because different sensor nodes use different frequency bands to transmit signals, the same as in previous studies [24; 25], the interference between nodes can be ignored accordingly. We pay attention to one layer and call it the optimization layer. We assume there are I SNs in this layer and use \(\mathcal{I}=\{1,2,3,\ldots,I\}\) to denote them. The layer above this layer is called the assisted layer, and it is denoted that there are J SNs in the assisted layer, using \(\mathcal{J}=\{1,2,3,\ldots J\}\) to denote them. For each SN in the optimization layer, we consider that there is only one piece of data to be transmitted, and this piece of data cannot be divided. We use \(W_{i}=\{D_{i},X_{i}\},i\in\mathcal{I}\) to represent the data of SN i, where \(D_{i}\) represents the data size, and \(X_{i}\) represents the number of CPU cycles required to process it. The considered three-layer model--the optimization layer, the assisted layer, and the water surface BS--is shown in Figure 3 below.