## 2 An Underwater Multi-DATA Train Protocol with Multi-RTS Reception and BACK
Figure 1 shows an example of the proposed underwater multi-DATA train protocol where \(T_{\text{RTS}}\) denotes the duration of RTS frame, \(T_{\text{CTS}}\) denotes the duration of CTS frame, and PROP denotes the underwater acoustic propagation delay between a sink node and the farthest underwater sensor node to the sink node in an underwater cell. For example, the sensor node 1 and the sensor node 3 send RTS frames simultaneously, then the RTS frames sent by the sensor nodes 1 and 3 may not overlap at the sink node due to long underwater acoustic propagation delay as shown in Figure 1.  
In Figure 1, using the recovered RTS frames each of which contains ID of the sensor node 1 or 3 and a timestamp, the sink node calculates the underwater propagation delay between the sensor node 1 or 3 and the sink node. Then, the underwater sink node broadcasts a CTS frame which contains the time information about when the sensor nodes 1 and 3 can transmit a DATA frame to the underwater sink node, respectively. From this time information in our CTS frame, the DATA frames transmitted from the sensor nodes 1 and 3 to the sink node can be formed as a train at the sink node. The time information in our CTS frame can make the sensor nodes 1 and 3 transmit a DATA frame to the sink node in ascending order of the calculated propagation delay between each RTS sending node and the sink node. The time information in our CTS frame can also make the sensor node 1 which is the nearest RTS sending node to the sink node transmit a DATA frame immediately after receiving the CTS frame and a short guard time. The multi-DATA train formed at the sink node can contain a short guard time between the DATA frames. After receiving the multi-DATA train from the sensor nodes 1 and 3, the underwater sink node broadcasts a BACK frame which contains the information about whether each DATA frame was successfully received or not. We also propose an underwater BACK protocol with multi-RTS reception, which can be shortly called an _underwater BACK protocol_. As shown in Figure 2, our proposed underwater BACK protocol is analogous to our proposed underwater multi-DATA train protocol except the multi-DATA train and the information contained in RTS and CTS frames. In the proposed underwater BACK protocol, an RTS frame does not need to contain a timestamp because an underwater sink node does not need to calculate the underwater propagation delay between the underwater sink node and each sensor node that sends the RTS frame. In the proposed underwater BACK protocol, a CTS frame does not need to contain the time information about when each sensor node that sent the recovered RTS frame can transmit a DATA frame to the underwater sink node. The CTS frame needs to contain the transmission order of DATA frames and ID of each sensor node that sent the recovered RTS frame. In this transmission order of DATA frames, each sensor node that sent the recovered RTS frame can transmit a DATA frame to the underwater sink node. After receiving DATA frames from the underwater sensor nodes, the underwater sink node broadcasts a BACK frame which contains the information about whether each DATA frame was successfully received or not. Figure 2 shows an example of the proposed underwater BACK protocol where \(T_{\text{DATA}}\) denotes the duration of DATA frame. For example, the sensor node 1 and the sensor node 3 send RTS frames simultaneously, then the RTS frames sent by the sensor nodes 1 and 3 may not overlap at the sink node due to long underwater acoustic propagation delay as shown in Figure 2. Then, the underwater sink node broadcasts a CTS frame which contains the transmission order of DATA frames and IDs of the sensor nodes 1 and 3 each of which sent the recovered RTS frame. In this transmission order of DATA frames, the sensor nodes 1 and 3 can transmit a DATA frame to the underwater sink node, respectively. Figure 1: An example of the proposed underwater multi-DATA train protocol. Figure 2: An example of the proposed underwater BACK protocol.