## 2 Deployment and Proposed Transmission/Reception Timing Schemes  
### Deployment and Environments  
Regarding sensor node deployment, although two-dimensional or three-dimensional deployment can be generally considered, in this paper, one-dimensional linear equidistant deployment is assumed to be the easiest form and the deployment may be expanded to other complicated forms in later studies. The places for the application of this deployment may include cases where the nodes are deployed along the seaside, perpendicularly to the seaside, or across the width of a river, as shown in Figure 1. The locations of the sink nodes that gather data can be the center or both ends, but both ends become one end if the nodes are divided into two groups. Each communication channel is assumed to be a shared common channel operating in a half-duplex mode. In underwater environments, the propagation delays are quite large, so the transmission/reception of neighboring nodes is restricted while a pair of omni-directional nodes is transmitting/receiving signals. That is, other nodes around the receiving node might not transmit signals to any node because interfering signals should not be given to the receiving node. In addition, other nodes around the transmitting node may not receive any other signal because the signals coming from the transmitting node become interfering signals. That is, if a pair of nodes transmit/receive signals, the time sections during which individual neighbor nodes may not transmit/receive signals will occur. The lengths of the node transmission times are regarded as frames to examine the three types of frame timing, as shown in Figure 2. \(T_{f}\) is the frame time and \(T_{p}\) is the one-way propagation delay. Figure 2a presents a case where \(T_{f}=T_{p}\), and because the last time point (A) of the frame in the transmission node is identical to the time point (B) of the beginning of the frame in the receiving node, the entire network can be made so that time slots in the length of \(T_{f}\) are synchronized for all nodes. Frame-level synchronization among the nodes is assumed in the paper. As propagation delays between all nodes should be identical at \(T_{p}\) to this end, equal spaces between the nodes should be assumed. That is, to apply the scheme proposed in this paper, one-dimensional underwater nodes are assumed to have been deployed linearly at equal spaces. Regarding the cases shown in Figure 2b (\(T_{f}\)\(>T_{p}\)) and Figure 2c (\(T_{f}\)\(<T_{p}\)), the complexity in management  
Figure 1: Place for the application of a one-dimensional linear sensor node deployment. increases and the cases cannot be more excellent than the case shown in Figure 2a (\(T_{f}=T_{p}\)) in terms of maximizing the channel utilization by minimizing the idle sections on the time axis. That is, the scheme shown in Figure 2a is used in this paper. In underwater environments, a packet size is generally greater than \(T_{p}\). To match the inconsistency between a packet and a frame, a packet is segmented into the size, \(T_{p}\). On the other hand, concatenation is also applicable. Because the idle spaces between the time slots are removed through the operation in the form of time slots synchronized through Figure 2a, obtaining the maximum channel utilization simply becomes an issue of minimizing the idle time slot frequency. Two one-dimensional linear node deployment and data flow models, as shown in Figure 3, are used. In these models, there is one sink node and if there are multiple sink nodes, the nodes can be divided based on the sink nodes into groups with a single sink node each. Figure 3b shows the cases where the sink node not located at the center are not considered because these cases are inferior to the cases where the sink node is located at the center. In cases where the sink node is located at the center, the total number of nodes shall be determined to be \(N=2M+1\) because cases where the total number of nodes is an odd number are more convenient.