## 1 Introduction  
Underwater sensor networks (UWSNs) have potential applications such as oceanic environmental monitoring, tactical surveillance, and communication among autonomous unmanned vehicles (AUVs), unmanned underwater vehicles (UUVs), divers, and sensors [1; 2; 3]. The underwater channel characteristics are significantly different from terrestrial ones; the communication bandwidth is narrow and the propagation delay of acoustic waves is large [1; 3; 4]. Therefore, new protocols for medium access control (MAC) in UWSNs have been developed despite there being sufficient terrestrial MAC protocols.  
The current research efforts on underwater MAC protocols have focused on increasing the channel utilization, avoiding hidden node problems, reducing delay, and enhancing fairness. First, to improve channel utilization, several underwater MAC protocols such as MACA-MN [5], MACA-UPT [6] and BiC-MAC [7], employ the packet train approach, where multiple consecutive data packets are transmitted in each round of a handshake. To address the hidden node problem, conventional underwater MAC protocols, such as Slotted-FAMA [8] and DACAP [9] have avoided the hidden node collisions by inserting a certain amount of waiting time, which results in a longer handshake exchange time and a longer delay. Recently, a way of reserving the channel through multi-hops at once is proposed, which is called cascading multi-hop reservation and transmission (CMRT) [10]. CMRT reduces the time taken for control packet exchange, and accordingly reduces the delay and increases the throughput. To enhance fairness, SF-MAC [11] has been proposed.  
Although power saving and reliable transmission have been of interest because of the poor channel characteristics, the demands for enhancing the data rates are also increasing because the currently supported rates are extremely low, and higher rates will enable new applications, such as video or security data transmission [2; 12; 13]. To enhance the data rate under limited channel capacity, the above-mentioned packet train scheme tries to fill the time-axis by transmitting multiple packets at once without individual handshaking. Such a high usage of time is a reasonable and straightforward way to increase the data rate. In this paper, the approach of packing time-axis is adopted to enlarge the channel utilization in one-dimensionally linearly configured multi-hop sensor networks, In particular, an internode transmission/reception timing schedule is designed to minimize the idle sections on the time axis. Thereafter, the scheme is analyzed mathematically to observe the power consumption at nodes through numerical results. Because data is gathered at the sink, the transmission/reception data cumulatively increases as they become closer to the sink along with rapid increases in power consumption. This will be analyzed quantitatively. That is, this paper first optimizes the data transmission rates through the proposed internode transmission/reception timing scheme and enables an estimation of the batteries necessary according to the node by observing the minimum power levels according to the node and the minimum overall necessary power. After that, the proposed scheme is compared with the existing packet train scheme by a computer simulation. The simulation environments reflect the realistic underwater channels in terms of the distances and path loss models.  
The paper is organized as follows: in Section 2, node deployment and frame timing are determined and the appropriate transmission/reception timing schemes are proposed. In Section 3, signal-to-interference-plus-noise ratio (SINR) and power consumption are derived, and the numerical results and discussion of the results are provided. The simulation results are given in Section 4, and Section 5 reports the conclusions.