## 1 Introduction
[31] proposed an analytical model to study the optimal depth threshold of a receiver-based opportunistic routing protocol for a UWSN. The UWSN consists of underwater motes and surface sonobuoys. The receiver-based opportunistic routing protocol decides to forward a packet using the depth difference between a transmitter and a receiver. They presented a numerical method for computing the optimal depth threshold by assuming homogeneous Poisson point processes. In this paper, we propose an underwater multi-DATA train protocol with multi-RTS reception and block ACK (BACK), shortly called an underwater multi-DATA train protocol, based on the CSMA/CA protocol using the RTS/CTS exchange method. We consider an underwater acoustic sensor network which consists of an underwater sink node and multiple underwater sensor nodes. Each underwater sensor node can transmit sensory information to the underwater sink node using our proposed protocol. Due to long underwater acoustic propagation delay, some RTS frames may not overlap at a sink node, even if the RTS frames were sent to the sink node simultaneously by different sensor nodes. We consider that our underwater sink node can recover these nonoverlapping RTS frames, that we can call multi-RTS reception. Since our RTS frame contains ID of the RTS sending node and a timestamp, the sink node calculates the propagation delay between the RTS sending node and the sink node, then broadcasts a CTS frame. Since our CTS frame contains the time information about when each RTS sending node can transmit a DATA frame to the sink node, multiple DATA frames transmitted from different sensor nodes to the sink node can be formed as a train, that we can call a multi-DATA train. Then, the sink node broadcasts a BACK frame which contains whether each DATA frame was successfully received or not. We also propose an underwater BACK protocol which is analogous to our proposed underwater multi-DATA train protocol except the multi-DATA train and the information contained in RTS and CTS frames. Then, we analyze normalized throughput and mean access delay of our proposed underwater multi-DATA train protocol, our proposed underwater BACK protocol, and the conventional protocols, respectively. The analytical results agree very well with the simulation results for throughput and delay performances of our proposed protocols and the conventional protocols, respectively, with various numbers of underwater sensor nodes and input parameters. The analytical results and the simulation results show that our proposed underwater multi-DATA outperform the conventional protocols. We also provide a more generalized and accurate analysis of the throughput and delay performance for the underwater multi-RTS reception protocol presented in our previous study [17]. The throughput and delay performance of the underwater multi-RTS reception protocol is compared with that of our proposed underwater multi-DATA train protocol and that of our proposed underwater BACK protocol, respectively, for various values of input parameters. The analytical results and the simulation results show that our proposed underwater multi-DATAtrain protocol and our proposed underwater BACK protocol outperform the underwater multi-RTS reception protocol in terms of normalized throughput and mean access delay.