## 1 Introduction  
Underwater sensor networks (UWSNs) have great potential in many areas, mainly in environmental monitoring, with applications in the fields of oceanography, defense and security, and fisheries, which include pollution control, the gathering of scientific data, or intruder's surveillance. Image transmission from remote sites is the most envisaged capability of UWSNs [1; 2; 3]. One important case is monitoring the behavior of river-fed sediment plumes in estuaries and deltas [4], because of their influence on water quality and the environment. UWSNs are long-overdue to reduce the cost of traditional monitoring methods, like campaigns of CTD (Conductivity-Temperature-Depth) and turbidity measurements on board ships. These measurement campaigns are also affected by bad weather, e.g., storms, which are frequently the reason for the campaigns. Furthermore, the data gathered and sent by the network can be available near real time in an on land data center for later processing. Nowadays, using optical wireless communications for the underwater medium is only possible up to a few meters [5], and even less if radiofrequency waves are used instead, while acoustic waves can reach distances in the range of kilometers. Therefore, the communication channel chosen in this work is the underwater acoustic channel (UAC), which has several important limitations: the low propagation speed of the acoustic waves, the limited available bandwidth, the high absorption, and the frequency-selective fading. The former causes underwater communications to suffer from a high latency, while the others only allow for transmission with a limited signaling rate. Special care must be taken in time scheduling to achieve a reasonable throughput in the network operation. In this paper, we cope with the latency so that it will not play against throughput. The first step to achieve a high throughput must be to employ a time-efficient MAC layer. In this work, the Time-Division Multiple Access (TDMA) operation has been adopted, since it is the most time-efficient technique [6]. Nevertheless, TDMA requires good scheduling to organize the node transmissions. We exploit the large propagation delay to choose the best scheduling, as we will see later in Section 2. Many TDMA techniques have already been presented and assessed in the literature when concerning the MAC layer in UWSNs [7]. A recent paper that also provides an exhaustive survey of the different TDMA variants in this type of networks is [8]. For example, the protocol named the Acoustic Communication network for Monitoring of Environment (ACMENet) [9], divides sensor nodes into two types: master and slave nodes, similar to protocol SBMAC [10]. In these protocols, propagation delays are measured and the resulting values are used to avoid packet collisions. Although slave nodes in the ACMENet protocol have a simple design, the master node is complex and can be a problem when the network size grows. In [11], protocol ST-MAC is designed to overcome the spatial-temporal uncertainty in the TDMA-based MAC scheduling, improving the throughput by means of resolving a conflict graph. Spatial TDMA (STDMA) was proposed as early as 1985 [12]. The idea is that two hop links of the network that are far enough apart, i.e., do not interfere each other, can be operating simultaneously. Scheduling is of paramount importance in STDMA networks. [PERSON], et al. [4] present optimal STDMA scheduling for linear networks where the sink node collects a single packet from every node in one frame. The problem of finding the shortest frame is addressed as a bin packing problem. However, no propagation delay was considered. The long propagation delay of the acoustic waves allows the nodes to overlap their transmissions in time without collisions. The idea of exploiting the time overlapping of travelling waves to increase the throughput in TDMA networks has been already proposed [6; 13; 14].