## 2 Deployment and Proposed Transmission/Reception Timing Schemes
### Proposed Schemes  
In general, in Figure 4, the horizontal axis is the spatial dimension that indicates the nodes and the vertical axis is the time axis that indicates the time slots. Data flows from the left to the right until it arrives at the diamond shaped sink node and time flows from the top to the bottom. The filled circles indicate that the nodes are transmitting data and the empty circles indicate that the nodes are receiving data. When nodes are idle, there is no circle on the intersection points. For easy explanation, the individual intersection points are shown with the coordinates. \((i,j)\) is the \(j\)th time slot from the top on the position of the \(i\)th node from the left. Owing to propagation delays, the transmitted frames are received by the neighboring nodes in the next time slot, which is indicated by the diagonal dotted lines in the figure. That is, the transmission from \((i,j)\) is received by \((i+1,j+1)\) and \((i-1,j+1)\). The diagonal dotted lines originally progress infinitely, not just one box, and the power of the signals attenuates greatly as the signals progress. On the other hand, each dotted line is drawn in only one box for easy understanding of the figure. Figure 3: One-dimensional linear data flow. (**a**) The sink node is located at the end; (**b**) The sink node is located at the center. Scheme 1 in Figure 4a shows the case where all nodes transmit data simultaneously and all nodes receive data simultaneously in the next time slot. From the standpoint of the receiving node \((i,j)\), the data comes from \((i-1,j-1)\), the immediate left upper box, and dominant interfering signals come from \((i+1,j-1)\), the immediate right upper box. If the transmission power levels of the two transmissions are the same, the SIR should be approximately 1(=0 dB). Note that, according to the calculations in the following section, the transmission power levels are different by the node. Because the data is received from two directions, left and right in the sink node, the time points of receiving should be alternated. Figure 4: Proposed transmission/reception timing schemes. (The thick arrows represent data transfer) (**a**) Scheme 1; (**b**) Scheme 2; (**c**) Scheme 3. Scheme 2 in Figure 4b is designed more elaborately. If the dominant interfering signals would not come from \((i+1,j-1)\), the immediate right upper box from the standpoint of receiving node \((i,j)\), the right upper box should not transmit data. Because the time axis use efficiency cannot be maximized if the box is idle, \((i+1,j-1)\) should be receiving data. This can be explained in Figure 4b with examples of coordinates following the circular arrow. The transmission by (3, 2) becomes a reception by (4, 3) and because the transmission by (5, 2) will cause great interference, (5, 2) should be receiving data. If (5, 2) is receiving data, (4, 1) should be transmitting data. Because transmission by \((i,j)\) requires transmission by \((i+1,j-1)\), the transmission is located in the diagonal direction in the figure and the reception corresponding to the transmission is located one box away in the diagonal direction. Figure 4b shows the overlapping deployment of two of this pattern. Because all points are filled with filled or empty circles, the time efficiency has a maximum value of 1/2, as observed with Figure 4a. On the other hand, Figure 4b is more advantageous than Figure 4a in terms of the SIR because the dominant interference occurs on the left upper region at a distance of three boxes. For example, the frame to be received by (6,4) comes from (5,3) but the interference comes from (3,1). If an underwater path loss exponent of 1.5 is assumed for practical spreading [14], three times the difference in distance will be calculated as \((1/3)^{1.5}\), indicating that the SIR gains of roughly 7.16 dB are provided. Because data is also received from two directions, left and right in the sink node in this case, the time points for receiving should be alternated to avoid a collision.