## 3 Intermittent Periodic Transmit (IPT)
### Round Robin IPT (RR-IPT): Efficient Extention for Two-Dimensional Topology  
RR-IPT exploits the tree-topology of MWBN where forwarding paths are constructed around the core node. Role of the core node is predetermined depending on the deployment environment where wired Ethernet gateway is available. The tree topology is suitable for IPT since the core node acts as a control station. Wireless relay links on MWBN should be tolerant of an environmental fluctuation, so we employ minimum path loss routing [45; 46] which can organize stable forwarding paths as well as ensure higher transmission rate. Its detailed routing algorithm is summarized in [46]. The core node intermittently transmits owing packets with predetermined interval and other nodes immediately relay received packets in a decode and forward (DF) manner. Figure 4 exemplifies detailed flow of RR-IPT. The core node sends out packets to surrounding nodes in successive order; consecutive transmission to the specific node is prohibited. With the conventional IPT in the string topology, the core node must wait for its transmission until the intermediate node in two (or more) hops away has finished transmitting. In other words, transmission period should be provided so that communication ranges (depicted as circles in the figure) cannot be overlapped.  
In the tree topology, the transmission period can be set shorter than in the string topology by round robin packet transmission since the forwarding path (branch) is different as long as transmitted signals cannot interfere with each other, as illustrated in Figure 4b. Here, we consider the transmission period to be set for RR-IPT. Assuming packet transmission duration is \(T_{p}\) for all nodes, let \(N\) and \(T_{i}\) (\(i=1,2,\ldots,N\)) denote the number of relay nodes next to the core node and the waiting time after the transmission to the \(i\)-th relay node, respectively, transmission period, \(P\), for the specific branch can be expressed as follows.  
\[P=\sum_{i=1}^{N}\left(T_{p}+T_{i}\right)=NT_{p}+\sum_{i=1}^{N}T_{i} \tag{1}\]  
Figure 4: Round robin IPT (RR-IPT). (**a**) Transmission flow; (**b**) Frequency reuse on RR-IPT.  
Defining the required frequency reuse space as \(M_{i}\), a required transmission period for the \(i\)-th forwarding path, \(S_{i}\), is given by  
\[S_{i}=\ M_{i}\ T_{p} \tag{2}\]  
In order to completely avoid intra-path interference, \(P\geq S_{i}\) is required for all \(i\)-th forwarding paths. From (1) and (2), following requirement can be derived;  
\[P-S_{i}=\ NT_{p}+\sum_{i=1}^{N}T_{i}-M_{i}T_{p}\ =\ (N-M_{i})\ T_{p}+\sum_{i=1}^{N}T_{i}\ \geq 0 \tag{3}\]  
It indicates that intra-path interference can be avoided when \(N\geq M_{i}\) even though \(T_{i}\) is set to negligibly small value. In order to satisfy the above condition for arbitrary \(i\)-th forwarding path,  
\[N\geq\max_{i}(M_{i}) \tag{4}\]  
is required. Meanwhile, inter-path interference should also be considered in RR-IPT since IPT is performed to multiple forwarding paths unlike the string topology case. Although the most of intra-path and inter-path interference can be avoided by the use of transmission period, the former occasionally happens. Here we set minimum contention window (MinCW) as a small value but not zero and keep random back-off function activated so as to autonomously avoid inter-path interference while suppressing the overhead of CSMA/CA. In case a relay node has multiple forwarding paths, it also chooses subordinating relay nodes in round robin manner.