# FD-LTDA-MAC: Full-Duplex Unsynchronised Scheduling in Linear Underwater Acoustic Chain Networks
## 2 FD-LTDA-MAC Protocol  
The FD-LTDA-MAC protocol is developed for full-duplex underwater multi-hop chain networks. It is an unsynchronised protocol that locally derives transmission times at the nodes by measuring the delays between nodes receiving a request (REQ) packet and transmitting their data packets. Consider a conceptual diagram of multi-hop chain Full-Duplex Relay (FDR) network shown in Figure 2.  
Each sensor node utilises two-way connections, it connects to the node one hop closer to the sink node up the chain and to a node further down the chain. Upon receiving an REQ packet, transmitting nodes forward REQ packets down the chain to the last node. Every transmitting node responds to the REQ packet query by either acting as a source node and transmitting its own data packet up the chain or by acting as a relay node forwarding data packets up the chain that it received from the node further down the chain. The sink node is responsible for sending the REQ packets to request data packets from the transmitting nodes and to handle eventual reception of data packets from the transmitting nodes. The last transmitting node down the chain does not relay packets, it  
Figure 2: Multi-hop chain FDR network. only transmits its own data packets. Every transmitting node serves as a data source or data forwarder except the last transmitting node, which serves only as a data source. It is assumed that the self-interference is totally cancelled. The new linear constraint is based on full-duplex communication structure to calculate transmit delays for an enhanced packet forwarding among full-duplex nodes. Additionally, a greedy scheduling algorithm uses full-duplex based initial starting point of search, this reduces the time wasted in waiting for an interference lapse before beginning a new transmission and the corresponding propagation delay components. The timing diagram of the FD-LTDA MAC schedule for a typical one-hop interference range full-duplex underwater chain network is shown in Figure 3. It consists of a master node, \(N_{m}\), which serves as the sink node, and three transmitting sensor nodes, \(N_{1}\), \(N_{2}\), and \(N_{3}\). The master node broadcasts REQ packets down the chain through nodes \(N_{1}\) and \(N_{2}\) to node \(N_{3}\). Nodes \(N_{1}\) and \(N_{2}\) forward the REQ packets after an allowable guard interval, \(\tau_{g}\). Upon the reception of a REQ packet by a node, it generates and schedules data packet for transmission or schedules forwarding of a relayed packet up the chain towards \(N_{m}\) after waiting a certain time called transmit delay. The wait time accounts for only REQ packet interval, \(\tau_{rp}\), but excludes the interference reception time, this is because, the FD-LTDA MAC protocol is able to schedule simultaneous transmission and reception of packets. The full-duplex gain (FD gain) is the measure of the transmit delay required for the FD-LTDA MAC protocol to successfully schedule packet transmissions without packet collisions. Examples of FD gain can be found in Figure 3 where \(N_{1}\) can transmit data packets (D2 and D3) much earlier than it could in the case of LTDA-MAC protocol. Additionally, D2 can be transmitted earlier by \(N_{2}\) due to the full-duplex capability compared with LTDA-MAC. The transmission scheduling is based on the timings and these timings are based on the scheduling algorithm which is described below. In order to find the transmission times, as labelled in Figure 3, the following algorithm is used. Extending the 4-nodes network of Figure 3 to the case with \(N_{m}\) transmitting sensor nodes, the FD-LTDA-MAC schedule transmit delays incurred by a node transmitting its own data packet to a node up the chain are represented by a triangular matrix,  
\[\mathbf{T_{tx}^{FD}}= \begin{pmatrix}T_{tom}^{FD}[1,1]&T_{tor}^{FD}[1,2]&\cdots&T_{ tor}^{FD}[1,N_{sn}]\\ \varnothing&T_{tom}^{FD}[2,2]&\cdots&T_{tor}^{FD}[2,N_{sn}]\\ \vdots&\vdots&\ddots&\vdots\\ \varnothing&\varnothing&\cdots&T_{tom}^{FD}[N_{sn},N_{sn}]\\ \end{pmatrix}