# Mutual-Information-Based Incremental Relay Communications for Wireless Biomedical Implant Systems
## 5 Analysis of Selected QoS Metrics
### Network Throughput  
The network throughput denotes the number of successfully received data packets at the coordinator. As stated in Equation (2), transmission of a higher number of data packets demands significant energy consumption. The maximization of the network throughput \(y_{D}\) can be expressed as  
\[\underset{P_{t},C_{SR_{j}},C_{R_{j}D},|N|}{\max}y_{D} \tag{21}\]  
where \(y_{D}=\alpha y_{SD}+\beta y_{RD}\) as mentioned in Equation (14).  
This is subject to  
\[P>P_{min}, \tag{22}\]  
\[P_{t}\leq P_{max}, \tag{23}\]  
\[C_{SR_{j}}=1,\ j=1,2, \tag{24}\]  
\[C_{R_{j}D}=1,\ j=1,2, \tag{25}\]  
\[0<|N|\leq i,\ i=1,2,\ldots,n. \tag{26}\]  
The objective of Equation (21) is to maximize the total number of received packets \(y_{D}\) at the coordinator from the implanted sensors and relay nodes during the network lifetime \(T\). To maximize \(y_{D}\), the coordinator implements a fixed-ratio combining strategy where the optimal ratio value of 2 for Equation (14) is taken into account in accordance with [29]. Equation (22) demonstrates that the OP should be higher than the minimum required value \(P_{min}\) as proved in Equation (6) under the minimum required BER of \(10^{-3}\)[25; 30]. According to Equations (5)-(7), higher transmission power \(P_{t}\) promises better link quality. However, this causes body temperature rise and may damage the human body; therefore, \(P_{t}\) should be carefully designated to guarantee human safety. The constraint in Equation (23) implies that the value of \(P_{t}\) should not be more than that of the maximum transmitting power \(P_{max}\) as regulated by the IEEE 802.15.6 technical standard [1]. Equation (23) fulfills the condition that all possible transmission paths from \(S\) to \(R\) can be established. The constraints in Equations (24) and (25) state that the network should minimize the number of dropped information packets when transmitting from \(S\) to \(R\) and \(R\) to \(D\), respectively. Moreover, it is worth noting that the number of transmitted packets from \(S\) to \(R\) should be no more than the flow from \(R\) to \(D\) as analyzed in Equation (18). Equation (26) offers that the total number of implanted sensors within a WBAN should be limited to reduce the channel access contention and data collision. Since the primary target is to maximize the network lifetime, there exists a tradeoff between network energy consumption and other performance metrics such as throughput, transmission distance, and so forth. One should note that by adopting the optimization of (15), unlike the work in [10], the transmission link is not always applicable to deliver data to the relay or the coordinator, which results in decreasing the number of transmitted packets. Moreover, due to the nature of human mobility and the instability of the intra-body channel, even when using the maximum allowed transmission power, numerous data packets are still dropped or lost during the transmission process. In this paper, we do not consider data retransmission and the computation capacity of wearable relays and the coordinator. To support retransmission of the dropped packets, surplus energy consumption is required and may significantly reduce the network lifetime as we analyzed in (16). Detailed information regarding retransmission can be found in [31; 32]. The computation capacity of the relay nodes and the coordinator is not considered. According to [33], computation-intensive or latency-sensitive medical data can be handled locally using edge computing techniques if the wearable device or the coordinator have enough local data storage size and calculation resources, or transfer data to the Internet of Things (IoT) cloud for further computing and analysis.