## 3 Materials and Methods
### Proposed Patient Information Transmission Scheme  
The proposed framework utilizes an IoMT communication system to facilitate the transfer of patient data from various smart monitoring devices to a medical reception, as depicted in Figure 4. The presented framework aims to address the entire process of  
Figure 3: Proposed deep learning model for risk classification. collecting data from different sensors, applying XAI models for recommendations and analysis, and finally, securely and efficiently transmitting the data to remote locations for further analysis, storage, or request for intervention. The proposed transmission scheme is an important part of this framework to ensure an optimized use of the wireless channels to achieve the lowest data loss during transmission with minimal energy consumption to produce the best possible quality of service (QoS). The IoMT transmission system consists of a patient's smart monitor device, which must access the wireless channel to effectively send the data through the gateway to the medical reception. The proposed IoMT transmission model is designed to efficiently transmit patient data, achieving the highest possible QoS to ensure that the transferred data are successfully received by the destination. For achieving the required goals, an optimized energy-efficient model is proposed to enhance the system energy efficiency (EE) with the minimum required system outage probability \((p_{out})\) to ensure that the information is sent with the best QoS, i.e.,  
\[Max\sum_{n=1}^{N}EE,\;\;s.t.\;\;C1:Q_{UL}\geq 1-p_{outUL},\;\;s.t.\;\;C2:Q_{DL} \geq 1-p_{outDL} \tag{1}\]  
where C1 and C2 represent the Lagrange multipliers for the optimization problem. C1 ensures that the uplink outage probability \(p_{\text{out,UL}}\) meets the needed uplink QoS \(U_{\text{UL}}\). C2 ensures that the downlink outage probability \(p_{\text{out,DL}}\) meets the required downlink QoS \(U_{\text{DL}}\). The link outage probability is defined as the probability that any receiver has a signal-to-interference plus noise ratio \((SINR)\) lower than the required threshold \((SINR_{th})\), let \((SINR_{th})\) be referred to as \(\xi\). The required signal-to-interference plus noise ratio threshold for the uplink \((SINR_{thIL})\) and downlink \((SINR_{thDL})\) data transmission are referred to as \(\xi_{UL}\) and \(\xi_{DL}\), respectively. Therefore, \((p_{outUL})\) and \((p_{outDL})\) can be formulated, respectively, as [25]  
\[p_{outUL}=p(SINR_{thUL}\leq\xi_{UL})=1-\frac{P_{S}|h_{SG}|^{2}}{\xi_{UL}\sum_{i= 1}^{K}P_{Util}|h_{IUHG}|^{2}+P_{S}|h_{SG}|^{2}}e^{\frac{-S_{UL}N}{P_{S}|h_{SG} |^{2}}} \tag{2}\]  
\[p_{outDL}=p(SINR_{thDL}\leq\xi_{DL})=1-\frac{P_{C}|h_{GD}|^{2}}{\xi_{DL}\sum_{j =1}^{L}P_{IDj}|h_{IDjD}|^{2}+P_{G}|h_{GD}|^{2}}e^{\frac{-S_{DI}N}{P_{D}|h_{GD} |^{2}}} \tag{3}\]  
\(N\) denotes the noise power spectral density, expressed as \(N=N_{o}B\), where \(B\) is the system bandwidth in hertz. Moreover, \(P_{S}\) and \(P_{G}\) represent the smart monitor device and the gateway  
Figure 4: Proposed patient monitoring transmission scheme. transmission power, respectively. The parameters \(|h_{SG}|^{2}\) and \(|h_{IIDi}|^{2}\) are the channel gain coefficients between the smart monitor device and the gateway and between any interfering devices and the gateway, respectively. Similarly, \(|h_{GD}|^{2}\) and \(|h_{IDD}|^{2}\) represent the channel gain coefficients between the gateway and the medical reception, and between any interfering device and the medical reception, respectively. \(P_{IIDi}\) and \(P_{IDj}\) denote the transmission powers of interfering devices to the gateway and the medical reception, respectively.