# A Cross-Layer Media Access Control Protocol for WBANs
## 4 The Proposed Cross-Layer MAC Protocol
### Base Transmission Power Determination  
Two efforts are made to enhance the packet reception ratio, mitigate packet collisions, and ensure sufficient signal strength. As the majority of packets transmitted are periodic health information, the TDMA scheme is employed during the CFP, allowing sensors to upload packets without collisions. During the CBP, only a smaller number of packets are transmitted, further reducing the chances of collisions. In the absence of collisions, the packet reception ratio depends on the signal-to-noise ratio. Taking non-coherent FSK as an illustration [31], the packet reception ratio can be mathematically expressed as follows:  
\[\Theta(\gamma)=(1-f(\gamma))^{L}=(1-\frac{1}{2}exp^{-\frac{2\beta}{2\pi}})^{L}, \tag{3}\]  
where \(f(\gamma)\) denotes the bit error rate, \(\gamma\), \(R\), \(L\), and \(B\) represent the signal-to-noise ratio (SNR) at the coordinator, the transmission rate, the packet length in bits, and the noise bandwidth, respectively. By improving its transmission power, a sensor can achieve a higher \(\gamma\), thereby increasing the probability of successful packet reception. However, higher transmission power leads to faster energy consumption and shorter network lifetime. Hence, there exists a trade-off between the packet reception ratio and network lifetime. To address this trade-off, a dynamic determination scheme is required to adjust the transmission power based on the data type. For instance, in the case of event-triggered emergency data, the loss of such data may result in serious consequences. Therefore, higher transmission power is desired to ensure the reliability of the data. Conversely, for periodic health monitoring, a longer network lifetime is preferred. As long as the user's state is healthy, the loss of a frame in the continuously detected periodic data would not have a significant impact. Thus, a relatively lower transmission power is acceptable to ensure that more packets can be uploaded within the sensor's life cycle.  
We need to determine a base transmission power to meet the requirements of low-priority data, and a transmission power adjustment scheme is also needed, which can choose the proper power for data with different priorities. The base transmission power is calculated according to the wireless channel state. When sensor \(n_{i}\) transmits data using power \(P_{i}\), the received SNR at the coordinator is  
\[\gamma_{ic}=\frac{p_{i}|g_{ic}|^{2}}{\sigma^{2}}, \tag{4}\]  
where \(\sigma\) and \(g_{ic}\) denote the power of the noise signal and the channel gain. Correspondingly, when the coordinator broadcast beacons using power \(P_{c}\), the received SNR at sensor \(n_{i}\) is  
\[\gamma_{ci}=\frac{p_{c}|g_{ci}|^{2}}{\sigma^{2}}, \tag{5}\]  
According to the wireless channel reciprocity, the receiver and the transmitter of one wireless link observe the same channel simultaneously [32], and the channel gains are equal as \(g_{ic}=g_{ci}\). Then, the base transmission power \(P_{i}^{*}\) can be calculated according to  
Figure 2: The overview of the superframe.  
\[(1-\frac{1}{2}exp^{-\frac{B_{\Psi_{2}i}}{2 RT\Phi}P_{i})}L^{\frac{1}{2}}\geqslant\Phi. \tag{6}\]  
where \(\Phi\) denotes the threshold value of the packet reception ratio.  
Instead of using a fixed transmission power \(P_{max}\), the lifetime of a sensor can be effectively improved by using the base transmission power \(P_{i}^{*}\). Then, sensors can upload low-priority data using \(P_{i}^{*}\) to prolong the lifetime and further improve the reliability of high-priority data through priority-based transmission power adjustment.