# Virtual Sensing Directional Hub MAC (VSDH-MAC) Protocol with Power Control
## 2 Medium Access Control Protocol
#### VSDH-MAC Channel Access Algorithm
Although the CMDMAC protocol provides better throughput performance compared with the VSDH-MAC protocol, under these conditions, the additional requirements mean that the throughput performance comes at the cost of increased node manufacturing cost and energy consumption. Moreover, Figure 7 shows that the throughput performance of applying an idealized antenna pattern is significantly higher than using realistic antenna patterns. Figure 6: Throughput of the VSDH-MAC and DIFS-VSDH-MAC protocols with different antennas patterns with \(M=4\), compared against the VSDH-MAC with a single omni-directional hub antenna. Figure 8 shows the average transmission energy required by the VSDH-MAC protocol with and without power control, for each successful data bit. The power control algorithm can reduce the average required transmission energy by a factor of two. One of the goals of the VSDH-MAC is to prolong the lifetime of the sensor and hence the network lifetime. To quantitatively compare these directional MAC protocols, we adopt the quoted values of current consumption values from MICAz more [26]. Two 1.5V batteries rated at 2000 mAh each are assumed for each sensor node. We assume the current draw and the size of the packets are fixed. Figure 9 shows the numerical comparison of the expected lifetime obtained from the directional MAC protocols including the directional CSMA/CA. Figures 8 and 9 highlights that the energy efficiency and lifetime expectancy of the VSDH-MAC outperforms the other protocols. Comparing to the VSDH-MAC protocol, the physical carrier sensing from the other directional MAC protocols contribute a significant amount of energy consumption to the sensor nodes. This mechanism with the lack of transmit power control further reduce the lifetime of the sensor nodes. It is important to have an accurate energy model and lifetime estimation of a sensor node, as it directly impacts the lifetime of a WSN. Figure 8: The required transmission energy per bit with and without the proposed power control scheme. Figure 7: Impact of antenna pattern on throughput performance with \(M=4\). Figures 10 and 11 show the fairness of the VSDH-MAC protocol. Figure 10 shows the impact of transmission distance on fairness performance and the effect of the power control strategy. It can be seen that the effect of distance on throughput is much less with the power control strategy, thus increasing the fairness of the network. In wireless communication, increasing the propagation distance would increase the path loss in the transmission which may cause the SINR to decrease with distance. However, the power control strategy in VSDH-MAC provides a uniform SINR for all sensor nodes regardless of the propagation distance, thus increasing the per node fairness. Figure 10: The proportion successful transmissions as a function of distance from the hub at maximum throughput. Figure 9: Comparison of expected sensor node lifetime with different network traffic load. Figure 11 compares the fairness performance of VSDH-MAC protocol and IEEE 802.11 DCF using [PERSON]'s fairness index [27]. [PERSON]'s fairness index is used to determine the fairness of the network at different offered loads, and is defined by:

\[FI=\frac{\left(\sum_{i=0}^{n}\ x_{i}\ \right)^{2}}{n\sum_{i=0}^{n}\ x_{i}^{2}}, \tag{9}\]

where \(n\) is the number of nodes in the network, \(x_{i}\) is the throughput of the \(i\)th node within the network. The fairness index ranges from \(\frac{1}{n}\) to 1. Ideally, when all sensor nodes share the channel equitably, the fairness index should be equal to 1. Figure 11 indicates that the VSDH-MAC protocol with the power control strategy achieves a higher fairness index than the case without power control and the directional CSMA/CA. At the low offered load, VSDH-MAC provides a very high Jain's fairness index value. This indicates that all sensor nodes within the network have an equal opportunity to transmit a packet to the hub and of being received successfully.