# Virtual Sensing Directional Hub MAC (VSDH-MAC) Protocol with Power Control
## 2 Medium Access Control Protocol
#### VSDH-MAC Channel Access Algorithm
The average energy consumption during data transmission, reception and control packets is given below: successful data packet transmission (\(E_{tx}\)):

\[E_{tx}=P_{tx_{RTS}}\ T_{RTS}+P_{tx_{DATA}}\ T_{DATA}+P_{rx}\left(T_{CTS}+T_{ACK}+2 \ x\left(T_{p}+T_{SIFS}\right)\right)\!, \tag{1}\]

colliding RTS or CTS transmission (\(E_{c\_RTS}\)):

\[E_{c\_RTS}=P_{tx_{RTS}}\ T_{RTS}+P_{rx}\left(T_{CTS}+T_{p}\right)\!, \tag{2}\]

colliding DATA or ACK transmission (\(E_{c\_DATA}\)):

\[E_{c\_DATA}=E_{c\_RTS}+P_{tx_{DATA}}\ T_{DATA}+P_{rx}\left(\ T_{ACK}+T_{p}+T_{ SIFS}\right)\!, \tag{3}\]

back-off due to unsuccessful RTS/CTS communication (\(E_{BO}\)):

\[E_{BO}=E_{c\_RTS}+P_{slap}\ (T_{CW})\!, \tag{4}\]

overhearing reception destined to other user after RTS transmission, (\(E_{OH}\)):

\[E_{OH}=E_{c\_RTS}+P_{rx}\ (\ T_{SIFS})+P_{slep}\ (T_{NAV}+T_{CW})\!, \tag{5}\]

sleep when no packet transmission is required (\(E_{slap}\)):

\[E_{Slap}=P_{Slap}\ T_{Slap}\!, \tag{6}\]

in addition, when carrier (DIFS) sensing is used, additional energy (\(E_{DIFS}\)) is consumed:

\[E_{DIFS}=P_{rx}\ T_{DIFS}\!, \tag{7}\]

where \(T_{DIFS}\) is the time during which the carrier is sensed. If a transmission is detected during \(T_{DIFS}\) then additional energy is expended (\(E_{OH\_DIFS}\)) whilst the node waits before attempting to transmit again:

\[E_{OH\_DIFS}=E_{DIFS}+P_{slep}\ (T_{NAV}+T_{CW})\!, \tag{8}\]

where, \(P_{slap}\), \(P_{tx_{RTS}}\), \(P_{tx_{DATA}}\), and \(P_{rx}\) are the power consumed in sleep, transmit and receive mode respectively. \(T_{SIFS}\), \(T_{DIFS}\) and \(T_{p}\) are the SIFS and DIFS time duration from IEEE 802.11 DCF standard and the propagation time of the packet. \(T_{CW}\) is the back-off time duration. \(T_{RTS}\), \(T_{CTS}\), \(T_{DATA}\), and \(T_{ACK}\) denotes the packet transmission time for RTS, CTS, DATA, and ACK packets respectively. \(T_{slap}\) is the time for the node to stay in the sleep state. \(T_{NAV}\) represents the back-off time indicated from the received NAV. Figure 3 shows a breakdown of the average energy consumption per successful data bit in a sensor node with respect to the channel offered load. Figure 3a is the energy consumption of the VSDH-MAC protocol with power control strategy. Figure 3b is the energy consumption of the VSDH-MAC protocol without the power control strategy. Figure 3c is the energy consumption of the IEEE 802.11 DCF protocol. By comparing those figures, it can be seen that the VSDH-MAC protocol provides a far higher energy efficiency than CSMA/CA protocol. Figure 4 shows the additional transmission required for the DIFS sensing. Table 2 shows the operation states of the sensor node and the power consumption of each state. The values are based on typical figures for current radio modules and serve only for comparative purposes. Figure 2:0 The transmission energy per bit for a four antennas DIFS-VSDH-MAC protocol showing the proportion of energy used by DIFS (DCF Interframe Space) carrier sensing. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**State** & **Activity** & **Tx** & **Rx** & **Power Required** \\ \hline \(S_{0}\) & Sleep & Off & Off & 0.003 mW \\ \(S_{1}\) & RTS Tx & On & Off & 52 mW \\ \(S_{2}\) & Receiving & Off & On & 59 mW \\ \(S_{3}\) & Data Tx & On & Off & 26 mW (Average) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Operational states for Finite State Machine (FSM) of sensor nodes. Figure 3: The comparison of required transmission energy per bit virtual sensing directional hub, medium access control protocol (VSDH-MAC) protocol with power control (**a**) and without power control (**b**), and carrier sense multiple access with collision avoidance (CSMA/CA)/distributed coordination function (DCF) protocol (**c**). We expect the number of hub antennas to have a small impact on the node energy usage in a given scenario. Firstly, as the number of nodes in each sector is reduced there is likely to be fewer collisions which would reduce the energy wasted by this mechanism.