## 2 Original Star-Based Configuration
### Node Energy Model  
In a real implementation of a node it is necessary to consider all energy requirements, including energy requirements for sensors, microcontrollers, RF chip, _etc._ The energy requirements in Joules of each aspect of the node can be calculated using:  
\[E=I\times V\times t \tag{1}\]  
where I is the current in Amperes, V is the voltage in Volts and t is the time in seconds. The complexity of the RF protocol will influence the requirements because it will involve higher processing requirements at the microcontroller level. Depending on the state of the node, the requirements of energy will be different. The total requirements of energy can be expressed as:  
\[E_{total}=E_{\sigma}+E_{protocol}+E_{sens\,sing} \tag{2}\]  
where \(E_{\sigma}\) is the energy required by the radio modem portion of the node; \(E_{protocol}\) is the energy needed to handle data to be transferred, the protocol overhead, and the radio modem signals handling (for instance, the communications signals between a microcontroller and independent radio modem); \(E_{sensing}\) are the energy requirements for the sensing aspects and it is independent of the RF portion.  
\(E_{\sigma}\) is the only parameter that was considered when comparing WSN protocols and it is the one that was estimated in the simulations section.  
The radio-modem has different energy requirements depending on whether it is transmitting, receiving, idle or sleeping. For example, the Texas Instruments/Chipcon CC1101 ISM band transceiver used in our implementation has four main states: idle, receiving, transmitting and shut-down. Table 1 summarizes some of the current requirements for the different states. Table 1 also includes real measured values. We also tested salient parameters for low power devices such as pin leakage that are not documented in datasheets.  
For estimating the energy required for the radio modem Erf we used the following equation:  
\[E_{\sigma}=V\times\left(I_{sleep}\times T_{sleep}+I_{idle}\times t_{idle}+I_{ rx}+t_{rx}+I_{rx}\times t_{rx}\right) \tag{3}\]  
where the definition of each state is:  
* Sleep: Radio modem in sleep-mode. This is the lowest possible power mode;
* Idle: Radio modem chip is ready to switch to receiving or transmitting mode. This mode requires significant energy because oscillator is running;  
\begin{table}
\begin{tabular}{|l|c|c|c|} \hline
**Parameter** & **Current according** & **Measured** & **Units** \\  & **datasheet** & **current** & \\ \hline Receiving mode for 898 MHz (SRX) & 15.7 (reduced mode) & 19.6 & mA \\ “SLEEP” mode (SPWD) & 0.2 & 0.07 & uA \\ Transmission mode, 868 MHz, FSK, 10 dBm & 35.5 & - & mA \\ Leakage current at pin CS (chip not selected) & Not documented & \textless{}1 μA & N/A \\ Current leakage at pin GD0 & Not documented & 0.1 & mA \\ \hline \end{tabular}
\end{table}
Table 1: Current requirements measured and specified in datasheets. VDD = 3.3 V.  
* Tx (transmission): RF data is being transmitted;
* Rx (reception): RF modem is in receiving mode. The energy requirements while receiving data and waiting for data are not significant.  
The main objective of a low power protocol will be to maximize the time that the radio modem is in sleep mode. In real implementations, the energy requirement of each electronic part depends on its state. It is fundamental to test each part individually in different configurations in order to check whether the energy requirements specified on the datasheets are correct before considering its inclusion in the project (a mistake the authors have experienced first-hand in previous work). For the calculations, the maximum energy consumption must be considered.