## 5 Analysis of Alternatives for CB  
Finally, the phase offset for the independent transmission at the motes is the most important to do CB. Defining the optimal offset is a challenging task due to the difficulties in performing an accurated synchronization. In this section, we state and analyze different feasible alternatives and their assumptions, taking into account the constraints imposed by existing commercial motes. _Alternative 1_: We could synchronize all motes in a WSN with a broadcast packet transmission (or trigger), sent by a coordinator to start the transmission at each mote to perform the CB, where the required offset is introduced beforehand by the location (distance) of each mote to the coordinator. That is, each delay is introduced indirectly by the time propagation of the broadcast packet (trigger) to reach the different motes in the deployment assuming that the trigger propagates at the speed of light (\(c\)). Thus, once the motes receive this trigger, they could start the transmission. In this alternative, the required offsets will be related to the exact location of each mote in the deployment. In order to evaluate this alternative and its accuracy, we analyze the variation of the delay of the SFD activation for different motes that receive the same broadcast packet, in a receiver-to-receiver model using TelosB motes. The motes run a program written in NesC language [26] that activates the SFD outpin when receiving the broadcast packet, and, with a digital oscilloscope, we measure the time differences. The motes use a TinyOS [27] operating system. Figure 4 shows this scheme between two motes (approximately 1 m apart), where \(T_{1}\) and \(T_{2}\) are the delays to activate the SFD at each mote and \(T_{3}\) is the measured time difference. \(T_{3}\) is experimentally obtained using two motes analyzing the symbol transmission. Figure 5 shows the histogram of the time delay for 1948 measurements, and the average is \(\mu\) = 0 ns and \(\sigma\) = 165 ns (95% Confidence Interval [\(-\)7.3, +7.3] ns). These results agree with [28]. It is important to note that this delay is affected by the uncertainty both of time synchronization and location. Unfortunately, unless we find different commercial motes with another design, it is impossible to meet _R_-6 with such stretch standard deviation. These results also apply to the algorithms proposed for open and closed loop phase synchronization in [3; 5; 7] seen in Section 2. In addition, we should take  
Figure 4: Measuring the Start Frame Delimiter delay with a receiver–receiver scheme. into account that in case we use a GPS for the location of the motes, it has a resolution of \(\sim\)3.5 m [21] as stated previously. _Alternative 2_: We could consider a different procedure to achieve a better synchronization using extra equipment. We could use synchronization techniques based on GPS, but they offer a synchronization error on the order of microseconds [29]. A recent technological advancement is the development of high precision oscillators that use atomic standards, such as cesium and rubidium standards, both implemented in a chip scale size. The first Chip-Scale Atomic Clock (CSAC) was presented in 2004, and it has been commercially available since 2011 [30]. It provides high accuracy phase synchronization between motes for relatively long time durations with precision of around hundredths of nanoseconds. Nevertheless, on one hand, at the time of the present work, the cost of a CSAC was tremendously higher than the price of a single mote. On the other hand, in spite of the fact that recent atomic clocks were made to be low in power consumption, compared to the power used in motes, it is considered extremely high. For example, TelosB and MicaZ motes draw 1.8 mA and 8 mA, respectively, in the active mode using 2 AA batteries, compared with 36.3 mA with an input power of 3.3 V (120 mW) for a CSAC. Then, an additional power supply might be needed in a practical implementation.