# End to End Delay and Energy Consumption in a Two Tier Cluster Hierarchical Wireless Sensor Networks
## 4 Communication
### Synchronization of the WSN
For tracking purposes, both, the \(FB\) and the \(SB\) are repeated regularly 5 times per each multiframe, in particular in \(TS=0\) and frames \((FB,SB)=(0,1)\); \((FB,SB)=(10,11)\); \((FB,SB)=(20,21)\); \((FB,SB)=(30,31)\) and \((FB,SB)=(40,41)\). It means that on average, the \(FB\) and the \(SB\) are transmitted once each 47.0769 ms approximately. The repetition of \(FB\) and \(SB\) are also named frequency correction channel (FCCH) and synchronization channel (SCH), respectively. Some similar figures can be found in WSN that operate in the 868-868.8 MHz (EU), the 902-928 MHz (USA, Canada, etc.) or 2.4 GHz Industrial Scientific and Medical (ISM) bands. They are built upon IEEE 802.15.4 protocol using 5 MHz channels and able to transmit up to 250 Kbps (due to protocol overload, the net bit rate is reduced by half, approximately). In fact, the PHY/MAC layer determines the frame size, for instance in the referred IEEE 802.15.4 standard says the frame size is 127 bytes, so we can assume data packets of size around 1000 bits, including overheads (preamble, identifiers, CRC, etc.). Then, the transmission time of a WSN data packet turns to be equal to 1000 bits/(\(250\times 10^{3}\) bits/s)= 4 ms, i.e., 4 us per bit. In addition, for coverage areas of our WSN with radio less than 600 m, the propagation delay from the sink to the edge of the WSN is around \(600/3\times 10^{8}=2\) us which means half a bit \"in the air\", a very significant difference compared with the 34.125 bits in GSM. So we surmise that, in our WSN scenario, a TA algorithm is not of imperative necessity and can be avoided by using guard periods as suggested in [12]. On the other hand, we need to take into account the quality of the clocks. For example, as is reported in [32], according to the data sheet of a typical crystal-quartz oscillator commonly used in sensor networks, the frequency of a clock varies up to 40 ppm, which means clocks of different nodes can loose as much as 40 us in a second (or 0.16 us per data packet or data slot, i.e., 1/25 part of a bit). Then, some guard bands can be inserted into the time slot structure to cover practical aspects of synchronization errors. At first glance, in a parallel way to the GSM time-slot structure, if a GP of 8.25 bits is added to the 148 real bits of the normal burst i.e., 5.55%, keeping the same proportion to our WSN we could have a GP of 53 bits added to the 947 real bits, in total the 1000 bits that fill our data slot of 4 ms. Regarding the frequency synchronization and the time synchronization both can be periodically updated, for instance at the beginning of each Combi-Frame, see Figure 3, i.e., one \(FB_{WSN}\) at the beginning of the CONT sub-frame and one \(SB_{WSN}\) at the beginning of the TDMA sub-frame. The repetition rate of both burst will depend on the final length of the Combi-Frame. We recall that the \(FB_{WSN}\) is the beacon signaling used to synchronize receiver radio to the carrier frequency and the \(SB_{WSN}\) for time synchronization, including some WSN parameters such as the Combi-Frame numbering.