## 6 Achievability Analysis: Proposal of Random CB  
Once we have seen unsuccessfully the different alternatives, to find a feasible solution for CB in WSN, we suggest relaxing the \(R\)-2 requirement. This means that instead of pointing to a fixed and known BS, because of the inability to control the phase offset of the transmissions at each mote, we could generate a random phase offset to perform CB, where the beam is pointing to a random point, covering the upper hemisphere. Statistically, we could assume that, under certain circumstances, we can reach the BS. An example of such random communications is present in Meteor Burst Communications (MBC) [32], as seen in Figure 7. MBC are based on the radio signal reflection at the ionized electron trails (called bursts) of meteors when entering the atmosphere. These trails are random in space, time and duration, but predictable in quantity. Commercial systems [33; 34] can perform long-distance burst data communications within a range of 500 to 1930 km at low bit rates (on the order of bps), but they are not suitable for real-time communications since the time window is very short and unpredictable (up to a few seconds). In Figure 7, the master station is sending a Request to the slave, that gives a Reply and finally the master sends an Acknowledgment (Ack). Thus, inspired by this approach, it is not necessary to meet \(R\)-1, \(R\)-2 and \(R\)-6, at the expense of increasing the energy demands due to the randomness introduced by the communication process. Now, we propose a long range communication based on CB, named random CB. In the proposed scheme, the motes will randomly generate different random offsets for a CB that randomly will scan the sky (upper hemisphere). In this case, the BS could be located at an helicopter, unmanned aerial vehicle (drone), an LEO (Low Earth Orbit) satellite (with an altitude between 20 to 200 km) or a special mote located high above the WSN, always at the line of sight. In a practical scenario, if we want to send the information gathered by the WSN outside the network, one feasible option should be sending it to a satellite because it provides better performances in terms of directivity (antenna gain), power transmission as well as sensitivity at reception. Then, when the satellite is flying above the WSN, it could move the antenna to point at the WSN and wait for a transmission. In this case, the motes should only follow \(R\)-3, \(R\)-4 and \(R\)-5 requirements. Figure 6: System on Chip: design of a mote with internal connection between the MicroController Units (MCU) and the radio transceiver. It is important to highlight that CB can only be implemented in the transmission, but it is not feasible in the reception, and it is always simplex. In the transmission, the sum of signals for the CB is done at the receiving antenna, However, in the reception, each receiver is independent and the signal can not be added coherently into a constructive interference to get a CB in a distributed way inside the WSN. This is a clear difference between antenna arrays of a single transmitter and cooperative transmission of many transmitters. In this case, we have a simplex communication channel and the WSN would work as a cooperative broadcast emitter, but it would not work as a cooperative receiver. However, we could get feedback from the satellite. To achieve this, it should be necessary to schedule different slots of time, where alternatively the WSN transmits and the satellite sends an acknowledgment in case it receives the message. Notice that the transceivers of the commercial motes are half duplex, thus while transmitting they cannot receive, as stated in the standard IEEE 802.15.4 [1]. In this case, the reception at the motes could be achieved if the satellite is able to send an acknowledgment, pointing at the WSN. The motes could receive this signal with an omnidirectional antenna. In particular, the TI CC2420 radio chip [19] has a receiver sensitivity of \(-94\) dBm.