## 4 Cooperative Stochastic Transmission Planning  
As stated, without lack of generalizability, and to ease the understanding, we will assume the BS is placed in a Low Earth Orbit (LEO) satellite, with an altitude between 200 and 2000 km. In this scenario, we must find a way to achieve constructive interference in the direction of the receiver. It is assumed that the distant BS has enough energy to communicate with the motes (non-cooperative reception), but the motes independently do not reach the BS or satellite. Thus, the motes need to make a coherent transmission with constructive interference in the direction of the BS. We are facing an asymmetric or non-reciprocal situation in which the BS would have enough power to send a signal of sufficient intensity to the motes, but not the other way around. It is assumed that the WSN is distributed on the ground, and the BS are in some direction above them at a great distance, in a LEO a satellite. So, the BS transmits a beacon to the WSN motes to indicate that it is above them, because the BS (with more powerful hardware and a precise clock) knows where it is at all times and where the WSN is too. This broadcast communication is done directly from the emitter to all the motes. The motes when receiving the beacon are aware that the satellite or BS is in its upper space. This communication takes place for all the motes at the same time, except for the small delay associated with their different spatial positions. The reception of the beacon starts the synchronization and the transmission from all the motes of the WSN simultaneously. Thus, the motes start to emit the same message, following a loop until the BS receives the message as shown in the next algorithm:  
Figure 3: Deployment of motes to cover an area of 2 Ha in vineyards in the Sierra de Negrete (Valencia): (**a**) Vineyards land; (**b**) Screenshot of SIGPAC web tool used to manage plots of fields ([[http://sigpac.mapa.es/](http://sigpac.mapa.es/)]([http://sigpac.mapa.es/](http://sigpac.mapa.es/))). In this case, the motes are trying to receive from the BS. Then, when the BS sends the broadcast beacon, the receiving motes will be synchronized (assuming their internal accuracy). The motes are ordered to synchronize with a relative delay between them due to their different spatial position in receiving the triggering signal from the BS. The synchronization process is carried out between the motes of the WSN, which adjust the offsets of their respective clocks communicating with each other. The errors of clock and synchronism mean that the time offsets vary randomly between all the motes. These random time offsets have a certain probability of generating a constructive interference and to give rise to a random pointing. The pointing direction in which the constructive interference is achieved varies randomly for each instant due to clock errors. In this way, a random pointing or stochastic pointing is achieved, which in principle, and after a number of M repetitions of the message, manages to be high enough to get the signal to the BS. Finally, when the BS receives the message, it will send a new beacon (acknowledgment) to the motes of the WSN to notify of the correct reception and put an end to the repetition. It is important to highlight, that due to the half-duplex communication scheme of the motes, as well as their limited energy, the receiving process is always done asynchronously and in duty-cycles. This must be taken into account, both at the initial beacon from the BS and the acknowledgment. In both cases, once a mote had received the message (beacon from the BS), it will spread the information among their neighboring motes in the WSN. Also, notice that meanwhile the motes are transmitting in order to make a CB, they will switch periodically to reception mode in order to receive the acknowledgement of the BS. In addition, if the BS on the satellite knows the position of the WSN, it can send the beacon when it is on the vertical to minimize the distance of transmission.