## 2 Related Work
### Beamforming  
Initial work was directed to study the effect on beamforming of antenna clusters with random spatial distributions based on the theory of antenna array [15], and also to the study of synchronization [19; 20]. Although the CB-DCB proposals are old, little progress has been made in the last 14 years in terms of their practical application in a real WSN deployment [21]. The main problem is the synchronization and the introduction of time delays, the mote cannot introduce the necessary delays for the strict beamforming and electronic steering that an array can perform, and this is because its architecture is very simple and low cost [14]. It needs to be remembered that the hardware of the motes is little more than a microcontroller capable of communicating at short distances with the standard IEEE 802.15.4, [14]. The fundamental difference between CB or DCB in WSN and an array of antennas is that in an array there is only one oscillator that generates the carrier, and with WSN-CB-DCB independent oscillators are treated, one in each mote, and this imposes many technical limitations [14]. This also imposes the use of WSN-CB-DCB in emission but prevents its use in reception, which is why the utility of WSN-CB-DCB is to achieve a higher transmission gain only, to get with sufficient intensity (RSSI) to a receiver that would be at a large distance from the WSN, [22]. The WSN-CB-DCB starting point was the theory of antenna clusters with random spatial distributions, and has been based on the hypothesis that phase (temporal offset) and frequency (frequency offset) synchronization is possible, and they theorize about beamforming from those assumptions. For instance, using the theory of antenna arrays with Gaussian spatial distribution [23; 24], with random or arbitrary spatial distribution of the nodes [25; 26], using a closed loop with 1-bit feedback to correct the phase offsets [27], or by changing the direction of the beam [28]. The control of the radiation pattern by a proper adjustment of nulls and sidelobe levels was theorized [29; 30], because the power that is radiated in the undesired directions is wasted (as are the side lobes). The final objective of these proposals is to save battery power [31]. Finally, it was also proposed that the CB-DCB sends the signal to multiple directions [32]. At the same time, the development of CB-DCB techniques seeks an intelligent choice of emitting nodes to minimize energy consumption [33; 34]. Battery power is extremely important for the survival of the WSN. If one of the nodes depletes its energy it can no longer monitor or transmit. This node is lost to the network, and if more nodes are lost the WSN may cease to be useful. The energy of the nodes is therefore a precious asset that must be used to the maximum because this will determine the longevity of the WSN. In this way a line of work arises that focuses on looking for synchronization procedures and choice of nodes for CB-DCB that are very efficient in order to minimize energy consumption, for example [35; 36]. In [37], a convex optimization procedure is formulated to maximize the network lifetime taking in account other miscellaneous sources of battery depletion different from that of communications, and genetic algorithms are also used to obtain the maximum lifetime [38], looking for optimal phase and amplitudes at each node. However, there is no clearly defined and widely accepted metric to evaluate the energy and longevity of a WSN. There are several metrics used by different researchers that also change their definition according to the author, for example for some authors the longevity of the WSN is the period of time that the WSN can attend a QoS, [37]. For others, it is defined as the number of operational motes, with enough battery, after a CB-DCB, and finally other researchers calculate it as the time it takes to remain inoperative (without battery) the first node [38].