## 4 Cooperative Stochastic Transmission Planning
### SCB from a WSN with Linear Distribution of Motes in Horizontal Plane
#### 4.2.2 Random Linear Distribution and Stochastic Transmission Activation  
This type of spatial distribution would not be the one initially proposed to monitor the area of study, but it is interesting to analyze it because it would be applicable to a deployment of motes made from the air by a helicopter or a drone over an inaccessible area. We consider up to \(N=20\) motes in which the clock offsets are obtained from measurements (Figure 4), but now these are located in a random way along a line of length of 1.0 km. We make a Monte Carlo simulation in which we introduce again the random delays measured in the motes [13; 14]. In addition, 20 cases are considered in which the number of distributed motes that are activated to transmit change from \(i=2\) to \(i=N/2\) motes. For example, the WSN can activate the emission of 2.3,... \(N/2\) motes randomly for each WSN-N case. This case would respond to the possibility that not all motes transmit at every attempt, because the motes do not have enough energy in the battery, because they have deteriorated over time or because some physical obstacle blocks the trigger signal from the BS or its own signal. Figure 9 shows the maximum gain obtained in the broadside direction as a function of the number of motes, and the maximum gain normalized to the theoretical maximum as a function of the number of motes used. It is observed how the gain increases logarithmically when the number of motes increases. If we take into account the maximum achievable gain, normalizing the maximum gain, this decrease from \(N=5\), but always being above 40% of the theoretical maximum gain. This result indicates that it is necessary to look for a trade-off solution: with a number of motes that allows a sufficient gain, from a certain number of motes that the gain increase is reduced. The activation of the transmission would be stochastic, given that a priori the state of the motes would not be known, nor all have received the trigger correctly from the BS.  
Figure 8: Gain distribution in the experiment of 100 stochastic transmissions for a linear WSN of 20 motes (WSN-20), a WSN of nine motes (WSN-9) and WSN of five motes (WSN-5).  
Figure 9: Gain as a function of the number of motes for random spatial distribution. (**a**) Maximum Gain versus number of motes. (**b**) Normalized Maximum Gain versus number of motes.  
Figure 9 also shows the case in which not all the motes radiate the same energy. This is the case of the WSN with a linear distribution with random spacing but with an emission power lower than the maximum at all the motes. This case would be similar to the previous one, but instead of several motes not being operative, all of them would be, but with a power lower than the maximum. This would correspond better with a real deployment in which the motes are not at the same distance, and in which by different circumstances associated to the characteristics of the terrain and the environment, they transmit with less energy. The results show deterioration in the WSN's gain, but still gain is achieved in this case, that we consider as the most unfavorable.