## 6 Sidelobe Reduction via Optimizing the Sensor Selection Algorithm
### The Sensor Selection Algorithm  
Node selection procedure works on the basis that the positions of the sensors forming an antenna array are selected such that their mutual phase offset due to their locations creates a coherently combined signal at the cluster head. Consequently, the node selection algorithm involves carefully selecting the best position for each collaborative sensor and then positioning according to the logical connectivity such that the beampattern is optimal. Assume \(\aleph^{\kappa}\) be a set of collaborative sensors to be selected from \(N^{\kappa}\), i.e., \(\aleph^{\kappa}\subset N^{\kappa}\), to form beampattern towards the base station. The path connectivity assigns a set of collaborative sensors to each source-destination pair that forms a specific topology. Each cluster consists of many sensors, thus the mainlobe of the beampattern is unstable for different number of \(\aleph^{\kappa}\) of different subsets \(N^{\kappa}\). This occurs as long as the coverage area does dynamically change according to IoT environment as well as the requirements of the applications in that environment. It is necessary to take into consideration these two conditions to maximize mainlobe towards the intended base station and minimize the sidelobes. We have developed an algorithm for sensor selection based on robust optimization scheme satisfying certain objective functions. First, to find an optimal solution for uncertain objective function which guarantees that the sidelobe levels at the direction of intended base station are below a certain prescribed value. Second, to find an optimal solution that is stable under fluctuations of the channel environments. However, it seems a challenge to find a robust optimal solution for the objective function \(f(\vec{x})\rightarrow\max(mainlobe)/\min(sidelobe)\) on a continuous optimization problem with uncertainty fluctuations in the collaborative sensors. This is because of the difficulty of realizing the gain achieved from the fluctuations in input variables to get an optimal solution. Hence, to assess the robustness of a solution for the objective function, there are common measures to calculate the expected fitness function taking into account the input variable fluctuations and their probability of deployment via a probability distribution function \(pdf(\vec{x})\) over the whole input variable space \([\vec{x}_{i}=\{(x_{i1},y_{i1}),(x_{i2},y_{i2}),\ldots,(x_{iK},y_{K})\}]^{ \aleph\subset N}\), where \(\aleph\subset N\) is the problem's dimension. As mentioned in the previous section, the spacing among the collaborative sensors affects the beampattern shape of the antenna array. Thus, selecting random sensors positions i.e., uncertain sensor positions may lead to positions errors. However, the minimum SLL of an antenna array with fixed and selected sensors positions is higher than that of the antenna array with randomly selected sensors if the number of antenna array is the same, since the distance among the randomly selected sensors has maximum Euclidean distance corresponding to a certain hop-distance which is considered to be a practical metric for modeling spatially random sensor network. Specifically, the connectivity in terms of estimating the area of interest is defined by maximum distance that can be covered in multihop paths. Furthermore, the maximum Euclidean distance is directly related to the estimated hop-distance which is equal to the least number of hops overall multihop paths between any two locations. Therefore, CPSO is used for the optimization of sensor selection whereasthe topology of random selection becomes regular topology such as linear, mesh, tree, or ring and the SLL deteriorates further.