# Cost and Performance Tradeoff Analysis of Cell Planning Levels

#### Written by Jun Gao

#### Paper category

### Master Thesis

#### Subject

### Business Administration>Finance

#### Year

### 2013

#### Abstract

Master Thesis: The basic principle of point process Point process represents a random process composed of a set of points in statistics and probability theory. These points are isolated in time and space. The isolation here means that the appearance of one point will not affect the appearance of other points. In addition, the space here can be applied to a more general space defined by mathematics. Usually, the problem is not that complicated and abstract, and the space is limited by time and 2 or 3 dimensions. In this particular case, it can be called a point-in-space process [9]. Generally speaking, the point process is to study the distribution of random points. The dots here can represent events and are composed of time and place of occurrence. For example, it may be the impulse of neurons in the human brain. It is not only useful in the field of telecommunications, but also in many other fields, such as epidemiology, materials science, economics, neuroscience, etc. 2.2 Poisson point process In the field of telecommunications, the most commonly used space when considering point process problems is the Euclidean space, expressed as Rd. And nor-mallydis is equal to 2 or 3. SoR2 represents a 2-dimensional plane space, and R3 represents a 3-dimensional space. An example of the ubiquitous point process in R is the Poisson point process, which is the expression of the Poisson process in space. Since the Poisson process has two 2.3. 9 attributes of other point processes. One is that the number of events in each interval is independent, and the other is that the probability of occurrence of different events in an interval is Poisson distribution, as shown in Equation 2.3: Pr(X=k) =λke−λk!(2.3 ) Among them, kmeans is the number of events that occurred in the same interval, and λ is the expected value of the random variable K. A Poisson point process can be described as follows. Intensity μ is the set of random variables N(A,ω), A∈Rdandω∈Ω, and Ω is the sample space. 1. If A1, A2,... are disjoint sets, then N(A1,•),N(A2,•),... are independent. 2.N(A,•) is the Poisson average μ(A): Pr(N(A) =k) =e−μ(A)μ(A)kk!. In order to generate the Poisson point process to simulate the base station For deployment, Poisson distribution is used to generate the number of points that appear each time, and uniform distribution is used to allocate BS in a simulation. 2.3 Other point processes In addition to PPP, there are many other types of point processes. Some of them are listed in Table 2.1 [9]. The Matern hard-core point process forms a general point process, the distance between the points is never closer than some predefined distance, while the Poisson point process has no such limitation [11]. The hard core model can be constructed by removing certain points from the Poisson point process to achieve distance control.
3.1 Assumptions It is difficult to decide which planning scheme has the best system performance for the wireless system. However, it was observed in [8] that regular deployment provides better performance than random deployment. In this article, the hexagonal model is assumed to be the optimal planning solution. At the same time, a self-deployment plan is generated through BPP. In addition, we assume that by increasing the minimum inter-site distance in the self-deployment scheme, the final deployment can approach the optimal planning scheme. This hypothesis is based on the hexagonal tile is the way the dentist arranges circles in a two-dimensional plane. When the area and number of base stations are determined. If there is no transmission power control scheme, we can treat each base station and its coverage area as the same circle. Therefore, the dentist and the fairest way to deploy all BSs to the area is based on the hexagonal model. 3.2 Residential Area Planning Level The Residential Area Planning Level is a parameter indicating the degree of wireless system planning. According to our assumptions, the minimum inter-site distance is used to control the change of the system deployment from the self-deployment scheme to the optimal planning scheme. The final value of the minimum inter-site distance should be equal to the inter-site distance of the hexagonal model. Therefore, we define the cell planning level as 3.3 network model. Since the self-deployment scheme is simulated by BPP. It is simpler to allocate all base stations in a square area and use Voronoi tessellation to divide the boundary of each unit, as shown in Figure 3.1. However, there are some limitations to dividing a square area with a hexagonal pattern. The first is that the number of hexagons cannot be arbitrary, and the second is that the divided edges are not smooth. Therefore, in order to avoid these limitations, the square coverage area was removed from the hexagonal model. On the contrary, in order to generate the covering shape, the first hexagon is arranged in the center, and the remaining hexagons surround the central hexagon one by one, until all the hexagons are arranged. We try to maintain the symmetry of the entire pattern, which means that on the outermost tire, the remaining hexagons are not arranged in succession on one side, but arranged one by one on the opposite side. The total number of hexagons is equal to the number of base stations, and the entire area covered by the hexagons is equal to the square area in the self-deployment scheme. This mode is shown in Figure 3.2. Because the area covered by the two models is not the same. It is unfair to compare these two models directly. In order to solve this problem, an interesting area was introduced into the system. An interesting area is the circular area around the center of the coverage area. It is shown as a red circle in Figure 3.1 and Figure 3.2. An interesting area is designed to cover a certain part of the entire area. Its radius is determined in part. Because sampling and analysis work are concentrated in this area. The results of these two models are comparable. Read Less