Processing Time

Condition of Experiments. Tests were conducted on a PC that is equipped with a Pentium

(R) processor, a CPU of 3 GHz, and 496 MB of RAM. Codes are written in C++.

one. This can be explained by the presence of a logarithm function in the path loss model, which slows down calculations.

We can also observe that the processing time increases drastically with the number of APs needed (see Figures 2.8 and 2.9 where processing time is measured for Pt = 20 dBm and Rth ∈ [−85, −55]).

Figure 2.8: Path loss-based model – total processing time when Pt = 20 dBm and Rth is changing form -85 to -55 dBm

Figure 2.9: Power-based model – total processing time when Pt = 20 dBm and Rth is changing form -85 to -55 dBm

2.4

Conclusion

In this chapter, we developed two models for WLAN planning. One is based on path losses while the other is based on power. For each of these models, two objective functions are proposed in order to take into account the average and the worst signal quality. A balancing

Evaluation of a Multi-objective Functions Model 2.4. Conclusion

that the acceptable signal quality can be received from everywhere in the design area. A scheme to find the minimum number of APs satisfying the constraint is also developed.

Extensive experiments have been conducted in order to test these models. They aim at evaluating the following aspects:

• Finding the minimum number of the APs • The solutions of each objective function. • The impact of the balancing parameter.

The scheme produces satisfactory results, as the number of APs in the design of WLAN changes as expected when the coverage distance changes. This is observed for both models. Although the path loss-based model computationally is more expensive than the power- based one, it produces better solutions in finding the minimum number of APs. Hence, the models designed subsequently will be based on path losses.

It appears that the use of balancing parameters is difficult, as both models showed an abrupt change from one solution to another at a given value of ψ. Hence other strategies will be suggested in the following chapters for planning WLANs when environment includes obstacles. These strategies will be compared with other approaches found in the literature.

Network Planning – Proposed

Optimisation Model

In the last chapter, a multi-objective functions model based on path losses and power was developed to find the number of APs and their distribution. The two functions in the model were combined together by using a balancing parameter that can take any value between 0 and 1. The purpose of combining the two functions was to obtain good coverage for all users. An iterative scheme was developed to find the minimum number of APs. A nonsmooth continuous optimisation algorithm was used to solve the problem. Satisfactory results were obtained in finding the number of APs. However, we found that choosing the best possible value of the balancing parameter to satisfy the operation of both functions is quite difficult.

The aim of this chapter is to introduce a simple yet effective optimisation model we developed for minimising the number of APs in a WLAN system. The model does not include a balancing parameter. Once the minimal number of APs is determined, it will be possible to incorporate other objective functions into the model to achieve other goals. This step-by-step approach allows us to reduce a complicated problem to a series of simpler ones. We will also demonstrate the validity and advantages of this model.

We use the Global Optimisation Algorithm (AGOP) developed at the University of Bal- larat for solving the optimisation problem. This algorithm, which is not used by previous researchers, is suitable for discontinuous functions and large size problems.

Network Planning – Proposed Optimisation Model 3.1. Path Loss Model

3.1

Path Loss Model

Path loss model is the core of signal coverage calculation in any environment [29,60,63,69]. It allows one to calculate the coverage distance of an AP, the distance between users and APs, and the distance between two terminals. In addition, it is also possible to incorporate the loss associated with obstacles into the model. Many researchers [1, 2, 6, 24, 28, 41, 42, 64, 65, 67, 75, 81, 82, 90] developed their optimisation models based on path losses.

The proposed optimisation model will be based on the path loss function that takes into account loss in the free space areas, as well as loss associated with the building materials at each point: pl(aj, ri)[dB] = pl(d0)[dB] + 20 log  d(a_j, ri) d0  | {z } 1 + T X t=1 ntlt, | {z } 2 (3.1)

where pl(aj, ri) [dB] represents the loss of signal from AP aj to user ri(measured in deci- bels), pl(d0) is the loss of signal at the reference distance d0, d(aj, ri) is the distance from AP aj to user ri, ntis the number of obstacles of type t (for example, walls, windows), and ltrepresents the loss attributed to the type of an obstacle. There are T types of obstacles.

The right hand side of (3.1) contains two parts associated to two different types of environments. Part one corresponds to environments where a line of sight exists between the transmitter and the receiver (eg: hallways). Part two calculates the loss of signal in indoor areas where obstacles (walls, doors, windows) are obstructing the line of sight between the AP and the user. Due to the presence of obstacles, the radio signal drops abruptly. The rate of loss depends on the structure of the obstacles. The sudden change in the received signal causes the path loss model (3.1) and, consequently, the objective function in the corresponding optimisation problem, to be discontinuous [1, 23–25, 30, 42, 65, 68, 72, 75].

It should be noted that this model can be used for carrier frequencies of 900 MHz, 2.4 GHz, and 5.x GHz bands because the attenuation factor related to different types of partitions is more dependent upon construction materials than upon carrier frequencies [60].