CAREER EPISODE ONE
Analysis of Statistical Models for the Simulation of Rayleigh Faded Cellular Channels

1.2 Background
1.2.1 Nature of the project
The successful design and testing of mobile communication systems requires a thorough understanding of the underlying radio propagation environment. This has motivated the development of standardized channel models and methods for the simulation of mobile radio channels. The primary goal of any channel simulation model is to reproduce the statistical properties of the real world channel as faithfully as possible. The main idea behind a class of sum-of-sinusoids (SoS) channel models is to simulate the channel as a stationary complex Gaussian random process, formed by the sum of multiple sinusoidal waveforms having frequencies, amplitudes and phases that are appropriately selected to accurately reproduce the desired statistical properties.

1.2.2 Aims of the project
This project aims to compare the statistical SoS methods in terms of their complexity and performance. My partner and I decided to compare the Level Crossing Rate (LCR) and Average Fade Duration (AFD) for various models.

1.2.3 Chart of team organization
This project was carried out in a two-member team. I was in charge of the team. The organization of the team is shown as below (Table 1):

|Stage 1 |Literature Review; |
| |Model Selection |
|Stage 2 |Hardware Prepare |Mathematic Description for Models |
|Stage 3 |Hardware Implementation |Model Simulation& Analysis |
|Stage 4 |Project Report |

Table 1 Team Organization

1.2.4 Brief statement of my duties • Take responsibility of the team • Organize the resources and time table of the project • Work out the detailed requirement of the project • Find SoS simulation models with Shuo Zhang • Build up and implement simulation model • Finish the project reports

1.3 Personal Workplace Activity

1.3.1 Team Management
In this project, I was the leader of the group. As a leader, I organized several meetings with Shuo Zhang. In those meetings, I made clear the requirements about the project, such as the simulation model and the time limitation. Then, discussions were held to come up with a timetable. I set a deadline for every stage to ensure the project can be finished on time. Planning is very important in any project. Therefore, regular meetings were held to discuss the work being done and any problems met. If alterations were required, I went back and did more research and had brainstorming sessions with Shuo Zhang to come up with more efficient solutions.

1.3.2 Literature Review and Models Selection
In the first stage of the project, I firstly stated with the literature review to be familiar with many different approaches to the modeling and simulation of mobile radio channels. Among them, I found that the well-known mathematical reference model due to Jakes has been widely used for Rayleigh fading channels for about 30 years. So I decided Jake’s model was the one we have to investigate. Besides, Zheng&Xiao model-1 and Zheng&Xiao model-2 were the newest ones, so the two models were chosen as our candidates.

1.3.3 Mathematic Description for Models
After three models have been selected, the next step is to determine mathematic description for three models. This is the most important stage of this project.

According to several papers, I found that in a multipath fading wireless channel, the transmitted signal is reflected and refracted, such that the received signal is made up of a superposition of waves. These waves may add constructively or destructively giving rise to received signal fading. It is of interest to characterize the channel response, in order that systems may be designed which operate at acceptable performance levels during fades. Since the orientation and material properties of the obstacles between transmitter and receiver are not known in advance, or may be time varying, it is common to characterize the received signal as stochastic. In the case of SOS simulators, the received signal is a sum of randomly-phased sinusoids. Jake’s model is based this idea, which is shown below.
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[pic] is statistically independent and uniformly distributed over (-[pic],[pic]) for all n. [pic] is the maximum Doppler frequency, S is the number of subpath.

Based on Jake’s model, Zheng&Xiao propose their own model.
Zheng&Xiao-1 Impulse Response:
[pic]
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Zheng&Xiao-2 Impulse Response:
[pic] [pic] [pic]
[pic]

1.3.4 Model Simulation
In order to simulate three models, firstly, I needed to determine the parameter settings of the model. The parameters used in simulation are shown in Table 2.

|Parameters |Values |
|Operating frequency |2Ghz |
|Channel Samples |20000 |
|Sample density |8 |
|Subpaths No. |25 |
|MS velocity |54km/hr |
|Channel environment |Rayleigh fading |
|Mean Angle of Arrival |60 degree |
|PDF in AOA |Gaussian |

Table 2 Parameter used for simulating cellular channel model
After I studied the Matlab language especially the communication tool box and then apply them to the simulation. In the simulation process, I used one main function to calculate the channel impulse response and two sub-functions to calculate and display the level crossing rate and average fade duration.

1.3.5 Comparative Analysis of Models
The simulation results obtained from the previous stage is shown in figure 1 and figure 2.
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Figure 1 LCR for cellular channel model
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Figure 2 AFD for cellular channel model

According to the figures, I got the conclusion that regarding the performance the three models nearly have the performance. All the three models match the theory curve very well. But in terms of complexity, Jake’s model and Zheng&Xiao-1 have the same channel impulse response, their angle of arrival (AOA) is different. Zheng&Xiao-2 is the most complex model among the three, both the impulse response and angle of arrival (AOA) are harder than other two models.

1.3.6 Project Report
The last stage of the project was to write reports to document all the technique details of the project. I finished the “Analysis of Statistical Models for the Simulation of Rayleigh Faded Cellular Channels”. Then Shuo Zhang and I submitted the report and did the presentation in Australia National University to report the process of the project.

1.4 Summary
Finally, the overall project was finished successfully and met all the requirements. I compare Jakes’s model, Zheng&Xiao-1 and Zheng&Xiao-2 in terms of their complexity and performance. The Project management approach helped me to manage the process and come up with the most appropriate technical solution. We did regular meeting to find causes of the problem, choose method to solve the problem. Finally, from simulation results, I made the conclusion that the three model nearly have the same performance and Zheng&Xiao-2 in the most complex one among the three.