Generating Generalized Exponentially Distributed Random Variates with Transformed Density Rejection and Ratio-of-Uniform Methods

To analyze a communication system without the aid of simulation, the channel noise for the simulation must be assumed to be normal. The assumption is often valid, but the normal distribution may not be able to model the channel noise adequately in some environments. This thesis will explore the generalized exponential distribution for better noise modeling and robustness testing in communication system.

When using the generalized exponential distribution for the channel noise, the analysis will become analytically intractable, and simulation becomes mandatory. To generate the noise with the distribution, the rejection method can be used. However, since the distribution can take on different shapes, finding the appropriate Upper Bounding Function (UBF) for the method is very difficult. Thus, two modified versions of the rejection method will be examined. They are the Transformed Density Rejection (TDR) and Ratio-of-Uniform (RoU) method; their quality, efficient, trade-offs, etc will be discussed.

Choosing TDR, a simulation of a BPSK communication system will be performed.

With the simulation, it can further ascertain that the random variates generated by TDR can be used to model the channel noise and to test the robustness of a communication system.