Simulation methods are used when closed-form solutions do not exist. An interesting simulation method that has been widely used in many scientific fields is the Monte Carlo method. Not only it is a simple technique that enables to estimate the
quantity of interest, but it can also provide relevant information about the value to be
estimated through its confidence interval. However, the use of classical Monte Carlo
method is not a reasonable choice when dealing with rare event probabilities. In fact,
very small probabilities require a huge number of simulation runs, and thus, the computational time of the simulation increases significantly. This observation lies behind the main motivation of the present work. In this thesis, we propose efficient importance sampling estimators to evaluate rare events probabilities. In the first part of
the thesis, we consider a variety of turbulence regimes, and we study the outage probability of free-space optics communication systems under a generalized pointing error model with both a nonzero boresight component and different horizontal and vertical jitter effects. More specifically, we use an importance sampling approach,based on the exponential twisting technique to offer fast and accurate results. We also
show that our approach extends to the multihop scenario. In the second part of the
thesis, we are interested in assessing the outage probability achieved by some diversity techniques over generalized fading channels. In many circumstances, this is related to the difficult question of analyzing the statistics of the sum of random variables.
More specifically, we propose robust importance sampling schemes that efficiently evaluate the outage probability of diversity receivers over Gamma-Gamma, α − µ, κ − µ, and η − µ fading channels. The proposed estimators satisfy the well-known bounded relative error criterion for both maximum ratio combining and equal gain
combining cases. We show the accuracy and the efficiency of our approach compared
to naive Monte Carlo via some selected numerical simulations in both case studies.
In the last part of this thesis, we propose efficient importance sampling estimators
for the left tail of positive Gaussian quadratic forms in both real and complex settings. We show that these estimators possess the bounded relative error property.
These estimators are then used to estimate the outage probability of maximum ratio
combining diversity receivers over correlated Nakagami-m or correlated Rician fading
|Date of Award||Nov 12 2019|
|Original language||English (US)|
- Computer, Electrical and Mathematical Science and Engineering
|Supervisor||Mohamed-Slim Alouini (Supervisor)|
- rare events
- bounded relative error
- importance sampling
- outage probability
- diversity techniques