Importance Sampling in Wireless Communication Systems with Ultra-Low Error Rates

Abstract: Simulation mimics the behaviour of real world processes or the system over time. It helps us to understand the impact of modification and the effect of introducing various interventions to a system. One such simulation method is known as Monte Carlo (MC) simulation, which has been utilized to evaluate the performance of digital communication systems over the last 70 years. MC has been the most exploited simulation method to assess modern communication systems due to its ability to cope with arbitrary complex system. This method utilizes the concept of repeated sampling, i.e., it blindly samples from a pseudo-random number generator without any knowledge of rare (error) events, to obtain the statistical properties of the system. Hence, to estimate the performance metric down to very low probabilities with high accuracy, long MC simulations are needed and require significant computational power. Therefore, in this thesis we will explore a modified MC simulation technique called importance sampling (IS), which reduces the variance of the estimator by sampling from the error (rare) events of the input space and thus achieves a given accuracy with shorter simulation time. A detailed evaluation and implementation of current state-of-the-art IS techniques is presented across the additive white Gaussian noise (AWGN) and the Rayleigh fading channel. The limitation of IS is the requirement of the input probability density function (pdf) which helps in identifying the error region. Obtaining a pdf for 3rd generation partnership project (3GPP) channel models is often not possible and therefore researchers and standardization engineers still resort to MC for system evaluations. In this thesis, we derive an optimal channel pdf for a multiple importance sampling (MIS) technique called ALOE (“At Least One rare Event”) in an orthogonal frequency-division multiplexing (OFDM) system. It is further observed that channel samples from the optimal pdf are obtainable via rejection sampling (RS). Significant gain over MC, and better or satisfactory performance compared to the current state-of-the-art IS technique for the Rayleigh fading channel is obtained. Also, a significant improvement over the current state-of-the-art IS technique for the Rayleigh fading channel has been achieved. This is accomplished by using the Kullback-Leibler divergence (KLD) to estimate an optimal pdf for ALOE using another Rayleigh channel pdf. The system and methods are implemented using MATLAB, and to obtain 3GPP channel models we have utilized QuaDRiGai version 2.6.1. Keywords: error region, Monte Carlo, importance sampling, rejection sampling, Kullback-Leibler divergence.