Importance Sampling in Wireless Communication Systems with Ultra-Low Error Rates
(2022) EITM02 20221Department of Electrical and Information Technology
- 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,... (More) - 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. (Less) - Popular Abstract
- Performing simulations using the statistical sampling techniques was made possible by the miraculous development of the first digital computer called electronic numerical integrator and computer (ENIAC) in 1945. Since then, utilization of simulation to asses communication systems has increased significantly, as it provides an insight about the system behaviour under different conditions before the actual implementation with hardware and is much more cost effective than a hardware prototype. One of the vastly utilized method to evaluate communication systems is MC simulation.
MC simulates the system without any knowledge of the systems error region, using the repeated sampling technique in order to obtain the performance of a
system... (More) - Performing simulations using the statistical sampling techniques was made possible by the miraculous development of the first digital computer called electronic numerical integrator and computer (ENIAC) in 1945. Since then, utilization of simulation to asses communication systems has increased significantly, as it provides an insight about the system behaviour under different conditions before the actual implementation with hardware and is much more cost effective than a hardware prototype. One of the vastly utilized method to evaluate communication systems is MC simulation.
MC simulates the system without any knowledge of the systems error region, using the repeated sampling technique in order to obtain the performance of a
system under certain conditions, which results in very long simulations time to estimate the low error probabilities with good accuracy. Therefore, in this thesis we will investigate a variance reduction (VR) technique known as IS, to obtain a superior performance compared to MC, which utilizes the knowledge of the input pdf to locate the rare event or error region. The main idea of this thesis work can
be understood by the following example:
Consider a supermarket where there are different sections and each section has a worker assigned to it. MC corresponds to you blindly going around in the market looking for the taco (error region) without asking anyone. IS without considering channel pdf corresponds to you blindly going to different sections (bathroom, gardening, food, etc.) and asking the corresponding worker whether the tortilla is in his section. If it is, the worker shows you and you are done. If it is not, you move randomly to the next section. Now, adding signs into the supermarket (or each worker recommending which worker to ask next) corresponds to changing the channel pdf, so that you move only to the relevant sections and reject others. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9089254
- author
- Maheshwari, Bharat LU and Zhou, Yewen LU
- supervisor
- organization
- course
- EITM02 20221
- year
- 2022
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- error region, Monte Carlo, importance sampling, rejection sampling, Kullback-Leibler divergence.
- report number
- LU/LTH-EIT 2022-870
- language
- English
- id
- 9089254
- date added to LUP
- 2022-06-21 10:39:09
- date last changed
- 2022-06-21 10:39:09
@misc{9089254,
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.}},
author = {{Maheshwari, Bharat and Zhou, Yewen}},
language = {{eng}},
note = {{Student Paper}},
title = {{Importance Sampling in Wireless Communication Systems with Ultra-Low Error Rates}},
year = {{2022}},
}