Efficient Importance Sampling for the Left Tail of Positive Gaussian Quadratic Forms
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramCommunication Theory Lab
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Stochastic Numerics Research Group
Date
2020Preprint Posting Date
2020-09-06Permanent link to this record
http://hdl.handle.net/10754/665134
Metadata
Show full item recordAbstract
Estimating the left tail of quadratic forms in Gaussian random vectors is of major practical importance in many applications. In this letter, we propose an efficient importance sampling estimator that is endowed with the bounded relative error property. This property significantly reduces the number of simulation runs required by the proposed estimator compared to naive Monte Carlo (MC), especially when the probability of interest is very small. Selected simulation results are presented to illustrate the efficiency of our estimator compared to naive MC as well as some of the well-known approximations.Citation
Issaid, C. B., Alouini, M.-S., & Tempone, R. (2020). Efficient Importance Sampling for the Left Tail of Positive Gaussian Quadratic Forms. IEEE Wireless Communications Letters, 1–1. doi:10.1109/lwc.2020.3036588Sponsors
This work was supported by KAUST and the Alexander von Humboldt foundation.Publisher
IEEEarXiv
2009.03677Additional Links
https://ieeexplore.ieee.org/document/9250477/https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9250477
ae974a485f413a2113503eed53cd6c53
10.1109/LWC.2020.3036588