University of Oulu

C. B. Issaid, M. -S. Alouini and R. Tempone, "Efficient Importance Sampling for the Left Tail of Positive Gaussian Quadratic Forms," in IEEE Wireless Communications Letters, vol. 10, no. 3, pp. 527-531, March 2021, doi: 10.1109/LWC.2020.3036588

Efficient importance sampling for the left tail of positive Gaussian quadratic forms

Saved in:
Author: Issaid, Chaouki Ben1; Alouini, Mohamed-Slim1; Tempone, Raúl1,2
Organizations: 1King Abdullah University of Science and Technology (KAUST), Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division, Thuwal 23955-6900, Saudi Arabia
2Alexander von Humboldt Professor in Mathematics for UQ, RWTH Aachen University, 52062 Aachen, Germany
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
Persistent link:
Language: English
Published: Institute of Electrical and Electronics Engineers, 2021
Publish Date: 2021-03-17


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.

see all

Series: IEEE wireless communications letters
ISSN: 2162-2337
ISSN-E: 2162-2345
ISSN-L: 2162-2337
Volume: 10
Issue: 3
Pages: 527 - 531
DOI: 10.1109/LWC.2020.3036588
Type of Publication: A1 Journal article – refereed
Field of Science: 213 Electronic, automation and communications engineering, electronics
Copyright information: © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.