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

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.

Issaid Chaouki Ben, Alouini Mohamed-Slim, Tempone Raúl

A1 Journal article – refereed

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

https://doi.org/10.1109/LWC.2020.3036588 http://urn.fi/urn:nbn:fi-fe202103177627