Efficient Importance Sampling for the Left Tail of Positive Gaussian Quadratic Forms
KAUST DepartmentApplied Mathematics and Computational Science Program
Communication Theory Lab
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Stochastic Numerics Research Group
Preprint Posting Date2020-09-06
Permanent link to this recordhttp://hdl.handle.net/10754/665134
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AbstractEstimating 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.
CitationIssaid, 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.2020.3036588
SponsorsThis work was supported by KAUST and the Alexander von Humboldt foundation.