Multiple importance sampling for efficient symbol error rate estimation

Victor Elvira*, Ignacio Santamaria

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Digital constellations formed by hexagonal or other non-square two-dimensional lattices are often used in advanced digital communication systems. The integrals required to evaluate the symbol error rate (SER) of these constellations in the presence of Gaussian noise are in general difficult to compute in closed form, and therefore Monte Carlo simulation is typically used to estimate the SER. However, naive Monte Carlo simulation can be very inefficient and requires very long simulation runs, especially at high signal-to-noise ratios. In this letter, we adapt a recently proposed multiple importance sampling technique, called ALOE (for 'at least one rare event'), to this problem. Conditioned to a transmitted symbol, an error (or rare event) occurs when the observation falls in a union of half-spaces or, equivalently, outside a given polytope. The proposal distribution for ALOE samples the system conditionally on an error taking place, which makes it more efficient than other importance sampling techniques. ALOE provides unbiased SER estimates with simulation times orders of magnitude shorter than conventional Monte Carlo.

Original languageEnglish
Article number8611088
Pages (from-to)420-424
Number of pages5
JournalIEEE Signal Processing Letters
Volume26
Issue number3
Early online date14 Jan 2019
DOIs
Publication statusPublished - 1 Mar 2019

Keywords

  • Improper constellations
  • lattices
  • Monte Carlo
  • multiple importance sampling
  • symbol error rate

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