## 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 language | English |
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Article number | 8611088 |

Pages (from-to) | 420-424 |

Number of pages | 5 |

Journal | IEEE Signal Processing Letters |

Volume | 26 |

Issue number | 3 |

Early online date | 14 Jan 2019 |

DOIs | |

Publication status | Published - 1 Mar 2019 |

## Keywords

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