### Abstract

The symbol error rate of the maximum likelihood detector for an arbitrary multi-dimensional constellation impaired by additive white Gaussian noise is characterized as the product of a completely monotone function with a non-negative power of the signal to noise ratio. Using this general result, it is proved that the symbol error rate is completely monotone if the rank of its constellation matrix is either one or two. Further, it is shown that, if the rank of the constellation matrix is greater than or equal to four, then the symbol error rate cannot be a completely monotone function of the SNR. Applications to stochastic ordering of wireless system performance is also discussed.

Original language | English (US) |
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Title of host publication | Conference Record of the 46th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2012 |

Pages | 148-152 |

Number of pages | 5 |

DOIs | |

State | Published - Dec 1 2012 |

Event | 46th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2012 - Pacific Grove, CA, United States Duration: Nov 4 2012 → Nov 7 2012 |

### Publication series

Name | Conference Record - Asilomar Conference on Signals, Systems and Computers |
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ISSN (Print) | 1058-6393 |

### Other

Other | 46th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2012 |
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Country | United States |

City | Pacific Grove, CA |

Period | 11/4/12 → 11/7/12 |

### Fingerprint

### Keywords

- Communication Systems
- Modulation and Detection
- Symbol error rate
- canonical representation
- complete monotonicity
- convex
- stochastic ordering

### ASJC Scopus subject areas

- Signal Processing
- Computer Networks and Communications

### Cite this

*Conference Record of the 46th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2012*(pp. 148-152). [6488978] (Conference Record - Asilomar Conference on Signals, Systems and Computers). https://doi.org/10.1109/ACSSC.2012.6488978