## Abstract

We investigate how pilot signals affect complexity and accuracy of maximum likelihood (ML) frequency estimation in frequency-flat channels with transmit diversity. We show that for arbitrary pilot signals, the complexity can be as low as O(N-t), where N-t is the number of transmit antennas. For linearly dependent pilot signals this can be further reduced down to O(1) with even better estimation accuracy. Lower and upper bounds of the Cramer-Rao lower bound (CRLB) over possible channel gains are derived. We define locally optimal pilot signals as those minimising the upper bound and show how to find such signals. The CRLB characterises local properties of ML estimates, while the ambiguity function allows analysis of global properties of estimates in the whole acquisition range. We analyse the ambiguity function for binary pilot signals, in particular Hadamard sequences, and show how it relates to behaviour of frequency estimates over the signal-to-noise ratio and frequency acquisition range.

Original language | English |
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Title of host publication | 2004 IEEE 15TH INTERNATIONAL SYMPOSIUM ON PERSONAL, INDOOR AND MOBILE RADIO COMMUNICATIONS, VOLS 1-4, PROCEEDINGS |

Place of Publication | NEW YORK |

Publisher | IEEE |

Pages | 2023-2028 |

Number of pages | 6 |

ISBN (Print) | 0-7803-8523-3 |

Publication status | Published - 2004 |

Event | 15th IEEE International Symposium on Personal, Indoor, Mobile, Radio Communications (PIMRC 2004) - Barcelona Duration: 5 Sep 2004 → 8 Sep 2004 |

### Conference

Conference | 15th IEEE International Symposium on Personal, Indoor, Mobile, Radio Communications (PIMRC 2004) |
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City | Barcelona |

Period | 5/09/04 → 8/09/04 |

## Keywords

- frequency estimation
- transmit diversity
- pilot signals
- PARAMETER-ESTIMATION
- SELECTIVE CHANNELS
- MULTIPATH CHANNEL