## Abstract

This paper considers the problem of estimating the bearing of a single, far-field source using passive sensor array measurements when the spatial propagation channel formed between the source and the array may be described as "Ricean." Such a channel consists of a direct, line-of-sight (LOS) component as well as an indirect, nonline-of-sight (NLOS) component due to scattering. A parametric description of the resulting spatial propagation channel is presented. A related source-bearing estimation problem is formulated, and the associated Cramér-Rao lower bound (CRLB) is evaluated. The bound is used to study the relationship among the bearing estimation problems under the Ricean (LOS/NLOS), point source (LOS), and scattered source (NLOS) models. Exact and simplified approximate forms of the bound are derived explicitly in terms of the point source and scattered source CRLBs. A number of properties of the bound are presented. In particular, it is shown that the bound is monotonically decreasing function of Rice factor (the ratio of the LOS component power to the NLOS component power). This implies that for a given signal-to-noise ratio (SNR), the CRLB is bounded from below by the point source bound and bounded from above by the scattered source bound. It is also shown that given a NLOS component, the addition of a LOS component necessarily makes the bearing estimation problem easier. On the other hand, given an LOS component, the addition of an NLOS component does not necessarily make the bearing estimation problem easier (and may even make it harder). Last, the CRLB for estimation of the Rice factor is considered, and some of its properties are studied.

Original language | English |
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Pages (from-to) | 925-937 |

Number of pages | 13 |

Journal | IEEE Transactions on Signal Processing |

Volume | 49 |

Issue number | 5 |

DOIs | |

State | Published - May 2001 |

Externally published | Yes |

### Bibliographical note

Funding Information:Manuscript received January 17, 2000; revised February 5, 2001. This work was supported by the Israeli Science Foundation founded by the Academy of Sciences and Humanities. The associate editor coordinating the review of this paper and approving it for publication was Prof. Jian Li.