Bearing estimation in a Ricean channel .I. Inherent accuracy limitations

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 Cramer-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 a monotonically decreasing function of the 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). Lastly, the CRLB for estimation of the Rice factor is considered, and some of its properties are studied.