Abstract

The extended Ziv-Zakai bound for vector parameters is used to develop a lower bound on the mean square error in estimating the 2-D bearing of a narrowband planewave signal using planar arrays of arbitrary geometry. The bound has a simple closed-form expression that is a function of the signal wavelength, the signal-to-noise ratio (SNR), the number of data snapshots, the number of sensors in the array, and the array configuration. Analysis of the bound suggests that there are several regions of operation, and expressions for the thresholds separating the regions are provided. In the asymptotic region where the number of snapshots and/or SNR are large, estimation errors are small, and the bound approaches the inverse Fisher information. This is the same as the asymptotic performance predicted by the local Cramer-Rao bound for each value of bearing. In the a priori performance region where the number of snapshots or SNR is small, estimation errors are distributed throughout the a priori parameter space and the bound approaches the a priori covariance. In the transition region, both small and large errors occur, and the bound varies smoothly between the two extremes. Simulations of the maximum likelihood estimator (MLE) demonstrate that the bound closely predicts the performance of the MLE in all regions.

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.