Cramér-Rao Bounds for Direction Estimation in the Presence of Circular and Noncirular Signals

Abstract

In direction finding, the use of noncircularity of signals arriving at a sensor array can allow us to improve estimation performance. It will be more realistic, rather than the assumption of all noncircular sources, to consider some sources transmitting circular signals. In the presence of both circular and noncircular signals, this paper presents the deterministic Cramér-Rao bound (CRB) of direction estimation. The derivation of the CRB is quite general so that the bounds with unknown signal structures and with known waveforms can be readily obtained from it. Moreover, we show that the more information on signal structures is available the less the CRB is. And we present general conditions under which the CRBs for the direction parameters obtained from different Fisher information matrices are equal. Based on these basic theoretical results, the bounds with different information are analytically compared. Numerical results confirm the theoretical results.

Efficient Approach to Decoupled Localization for Noncircular Sources in the Presence of Doppler Effect

“…The associate editor coordinating the review of this manuscript and approving it for publication was Chengpeng Hao . nonzero, the noncircularity can be exploited to improve estimation performance [7], [8]. Various methods for direction finding have been suggested that use noncircularity [8]- [14], but without the consideration of the Doppler effect.…”