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

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.