Closed form expression for the Cramér-Rao lower bound for the DOA estimates from spatially and temporally correlated narrowband signals considering noncircular sources

Abstract

In this paper, we derive for the first time an explicit expression for the stochastic Cramér-Rao lower bound (CRLB or CRB) of the DOA estimates from spatially and temporally correlated signals generated from noncircular sources. The new CRB is compared to those of circular temporally correlated and noncircular independent and identically distributed (iid) signals. It will be shown that the CRB obtained assuming both noncircular sources and temporally correlated signals is lower than the CRBs derived considering only one of these two assumptions. This illustrates the potential gain that both the noncircularity and the temporal correlation provide when considered together. It will also be proved that the difference between the three CRBs increases with the number of snapshots. However, as the signal-to-noise ratio (SNR) increases, the CRBs merge together and decrease linearly. Moreover, we notice that in low SNR values the temporal correlation is more informative about the unknown DOA parameters than the noncircularity. Finally, we show the dependence of the CRB on the noncircularity rate, the noncircularity phase separation and the DOA separation.