Cramer-Rao Lower Bounds for Angular Parameters Estimates from Incoherently Distributed Signals Generated by Noncircular Sources

In this paper, we derive for the first time analytical expressions for the stochastic Cramér- Rao lower bound (CRLB or CRB) of the angular parameters (central DOAs and angular spreads) estimates from incoherently distributed (ID) signals generated by noncircular sources. The new CRBs of the angular parameters are compared to those obtained from circular ID signals. The CRB of the central DOAs, however, are compared to those obtained from both circular and noncircular point sources. It will be shown that the CRB of both the central DOAs and the angular spreads obtained assuming noncircular ID sources are lower than those obtained using circular ID sources. This illustrates the potential gain that the noncircularity characteristic of the sources provides for the estimation of the angular parameters, especially in presence of different sources' distributions and for high angular spreads. Finally, the CRBs derived assuming noncircular ID signals decrease as the noncircularity rate increases. Furthermore, this decrease is more prominent at low DOA separations where the CRBs are sensitive to the noncircularity phase separation.