  In this paper, we consider the Cramer-Rao lower bound (CRLB) for estimation
of a lens-embedded antenna array with deterministic parameters. Unlike CRLB of
uniform linear array (ULA), it is noted that CRLB for direction of arrival
(DoA) of lens-embedded antenna array is dominated by not only angle but
characteristics of lens. Derivation is based on the approximation that
amplitude of received signal with lens is approximated to Gaussian function. We
confirmed that parameters needed to design a lens can be derived by standard
deviation of Gaussian, which represents characteristic of received signal, by
simulation of beam propagation method. Well-designed lens antenna shows better
performance than ULA in terms of estimating DoA. This is a useful derivation
because, result can be the guideline for designing parameters of lens to
satisfy certain purpose.
