  In this paper we investigate the design of compressive antenna arrays for
direction of arrival (DOA) estimation that aim to provide a larger aperture
with a reduced hardware complexity by a linear combination of the antenna
outputs to a lower number of receiver channels. We present a basic receiver
architecture of such a compressive array and introduce a generic system model
that includes different options for the hardware implementation. We then
discuss the design of the analog combining network that performs the receiver
channel reduction, and propose two design approaches. The first approach is
based on the spatial correlation function which is a low-complexity scheme that
in certain cases admits a closed-form solution. The second approach is based on
minimizing the Cramer-Rao Bound (CRB) with the constraint to limit the
probability of false detection of paths to a pre-specified level. Our numerical
simulations demonstrate the superiority of the proposed optimized compressive
arrays compared to the sparse arrays of the same complexity and to compressive
arrays with randomly chosen combining kernels.
