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.