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In this paper we propose a multi-carrier (MC) based sparse array for improved direction-of-arrival (DOA) estimation. We use a spatial (physical or virtual) array of a small number of antennas, but with a large aperture to achieve a high DOA estimation accuracy. The resulting problem of grating lobes (spatial aliasing) is addressed by using multiple carrier frequencies. In contrast to the single-carrier case, by a suitable choice of multiple carrier frequencies the resulting antenna position-to-wavelength ratios can be used to satisfy the spatial anti-aliasing condition. We present such design rules in this paper.A new problem, however, is that a target range results in different phase changes for different carriers. This is the MC range-DOA coupling. We both discuss the joint range-DOA deterministic maximum likelihood estimation and a simplified DOA estimation algorithm with range elimination. Their performance in simulations are compared to the Cramer-Rao bound.