  We consider the problem of direction of arrival (DOA) estimation using a
newly proposed structure of non-uniform linear arrays, referred to as co-prime
arrays, in this paper. By exploiting the second order statistical information
of the received signals, co-prime arrays exhibit O(MN) degrees of freedom with
only M + N sensors. A sparsity based recovery method is proposed to fully
utilize these degrees of freedom. Unlike traditional sparse recovery methods,
the proposed method is based on the developing theory of super resolution,
which considers a continuous range of possible sources instead of discretizing
this range into a discrete grid. With this approach, off-grid effects inherited
in traditional sparse recovery can be neglected, thus improving the accuracy of
DOA estimation. In this paper we show that in the noiseless case one can
theoretically detect up to M N sources with only 2M + N sensors. The noise 2
statistics of co-prime arrays are also analyzed to demonstrate the robustness
of the proposed optimization scheme. A source number detection method is
presented based on the spectrum reconstructed from the sparse method. By
extensive numerical examples, we show the superiority of the proposed method in
terms of DOA estimation accuracy, degrees of freedom, and resolution ability
compared with previous methods, such as MUSIC with spatial smoothing and the
discrete sparse recovery method.
