  Recently, coprime arrays have been in the focus of research because of their
potential in exploiting redundancy in spanning large apertures with fewer
elements than suggested by theory. A coprime array consists of two uniform
linear subarrays with inter-element spacings $M\lambda/2$ and $N\lambda/2$,
where $M$ and $N$ are coprime integers and $\lambda$ is the wavelength of the
signal. In this paper, we propose a fast search-free method for
direction-of-arrival (DOA) estimation with coprime arrays. It is based on the
use of methods that operate on the uniform linear subarrays of the coprime
array and that enjoy many processing advantages. We first estimate the DOAs for
each uniform linear subarray separately and then combine the estimates from the
subarrays. For combining the estimates, we propose a method that projects the
estimated point in the two-dimensional plane onto one-dimensional line segments
that correspond to the entire angular domain. By doing so, we avoid the search
step and consequently, we greatly reduce the computational complexity of the
method. We demonstrate the performance of the method with computer simulations
and compare it with that of the FD-root MUSIC method.
