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 $M��/2$ and $N��/2$, where $M$ and $N$ are coprime integers and $��$ 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.

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