  Despite many advantages of direction-of-arrivals (DOAs) in sparse
representation domain, they have high computational complexity. This paper
presents a new method for real-valued 2-D DOAs estimation of sources in a
uniform circular array configuration. This method uses a transformation based
on phase mode excitation in uniform circular arrays which called real beamspace
L1-SVD (RB-L1SVD). This unitary transformation converts complex manifold matrix
to real one, so that the computational complexity is decreased with respect to
complex valued computations,its computation, at least, is one,fourth of the
complex-valued case; moreover, some benefits from using this transformation are
robustness to array imperfections, a better noise suppression because of
exploiting an additional real structure, and etc. Numerical results demonstrate
the better performance of the proposed approach over previous techniques such
as C-L1SVD, RB-ESPRIT, and RB-MUSIC, especially in low signal-to-noise ratios.
