  In this work, we consider the Direction-of-Arrival (DOA) estimation problem
in a low-cost architecture where only one antenna as the receiver is aided by a
reconfigurable intelligent surface (RIS). We introduce the one-bit RIS as a
signal reflector to enhance signal transmission in non-line-of-sight (NLOS)
situations and substantially simplify the physical hardware for DOA estimation.
We optimize the beamforming scheme called measurement matrix to focus the echo
power on the receiver with the coarse localization information of the targets
as the prior. A beamforming scheme based on the modified genetic algorithm is
proposed to optimize the measurement matrix, guaranteeing restricted isometry
property (RIP) and meeting single beamforming requirements. The DOA results are
finely estimated by solving an atomic-norm based sparse reconstruction problem.
Simulation results show that the proposed method outperforms the existing
methods in the DOA estimation performance.
