Direction-of-arrival (DOA) estimation is a classic research topic with numerous applications in the field of signal processing. However, multiple radio frequency channels are required to receive array signals in order to achieve excellent performance, which is complicated in hardware to be applied to portable or cost-effective equipment. In this paper, we investigate the DOA estimation for transmissive metasurface antenna systems, where the signals are modulated by metasurface elements before reaching the receiving antennas. Then, we proposed an off-grid sparse Bayesian learning algorithm for metasurface aided systems, where the DOA estimation process consists of three stages, i.e., off-grid operation, calculation of posterior probability, and iterative update for hyperparameters using expectation maximization algorithm. Simulation results show that the proposed method can obtain superior estimation performance with a low number of snapshots and low signal-to-noise ratio. Meanwhile, it can achieve satisfactory performance even when the angle interval of the incoming signal is small.
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