The L-band digital aeronautical communication system (LDACS) is one of the essential infrastructures for future aviation broadband communication. To address the problem of interference from adjacent high-power distance measuring equipment (DME) signals, a joint orthogonal projection interference suppression and single-snapshot sparse decomposition direction of arrival (DOA) estimation method is proposed. Firstly, the DME interference is suppressed by using the subspace projection, and then a pseudo-covariance matrix is constructed by using single-snapshot data. High-order power of the pseudo-covariance matrix is calculated, followed by singular value decomposition and sparse solution obtained using constraints to estimate the desired target. The proposed method in this paper reduces the impact of noise by utilizing high-order pseudo-covariance matrix, enabling accurate estimation of the DOA of OFDM signals with only a single snapshot. Simulation results show that the estimation accuracy by using ISS-HOP-L1-SVD algorithm is better than that via ISS-HOP-MUSIC algorithm. This method can effectively suppress DME interference and improve the performance of the OFDM receiver.