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In underwater acoustics, compressive sensing was applied to the separation of multiple raypaths based on direction of arrival (DOA) estimation. While it is impossible to separate raypaths directly without eliminating the interference between raypaths. This paper proposes a subspace-based higher-order compressive sensing algorithm, which enables separating raypaths interrupted by colored noise. In the algorithm, a trispectrum matrix is first calculated from the signal received on the reception array. To improve the robustness against noise, the trispectrum matrix is decomposed into signal and noise subspaces using an eigenvalue decomposition. Then, a subspace-based higher-order convex optimization problem is designed based on the signal subspace. The separation of raypaths is cast as the optimization problem solved in a greedy strategy approximation. The results obtained in both simulations and experiments show that the present method not only achieves the more precise separation of raypaths, but it also provides better suppression of noise as compared to the other algorithms. [ABSTRACT FROM AUTHOR]