The direction of arrival (DOA) estimation of multiple radio frequency (RF) coherent signals using conventional algorithms such as Multiple Signal Classification (MUSIC), Estimation of the Signal Parameters via the Rotational Invariance Technique (ESPRIT), and their variants is computationally complex and usually requires a large number of data snapshots for accurate estimation. As the number of antenna elements grows, particularly in massive MIMO systems, the complexity of real-time DOA estimation algorithms significantly rises, placing higher demands on computational power and memory resources. In this paper, we present an efficient approach that operates effectively with just a single snapshot for DOA estimation of multiple coherent and non-coherent signals. The proposed method has the following advantages over existing methods: 1) constructs a Toeplitz structure data matrix from a single data snapshot, 2) applies forward-backward averaging operation to the data matrix instead of the covariance matrix constructed using hundreds of snapshots, 3) resolves the differences in the noise elements of the data matrix, preserving the conjugate symmetry property of the Toeplitz matrix, 4) converts the complex Toeplitz data matrix to a realvalued matrix in an efficient way without unitary transformations, and 5) employs QR decomposition to extract the signal and noise subspaces, eliminating the need for computationally complex eigenvalue (EVD) or singular value decomposition (SVD). Finally, we establish the effectiveness of our proposed method through both MATLAB simulations and real-time experiments. Compared to existing methods like Unitary root-MUSIC, the proposed approach demonstrates significantly reduced complexity and faster estimation times.
