Decomposition-Free DOA Estimation Method for Multiple Coherent Sources

Direction of Arrival (DOA) estimation of highly correlated or coherent sources remains a challenging problem, particularly for subspace-based methods such as MUSIC and Root-MUSIC, which require spatial smoothing or eigenvalue decomposition. This work introduces a decomposition-free DOA estimation algorithm that exploits the inherent Toeplitz structure of uniform linear arrays (ULAs). The method constructs a structured Toeplitz matrix directly from the received data vector, forms a real, symmetric compound matrix to enable real-valued processing, and extracts structured sub-blocks without matrix decomposition. A polynomial matrix is then generated, and the DOAs are obtained by solving its roots, thereby bypassing covariance decomposition entirely. This design reduces computational burden, improves numerical stability, and inherently accommodates coherent sources without the need for spatial smoothing. Computational complexity analysis shows significant savings compared to subspace methods, while MATLAB simulations across various SNR, snapshot, and array size conditions validate estimation accuracy. Furthermore, a hardware realization on the NI PXIe-7993 FPGA platform demonstrates that the decomposition-free structure requires minimal hardware resources and execution cycles, making the algorithm highly suitable for real-time embedded applications.