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A novel real-valued algorithm of the popular root multiple signal classification of non-circular sources (NC-root-MUSIC) is developed for low-complexity direction of arrival (DOA) estimation. The proposed real-valued NC-root-MUSIC (RV-NC-root-MUSIC) reduces the computational burden mainly in following three aspects. First, unlike the classical real-valued algorithms, such as unitary transform, the complex-valued operation is still implemented when acquiring DOAs. However, the proposed RV-NC-root-MUSIC implements real-valued received data. Therefore, both tasks of eigenvalue decomposition (EVD) (or singular value decomposition (SVD)) and polynomial rooting can be implemented completely by real-valued computations in the proposed RV-NC-root-MUSIC. Next, due to the conjugate expansion of the non-circular sources, the steering vector dimension is extended by a factor of two, and the real-valued signal- and noise-subspace can be calculated by two reduced-dimension sub-matrices. As such, large-scale EVD/SVD computation is avoided. Finally, a real coefficient rooting polynomial with a similar order as NC-root-MUSIC is constructed. A variable substitution technique is further proposed to reduce the degree of this polynomial by half without sacrificing accuracy, which allows fast coefficient computation and real-valued rooting. The real-valued computation and reduced-order polynomial rooting in the proposed method result in a significant reduction in computational cost as compared to state-of-the-art methods. Numerical computer simulations illustrate that with significantly reduced complexity, the fast RV-NC-root-MUSIC algorithm can provide similar root mean square errors (RMSE) close to the conventional methods.

Real-Valued DOA Estimation for Non-Circular Sources via Reduced-Order Polynomial Rooting